%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU664^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:46:08 AM UTC 2026
% Result : Theorem 41.62s 7.19s
% Output : CNFRefutation 7.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 185
% Syntax : Number of formulae : 3509 (1141 unt; 0 typ; 184 def)
% Number of atoms : 29230 (12705 equ; 0 cnn)
% Maximal formula atoms : 182 ( 8 avg)
% Number of connectives : 63719 (13486 ~;11335 |; 197 &;37052 @)
% ( 56 <=>;1593 =>; 0 <=; 0 <~>)
% Maximal formula depth : 188 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2439 (2439 >; 0 *; 0 +; 0 <<)
% Number of symbols : 357 ( 354 usr; 187 con; 0-4 aty)
% Number of variables : 14439 (1235 ^;13003 !; 201 ?;14439 :)
% Comments :
%------------------------------------------------------------------------------
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_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_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_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_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_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_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_sK100_SY1852,type,
sK100_SY1852: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK101_SY1853,type,
sK101_SY1853: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK102_SY1841,type,
sK102_SY1841: $i > $i > $i > $i ).
thf(tp_sK103_SY1878,type,
sK103_SY1878: $i > $i > $i > $i ).
thf(tp_sK104_SY1562,type,
sK104_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK105_SY1228,type,
sK105_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK106_SY1859,type,
sK106_SY1859: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK107_SY1890,type,
sK107_SY1890: $i > $i > $i > $i ).
thf(tp_sK108_SY1862,type,
sK108_SY1862: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK109_SY1863,type,
sK109_SY1863: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK10_SY1558,type,
sK10_SY1558: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK110_SY1860,type,
sK110_SY1860: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK111_SY1870,type,
sK111_SY1870: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK112_SY1871,type,
sK112_SY1871: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK113_SY1872,type,
sK113_SY1872: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK114_SY1873,type,
sK114_SY1873: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK115_SY1868,type,
sK115_SY1868: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK116_SY1886,type,
sK116_SY1886: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK117_SY1887,type,
sK117_SY1887: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK118_SY1562,type,
sK118_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK119_SY1228,type,
sK119_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK11_SY1274,type,
sK11_SY1274: $i > $i ).
thf(tp_sK120_SY1896,type,
sK120_SY1896: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK121_SY1562,type,
sK121_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK122_SY1228,type,
sK122_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK123_SY1562,type,
sK123_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK124_SY1228,type,
sK124_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK125_SY1562,type,
sK125_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK126_SY1228,type,
sK126_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK127_SY1899,type,
sK127_SY1899: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK128_SY1562,type,
sK128_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK129_SY1228,type,
sK129_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK12_SY1624,type,
sK12_SY1624: $i > $i > $i ).
thf(tp_sK130_SY1562,type,
sK130_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK131_SY1228,type,
sK131_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK132_SY1562,type,
sK132_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK133_SY1228,type,
sK133_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK134_SY1562,type,
sK134_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK135_SY1228,type,
sK135_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK136_SY1908,type,
sK136_SY1908: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK137_SY1911,type,
sK137_SY1911: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK138_SY1912,type,
sK138_SY1912: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK139_SY1913,type,
sK139_SY1913: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK13_SY1625,type,
sK13_SY1625: $i > $i > $i ).
thf(tp_sK140_SY1921,type,
sK140_SY1921: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK141_SY1922,type,
sK141_SY1922: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK142_SY1923,type,
sK142_SY1923: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK143_SY1931,type,
sK143_SY1931: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK14_SY1630,type,
sK14_SY1630: ( $i > $o ) > $i > $i ).
thf(tp_sK15_SY1396,type,
sK15_SY1396: $i > $i ).
thf(tp_sK16_SY1651,type,
sK16_SY1651: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK17_SY1659,type,
sK17_SY1659: $i > $i > $i ).
thf(tp_sK18_SY1663,type,
sK18_SY1663: ( $i > $o ) > $i > $i ).
thf(tp_sK19_SY1689,type,
sK19_SY1689: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY1762,type,
sK20_SY1762: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK21_SY1296,type,
sK21_SY1296: $i > $i ).
thf(tp_sK22_SY1599,type,
sK22_SY1599: $i > $i > $i ).
thf(tp_sK23_SY1317,type,
sK23_SY1317: $i > $i ).
thf(tp_sK24_SY1779,type,
sK24_SY1779: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK25_SY1545,type,
sK25_SY1545: ( $i > $o ) > $i > $i ).
thf(tp_sK26_SY1591,type,
sK26_SY1591: ( $i > $o ) > $i > $i ).
thf(tp_sK27_SY1607,type,
sK27_SY1607: $i > $i > $i ).
thf(tp_sK28_SY1725,type,
sK28_SY1725: $i > $i > $i > $i ).
thf(tp_sK29_SY1770,type,
sK29_SY1770: $i > ( $i > $o ) > $i ).
thf(tp_sK2_SY1628,type,
sK2_SY1628: $i ).
thf(tp_sK30_SY1771,type,
sK30_SY1771: ( $i > $o ) > $i > $i ).
thf(tp_sK31_SY1780,type,
sK31_SY1780: ( $i > $o ) > $i > $i ).
thf(tp_sK32_SY1253,type,
sK32_SY1253: $i > $i ).
thf(tp_sK33_SY1614,type,
sK33_SY1614: $i > $i > $i ).
thf(tp_sK34_SY1371,type,
sK34_SY1371: $i > $i > $i ).
thf(tp_sK35_SY1781,type,
sK35_SY1781: $o > $i > $i > $i ).
thf(tp_sK36_SX0,type,
sK36_SX0: $i > $i > $i ).
thf(tp_sK37_SX0,type,
sK37_SX0: $i > $i > $i ).
thf(tp_sK38_SY1206,type,
sK38_SY1206: $i > ( $i > $o ) > $i ).
thf(tp_sK39_SY1585,type,
sK39_SY1585: $i > $i > $i ).
thf(tp_sK3_SY1423,type,
sK3_SY1423: $i > $i ).
thf(tp_sK40_SY1626,type,
sK40_SY1626: $i > $i > $i ).
thf(tp_sK41_SY1788,type,
sK41_SY1788: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK42_SY1692,type,
sK42_SY1692: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK43_SY1804,type,
sK43_SY1804: $i > ( $i > $o ) > $i ).
thf(tp_sK44_SY1595,type,
sK44_SY1595: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK45_SY1729,type,
sK45_SY1729: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK46_SY1626,type,
sK46_SY1626: $i > $i > $i ).
thf(tp_sK47_SY1679,type,
sK47_SY1679: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK48_SY1761,type,
sK48_SY1761: $i > ( $i > $o ) > $i ).
thf(tp_sK49_SY1763,type,
sK49_SY1763: $i > ( $i > $o ) > $i ).
thf(tp_sK4_SY1297,type,
sK4_SY1297: $i > $i ).
thf(tp_sK50_SY1767,type,
sK50_SY1767: $i > ( $i > $o ) > $i ).
thf(tp_sK51_SY1768,type,
sK51_SY1768: $i > ( $i > $o ) > $i ).
thf(tp_sK52_SY1769,type,
sK52_SY1769: $i > ( $i > $o ) > $i ).
thf(tp_sK53_SY1805,type,
sK53_SY1805: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK54_SY1785,type,
sK54_SY1785: $i > ( $i > $o ) > $i ).
thf(tp_sK55_SY1786,type,
sK55_SY1786: $i > ( $i > $o ) > $i ).
thf(tp_sK56_SY1794,type,
sK56_SY1794: $i > $i > $i > $i ).
thf(tp_sK57_SY1686,type,
sK57_SY1686: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK58_SY1208,type,
sK58_SY1208: $i > ( $i > $o ) > $i ).
thf(tp_sK59_SY1208,type,
sK59_SY1208: $i > ( $i > $o ) > $i ).
thf(tp_sK5_SY1343,type,
sK5_SY1343: $i > $i ).
thf(tp_sK60_SY1260,type,
sK60_SY1260: $i > ( $i > $o ) > $i ).
thf(tp_sK61_SY1322,type,
sK61_SY1322: $i > ( $i > $o ) > $i ).
thf(tp_sK62_SY1351,type,
sK62_SY1351: $i > ( $i > $o ) > $i ).
thf(tp_sK63_SY1621,type,
sK63_SY1621: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK64_SY1621,type,
sK64_SY1621: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK65_SY1646,type,
sK65_SY1646: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK66_SY1796,type,
sK66_SY1796: $i > $i > $i ).
thf(tp_sK67_SY1803,type,
sK67_SY1803: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK68_SY1509,type,
sK68_SY1509: $i > ( $i > $o ) > $i ).
thf(tp_sK69_SY1208,type,
sK69_SY1208: $i > ( $i > $o ) > $i ).
thf(tp_sK6_SY1733,type,
sK6_SY1733: $i ).
thf(tp_sK70_SY1260,type,
sK70_SY1260: $i > ( $i > $o ) > $i ).
thf(tp_sK71_SY1322,type,
sK71_SY1322: $i > ( $i > $o ) > $i ).
thf(tp_sK72_SY1351,type,
sK72_SY1351: $i > ( $i > $o ) > $i ).
thf(tp_sK73_SY1621,type,
sK73_SY1621: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK74_SY1375,type,
sK74_SY1375: $i > ( $i > $o ) > $i ).
thf(tp_sK75_SY1509,type,
sK75_SY1509: $i > ( $i > $o ) > $i ).
thf(tp_sK76_SY1375,type,
sK76_SY1375: $i > ( $i > $o ) > $i ).
thf(tp_sK77_SY1375,type,
sK77_SY1375: $i > ( $i > $o ) > $i ).
thf(tp_sK78_SY1375,type,
sK78_SY1375: $i > ( $i > $o ) > $i ).
thf(tp_sK79_SY1692,type,
sK79_SY1692: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK7_SY1538,type,
sK7_SY1538: $i > $i > $i ).
thf(tp_sK80_SY1633,type,
sK80_SY1633: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK81_SY1814,type,
sK81_SY1814: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK82_SY1666,type,
sK82_SY1666: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK83_SY1812,type,
sK83_SY1812: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK84_SY1692,type,
sK84_SY1692: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK85_SY1633,type,
sK85_SY1633: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK86_SY1666,type,
sK86_SY1666: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK87_SY1834,type,
sK87_SY1834: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY1835,type,
sK88_SY1835: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY1633,type,
sK89_SY1633: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY1539,type,
sK8_SY1539: $i > $i > $i ).
thf(tp_sK90_SY1633,type,
sK90_SY1633: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK91_SY1798,type,
sK91_SY1798: $i > $i > $i > $i ).
thf(tp_sK92_SY1666,type,
sK92_SY1666: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK93_SY1666,type,
sK93_SY1666: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK94_SY1633,type,
sK94_SY1633: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK95_SY1798,type,
sK95_SY1798: $i > $i > $i > $i ).
thf(tp_sK96_SY1666,type,
sK96_SY1666: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK97_SY1846,type,
sK97_SY1846: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK98_SY1562,type,
sK98_SY1562: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK99_SY1228,type,
sK99_SY1228: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK9_SY1552,type,
sK9_SY1552: ( $i > $o ) > $i > $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_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(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(cartprodfstin,definition,
( cartprodfstin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodfstpairEq,definition,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodpairin,definition,
( cartprodpairin
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodpairmemEL,definition,
( cartprodpairmemEL
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,definition,
( cartprodpairmemER
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodsndin,definition,
( cartprodsndin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodsndpairEq,definition,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,definition,
( ex1E1
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,definition,
( ex1I
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,definition,
( ex1I2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kfstsingleton,definition,
( kfstsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(kpairsurjEq,definition,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,definition,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(ksndsingleton,definition,
( ksndsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(setukpairinjL,definition,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjL1,definition,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(setukpairinjL2,definition,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR,definition,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(setukpairinjR1,definition,
( setukpairinjR1
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(setukpairinjR11,definition,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,definition,
( setukpairinjR12
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR2,definition,
( setukpairinjR2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,definition,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(singletonprop,definition,
( singletonprop
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,definition,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairequniteq,definition,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsubunion,definition,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(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
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY20: $i > $i > $o,SY21: $i] :
( ! [SY22: $i] :
( ( in @ SY22 @ SY21 )
=> ? [SY24: $i] :
( ( SY20 @ SY22 @ SY24 )
& ! [SY25: $i] :
( ( SY20 @ SY22 @ SY25 )
=> ( SY24 = SY25 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY21 )
& ( SY20 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY52: $i > $o] :
( ? [SY54: $i] :
( ( SY52 @ SY54 )
& ! [SY55: $i] :
( ( SY52 @ SY55 )
=> ( SY54 = SY55 ) ) )
=> ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY69: $i > $o] :
( ? [SY71: $i] :
( ( SY69 @ SY71 )
& ! [SY72: $i] :
( ( SY69 @ SY72 )
=> ( SY71 = SY72 ) ) )
=> ? [Xx: $i] :
( ( SY69 @ Xx )
& ! [Xy: $i] :
( ( SY69 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY81: $i > $o] :
( ? [SY83: $i] :
( ( SY81 @ SY83 )
& ! [SY84: $i] :
( ( SY81 @ SY84 )
=> ( SY83 = SY84 ) ) )
=> ? [Xx: $i] : ( SY81 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY98: $i] :
( ( SY98 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY98 ) )
=> ( ! [SY100: $i,SY101: $i > $o,SY102: $i] :
( ( in @ SY102 @ SY100 )
=> ( ( SY101 @ SY102 )
=> ( ( dsetconstr @ SY100
@ ^ [Xy: $i] : ( SY101 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY104: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY104 )
=> ( SY104 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
=> ( ! [SY137: $i > $o] :
( ? [SY139: $i] :
( ( SY137 @ SY139 )
& ! [SY140: $i] :
( ( SY137 @ SY140 )
=> ( SY139 = SY140 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY137 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY143: $i] :
( ( SY143 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY143 )
& $true ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) )
=> ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [SY192: $i > $o] :
( ? [Xx: $i] :
( ( SY192 @ Xx )
& ! [Xy: $i] :
( ( SY192 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY196: $i] :
( ( SY192 @ SY196 )
& ! [SY197: $i] :
( ( SY192 @ SY197 )
=> ( SY196 = SY197 ) ) ) )
=> ( ! [SY198: $i > $o] :
( ? [Xx: $i] : ( SY198 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY198 @ Xx )
=> ( ( SY198 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY203: $i] :
( ( SY198 @ SY203 )
& ! [SY204: $i] :
( ( SY198 @ SY204 )
=> ( SY203 = SY204 ) ) ) ) )
=> ( ! [SY205: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY205 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY209: $i] :
( ( SY205 @ SY209 )
& ! [SY210: $i] :
( ( SY205 @ SY210 )
=> ( SY209 = SY210 ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [SY219: $i > $o] :
( ? [SY221: $i] :
( ( SY219 @ SY221 )
& ! [SY222: $i] :
( ( SY219 @ SY222 )
=> ( SY221 = SY222 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY219 @ Xx )
=> ( ( SY219 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY225: $i > $o,SY226: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY225 @ Xx )
<=> ( SY226 @ Xy ) ) )
=> ( ? [SY230: $i] :
( ( SY225 @ SY230 )
& ! [SY231: $i] :
( ( SY225 @ SY231 )
=> ( SY230 = SY231 ) ) )
<=> ? [SY233: $i] :
( ( SY226 @ SY233 )
& ! [SY234: $i] :
( ( SY226 @ SY234 )
=> ( SY233 = SY234 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ( omega = omega )
=> ( ! [SY243: $i > $o] :
( ? [SY245: $i] :
( ( SY243 @ SY245 )
& ! [SY246: $i] :
( ( SY243 @ SY246 )
=> ( SY245 = SY246 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY243 @ Xx )
=> ( ( SY243 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY249: $i > $o,SY250: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY249 @ Xx )
<=> ( SY250 @ Xy ) ) )
=> ( ? [SY254: $i] :
( ( SY249 @ SY254 )
& ! [SY255: $i] :
( ( SY249 @ SY255 )
=> ( SY254 = SY255 ) ) )
=> ( ? [SY257: $i] :
( ( SY250 @ SY257 )
& ! [SY258: $i] :
( ( SY250 @ SY258 )
=> ( SY257 = SY258 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY249 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] : ( subset @ emptyset @ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) )
=> ( ! [A: $i] : ( subset @ A @ A )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) )
=> ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i] : ( in @ A @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) )
=> ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
=> ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
=> ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx )
=> ( ! [SY471: $i,SY472: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY471 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY471 )
=> ( ( SY472 @ Xx )
=> ( ( SY472 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY471 )
& ( SY472 @ Xx ) )
=> ? [SY477: $i] :
( ( in @ SY477
@ ( dsetconstr @ SY471
@ ^ [Xx: $i] : ( SY472 @ Xx ) ) )
& ( ( dsetconstr @ SY471
@ ^ [Xx: $i] : ( SY472 @ Xx ) )
= ( setadjoin @ SY477 @ emptyset ) ) ) ) )
=> ( ! [SY478: $i,SY479: $i > $o] :
( ? [SY484: $i] :
( ( in @ SY484
@ ( dsetconstr @ SY478
@ ^ [SY485: $i] : ( SY479 @ SY485 ) ) )
& ( ( dsetconstr @ SY478
@ ^ [SY486: $i] : ( SY479 @ SY486 ) )
= ( setadjoin @ SY484 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY478 )
& ( SY479 @ Xx ) ) )
=> ( ! [SY488: $i,SY489: $i > $o,SY490: $i] :
( ( in @ SY490 @ SY488 )
=> ( ( SY489 @ SY490 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY488 )
=> ( ( SY489 @ Xy )
=> ( Xy = SY490 ) ) )
=> ? [SY496: $i] :
( ( in @ SY496
@ ( dsetconstr @ SY488
@ ^ [SY497: $i] : ( SY489 @ SY497 ) ) )
& ( ( dsetconstr @ SY488
@ ^ [SY498: $i] : ( SY489 @ SY498 ) )
= ( setadjoin @ SY496 @ emptyset ) ) ) ) ) )
=> ( ! [SY499: $i,SY500: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY499 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY499 )
=> ( ( SY500 @ Xx )
=> ( ( SY500 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY499 )
& ( SY500 @ Xx ) )
=> ? [SY508: $i] :
( ( in @ SY508
@ ( dsetconstr @ SY499
@ ^ [SY509: $i] : ( SY500 @ SY509 ) ) )
& ( ( dsetconstr @ SY499
@ ^ [SY510: $i] : ( SY500 @ SY510 ) )
= ( setadjoin @ SY508 @ 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 ) )
=> ( ! [SY516: $i] :
( ( iskpair @ SY516 )
=> ? [SY518: $i] :
( ( in @ SY518
@ ( dsetconstr @ ( setunion @ SY516 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY516 ) ) )
& ( ( dsetconstr @ ( setunion @ SY516 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY516 ) )
= ( setadjoin @ SY518 @ emptyset ) ) ) )
=> ( ! [SY519: $i] :
( ? [SY520: $i] :
( ( in @ SY520 @ SY519 )
& ( SY519
= ( setadjoin @ SY520 @ emptyset ) ) )
=> ( in @ ( setunion @ SY519 ) @ SY519 ) )
=> ( ! [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 ) )
=> ( ! [SY553: $i] :
( ( iskpair @ SY553 )
=> ? [SY555: $i] :
( ( in @ SY555
@ ( dsetconstr @ ( setunion @ SY553 )
@ ^ [Xx: $i] :
( SY553
= ( kpair @ ( kfst @ SY553 ) @ Xx ) ) ) )
& ( ( dsetconstr @ ( setunion @ SY553 )
@ ^ [Xx: $i] :
( SY553
= ( kpair @ ( kfst @ SY553 ) @ Xx ) ) )
= ( setadjoin @ SY555 @ 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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,
( ( ! [SY20: $i > $i > $o,SY21: $i] :
( ! [SY22: $i] :
( ( in @ SY22 @ SY21 )
=> ? [SY24: $i] :
( ( SY20 @ SY22 @ SY24 )
& ! [SY25: $i] :
( ( SY20 @ SY22 @ SY25 )
=> ( SY24 = SY25 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY21 )
& ( SY20 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY52: $i > $o] :
( ? [SY54: $i] :
( ( SY52 @ SY54 )
& ! [SY55: $i] :
( ( SY52 @ SY55 )
=> ( SY54 = SY55 ) ) )
=> ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY69: $i > $o] :
( ? [SY71: $i] :
( ( SY69 @ SY71 )
& ! [SY72: $i] :
( ( SY69 @ SY72 )
=> ( SY71 = SY72 ) ) )
=> ? [Xx: $i] :
( ( SY69 @ Xx )
& ! [Xy: $i] :
( ( SY69 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY81: $i > $o] :
( ? [SY83: $i] :
( ( SY81 @ SY83 )
& ! [SY84: $i] :
( ( SY81 @ SY84 )
=> ( SY83 = SY84 ) ) )
=> ? [Xx: $i] : ( SY81 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY98: $i] :
( ( SY98 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY98 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY100: $i,SY101: $i > $o,SY102: $i] :
( ( in @ SY102 @ SY100 )
=> ( ( SY101 @ SY102 )
=> ( ( dsetconstr @ SY100
@ ^ [Xy: $i] : ( SY101 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY104: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY104 )
=> ( SY104 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [SY137: $i > $o] :
( ? [SY139: $i] :
( ( SY137 @ SY139 )
& ! [SY140: $i] :
( ( SY137 @ SY140 )
=> ( SY139 = SY140 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY137 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY143: $i] :
( ( SY143 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY143 )
& $true ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(47,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(49,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(52,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(53,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(54,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(55,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(56,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(57,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(58,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(59,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(60,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [SY192: $i > $o] :
( ? [Xx: $i] :
( ( SY192 @ Xx )
& ! [Xy: $i] :
( ( SY192 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY196: $i] :
( ( SY192 @ SY196 )
& ! [SY197: $i] :
( ( SY192 @ SY197 )
=> ( SY196 = SY197 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY198: $i > $o] :
( ? [Xx: $i] : ( SY198 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY198 @ Xx )
=> ( ( SY198 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY203: $i] :
( ( SY198 @ SY203 )
& ! [SY204: $i] :
( ( SY198 @ SY204 )
=> ( SY203 = SY204 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY205: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY205 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY209: $i] :
( ( SY205 @ SY209 )
& ! [SY210: $i] :
( ( SY205 @ SY210 )
=> ( SY209 = SY210 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [SY219: $i > $o] :
( ? [SY221: $i] :
( ( SY219 @ SY221 )
& ! [SY222: $i] :
( ( SY219 @ SY222 )
=> ( SY221 = SY222 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY219 @ Xx )
=> ( ( SY219 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY225: $i > $o,SY226: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY225 @ Xx )
<=> ( SY226 @ Xy ) ) )
=> ( ? [SY230: $i] :
( ( SY225 @ SY230 )
& ! [SY231: $i] :
( ( SY225 @ SY231 )
=> ( SY230 = SY231 ) ) )
<=> ? [SY233: $i] :
( ( SY226 @ SY233 )
& ! [SY234: $i] :
( ( SY226 @ SY234 )
=> ( SY233 = SY234 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(71,plain,
( ( emptyset = emptyset )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(72,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(75,plain,
( ( omega = omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(76,plain,
( ( ! [SY243: $i > $o] :
( ? [SY245: $i] :
( ( SY243 @ SY245 )
& ! [SY246: $i] :
( ( SY243 @ SY246 )
=> ( SY245 = SY246 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY243 @ Xx )
=> ( ( SY243 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY249: $i > $o,SY250: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY249 @ Xx )
<=> ( SY250 @ Xy ) ) )
=> ( ? [SY254: $i] :
( ( SY249 @ SY254 )
& ! [SY255: $i] :
( ( SY249 @ SY255 )
=> ( SY254 = SY255 ) ) )
=> ( ? [SY257: $i] :
( ( SY250 @ SY257 )
& ! [SY258: $i] :
( ( SY250 @ SY258 )
=> ( SY257 = SY258 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY249 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(83,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(84,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(89,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(91,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(92,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(98,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(100,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(101,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(103,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(104,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(105,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(120,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(136,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(137,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(138,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(139,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(140,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(141,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(142,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(143,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(144,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(147,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(149,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(150,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(151,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(153,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(154,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(155,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(156,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(157,plain,
( ( ! [SY471: $i,SY472: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY471 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY471 )
=> ( ( SY472 @ Xx )
=> ( ( SY472 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY471 )
& ( SY472 @ Xx ) )
=> ? [SY477: $i] :
( ( in @ SY477
@ ( dsetconstr @ SY471
@ ^ [Xx: $i] : ( SY472 @ Xx ) ) )
& ( ( dsetconstr @ SY471
@ ^ [Xx: $i] : ( SY472 @ Xx ) )
= ( setadjoin @ SY477 @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(158,plain,
( ( ! [SY478: $i,SY479: $i > $o] :
( ? [SY484: $i] :
( ( in @ SY484
@ ( dsetconstr @ SY478
@ ^ [SY485: $i] : ( SY479 @ SY485 ) ) )
& ( ( dsetconstr @ SY478
@ ^ [SY486: $i] : ( SY479 @ SY486 ) )
= ( setadjoin @ SY484 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY478 )
& ( SY479 @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(159,plain,
( ( ! [SY488: $i,SY489: $i > $o,SY490: $i] :
( ( in @ SY490 @ SY488 )
=> ( ( SY489 @ SY490 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY488 )
=> ( ( SY489 @ Xy )
=> ( Xy = SY490 ) ) )
=> ? [SY496: $i] :
( ( in @ SY496
@ ( dsetconstr @ SY488
@ ^ [SY497: $i] : ( SY489 @ SY497 ) ) )
& ( ( dsetconstr @ SY488
@ ^ [SY498: $i] : ( SY489 @ SY498 ) )
= ( setadjoin @ SY496 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(160,plain,
( ( ! [SY499: $i,SY500: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY499 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY499 )
=> ( ( SY500 @ Xx )
=> ( ( SY500 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY499 )
& ( SY500 @ Xx ) )
=> ? [SY508: $i] :
( ( in @ SY508
@ ( dsetconstr @ SY499
@ ^ [SY509: $i] : ( SY500 @ SY509 ) ) )
& ( ( dsetconstr @ SY499
@ ^ [SY510: $i] : ( SY500 @ SY510 ) )
= ( setadjoin @ SY508 @ 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,
( ( ! [SY516: $i] :
( ( iskpair @ SY516 )
=> ? [SY518: $i] :
( ( in @ SY518
@ ( dsetconstr @ ( setunion @ SY516 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY516 ) ) )
& ( ( dsetconstr @ ( setunion @ SY516 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY516 ) )
= ( setadjoin @ SY518 @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(164,plain,
( ( ! [SY519: $i] :
( ? [SY520: $i] :
( ( in @ SY520 @ SY519 )
& ( SY519
= ( setadjoin @ SY520 @ emptyset ) ) )
=> ( in @ ( setunion @ SY519 ) @ SY519 ) ) )
= $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,
( ( ! [SY553: $i] :
( ( iskpair @ SY553 )
=> ? [SY555: $i] :
( ( in @ SY555
@ ( dsetconstr @ ( setunion @ SY553 )
@ ^ [Xx: $i] :
( SY553
= ( kpair @ ( kfst @ SY553 ) @ Xx ) ) ) )
& ( ( dsetconstr @ ( setunion @ SY553 )
@ ^ [Xx: $i] :
( SY553
= ( kpair @ ( kfst @ SY553 ) @ Xx ) ) )
= ( setadjoin @ SY555 @ 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 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(185,plain,
( ( ~ ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[184]) ).
thf(186,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(187,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(188,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(189,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(190,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(191,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(192,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(193,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(194,plain,
( ( ! [SY553: $i] :
( ( iskpair @ SY553 )
=> ? [SY555: $i] :
( ( in @ SY555
@ ( dsetconstr @ ( setunion @ SY553 )
@ ^ [Xx: $i] :
( SY553
= ( kpair @ ( kfst @ SY553 ) @ Xx ) ) ) )
& ( ( dsetconstr @ ( setunion @ SY553 )
@ ^ [Xx: $i] :
( SY553
= ( kpair @ ( kfst @ SY553 ) @ Xx ) ) )
= ( setadjoin @ SY555 @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(195,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(196,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(197,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(198,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(199,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(200,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(201,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(202,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(203,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(204,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(205,plain,
( ( ! [SY519: $i] :
( ? [SY520: $i] :
( ( in @ SY520 @ SY519 )
& ( SY519
= ( setadjoin @ SY520 @ emptyset ) ) )
=> ( in @ ( setunion @ SY519 ) @ SY519 ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(206,plain,
( ( ! [SY516: $i] :
( ( iskpair @ SY516 )
=> ? [SY518: $i] :
( ( in @ SY518
@ ( dsetconstr @ ( setunion @ SY516 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY516 ) ) )
& ( ( dsetconstr @ ( setunion @ SY516 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY516 ) )
= ( setadjoin @ SY518 @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(207,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(208,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(209,plain,
( ( ! [SY499: $i,SY500: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY499 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY499 )
=> ( ( SY500 @ Xx )
=> ( ( SY500 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY499 )
& ( SY500 @ Xx ) )
=> ? [SY508: $i] :
( ( in @ SY508
@ ( dsetconstr @ SY499
@ ^ [SY509: $i] : ( SY500 @ SY509 ) ) )
& ( ( dsetconstr @ SY499
@ ^ [SY510: $i] : ( SY500 @ SY510 ) )
= ( setadjoin @ SY508 @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(210,plain,
( ( ! [SY488: $i,SY489: $i > $o,SY490: $i] :
( ( in @ SY490 @ SY488 )
=> ( ( SY489 @ SY490 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY488 )
=> ( ( SY489 @ Xy )
=> ( Xy = SY490 ) ) )
=> ? [SY496: $i] :
( ( in @ SY496
@ ( dsetconstr @ SY488
@ ^ [SY497: $i] : ( SY489 @ SY497 ) ) )
& ( ( dsetconstr @ SY488
@ ^ [SY498: $i] : ( SY489 @ SY498 ) )
= ( setadjoin @ SY496 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(211,plain,
( ( ! [SY478: $i,SY479: $i > $o] :
( ? [SY484: $i] :
( ( in @ SY484
@ ( dsetconstr @ SY478
@ ^ [SY485: $i] : ( SY479 @ SY485 ) ) )
& ( ( dsetconstr @ SY478
@ ^ [SY486: $i] : ( SY479 @ SY486 ) )
= ( setadjoin @ SY484 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY478 )
& ( SY479 @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(212,plain,
( ( ! [SY471: $i,SY472: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY471 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY471 )
=> ( ( SY472 @ Xx )
=> ( ( SY472 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY471 )
& ( SY472 @ Xx ) )
=> ? [SY477: $i] :
( ( in @ SY477
@ ( dsetconstr @ SY471
@ ^ [Xx: $i] : ( SY472 @ Xx ) ) )
& ( ( dsetconstr @ SY471
@ ^ [Xx: $i] : ( SY472 @ Xx ) )
= ( setadjoin @ SY477 @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(213,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(214,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(215,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(216,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(217,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(218,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(219,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(220,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(221,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(222,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(223,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(224,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(225,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(226,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(227,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(228,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(229,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(230,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(231,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(232,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(233,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(234,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(235,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(236,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(237,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(238,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(239,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(240,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(241,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(242,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(243,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(244,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(246,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(247,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(248,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(249,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(250,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(254,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(255,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(258,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(259,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(260,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(261,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(263,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(264,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(265,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(266,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(267,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(268,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(269,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(270,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(271,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(274,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(276,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(277,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(278,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(279,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(280,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(281,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(282,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(283,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(284,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(285,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(286,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(289,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(291,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(292,plain,
( ( ! [SY249: $i > $o,SY250: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY249 @ Xx )
<=> ( SY250 @ Xy ) ) )
=> ( ? [SY254: $i] :
( ( SY249 @ SY254 )
& ! [SY255: $i] :
( ( SY249 @ SY255 )
=> ( SY254 = SY255 ) ) )
=> ( ? [SY257: $i] :
( ( SY250 @ SY257 )
& ! [SY258: $i] :
( ( SY250 @ SY258 )
=> ( SY257 = SY258 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY249 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(293,plain,
( ( ! [SY243: $i > $o] :
( ? [SY245: $i] :
( ( SY243 @ SY245 )
& ! [SY246: $i] :
( ( SY243 @ SY246 )
=> ( SY245 = SY246 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY243 @ Xx )
=> ( ( SY243 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(294,plain,
( ( omega = omega )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(297,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(298,plain,
( ( emptyset = emptyset )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(299,plain,
( ( ! [SY225: $i > $o,SY226: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY225 @ Xx )
<=> ( SY226 @ Xy ) ) )
=> ( ? [SY230: $i] :
( ( SY225 @ SY230 )
& ! [SY231: $i] :
( ( SY225 @ SY231 )
=> ( SY230 = SY231 ) ) )
<=> ? [SY233: $i] :
( ( SY226 @ SY233 )
& ! [SY234: $i] :
( ( SY226 @ SY234 )
=> ( SY233 = SY234 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(300,plain,
( ( ! [SY219: $i > $o] :
( ? [SY221: $i] :
( ( SY219 @ SY221 )
& ! [SY222: $i] :
( ( SY219 @ SY222 )
=> ( SY221 = SY222 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY219 @ Xx )
=> ( ( SY219 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(303,plain,
( ( ! [SY205: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY205 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY209: $i] :
( ( SY205 @ SY209 )
& ! [SY210: $i] :
( ( SY205 @ SY210 )
=> ( SY209 = SY210 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(304,plain,
( ( ! [SY198: $i > $o] :
( ? [Xx: $i] : ( SY198 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY198 @ Xx )
=> ( ( SY198 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY203: $i] :
( ( SY198 @ SY203 )
& ! [SY204: $i] :
( ( SY198 @ SY204 )
=> ( SY203 = SY204 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(305,plain,
( ( ! [SY192: $i > $o] :
( ? [Xx: $i] :
( ( SY192 @ Xx )
& ! [Xy: $i] :
( ( SY192 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY196: $i] :
( ( SY192 @ SY196 )
& ! [SY197: $i] :
( ( SY192 @ SY197 )
=> ( SY196 = SY197 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(306,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(307,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(308,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(309,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(310,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(311,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(312,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(313,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(314,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(315,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(316,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(317,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(318,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(319,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(320,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(321,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(322,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(323,plain,
( ( ! [SY143: $i] :
( ( SY143 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY143 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(324,plain,
( ( ! [SY137: $i > $o] :
( ? [SY139: $i] :
( ( SY137 @ SY139 )
& ! [SY140: $i] :
( ( SY137 @ SY140 )
=> ( SY139 = SY140 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY137 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(325,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(326,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(327,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(328,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(329,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(330,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(331,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(332,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(333,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(334,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(335,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(336,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(337,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(338,plain,
( ( ! [SY104: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY104 )
=> ( SY104 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(339,plain,
( ( ! [SY100: $i,SY101: $i > $o,SY102: $i] :
( ( in @ SY102 @ SY100 )
=> ( ( SY101 @ SY102 )
=> ( ( dsetconstr @ SY100
@ ^ [Xy: $i] : ( SY101 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(340,plain,
( ( ! [SY98: $i] :
( ( SY98 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY98 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(341,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(342,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(343,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(345,plain,
( ( ! [SY81: $i > $o] :
( ? [SY83: $i] :
( ( SY81 @ SY83 )
& ! [SY84: $i] :
( ( SY81 @ SY84 )
=> ( SY83 = SY84 ) ) )
=> ? [Xx: $i] : ( SY81 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(346,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(347,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(348,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(349,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(350,plain,
( ( ! [SY69: $i > $o] :
( ? [SY71: $i] :
( ( SY69 @ SY71 )
& ! [SY72: $i] :
( ( SY69 @ SY72 )
=> ( SY71 = SY72 ) ) )
=> ? [Xx: $i] :
( ( SY69 @ Xx )
& ! [Xy: $i] :
( ( SY69 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(351,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(352,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(353,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(354,plain,
( ( ! [SY52: $i > $o] :
( ? [SY54: $i] :
( ( SY52 @ SY54 )
& ! [SY55: $i] :
( ( SY52 @ SY55 )
=> ( SY54 = SY55 ) ) )
=> ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(355,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(356,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(357,plain,
( ( ! [SY20: $i > $i > $o,SY21: $i] :
( ! [SY22: $i] :
( ( in @ SY22 @ SY21 )
=> ? [SY24: $i] :
( ( SY20 @ SY22 @ SY24 )
& ! [SY25: $i] :
( ( SY20 @ SY22 @ SY25 )
=> ( SY24 = SY25 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY21 )
& ( SY20 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(358,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(359,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(360,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(361,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(362,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(363,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(364,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(366,plain,
( ( ~ ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(367,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| SX3 )
| ~ ( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(368,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(369,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(370,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(371,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX2 != SX3 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(372,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(373,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(374,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(375,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(376,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(377,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(378,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(379,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(380,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(381,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(382,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(383,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(384,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ( SX0 @ SX1 )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(385,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[347,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(386,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(387,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(388,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(389,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX1 @ SX3 ) )
| ~ ( ~ ( SX1 @ SX3 )
| ( SX0 @ SX2 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX0 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX0 @ SX3 )
| ( SX2 = SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(390,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(391,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(392,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(393,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(394,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(395,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(396,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(397,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(398,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(399,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(400,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( in @ emptyset @ SX0 )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( in @ SX1 @ omega )
| ~ ( in @ SX1 @ SX0 ) )
| ( in @ ( setadjoin @ SX1 @ SX1 ) @ SX0 ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(401,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(402,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(403,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(404,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(405,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(406,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(407,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(408,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(409,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(410,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(411,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(412,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX2: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX2 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX2: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX2 ) ) )
!= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(413,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(414,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(415,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(416,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(417,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(418,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(419,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(420,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(421,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(422,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(423,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(424,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(425,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(426,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(427,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(428,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(429,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(430,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(431,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(432,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(433,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(434,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(435,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(436,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(437,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(438,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX2 = SX1 ) )
| ~ ( ( SX2 != SX1 )
| ( SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(439,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(440,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(441,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ( SX2
!= ( kpair @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(442,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(443,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(444,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(445,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(446,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[348,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(447,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(448,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(449,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(450,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(451,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(452,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(453,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(454,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX3 )
| ( SX3 = SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3
@ ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX1 @ SX4 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX1 @ SX4 ) )
!= ( setadjoin @ SX3 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(455,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(456,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(457,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(458,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(459,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(460,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(461,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX2 = SX1 ) )
| ~ ( ( SX2 != SX1 )
| ( SX0 @ SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(462,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(463,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(464,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(465,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( iskpair @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(466,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i > $o,SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ( SX4 != SX5 )
| ~ ( ~ ( ~ ( SX2 @ SX4 )
| ( SX3 @ SX5 ) )
| ~ ( ~ ( SX3 @ SX5 )
| ( SX2 @ SX4 ) ) ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX2 @ SX4 ) )
= ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(467,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(468,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX2: $i] : ( in @ ( setadjoin @ SX2 @ emptyset ) @ SX0 ) ) )
| ( ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX2: $i] : ( in @ ( setadjoin @ SX2 @ emptyset ) @ SX0 ) )
!= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(469,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(470,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(471,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(472,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[315,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(473,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( subset @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(474,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(475,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX1 @ SX3 ) )
| ~ ( ~ ( SX1 @ SX3 )
| ( SX0 @ SX2 ) ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX0 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SX2: $i] : ( SX0 @ SX2 ) )
= ( descr
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(476,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(477,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX4 )
| ( in @ SX3 @ SX4 ) )
| ~ ( ~ ( in @ SX3 @ SX4 )
| ( in @ SX2 @ SX4 ) ) ) )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX2 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SX2 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(478,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( subset @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(479,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(480,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(481,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(482,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(483,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ( SX2 != SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(484,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(485,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kfst @ ( kpair @ SX2 @ SX3 ) )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(486,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(487,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(488,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(489,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $o] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) )
= $true ),
inference(unfold_def,[status(thm)],[264,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(490,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(491,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(492,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(493,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[349,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(494,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX1 @ SX3 )
| ~ ( in @ SX3 @ SX0 )
| SX2 )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(495,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(496,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ( ( setadjoin @ SX0 @ SX2 )
= ( setadjoin @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(497,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( SX0 @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( SX0 @ SX2 @ SX4 )
| ( SX3 = SX4 ) ) ) )
| ~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(498,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( ksnd @ ( kpair @ SX2 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(499,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(500,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(501,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(502,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(503,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(504,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(505,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(506,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( SX0
!= ( setadjoin @ SX1 @ emptyset ) ) )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(507,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(508,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(509,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(510,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kpair @ SX2 @ SX3 )
= ( kpair @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(511,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(512,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,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,inCongP,inPowerset,in__Cong,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,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,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(513,plain,
! [SV1: $i] :
( ( ! [SY1144: $i] :
( ( ksnd @ ( kpair @ SV1 @ SY1144 ) )
= SY1144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(514,plain,
! [SV2: $i] :
( ( ! [SY1145: $i] :
( ( kfst @ ( kpair @ SV2 @ SY1145 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(515,plain,
! [SV3: $i] :
( ( ( setunion @ ( setadjoin @ SV3 @ emptyset ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(516,plain,
! [SV4: $i] :
( ( subset @ SV4 @ ( setunion @ ( setadjoin @ SV4 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(517,plain,
! [SV5: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV5 @ emptyset ) ) @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(518,plain,
! [SV6: $i] :
( ( ! [SY1146: $i] : ( iskpair @ ( kpair @ SV6 @ SY1146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(519,plain,
! [SV7: $i] :
( ( ! [SY1147: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV7 @ ( setadjoin @ SY1147 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(520,plain,
! [SV8: $i] :
( ( ! [SY1148: $i] : ( in @ SY1148 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV8 @ ( setadjoin @ SY1148 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(521,plain,
! [SV9: $i] :
( ( ! [SY1149: $i] : ( in @ SV9 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SY1149 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(522,plain,
! [SV10: $i] :
( ( ! [SY1150: $i] : ( in @ SY1150 @ ( setadjoin @ SV10 @ ( setadjoin @ SY1150 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(523,plain,
! [SV11: $i] :
( ( ! [SY1151: $i] : ( subset @ ( setminus @ SV11 @ SY1151 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(524,plain,
! [SV12: $i] :
( ( ! [SY1152: $i,SY1153: $i] :
( ( binintersect @ SV12 @ ( binunion @ SY1152 @ SY1153 ) )
= ( binunion @ ( binintersect @ SV12 @ SY1152 ) @ ( binintersect @ SV12 @ SY1153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(525,plain,
! [SV13: $i] :
( ( ! [SY1154: $i] : ( subset @ ( binintersect @ SV13 @ SY1154 ) @ SY1154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(526,plain,
! [SV14: $i] :
( ( ! [SY1155: $i] : ( subset @ ( binintersect @ SV14 @ SY1155 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(527,plain,
! [SV15: $i] :
( ( ! [SY1156: $i] : ( subset @ SY1156 @ ( binunion @ SV15 @ SY1156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(528,plain,
! [SV16: $i] :
( ( ! [SY1157: $i] : ( subset @ SV16 @ ( binunion @ SV16 @ SY1157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(529,plain,
! [SV17: $i] :
( ( ! [SY1158: $i] : ( in @ SY1158 @ ( setadjoin @ SV17 @ ( setadjoin @ SY1158 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(530,plain,
! [SV18: $i] :
( ( ! [SY1159: $i > $o] :
( subset
@ ( dsetconstr @ SV18
@ ^ [Xx: $i] : ( SY1159 @ Xx ) )
@ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(531,plain,
! [SV19: $i] :
( ( ! [SY1161: $i > $o] :
( in
@ ( dsetconstr @ SV19
@ ^ [Xx: $i] : ( SY1161 @ Xx ) )
@ ( powerset @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(532,plain,
! [SV20: $i] :
( ( in @ SV20 @ ( powerset @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(533,plain,
! [SV21: $i] :
( ( ! [SY1163: $i] : ( subset @ SY1163 @ ( setadjoin @ SV21 @ SY1163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(534,plain,
! [SV22: $i] :
( ( subset @ SV22 @ SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(535,plain,
! [SV23: $i] :
( ( subset @ emptyset @ SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(536,plain,
! [SV24: $i] :
( ( ! [SY1164: $i] : ( in @ SY1164 @ ( setadjoin @ SV24 @ ( setadjoin @ SY1164 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(537,plain,
! [SV25: $i] :
( ( ! [SY1165: $i] : ( in @ SV25 @ ( setadjoin @ SV25 @ ( setadjoin @ SY1165 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(538,plain,
! [SV26: $i] :
( ( in @ emptyset @ ( powerset @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(539,plain,
! [SV27: $i] :
( ( in @ emptyset @ ( powerset @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(540,plain,
! [SV28: $i] :
( ( ( dsetconstr @ SV28
@ ^ [Xx: $i] : $true )
= SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(541,plain,
! [SV29: $i] :
( ( ! [SY1167: $i] : ( in @ SV29 @ ( setadjoin @ SV29 @ SY1167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(542,plain,
! [SV30: $i] :
( ( ~ ( in @ SV30 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(543,plain,
! [SV31: $i] :
( ( ~ ( in @ SV31 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(544,plain,
! [SV32: $i] :
( ( ! [SY1168: $i,SY1169: $i] :
( ~ ( in @ SY1169 @ ( symdiff @ SV32 @ SY1168 ) )
| ! [SY1170: $o] :
( ~ ( ~ ( in @ SY1169 @ SV32 )
| ~ ~ ( in @ SY1169 @ SY1168 )
| SY1170 )
| ~ ( ~ ~ ( in @ SY1169 @ SV32 )
| ~ ( in @ SY1169 @ SY1168 )
| SY1170 )
| SY1170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(545,plain,
! [SV33: $i] :
( ( ! [SY1171: $i,SY1172: $i] :
( ~ ( in @ SY1172 @ ( binunion @ SV33 @ SY1171 ) )
| ( in @ SY1172 @ SV33 )
| ( in @ SY1172 @ SY1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(546,plain,
! [SV34: $i] :
( ( ! [SY1173: $i] :
( ~ ! [SY1174: $i] :
( ~ ( in @ SY1174 @ SV34 )
| ( in @ SY1174 @ SY1173 ) )
| ( subset @ SV34 @ SY1173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(547,plain,
! [SV35: $i] :
( ( ! [SY1175: $i] :
( ~ ! [SY1176: $i] :
( ~ ( in @ SY1176 @ SV35 )
| ( in @ SY1176 @ SY1175 ) )
| ( subset @ SV35 @ SY1175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(548,plain,
! [SV36: $i] :
( ( ! [SY1177: $i,SY1178: $i,SY1179: $i] :
( ( ( setadjoin @ ( setadjoin @ SV36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV36 @ ( setadjoin @ SY1177 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1178 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1178 @ ( setadjoin @ SY1179 @ emptyset ) ) @ emptyset ) ) )
| ( SY1178 != SY1179 )
| ( SY1177 = SY1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(549,plain,
! [SV37: $i] :
( ( ! [SY1180: $i,SY1181: $i] :
( ~ ( in @ SY1180 @ SY1181 )
| ~ ( in @ SY1181 @ SV37 )
| ( in @ SY1180 @ ( setunion @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(550,plain,
! [SV38: $i] :
( ( ! [SY1182: $i,SY1183: $i] :
( ~ ( in @ SY1183 @ SV38 )
| ~ ~ ( in @ SY1183 @ SY1182 )
| ( in @ SY1183 @ ( setminus @ SV38 @ SY1182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(551,plain,
! [SV39: $i] :
( ( ! [SY1184: $i,SY1185: $i] :
( ~ ( in @ SY1185 @ SY1184 )
| ( in @ SY1185 @ ( binunion @ SV39 @ SY1184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(552,plain,
! [SV40: $i] :
( ( ! [SY1186: $i] :
( ~ ~ ( subset @ SV40 @ SY1186 )
| ( SV40 != SY1186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(553,plain,
! [SV41: $i] :
( ( ! [SY1187: $i > $o] :
( ~ ~ ~ ! [SY1188: $i] :
~ ~ ( ~ ( in @ SY1188 @ SV41 )
| ~ ( SY1187 @ SY1188 ) )
| ! [SY1189: $i] :
( ~ ( in @ SY1189 @ SV41 )
| ~ ( SY1187 @ SY1189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(554,plain,
! [SV42: $i] :
( ( ! [SY1190: $i,SY1191: $i] :
( ~ ( in @ SY1191 @ ( cartprod @ SV42 @ SY1190 ) )
| ( in @ ( ksnd @ SY1191 ) @ SY1190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(555,plain,
! [SV43: $i] :
( ( ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ SY1193 @ SV43 )
| ~ ( in @ SY1193 @ SY1192 )
| ( in @ SY1193 @ ( binintersect @ SV43 @ SY1192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(556,plain,
! [SV44: $i] :
( ( ! [SY1194: $i,SY1195: $i] :
( ~ ( in @ SY1195 @ SV44 )
| ( in @ SY1195 @ ( binunion @ SV44 @ SY1194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(557,plain,
! [SV45: $i] :
( ( ! [SY1196: $i] :
( ( ( binintersect @ SV45 @ SY1196 )
!= SY1196 )
| ( subset @ SY1196 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(558,plain,
! [SV46: $i > $o] :
( ( ~ ~ ! [SY1197: $i] :
~ ~ ( ~ ( SV46 @ SY1197 )
| ~ ! [SY1198: $i] :
( ~ ( SV46 @ SY1198 )
| ( SY1197 = SY1198 ) ) )
| ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(559,plain,
! [SV47: $i] :
( ( ! [SY1201: $i,SY1202: $i] :
( ~ ( in @ SY1202 @ SV47 )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SY1201 )
| ( in @ ( setadjoin @ SY1202 @ ( setadjoin @ SY1203 @ emptyset ) ) @ ( powerset @ ( binunion @ SV47 @ SY1201 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(560,plain,
! [SV48: $i] :
( ( ! [SY1204: $i] :
( ~ ( in @ SV48 @ ( setadjoin @ SY1204 @ emptyset ) )
| ( SV48 = SY1204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(561,plain,
! [SV49: $i > $o] :
( ( ~ ~ ! [SY1205: $i] :
~ ( SV49 @ SY1205 )
| ~ ! [SY1206: $i,SY1207: $i] :
( ~ ( SV49 @ SY1206 )
| ~ ( SV49 @ SY1207 )
| ( SY1206 = SY1207 ) )
| ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(562,plain,
! [SV50: $i] :
( ( ~ ( in @ SV50 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(563,plain,
! [SV51: $i] :
( ( ! [SY1210: $i > $o] :
( ~ ! [SY1211: $i] :
( ~ ( in @ SY1211 @ SV51 )
| ~ ( SY1210 @ SY1211 ) )
| ~ ~ ! [SY1212: $i] :
~ ~ ( ~ ( in @ SY1212 @ SV51 )
| ~ ( SY1210 @ SY1212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(564,plain,
! [SV52: $i] :
( ( ! [SY1213: $i,SY1214: $i] :
( ~ ( in @ SY1214 @ SV52 )
| ! [SY1215: $i] :
( ~ ( in @ SY1215 @ SY1213 )
| ( in @ ( kpair @ SY1214 @ SY1215 ) @ ( powerset @ ( powerset @ ( binunion @ SV52 @ SY1213 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(565,plain,
! [SV53: $i] :
( ( ! [SY1216: $i,SY1217: $i,SY1218: $i] :
( ( ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SY1216 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1217 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1217 @ ( setadjoin @ SY1218 @ emptyset ) ) @ emptyset ) ) )
| ( SV53 = SY1217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(566,plain,
! [SV54: $i > $o] :
( ( ! [SY1219: $i > $o] :
( ~ ! [SY1220: $i,SY1221: $i] :
( ( SY1220 != SY1221 )
| ~ ( ~ ( ~ ( SV54 @ SY1220 )
| ( SY1219 @ SY1221 ) )
| ~ ( ~ ( SY1219 @ SY1221 )
| ( SV54 @ SY1220 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1219 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1219 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1219 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1219 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(567,plain,
! [SV55: $i] :
( ( ! [SY1230: $i,SY1231: $i] :
( ( ( setadjoin @ SV55 @ ( setadjoin @ SY1230 @ emptyset ) )
!= ( setadjoin @ SY1231 @ emptyset ) )
| ( SV55 = SY1230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(568,plain,
! [SV56: $i] :
( ( ! [SY1232: $i,SY1233: $i,SY1234: $i] :
( ~ ( in @ ( kpair @ SY1233 @ SY1234 ) @ ( cartprod @ SV56 @ SY1232 ) )
| ( in @ SY1233 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(569,plain,
! [SV57: $i] :
( ( ! [SY1235: $i > $o,SY1236: $i] :
( ~ ( in @ SY1236
@ ( dsetconstr @ SV57
@ ^ [SX3: $i] : ( SY1235 @ SX3 ) ) )
| ( SY1235 @ SY1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(570,plain,
! [SV58: $i] :
( ( ! [SY1238: $i,SY1239: $i] :
( ~ ~ ( in @ SY1239 @ SV58 )
| ~ ( in @ SY1239 @ SY1238 )
| ( in @ SY1239 @ ( symdiff @ SV58 @ SY1238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(571,plain,
! [SV59: $i] :
( ( ! [SY1240: $i] :
( ( SV59 != SY1240 )
| ( subset @ SV59 @ SY1240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(572,plain,
! [SV60: $i] :
( ( ! [SY1241: $i,SY1242: $i] :
( ~ ( in @ SY1242 @ ( cartprod @ SV60 @ SY1241 ) )
| ( in @ ( kfst @ SY1242 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(573,plain,
! [SV61: $i] :
( ( ! [SY1243: $i,SY1244: $i,SY1245: $i] :
( ( ( kpair @ SV61 @ SY1243 )
!= ( kpair @ SY1244 @ SY1245 ) )
| ( SV61 = SY1244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(574,plain,
! [SV62: $i] :
( ( ! [SY1246: $i > $o,SY1247: $i] :
( ~ ( in @ SY1247 @ SV62 )
| ~ ( ~ ( ~ ( in @ SY1247
@ ( dsetconstr @ SV62
@ ^ [SX3: $i] : ( SY1246 @ SX3 ) ) )
| ( SY1246 @ SY1247 ) )
| ~ ( ~ ( SY1246 @ SY1247 )
| ( in @ SY1247
@ ( dsetconstr @ SV62
@ ^ [SX3: $i] : ( SY1246 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(575,plain,
! [SV63: $i] :
( ( ! [SY1250: $i,SY1251: $i] :
( ~ ( subset @ SV63 @ SY1250 )
| ~ ~ ( in @ SY1251 @ SY1250 )
| ~ ( in @ SY1251 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(576,plain,
! [SV64: $i] :
( ( ! [SY1252: $i] :
( ( SV64 != SY1252 )
| ( ( setadjoin @ SV64 @ ( setadjoin @ SY1252 @ emptyset ) )
= ( setadjoin @ SV64 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(577,plain,
! [SV65: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV65 )
| ~ ! [SY1253: $i] :
( ~ ~ ( ~ ( in @ SY1253 @ omega )
| ~ ( in @ SY1253 @ SV65 ) )
| ( in @ ( setadjoin @ SY1253 @ SY1253 ) @ SV65 ) ) )
| ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(578,plain,
! [SV66: $i] :
( ( ! [SY1255: $i > $o,SY1256: $i] :
( ~ ( in @ SY1256
@ ( dsetconstr @ SV66
@ ^ [SX3: $i] : ( SY1255 @ SX3 ) ) )
| ( in @ SY1256 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(579,plain,
! [SV67: $i > $o] :
( ( ~ ~ ! [SY1258: $i] :
~ ~ ( ~ ( SV67 @ SY1258 )
| ~ ! [SY1259: $i] :
( ~ ( SV67 @ SY1259 )
| ( SY1258 = SY1259 ) ) )
| ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(580,plain,
! [SV68: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
( ~ ( in @ ( setadjoin @ SY1263 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ ( setadjoin @ SY1262 @ emptyset ) ) @ emptyset ) ) )
| ( SV68 = SY1263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(581,plain,
! [SV69: $i] :
( ( ! [SY1264: $i,SY1265: $i] :
( ~ ( in @ SY1265 @ ( binintersect @ SV69 @ SY1264 ) )
| ( in @ SY1265 @ SY1264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(582,plain,
! [SV70: $i] :
( ( ! [SY1266: $i] :
~ ( ~ ( ~ ( in @ SY1266 @ ( setunion @ SV70 ) )
| ~ ! [SY1267: $i] :
~ ~ ( ~ ( in @ SY1266 @ SY1267 )
| ~ ( in @ SY1267 @ SV70 ) ) )
| ~ ( ~ ~ ! [SY1268: $i] :
~ ~ ( ~ ( in @ SY1266 @ SY1268 )
| ~ ( in @ SY1268 @ SV70 ) )
| ( in @ SY1266 @ ( setunion @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(583,plain,
! [SV71: $o] :
( ( ~ SV71
| ( in @ emptyset @ ( prop2set @ SV71 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[406]) ).
thf(584,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[406]) ).
thf(585,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[406]) ).
thf(586,plain,
! [SV72: $i] :
( ( ~ ~ ! [SY1269: $i] :
~ ( in @ SY1269 @ SV72 )
| ( SV72 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(587,plain,
! [SV73: $i] :
( ( ! [SY1270: $i] :
( ~ ( in @ SY1270 @ SV73 )
| ( in @ SY1270 @ ( powerset @ ( setunion @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(588,plain,
! [SV74: $i] :
( ( ! [SY1271: $i,SY1272: $i] :
( ~ ( in @ SY1272 @ SV74 )
| ~ ~ ( in @ SY1272 @ SY1271 )
| ( SV74 != SY1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(589,plain,
! [SV75: $i] :
( ( ~ ( subset @ SV75 @ emptyset )
| ( SV75 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(590,plain,
! [SV76: $i] :
( ( ! [SY1273: $i] :
( ~ ( in @ SV76 @ ( setadjoin @ SY1273 @ emptyset ) )
| ( in @ SY1273 @ ( setadjoin @ SV76 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(591,plain,
! [SV77: $i] :
( ( ~ ( iskpair @ SV77 )
| ~ ! [SY1274: $i] :
~ ~ ( ~ ( in @ SY1274
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
!= ( setadjoin @ SY1274 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(592,plain,
! [SV78: $i] :
( ( ! [SY1277: $i,SY1278: $i] :
( ~ ~ ( in @ SY1278 @ ( setminus @ SV78 @ SY1277 ) )
| ~ ~ ( in @ SY1278 @ SY1277 )
| ~ ( in @ SY1278 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(593,plain,
! [SV79: $i] :
( ( ! [SY1279: $i,SY1280: $i] :
( ~ ~ ( in @ SY1280 @ ( setminus @ SV79 @ SY1279 ) )
| ~ ( in @ SY1280 @ SV79 )
| ( in @ SY1280 @ SY1279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(594,plain,
! [SV80: $i] :
( ( ! [SY1281: $i] :
( ( ( setadjoin @ SV80 @ emptyset )
!= ( setadjoin @ SY1281 @ emptyset ) )
| ( SV80 = SY1281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(595,plain,
! [SV81: $i] :
( ( ! [SY1282: $i] :
( ~ ( in @ SY1282 @ SV81 )
| ( subset @ ( setadjoin @ SY1282 @ emptyset ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(596,plain,
! [SV82: $i] :
( ( ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SV82 )
| ( in @ ( setadjoin @ SY1283 @ emptyset ) @ ( powerset @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(597,plain,
! [SV83: $i] :
( ( ! [SY1284: $i] :
( ( SV83 != SY1284 )
| ( in @ SV83 @ ( setadjoin @ SY1284 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(598,plain,
! [SV84: $i] :
( ( ! [SY1285: $i,SY1286: $i] :
( ~ ( subset @ SY1286 @ SV84 )
| ~ ( subset @ SY1286 @ SY1285 )
| ( subset @ SY1286 @ ( binintersect @ SV84 @ SY1285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(599,plain,
! [SV85: $i] :
( ( ~ ( iskpair @ SV85 )
| ( ( kpair @ ( kfst @ SV85 ) @ ( ksnd @ SV85 ) )
= SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(600,plain,
! [SV86: $i] :
( ( ! [SY1287: $i > $o] :
( ~ ~ ~ ! [SY1288: $i] :
~ ~ ( ~ ( in @ SY1288 @ SV86 )
| ~ ( SY1287 @ SY1288 ) )
| ! [SY1289: $i] :
( ~ ( in @ SY1289 @ SV86 )
| ~ ( SY1287 @ SY1289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(601,plain,
! [SV87: $i] :
( ( ! [SY1290: $i,SY1291: $i] :
( ~ ( in @ SY1291 @ ( setadjoin @ SV87 @ ( setadjoin @ SY1290 @ emptyset ) ) )
| ( SY1291 = SV87 )
| ( SY1291 = SY1290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(602,plain,
! [SV88: $i] :
( ( ! [SY1292: $i] :
( ( SV88 != SY1292 )
| ( ( powerset @ SV88 )
= ( powerset @ SY1292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(603,plain,
! [SV89: $i] :
( ( ! [SY1293: $i > $o] :
( ~ ~ ! [SY1294: $i] :
( ~ ( in @ SY1294 @ SV89 )
| ( SY1293 @ SY1294 ) )
| ~ ! [SY1295: $i] :
~ ~ ( ~ ( in @ SY1295 @ SV89 )
| ~ ~ ( SY1293 @ SY1295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(604,plain,
! [SV90: $i] :
( ( ~ ( ( SV90 != emptyset ) )
| ~ ! [SY1296: $i] :
~ ~ ( ~ ( in @ SY1296 @ SV90 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(605,plain,
! [SV91: $i] :
( ( ~ ! [SY1297: $i] :
~ ( in @ SY1297 @ SV91 )
| ( SV91 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(606,plain,
! [SV92: $i] :
( ( ! [SY1298: $i,SY1299: $i,SY1300: $i] :
( ( ( kpair @ SV92 @ SY1298 )
!= ( kpair @ SY1299 @ SY1300 ) )
| ( SY1298 = SY1300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(607,plain,
! [SV93: $i] :
( ( ! [SY1301: $i,SY1302: $i] :
( ~ ( in @ SY1302 @ SY1301 )
| ( in @ SY1302 @ ( setadjoin @ SV93 @ SY1301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(608,plain,
! [SV94: $i] :
( ( ! [SY1303: $i] :
( ~ ( in @ SY1303 @ ( setunion @ SV94 ) )
| ~ ! [SY1304: $i] :
~ ~ ( ~ ( in @ SY1304 @ SV94 )
| ~ ( in @ SY1303 @ SY1304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(609,plain,
! [SV95: $i] :
( ( ! [SY1305: $i] :
( ~ ( subset @ SV95 @ SY1305 )
| ~ ( subset @ SY1305 @ SV95 )
| ( SV95 = SY1305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(610,plain,
! [SV96: $i] :
( ( ! [SY1306: $i,SY1307: $i,SY1308: $i] :
( ~ ( in @ ( kpair @ SY1307 @ SY1308 ) @ ( cartprod @ SV96 @ SY1306 ) )
| ( in @ SY1308 @ SY1306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(611,plain,
! [SV97: $i] :
( ( ! [SY1309: $i,SY1310: $i] :
( ~ ( in @ SY1310 @ ( binintersect @ SV97 @ SY1309 ) )
| ( in @ SY1310 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(612,plain,
! [SV98: $i] :
( ( ! [SY1311: $i] :
( ( SV98 != SY1311 )
| ! [SY1312: $i,SY1313: $i] :
( ( SY1312 != SY1313 )
| ~ ( ~ ( ~ ( in @ SY1312 @ SV98 )
| ( in @ SY1313 @ SY1311 ) )
| ~ ( ~ ( in @ SY1313 @ SY1311 )
| ( in @ SY1312 @ SV98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(613,plain,
! [SV99: $i] :
( ( ! [SY1314: $i,SY1315: $i] :
( ~ ( in @ SY1315 @ ( setadjoin @ SV99 @ ( setadjoin @ SY1314 @ emptyset ) ) )
| ( SY1315 = SV99 )
| ( SY1315 = SY1314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(614,plain,
! [SV100: $i] :
( ( ! [SY1316: $i] :
( ( ( setminus @ SV100 @ SY1316 )
!= emptyset )
| ( subset @ SV100 @ SY1316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(615,plain,
! [SV101: $i] :
( ( ~ ( ( SV101 != emptyset ) )
| ~ ! [SY1317: $i] :
~ ( in @ SY1317 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(616,plain,
! [SV102: $i] :
( ( ! [SY1318: $i,SY1319: $i] :
~ ( ~ ( ~ ( in @ SY1319 @ ( setadjoin @ SV102 @ SY1318 ) )
| ( SY1319 = SV102 )
| ( in @ SY1319 @ SY1318 ) )
| ~ ( ~ ( ( SY1319 = SV102 )
| ( in @ SY1319 @ SY1318 ) )
| ( in @ SY1319 @ ( setadjoin @ SV102 @ SY1318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(617,plain,
! [SV103: $i > $o] :
( ( ~ ~ ! [SY1320: $i] :
~ ~ ( ~ ( SV103 @ SY1320 )
| ~ ! [SY1321: $i] :
( ~ ( SV103 @ SY1321 )
| ( SY1320 = SY1321 ) ) )
| ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(618,plain,
! [SV104: $i] :
( ( ! [SY1324: $i] :
( ~ ~ ~ ! [SY1325: $i] :
~ ~ ( ~ ( in @ SY1325 @ SV104 )
| ~ ( in @ SY1325 @ SY1324 ) )
| ( ( binintersect @ SV104 @ SY1324 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(619,plain,
! [SV105: $i] :
( ( ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ SY1327 @ SV105 )
| ~ ~ ( in @ SY1327 @ SY1326 )
| ~ ( subset @ SV105 @ SY1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(620,plain,
! [SV106: $i] :
( ( ! [SY1328: $i,SY1329: $i] :
( ~ ( in @ SY1329 @ ( cartprod @ SV106 @ SY1328 ) )
| ~ ! [SY1330: $i] :
~ ~ ( ~ ( in @ SY1330 @ SV106 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY1328 )
| ( SY1329
!= ( kpair @ SY1330 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(621,plain,
! [SV107: $i > $o] :
( ( ~ ~ ! [SY1332: $i] :
~ ~ ( ~ ( SV107 @ SY1332 )
| ~ ! [SY1333: $i] :
( ~ ( SV107 @ SY1333 )
| ( SY1332 = SY1333 ) ) )
| ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(622,plain,
! [SV108: $i] :
( ( ! [SY1336: $i,SY1337: $i] :
( ~ ~ ( in @ SY1337 @ SV108 )
| ~ ~ ( in @ SY1337 @ SY1336 )
| ~ ( in @ SY1337 @ ( symdiff @ SV108 @ SY1336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(623,plain,
! [SV109: $i] :
( ( ! [SY1338: $i] :
~ ( ~ ( ~ ( in @ SY1338 @ ( powerset @ SV109 ) )
| ! [SY1339: $i] :
( ~ ( in @ SY1339 @ SY1338 )
| ( in @ SY1339 @ SV109 ) ) )
| ~ ( ~ ! [SY1340: $i] :
( ~ ( in @ SY1340 @ SY1338 )
| ( in @ SY1340 @ SV109 ) )
| ( in @ SY1338 @ ( powerset @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(624,plain,
! [SV110: $i] :
( ( ! [SY1341: $i] :
( ~ ( subset @ SV110 @ SY1341 )
| ( ( binintersect @ SV110 @ SY1341 )
= SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(625,plain,
! [SV111: $i] :
( ( ~ ( in @ SV111 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(626,plain,
! [SV112: $i] :
( ( ~ ! [SY1343: $i] :
~ ( in @ SY1343 @ SV112 )
| ( SV112 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(627,plain,
! [SV113: $o] :
( ( ~ SV113
| ( set2prop @ ( prop2set @ SV113 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[448]) ).
thf(628,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[448]) ).
thf(629,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[448]) ).
thf(630,plain,
! [SV114: $i > $o] :
( ( ! [SY1344: $i] :
( ~ ( in @ SY1344 @ emptyset )
| ( SV114 @ SY1344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(631,plain,
! [SV115: $i] :
( ( ! [SY1345: $i,SY1346: $i,SY1347: $i] :
( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SY1345 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1346 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1346 @ ( setadjoin @ SY1347 @ emptyset ) ) @ emptyset ) ) )
| ( SY1345 = SY1347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(632,plain,
! [SV116: $i] :
( ( ! [SY1348: $i] :
( ~ ( ( SV116 != SY1348 ) )
| ~ ( in @ SY1348 @ ( setadjoin @ SV116 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(633,plain,
! [SV117: $i > $o] :
( ( ~ ~ ! [SY1349: $i] :
~ ~ ( ~ ( SV117 @ SY1349 )
| ~ ! [SY1350: $i] :
( ~ ( SV117 @ SY1350 )
| ( SY1349 = SY1350 ) ) )
| ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(634,plain,
! [SV118: $i] :
( ( ! [SY1352: $i > $o,SY1353: $i] :
( ~ ( in @ SY1353 @ SV118 )
| ~ ( SY1352 @ SY1353 )
| ( ( dsetconstr @ SV118
@ ^ [SX3: $i] : ( SY1352 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(635,plain,
! [SV119: $i] :
( ( ! [SY1355: $i > $o,SY1356: $i] :
( ~ ( in @ SY1356 @ SV119 )
| ~ ( SY1355 @ SY1356 )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ SV119 )
| ~ ( SY1355 @ SY1357 )
| ( SY1357 = SY1356 ) )
| ~ ! [SY1358: $i] :
~ ~ ( ~ ( in @ SY1358
@ ( dsetconstr @ SV119
@ ^ [SX4: $i] : ( SY1355 @ SX4 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SX4: $i] : ( SY1355 @ SX4 ) )
!= ( setadjoin @ SY1358 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(636,plain,
! [SV120: $i] :
( ( ! [SY1361: $i] :
( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SY1361 )
| ( in @ SY1362 @ SV120 ) )
| ( in @ SY1361 @ ( powerset @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(637,plain,
! [SV121: $i] :
( ( ! [SY1363: $i] :
( ~ ! [SY1364: $i] :
( ~ ( in @ SY1364 @ SV121 )
| ( in @ SY1364 @ SY1363 ) )
| ~ ! [SY1365: $i] :
( ~ ( in @ SY1365 @ SY1363 )
| ( in @ SY1365 @ SV121 ) )
| ( SV121 = SY1363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(638,plain,
! [SV122: $i] :
( ( ! [SY1366: $i] :
( ~ ( subset @ SV122 @ SY1366 )
| ( ( setminus @ SV122 @ SY1366 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(639,plain,
! [SV123: $i] :
( ( ! [SY1367: $i] :
( ~ ( subset @ SY1367 @ SV123 )
| ( in @ SY1367 @ ( powerset @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(640,plain,
! [SV124: $i] :
( ( ! [SY1368: $i,SY1369: $i] :
( ~ ( subset @ SV124 @ SY1368 )
| ~ ( in @ SY1369 @ SV124 )
| ( in @ SY1369 @ SY1368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(641,plain,
! [SV125: $i] :
( ( ~ ~ ! [SY1370: $i] :
~ ( in @ SY1370 @ SV125 )
| ~ ! [SY1371: $i] :
~ ~ ( ~ ( in @ SY1371 @ SV125 )
| ~ ~ ~ ! [SY1372: $i] :
~ ~ ( ~ ( in @ SY1372 @ SY1371 )
| ~ ( in @ SY1372 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(642,plain,
! [SV126: $i > $o] :
( ( ~ ~ ! [SY1373: $i] :
~ ! [SY1374: $i] :
~ ( ~ ( ~ ( SV126 @ SY1374 )
| ( SY1374 = SY1373 ) )
| ~ ( ( SY1374 != SY1373 )
| ( SV126 @ SY1374 ) ) )
| ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(643,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(644,plain,
! [SV127: $i] :
( ( ! [SY1377: $i > $o] :
( ~ ! [SY1378: $i] :
( ~ ( in @ SY1378 @ SV127 )
| ! [SY1379: $i] :
( ~ ( in @ SY1379 @ SV127 )
| ~ ( SY1377 @ SY1378 )
| ~ ( SY1377 @ SY1379 )
| ( SY1378 = SY1379 ) ) )
| ~ ~ ! [SY1380: $i] :
~ ~ ( ~ ( in @ SY1380 @ SV127 )
| ~ ( SY1377 @ SY1380 ) )
| ~ ! [SY1381: $i] :
~ ~ ( ~ ( in @ SY1381
@ ( dsetconstr @ SV127
@ ^ [SX3: $i] : ( SY1377 @ SX3 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SX3: $i] : ( SY1377 @ SX3 ) )
!= ( setadjoin @ SY1381 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(645,plain,
! [SV128: $i] :
( ( ! [SY1384: $i] :
( ~ ( subset @ SV128 @ SY1384 )
| ( subset @ ( powerset @ SV128 ) @ ( powerset @ SY1384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(646,plain,
! [SV129: $i] :
( ( ! [SY1385: $i,SY1386: $i] :
( ~ ( in @ SY1386 @ ( cartprod @ SV129 @ SY1385 ) )
| ( iskpair @ SY1386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(647,plain,
! [SV130: $i] :
( ( ! [SY1387: $i] :
( ( SV130 != SY1387 )
| ! [SY1388: $i > $o,SY1389: $i > $o] :
( ~ ! [SY1390: $i] :
( ~ ( in @ SY1390 @ SV130 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY1387 )
| ( SY1390 != SX5 )
| ~ ( ~ ( ~ ( SY1388 @ SY1390 )
| ( SY1389 @ SX5 ) )
| ~ ( ~ ( SY1389 @ SX5 )
| ( SY1388 @ SY1390 ) ) ) ) )
| ( ( dsetconstr @ SV130
@ ^ [SX4: $i] : ( SY1388 @ SX4 ) )
= ( dsetconstr @ SY1387
@ ^ [SX4: $i] : ( SY1389 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(648,plain,
! [SV131: $i] :
( ( ! [SY1394: $i,SY1395: $i] :
( ~ ( subset @ SV131 @ SY1395 )
| ( subset @ SV131 @ ( setadjoin @ SY1394 @ SY1395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(649,plain,
! [SV132: $i] :
( ( ~ ( iskpair @ SV132 )
| ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) )
| ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
!= ( setadjoin @ SY1396 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(650,plain,
! [SV133: $i] :
( ( ! [SY1399: $i] :
( ( ( binintersect @ SV133 @ SY1399 )
!= SV133 )
| ( subset @ SV133 @ SY1399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(651,plain,
! [SV134: $i] :
( ( ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ SY1401 @ ( setadjoin @ SV134 @ SY1400 ) )
| ( SY1401 = SV134 )
| ( in @ SY1401 @ SY1400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(652,plain,
! [SV135: $i] :
( ( ! [SY1402: $i > $o] :
( ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ SV135 )
| ~ ~ ( SY1402 @ SY1403 ) )
| ~ ! [SY1404: $i] :
( ~ ( in @ SY1404 @ SV135 )
| ( SY1402 @ SY1404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(653,plain,
! [SV136: $i] :
( ( ! [SY1405: $i > $o] :
( ~ ~ ! [SY1406: $i] :
~ ~ ( ~ ( in @ SY1406 @ SV136 )
| ~ ( SY1405 @ SY1406 ) )
| ( ( dsetconstr @ SV136
@ ^ [SX2: $i] : ( SY1405 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(654,plain,
! [SV137: $i] :
( ( ! [SY1408: $i,SY1409: $i] :
( ~ ( in @ SY1409 @ SV137 )
| ! [SY1410: $i] :
( ~ ( in @ SY1410 @ SY1408 )
| ( subset @ ( setadjoin @ SY1409 @ ( setadjoin @ SY1410 @ emptyset ) ) @ ( binunion @ SV137 @ SY1408 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(655,plain,
! [SV138: $i] :
( ( ! [SY1411: $i] :
( ~ ( subset @ SV138 @ SY1411 )
| ( in @ SV138 @ ( powerset @ SY1411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(656,plain,
! [SV139: $i > $o] :
( ( ! [SY1412: $i > $o] :
( ~ ! [SY1413: $i,SY1414: $i] :
( ( SY1413 != SY1414 )
| ~ ( ~ ( ~ ( SV139 @ SY1413 )
| ( SY1412 @ SY1414 ) )
| ~ ( ~ ( SY1412 @ SY1414 )
| ( SV139 @ SY1413 ) ) ) )
| ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1412 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1412 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SX2: $i] : ( SY1412 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(657,plain,
! [SV140: $i] :
( ( ! [SY1421: $i] :
( ~ ! [SY1422: $i] :
~ ( ~ ( ~ ( in @ SY1422 @ SV140 )
| ( in @ SY1422 @ SY1421 ) )
| ~ ( ~ ( in @ SY1422 @ SY1421 )
| ( in @ SY1422 @ SV140 ) ) )
| ( SV140 = SY1421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(658,plain,
! [SV141: $i] :
( ( ~ ! [SY1423: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1424: $i] :
( ~ ( in @ SY1424 @ SY1423 )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1424 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1426: $i,SY1427: $i] :
( ~ ~ ( ~ ( in @ SY1426 @ SV141 )
| ~ ( in @ SY1427 @ SV141 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1423 )
| ~ ( ~ ( ~ ( in @ SY1426 @ SX4 )
| ( in @ SY1427 @ SX4 ) )
| ~ ( ~ ( in @ SY1427 @ SX4 )
| ( in @ SY1426 @ SX4 ) ) ) )
| ( SY1426 = SY1427 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY1423 )
| ~ ( in @ SX3 @ SY1423 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY1433: $i] :
( ~ ~ ( ~ ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SY1433 )
| ( in @ SY1434 @ SV141 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1433 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY1423 )
| ~ ( in @ SX4 @ SY1433 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY1433 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY1423 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(659,plain,
! [SV142: $i] :
( ( ! [SY1441: $i,SY1442: $i] :
( ~ ( in @ SY1442 @ SV142 )
| ! [SY1443: $i] :
( ~ ( in @ SY1443 @ SY1441 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1442 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1442 @ ( setadjoin @ SY1443 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV142 @ SY1441 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(660,plain,
! [SV143: $i] :
( ( ~ ( in @ SV143 @ omega )
| ( in @ ( setadjoin @ SV143 @ SV143 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(661,plain,
! [SV144: $i] :
( ( ! [SY1444: $i] :
( ~ ( subset @ SY1444 @ SV144 )
| ( ( binintersect @ SV144 @ SY1444 )
= SY1444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(662,plain,
! [SV145: $i] :
( ( ! [SY1445: $i,SY1446: $i] :
( ~ ( in @ SY1446 @ SY1445 )
| ~ ( in @ SY1446 @ ( setminus @ SV145 @ SY1445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(663,plain,
! [SV146: $i] :
( ( ! [SY1447: $i > $o] :
( ~ ! [SY1448: $i] :
( ~ ( in @ SY1448 @ SV146 )
| ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV146 )
| ~ ( SY1447 @ SY1448 )
| ~ ( SY1447 @ SY1449 )
| ( SY1448 = SY1449 ) ) )
| ~ ~ ! [SY1450: $i] :
~ ~ ( ~ ( in @ SY1450 @ SV146 )
| ~ ( SY1447 @ SY1450 ) )
| ~ ! [SY1451: $i] :
~ ~ ( ~ ( in @ SY1451
@ ( dsetconstr @ SV146
@ ^ [SX3: $i] : ( SY1447 @ SX3 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SX3: $i] : ( SY1447 @ SX3 ) )
!= ( setadjoin @ SY1451 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(664,plain,
! [SV147: $i] :
( ( ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ SY1455 @ ( setadjoin @ SV147 @ SY1454 ) )
| ! [SY1456: $o] :
( ~ ( ( SY1455 != SV147 )
| SY1456 )
| ~ ( ~ ( in @ SY1455 @ SY1454 )
| SY1456 )
| SY1456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(665,plain,
! [SV148: $i] :
( ( ! [SY1457: $i] :
( ( SV148 != SY1457 )
| ( subset @ SY1457 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(666,plain,
! [SV149: $i] :
( ( ! [SY1458: $i,SY1459: $i] :
( ~ ( in @ SY1459 @ SV149 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1458 )
| ( ( kfst @ ( kpair @ SY1459 @ SX3 ) )
= SY1459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(667,plain,
! [SV150: $i] :
( ( ! [SY1461: $i > $o,SY1462: $i] :
( ~ ( in @ SY1462 @ SV150 )
| ~ ( SY1461 @ SY1462 )
| ( in @ SY1462
@ ( dsetconstr @ SV150
@ ^ [SX3: $i] : ( SY1461 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(668,plain,
! [SV151: $i] :
( ( ! [SY1464: $i,SY1465: $i] :
( ~ ( in @ SY1464 @ ( powerset @ SV151 ) )
| ~ ( in @ SY1465 @ SY1464 )
| ( in @ SY1465 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(669,plain,
! [SV152: $i] :
( ( ! [SY1466: $i] :
( ( SV152 != SY1466 )
| ( ( setunion @ SV152 )
= ( setunion @ SY1466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(670,plain,
! [SV153: $i] :
( ( ! [SY1467: $i,SY1468: $i,SY1469: $o] :
( ~ ( in @ SY1468 @ ( binunion @ SV153 @ SY1467 ) )
| ~ ( ~ ( in @ SY1468 @ SV153 )
| SY1469 )
| ~ ( ~ ( in @ SY1468 @ SY1467 )
| SY1469 )
| SY1469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(671,plain,
! [SV154: $i] :
( ( ! [SY1470: $i] :
( ( SV154 != SY1470 )
| ( ( setadjoin @ ( setadjoin @ SV154 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV154 @ ( setadjoin @ SY1470 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV154 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(672,plain,
! [SV155: $i] :
( ( ! [SY1471: $i > $o] :
( ~ ~ ! [SY1472: $i] :
( ~ ( in @ SY1472 @ SV155 )
| ( SY1471 @ SY1472 ) )
| ~ ! [SY1473: $i] :
~ ~ ( ~ ( in @ SY1473 @ SV155 )
| ~ ~ ( SY1471 @ SY1473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(673,plain,
! [SV156: $i] :
( ( ! [SY1474: $i,SY1475: $i] :
( ~ ( in @ SY1475 @ SV156 )
| ( in @ ( setadjoin @ SY1475 @ emptyset ) @ ( powerset @ ( binunion @ SV156 @ SY1474 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(674,plain,
! [SV157: $o] :
( ( ! [SY1476: $i] :
( ~ ( in @ SY1476 @ ( prop2set @ SV157 ) )
| SV157 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[493]) ).
thf(675,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[493]) ).
thf(676,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[493]) ).
thf(677,plain,
! [SV158: $i] :
( ( ! [SY1477: $i] :
( ~ ( in @ SY1477 @ ( setunion @ SV158 ) )
| ! [SY1478: $o] :
( ~ ! [SY1479: $i] :
( ~ ( in @ SY1477 @ SY1479 )
| ~ ( in @ SY1479 @ SV158 )
| SY1478 )
| SY1478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(678,plain,
! [SV159: $i] :
( ( ! [SY1480: $i > $o] :
( ~ ~ ! [SY1481: $i] :
~ ~ ( ~ ( in @ SY1481
@ ( dsetconstr @ SV159
@ ^ [SX3: $i] : ( SY1480 @ SX3 ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SX3: $i] : ( SY1480 @ SX3 ) )
!= ( setadjoin @ SY1481 @ emptyset ) ) )
| ~ ! [SY1484: $i] :
~ ~ ( ~ ( in @ SY1484 @ SV159 )
| ~ ( SY1480 @ SY1484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(679,plain,
! [SV160: $i] :
( ( ! [SY1485: $i] :
( ( SV160 != SY1485 )
| ! [SY1486: $i,SY1487: $i] :
( ( SY1486 != SY1487 )
| ( ( setadjoin @ SV160 @ SY1486 )
= ( setadjoin @ SY1485 @ SY1487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(680,plain,
! [SV161: $i > $i > $o] :
( ( ! [SY1488: $i] :
( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ SY1488 )
| ~ ! [SY1490: $i] :
~ ~ ( ~ ( SV161 @ SY1489 @ SY1490 )
| ~ ! [SY1491: $i] :
( ~ ( SV161 @ SY1489 @ SY1491 )
| ( SY1490 = SY1491 ) ) ) )
| ~ ! [SY1492: $i] :
~ ! [SY1493: $i] :
~ ( ~ ( ~ ( in @ SY1493 @ SY1492 )
| ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SY1488 )
| ~ ( SV161 @ SY1494 @ SY1493 ) ) )
| ~ ( ~ ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495 @ SY1488 )
| ~ ( SV161 @ SY1495 @ SY1493 ) )
| ( in @ SY1493 @ SY1492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(681,plain,
! [SV162: $i] :
( ( ! [SY1496: $i,SY1497: $i] :
( ~ ( in @ SY1497 @ SV162 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1496 )
| ( ( ksnd @ ( kpair @ SY1497 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(682,plain,
! [SV163: $i] :
( ( ! [SY1499: $i,SY1500: $i] :
( ~ ( subset @ SV163 @ SY1499 )
| ~ ( subset @ SY1499 @ SY1500 )
| ( subset @ SV163 @ SY1500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(683,plain,
! [SV164: $i] :
( ( ! [SY1501: $i,SY1502: $i] :
( ~ ( in @ SY1502 @ ( setminus @ SV164 @ SY1501 ) )
| ( in @ SY1502 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(684,plain,
! [SV165: $i] :
( ( ! [SY1503: $i,SY1504: $i] :
( ~ ( in @ SY1504 @ SV165 )
| ~ ~ ( in @ SY1504 @ SY1503 )
| ( in @ SY1504 @ ( symdiff @ SV165 @ SY1503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(685,plain,
! [SV166: $i] :
( ( ! [SY1505: $i,SY1506: $i] :
( ~ ~ ( in @ SY1506 @ SV166 )
| ~ ( in @ SY1506 @ ( setminus @ SV166 @ SY1505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(686,plain,
! [SV167: $i > $o] :
( ( ~ ~ ! [SY1507: $i] :
~ ~ ( ~ ( SV167 @ SY1507 )
| ~ ! [SY1508: $i] :
( ~ ( SV167 @ SY1508 )
| ( SY1507 = SY1508 ) ) )
| ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(687,plain,
! [SV168: $i] :
( ( ! [SY1511: $i,SY1512: $i] :
( ~ ( in @ SY1512 @ ( setminus @ SV168 @ SY1511 ) )
| ~ ( in @ SY1512 @ SY1511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(688,plain,
! [SV169: $i] :
( ( ! [SY1513: $i,SY1514: $i] :
( ~ ( in @ SY1514 @ SV169 )
| ~ ( in @ SY1514 @ SY1513 )
| ~ ( in @ SY1514 @ ( symdiff @ SV169 @ SY1513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(689,plain,
! [SV170: $i] :
( ( ~ ~ ! [SY1515: $i] :
~ ~ ( ~ ( in @ SY1515 @ SV170 )
| ( SV170
!= ( setadjoin @ SY1515 @ emptyset ) ) )
| ( in @ ( setunion @ SV170 ) @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(690,plain,
! [SV171: $i] :
( ( ! [SY1516: $i,SY1517: $i] :
( ~ ( in @ SY1517 @ SV171 )
| ! [SY1518: $i] :
( ~ ( in @ SY1518 @ SY1516 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1517 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1517 @ ( setadjoin @ SY1518 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV171 @ SY1516 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(691,plain,
! [SV172: $i] :
( ( ! [SY1519: $i] :
( ~ ( in @ SY1519 @ ( powerset @ SV172 ) )
| ( subset @ SY1519 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(692,plain,
! [SV173: $i] :
( ( ! [SY1520: $i,SY1521: $i] :
( ~ ( in @ SY1521 @ SV173 )
| ! [SY1522: $i] :
( ~ ( in @ SY1522 @ SY1520 )
| ( in @ ( kpair @ SY1521 @ SY1522 ) @ ( cartprod @ SV173 @ SY1520 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(693,plain,
! [SV174: $i] :
( ( ! [SY1523: $i,SY1524: $i] :
( ~ ( in @ SY1524 @ SV174 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1523 )
| ( ( kpair @ SY1524 @ SX3 )
= ( kpair @ SY1524 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(694,plain,
! [SV175: $i > $o] :
( ( ~ ~ ! [SY1526: $i] :
~ ~ ( ~ ( SV175 @ SY1526 )
| ~ ! [SY1527: $i] :
( ~ ( SV175 @ SY1527 )
| ( SY1526 = SY1527 ) ) )
| ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(695,plain,
! [SV176: $i] :
( ( ! [SY1529: $i] :
( ( SV176 != SY1529 )
| ! [SY1530: $i,SY1531: $i] :
( ( SY1530 != SY1531 )
| ~ ( in @ SY1530 @ SV176 )
| ( in @ SY1531 @ SY1529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(696,plain,
! [SV177: $i,SV1: $i] :
( ( ( ksnd @ ( kpair @ SV1 @ SV177 ) )
= SV177 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(697,plain,
! [SV178: $i,SV2: $i] :
( ( ( kfst @ ( kpair @ SV2 @ SV178 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(698,plain,
! [SV179: $i,SV6: $i] :
( ( iskpair @ ( kpair @ SV6 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(699,plain,
! [SV180: $i,SV7: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV7 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV7 @ ( setadjoin @ SV180 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(700,plain,
! [SV8: $i,SV181: $i] :
( ( in @ SV181 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV8 @ ( setadjoin @ SV181 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(701,plain,
! [SV182: $i,SV9: $i] :
( ( in @ SV9 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SV182 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(702,plain,
! [SV10: $i,SV183: $i] :
( ( in @ SV183 @ ( setadjoin @ SV10 @ ( setadjoin @ SV183 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(703,plain,
! [SV184: $i,SV11: $i] :
( ( subset @ ( setminus @ SV11 @ SV184 ) @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(704,plain,
! [SV185: $i,SV12: $i] :
( ( ! [SY1532: $i] :
( ( binintersect @ SV12 @ ( binunion @ SV185 @ SY1532 ) )
= ( binunion @ ( binintersect @ SV12 @ SV185 ) @ ( binintersect @ SV12 @ SY1532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(705,plain,
! [SV186: $i,SV13: $i] :
( ( subset @ ( binintersect @ SV13 @ SV186 ) @ SV186 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(706,plain,
! [SV187: $i,SV14: $i] :
( ( subset @ ( binintersect @ SV14 @ SV187 ) @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(707,plain,
! [SV15: $i,SV188: $i] :
( ( subset @ SV188 @ ( binunion @ SV15 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(708,plain,
! [SV189: $i,SV16: $i] :
( ( subset @ SV16 @ ( binunion @ SV16 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(709,plain,
! [SV17: $i,SV190: $i] :
( ( in @ SV190 @ ( setadjoin @ SV17 @ ( setadjoin @ SV190 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(710,plain,
! [SV191: $i > $o,SV18: $i] :
( ( subset
@ ( dsetconstr @ SV18
@ ^ [SY1533: $i] : ( SV191 @ SY1533 ) )
@ SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(711,plain,
! [SV192: $i > $o,SV19: $i] :
( ( in
@ ( dsetconstr @ SV19
@ ^ [SY1534: $i] : ( SV192 @ SY1534 ) )
@ ( powerset @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(712,plain,
! [SV21: $i,SV193: $i] :
( ( subset @ SV193 @ ( setadjoin @ SV21 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(713,plain,
! [SV24: $i,SV194: $i] :
( ( in @ SV194 @ ( setadjoin @ SV24 @ ( setadjoin @ SV194 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(714,plain,
! [SV195: $i,SV25: $i] :
( ( in @ SV25 @ ( setadjoin @ SV25 @ ( setadjoin @ SV195 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(715,plain,
! [SV196: $i,SV29: $i] :
( ( in @ SV29 @ ( setadjoin @ SV29 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(716,plain,
! [SV30: $i] :
( ( in @ SV30 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(717,plain,
! [SV31: $i] :
( ( in @ SV31 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(718,plain,
! [SV197: $i,SV32: $i] :
( ( ! [SY1535: $i] :
( ~ ( in @ SY1535 @ ( symdiff @ SV32 @ SV197 ) )
| ! [SY1536: $o] :
( ~ ( ~ ( in @ SY1535 @ SV32 )
| ~ ~ ( in @ SY1535 @ SV197 )
| SY1536 )
| ~ ( ~ ~ ( in @ SY1535 @ SV32 )
| ~ ( in @ SY1535 @ SV197 )
| SY1536 )
| SY1536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(719,plain,
! [SV198: $i,SV33: $i] :
( ( ! [SY1537: $i] :
( ~ ( in @ SY1537 @ ( binunion @ SV33 @ SV198 ) )
| ( in @ SY1537 @ SV33 )
| ( in @ SY1537 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(720,plain,
! [SV199: $i,SV34: $i] :
( ( ~ ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV34 )
| ( in @ SY1538 @ SV199 ) )
| ( subset @ SV34 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(721,plain,
! [SV200: $i,SV35: $i] :
( ( ~ ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV35 )
| ( in @ SY1539 @ SV200 ) )
| ( subset @ SV35 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(722,plain,
! [SV201: $i,SV36: $i] :
( ( ! [SY1540: $i,SY1541: $i] :
( ( ( setadjoin @ ( setadjoin @ SV36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV36 @ ( setadjoin @ SV201 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1540 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1540 @ ( setadjoin @ SY1541 @ emptyset ) ) @ emptyset ) ) )
| ( SY1540 != SY1541 )
| ( SV201 = SY1541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(723,plain,
! [SV37: $i,SV202: $i] :
( ( ! [SY1542: $i] :
( ~ ( in @ SV202 @ SY1542 )
| ~ ( in @ SY1542 @ SV37 )
| ( in @ SV202 @ ( setunion @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(724,plain,
! [SV203: $i,SV38: $i] :
( ( ! [SY1543: $i] :
( ~ ( in @ SY1543 @ SV38 )
| ~ ~ ( in @ SY1543 @ SV203 )
| ( in @ SY1543 @ ( setminus @ SV38 @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(725,plain,
! [SV39: $i,SV204: $i] :
( ( ! [SY1544: $i] :
( ~ ( in @ SY1544 @ SV204 )
| ( in @ SY1544 @ ( binunion @ SV39 @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(726,plain,
! [SV205: $i,SV40: $i] :
( ( ~ ~ ( subset @ SV40 @ SV205 )
| ( SV40 != SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(727,plain,
! [SV206: $i > $o,SV41: $i] :
( ( ~ ~ ~ ! [SY1545: $i] :
~ ~ ( ~ ( in @ SY1545 @ SV41 )
| ~ ( SV206 @ SY1545 ) )
| ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(728,plain,
! [SV207: $i,SV42: $i] :
( ( ! [SY1547: $i] :
( ~ ( in @ SY1547 @ ( cartprod @ SV42 @ SV207 ) )
| ( in @ ( ksnd @ SY1547 ) @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(729,plain,
! [SV208: $i,SV43: $i] :
( ( ! [SY1548: $i] :
( ~ ( in @ SY1548 @ SV43 )
| ~ ( in @ SY1548 @ SV208 )
| ( in @ SY1548 @ ( binintersect @ SV43 @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(730,plain,
! [SV209: $i,SV44: $i] :
( ( ! [SY1549: $i] :
( ~ ( in @ SY1549 @ SV44 )
| ( in @ SY1549 @ ( binunion @ SV44 @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(731,plain,
! [SV210: $i,SV45: $i] :
( ( ( ( binintersect @ SV45 @ SV210 )
!= SV210 )
| ( subset @ SV210 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(732,plain,
! [SV46: $i > $o] :
( ( ( ~ ~ ! [SY1197: $i] :
~ ~ ( ~ ( SV46 @ SY1197 )
| ~ ! [SY1198: $i] :
( ~ ( SV46 @ SY1198 )
| ( SY1197 = SY1198 ) ) ) )
= $true )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(733,plain,
! [SV211: $i,SV47: $i] :
( ( ! [SY1550: $i] :
( ~ ( in @ SY1550 @ SV47 )
| ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV211 )
| ( in @ ( setadjoin @ SY1550 @ ( setadjoin @ SY1551 @ emptyset ) ) @ ( powerset @ ( binunion @ SV47 @ SV211 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(734,plain,
! [SV212: $i,SV48: $i] :
( ( ~ ( in @ SV48 @ ( setadjoin @ SV212 @ emptyset ) )
| ( SV48 = SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(735,plain,
! [SV49: $i > $o] :
( ( ( ~ ~ ! [SY1205: $i] :
~ ( SV49 @ SY1205 ) )
= $true )
| ( ( ~ ! [SY1206: $i,SY1207: $i] :
( ~ ( SV49 @ SY1206 )
| ~ ( SV49 @ SY1207 )
| ( SY1206 = SY1207 ) )
| ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(736,plain,
! [SV50: $i] :
( ( ( ~ ( in @ SV50 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(737,plain,
! [SV213: $i > $o,SV51: $i] :
( ( ~ ! [SY1552: $i] :
( ~ ( in @ SY1552 @ SV51 )
| ~ ( SV213 @ SY1552 ) )
| ~ ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(738,plain,
! [SV214: $i,SV52: $i] :
( ( ! [SY1554: $i] :
( ~ ( in @ SY1554 @ SV52 )
| ! [SY1555: $i] :
( ~ ( in @ SY1555 @ SV214 )
| ( in @ ( kpair @ SY1554 @ SY1555 ) @ ( powerset @ ( powerset @ ( binunion @ SV52 @ SV214 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(739,plain,
! [SV215: $i,SV53: $i] :
( ( ! [SY1556: $i,SY1557: $i] :
( ( ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV215 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1556 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1556 @ ( setadjoin @ SY1557 @ emptyset ) ) @ emptyset ) ) )
| ( SV53 = SY1556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(740,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ~ ! [SY1558: $i,SY1559: $i] :
( ( SY1558 != SY1559 )
| ~ ( ~ ( ~ ( SV54 @ SY1558 )
| ( SV216 @ SY1559 ) )
| ~ ( ~ ( SV216 @ SY1559 )
| ( SV54 @ SY1558 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(741,plain,
! [SV217: $i,SV55: $i] :
( ( ! [SY1568: $i] :
( ( ( setadjoin @ SV55 @ ( setadjoin @ SV217 @ emptyset ) )
!= ( setadjoin @ SY1568 @ emptyset ) )
| ( SV55 = SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(742,plain,
! [SV218: $i,SV56: $i] :
( ( ! [SY1569: $i,SY1570: $i] :
( ~ ( in @ ( kpair @ SY1569 @ SY1570 ) @ ( cartprod @ SV56 @ SV218 ) )
| ( in @ SY1569 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(743,plain,
! [SV219: $i > $o,SV57: $i] :
( ( ! [SY1571: $i] :
( ~ ( in @ SY1571
@ ( dsetconstr @ SV57
@ ^ [SY1572: $i] : ( SV219 @ SY1572 ) ) )
| ( SV219 @ SY1571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(744,plain,
! [SV220: $i,SV58: $i] :
( ( ! [SY1573: $i] :
( ~ ~ ( in @ SY1573 @ SV58 )
| ~ ( in @ SY1573 @ SV220 )
| ( in @ SY1573 @ ( symdiff @ SV58 @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(745,plain,
! [SV221: $i,SV59: $i] :
( ( ( SV59 != SV221 )
| ( subset @ SV59 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(746,plain,
! [SV222: $i,SV60: $i] :
( ( ! [SY1574: $i] :
( ~ ( in @ SY1574 @ ( cartprod @ SV60 @ SV222 ) )
| ( in @ ( kfst @ SY1574 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(747,plain,
! [SV223: $i,SV61: $i] :
( ( ! [SY1575: $i,SY1576: $i] :
( ( ( kpair @ SV61 @ SV223 )
!= ( kpair @ SY1575 @ SY1576 ) )
| ( SV61 = SY1575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(748,plain,
! [SV224: $i > $o,SV62: $i] :
( ( ! [SY1577: $i] :
( ~ ( in @ SY1577 @ SV62 )
| ~ ( ~ ( ~ ( in @ SY1577
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) )
| ( SV224 @ SY1577 ) )
| ~ ( ~ ( SV224 @ SY1577 )
| ( in @ SY1577
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(749,plain,
! [SV225: $i,SV63: $i] :
( ( ! [SY1580: $i] :
( ~ ( subset @ SV63 @ SV225 )
| ~ ~ ( in @ SY1580 @ SV225 )
| ~ ( in @ SY1580 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(750,plain,
! [SV226: $i,SV64: $i] :
( ( ( SV64 != SV226 )
| ( ( setadjoin @ SV64 @ ( setadjoin @ SV226 @ emptyset ) )
= ( setadjoin @ SV64 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(751,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV65 )
| ~ ! [SY1253: $i] :
( ~ ~ ( ~ ( in @ SY1253 @ omega )
| ~ ( in @ SY1253 @ SV65 ) )
| ( in @ ( setadjoin @ SY1253 @ SY1253 ) @ SV65 ) ) ) )
= $true )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(752,plain,
! [SV227: $i > $o,SV66: $i] :
( ( ! [SY1581: $i] :
( ~ ( in @ SY1581
@ ( dsetconstr @ SV66
@ ^ [SY1582: $i] : ( SV227 @ SY1582 ) ) )
| ( in @ SY1581 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(753,plain,
! [SV67: $i > $o] :
( ( ( ~ ~ ! [SY1258: $i] :
~ ~ ( ~ ( SV67 @ SY1258 )
| ~ ! [SY1259: $i] :
( ~ ( SV67 @ SY1259 )
| ( SY1258 = SY1259 ) ) ) )
= $true )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(754,plain,
! [SV228: $i,SV68: $i] :
( ( ! [SY1583: $i] :
( ~ ( in @ ( setadjoin @ SY1583 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ ( setadjoin @ SV228 @ emptyset ) ) @ emptyset ) ) )
| ( SV68 = SY1583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(755,plain,
! [SV229: $i,SV69: $i] :
( ( ! [SY1584: $i] :
( ~ ( in @ SY1584 @ ( binintersect @ SV69 @ SV229 ) )
| ( in @ SY1584 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(756,plain,
! [SV70: $i,SV230: $i] :
( ( ~ ( ~ ( ~ ( in @ SV230 @ ( setunion @ SV70 ) )
| ~ ! [SY1585: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1585 )
| ~ ( in @ SY1585 @ SV70 ) ) )
| ~ ( ~ ~ ! [SY1586: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1586 )
| ~ ( in @ SY1586 @ SV70 ) )
| ( in @ SV230 @ ( setunion @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(757,plain,
! [SV71: $o] :
( ( ( ~ SV71 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(758,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(759,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(760,plain,
! [SV72: $i] :
( ( ( ~ ~ ! [SY1269: $i] :
~ ( in @ SY1269 @ SV72 ) )
= $true )
| ( ( SV72 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(761,plain,
! [SV73: $i,SV231: $i] :
( ( ~ ( in @ SV231 @ SV73 )
| ( in @ SV231 @ ( powerset @ ( setunion @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(762,plain,
! [SV232: $i,SV74: $i] :
( ( ! [SY1587: $i] :
( ~ ( in @ SY1587 @ SV74 )
| ~ ~ ( in @ SY1587 @ SV232 )
| ( SV74 != SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(763,plain,
! [SV75: $i] :
( ( ( ~ ( subset @ SV75 @ emptyset ) )
= $true )
| ( ( SV75 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(764,plain,
! [SV233: $i,SV76: $i] :
( ( ~ ( in @ SV76 @ ( setadjoin @ SV233 @ emptyset ) )
| ( in @ SV233 @ ( setadjoin @ SV76 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(765,plain,
! [SV77: $i] :
( ( ( ~ ( iskpair @ SV77 ) )
= $true )
| ( ( ~ ! [SY1274: $i] :
~ ~ ( ~ ( in @ SY1274
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
!= ( setadjoin @ SY1274 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(766,plain,
! [SV234: $i,SV78: $i] :
( ( ! [SY1588: $i] :
( ~ ~ ( in @ SY1588 @ ( setminus @ SV78 @ SV234 ) )
| ~ ~ ( in @ SY1588 @ SV234 )
| ~ ( in @ SY1588 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(767,plain,
! [SV235: $i,SV79: $i] :
( ( ! [SY1589: $i] :
( ~ ~ ( in @ SY1589 @ ( setminus @ SV79 @ SV235 ) )
| ~ ( in @ SY1589 @ SV79 )
| ( in @ SY1589 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(768,plain,
! [SV236: $i,SV80: $i] :
( ( ( ( setadjoin @ SV80 @ emptyset )
!= ( setadjoin @ SV236 @ emptyset ) )
| ( SV80 = SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(769,plain,
! [SV81: $i,SV237: $i] :
( ( ~ ( in @ SV237 @ SV81 )
| ( subset @ ( setadjoin @ SV237 @ emptyset ) @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(770,plain,
! [SV82: $i,SV238: $i] :
( ( ~ ( in @ SV238 @ SV82 )
| ( in @ ( setadjoin @ SV238 @ emptyset ) @ ( powerset @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(771,plain,
! [SV239: $i,SV83: $i] :
( ( ( SV83 != SV239 )
| ( in @ SV83 @ ( setadjoin @ SV239 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(772,plain,
! [SV240: $i,SV84: $i] :
( ( ! [SY1590: $i] :
( ~ ( subset @ SY1590 @ SV84 )
| ~ ( subset @ SY1590 @ SV240 )
| ( subset @ SY1590 @ ( binintersect @ SV84 @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(773,plain,
! [SV85: $i] :
( ( ( ~ ( iskpair @ SV85 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV85 ) @ ( ksnd @ SV85 ) )
= SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(774,plain,
! [SV241: $i > $o,SV86: $i] :
( ( ~ ~ ~ ! [SY1591: $i] :
~ ~ ( ~ ( in @ SY1591 @ SV86 )
| ~ ( SV241 @ SY1591 ) )
| ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(775,plain,
! [SV242: $i,SV87: $i] :
( ( ! [SY1593: $i] :
( ~ ( in @ SY1593 @ ( setadjoin @ SV87 @ ( setadjoin @ SV242 @ emptyset ) ) )
| ( SY1593 = SV87 )
| ( SY1593 = SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(776,plain,
! [SV243: $i,SV88: $i] :
( ( ( SV88 != SV243 )
| ( ( powerset @ SV88 )
= ( powerset @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(777,plain,
! [SV244: $i > $o,SV89: $i] :
( ( ~ ~ ! [SY1594: $i] :
( ~ ( in @ SY1594 @ SV89 )
| ( SV244 @ SY1594 ) )
| ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV89 )
| ~ ~ ( SV244 @ SY1595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(778,plain,
! [SV90: $i] :
( ( ( ~ ( ( SV90 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY1296: $i] :
~ ~ ( ~ ( in @ SY1296 @ SV90 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(779,plain,
! [SV91: $i] :
( ( ( ~ ! [SY1297: $i] :
~ ( in @ SY1297 @ SV91 ) )
= $true )
| ( ( SV91 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(780,plain,
! [SV245: $i,SV92: $i] :
( ( ! [SY1596: $i,SY1597: $i] :
( ( ( kpair @ SV92 @ SV245 )
!= ( kpair @ SY1596 @ SY1597 ) )
| ( SV245 = SY1597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(781,plain,
! [SV93: $i,SV246: $i] :
( ( ! [SY1598: $i] :
( ~ ( in @ SY1598 @ SV246 )
| ( in @ SY1598 @ ( setadjoin @ SV93 @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(782,plain,
! [SV94: $i,SV247: $i] :
( ( ~ ( in @ SV247 @ ( setunion @ SV94 ) )
| ~ ! [SY1599: $i] :
~ ~ ( ~ ( in @ SY1599 @ SV94 )
| ~ ( in @ SV247 @ SY1599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(783,plain,
! [SV248: $i,SV95: $i] :
( ( ~ ( subset @ SV95 @ SV248 )
| ~ ( subset @ SV248 @ SV95 )
| ( SV95 = SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(784,plain,
! [SV249: $i,SV96: $i] :
( ( ! [SY1600: $i,SY1601: $i] :
( ~ ( in @ ( kpair @ SY1600 @ SY1601 ) @ ( cartprod @ SV96 @ SV249 ) )
| ( in @ SY1601 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(785,plain,
! [SV250: $i,SV97: $i] :
( ( ! [SY1602: $i] :
( ~ ( in @ SY1602 @ ( binintersect @ SV97 @ SV250 ) )
| ( in @ SY1602 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(786,plain,
! [SV251: $i,SV98: $i] :
( ( ( SV98 != SV251 )
| ! [SY1603: $i,SY1604: $i] :
( ( SY1603 != SY1604 )
| ~ ( ~ ( ~ ( in @ SY1603 @ SV98 )
| ( in @ SY1604 @ SV251 ) )
| ~ ( ~ ( in @ SY1604 @ SV251 )
| ( in @ SY1603 @ SV98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(787,plain,
! [SV252: $i,SV99: $i] :
( ( ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( setadjoin @ SV99 @ ( setadjoin @ SV252 @ emptyset ) ) )
| ( SY1605 = SV99 )
| ( SY1605 = SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(788,plain,
! [SV253: $i,SV100: $i] :
( ( ( ( setminus @ SV100 @ SV253 )
!= emptyset )
| ( subset @ SV100 @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(789,plain,
! [SV101: $i] :
( ( ( ~ ( ( SV101 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY1317: $i] :
~ ( in @ SY1317 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(790,plain,
! [SV254: $i,SV102: $i] :
( ( ! [SY1606: $i] :
~ ( ~ ( ~ ( in @ SY1606 @ ( setadjoin @ SV102 @ SV254 ) )
| ( SY1606 = SV102 )
| ( in @ SY1606 @ SV254 ) )
| ~ ( ~ ( ( SY1606 = SV102 )
| ( in @ SY1606 @ SV254 ) )
| ( in @ SY1606 @ ( setadjoin @ SV102 @ SV254 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(791,plain,
! [SV103: $i > $o] :
( ( ( ~ ~ ! [SY1320: $i] :
~ ~ ( ~ ( SV103 @ SY1320 )
| ~ ! [SY1321: $i] :
( ~ ( SV103 @ SY1321 )
| ( SY1320 = SY1321 ) ) ) )
= $true )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(792,plain,
! [SV255: $i,SV104: $i] :
( ( ~ ~ ~ ! [SY1607: $i] :
~ ~ ( ~ ( in @ SY1607 @ SV104 )
| ~ ( in @ SY1607 @ SV255 ) )
| ( ( binintersect @ SV104 @ SV255 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(793,plain,
! [SV256: $i,SV105: $i] :
( ( ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV105 )
| ~ ~ ( in @ SY1608 @ SV256 )
| ~ ( subset @ SV105 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(794,plain,
! [SV257: $i,SV106: $i] :
( ( ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( cartprod @ SV106 @ SV257 ) )
| ~ ! [SY1610: $i] :
~ ~ ( ~ ( in @ SY1610 @ SV106 )
| ~ ~ ! [SY1611: $i] :
~ ~ ( ~ ( in @ SY1611 @ SV257 )
| ( SY1609
!= ( kpair @ SY1610 @ SY1611 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(795,plain,
! [SV107: $i > $o] :
( ( ( ~ ~ ! [SY1332: $i] :
~ ~ ( ~ ( SV107 @ SY1332 )
| ~ ! [SY1333: $i] :
( ~ ( SV107 @ SY1333 )
| ( SY1332 = SY1333 ) ) ) )
= $true )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(796,plain,
! [SV258: $i,SV108: $i] :
( ( ! [SY1612: $i] :
( ~ ~ ( in @ SY1612 @ SV108 )
| ~ ~ ( in @ SY1612 @ SV258 )
| ~ ( in @ SY1612 @ ( symdiff @ SV108 @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(797,plain,
! [SV109: $i,SV259: $i] :
( ( ~ ( ~ ( ~ ( in @ SV259 @ ( powerset @ SV109 ) )
| ! [SY1613: $i] :
( ~ ( in @ SY1613 @ SV259 )
| ( in @ SY1613 @ SV109 ) ) )
| ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ SV259 )
| ( in @ SY1614 @ SV109 ) )
| ( in @ SV259 @ ( powerset @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(798,plain,
! [SV260: $i,SV110: $i] :
( ( ~ ( subset @ SV110 @ SV260 )
| ( ( binintersect @ SV110 @ SV260 )
= SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(799,plain,
! [SV111: $i] :
( ( ( ~ ( in @ SV111 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(800,plain,
! [SV112: $i] :
( ( ( ~ ! [SY1343: $i] :
~ ( in @ SY1343 @ SV112 ) )
= $true )
| ( ( SV112 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(801,plain,
! [SV113: $o] :
( ( ( ~ SV113 ) = $true )
| ( ( set2prop @ ( prop2set @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(802,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(803,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(804,plain,
! [SV114: $i > $o,SV261: $i] :
( ( ~ ( in @ SV261 @ emptyset )
| ( SV114 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(805,plain,
! [SV262: $i,SV115: $i] :
( ( ! [SY1615: $i,SY1616: $i] :
( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV262 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1615 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1615 @ ( setadjoin @ SY1616 @ emptyset ) ) @ emptyset ) ) )
| ( SV262 = SY1616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(806,plain,
! [SV263: $i,SV116: $i] :
( ( ~ ( ( SV116 != SV263 ) )
| ~ ( in @ SV263 @ ( setadjoin @ SV116 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(807,plain,
! [SV117: $i > $o] :
( ( ( ~ ~ ! [SY1349: $i] :
~ ~ ( ~ ( SV117 @ SY1349 )
| ~ ! [SY1350: $i] :
( ~ ( SV117 @ SY1350 )
| ( SY1349 = SY1350 ) ) ) )
= $true )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(808,plain,
! [SV264: $i > $o,SV118: $i] :
( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV118 )
| ~ ( SV264 @ SY1617 )
| ( ( dsetconstr @ SV118
@ ^ [SY1618: $i] : ( SV264 @ SY1618 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(809,plain,
! [SV265: $i > $o,SV119: $i] :
( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV119 )
| ~ ( SV265 @ SY1619 )
| ~ ! [SY1620: $i] :
( ~ ( in @ SY1620 @ SV119 )
| ~ ( SV265 @ SY1620 )
| ( SY1620 = SY1619 ) )
| ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(810,plain,
! [SV120: $i,SV266: $i] :
( ( ~ ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV266 )
| ( in @ SY1624 @ SV120 ) )
| ( in @ SV266 @ ( powerset @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(811,plain,
! [SV267: $i,SV121: $i] :
( ( ~ ! [SY1625: $i] :
( ~ ( in @ SY1625 @ SV121 )
| ( in @ SY1625 @ SV267 ) )
| ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) )
| ( SV121 = SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(812,plain,
! [SV268: $i,SV122: $i] :
( ( ~ ( subset @ SV122 @ SV268 )
| ( ( setminus @ SV122 @ SV268 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(813,plain,
! [SV123: $i,SV269: $i] :
( ( ~ ( subset @ SV269 @ SV123 )
| ( in @ SV269 @ ( powerset @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(814,plain,
! [SV270: $i,SV124: $i] :
( ( ! [SY1627: $i] :
( ~ ( subset @ SV124 @ SV270 )
| ~ ( in @ SY1627 @ SV124 )
| ( in @ SY1627 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(815,plain,
! [SV125: $i] :
( ( ( ~ ~ ! [SY1370: $i] :
~ ( in @ SY1370 @ SV125 ) )
= $true )
| ( ( ~ ! [SY1371: $i] :
~ ~ ( ~ ( in @ SY1371 @ SV125 )
| ~ ~ ~ ! [SY1372: $i] :
~ ~ ( ~ ( in @ SY1372 @ SY1371 )
| ~ ( in @ SY1372 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(816,plain,
! [SV126: $i > $o] :
( ( ( ~ ~ ! [SY1373: $i] :
~ ! [SY1374: $i] :
~ ( ~ ( ~ ( SV126 @ SY1374 )
| ( SY1374 = SY1373 ) )
| ~ ( ( SY1374 != SY1373 )
| ( SV126 @ SY1374 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(817,plain,
( ( ! [SY1628: $i,SY1629: $i] :
( ~ ( in @ SY1629 @ ( cartprod @ sK1_SX0 @ SY1628 ) )
| ( ( kpair @ ( kfst @ SY1629 ) @ ( ksnd @ SY1629 ) )
= SY1629 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[643]) ).
thf(818,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ~ ! [SY1630: $i] :
( ~ ( in @ SY1630 @ SV127 )
| ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV127 )
| ~ ( SV271 @ SY1630 )
| ~ ( SV271 @ SY1631 )
| ( SY1630 = SY1631 ) ) )
| ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(819,plain,
! [SV272: $i,SV128: $i] :
( ( ~ ( subset @ SV128 @ SV272 )
| ( subset @ ( powerset @ SV128 ) @ ( powerset @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(820,plain,
! [SV273: $i,SV129: $i] :
( ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ ( cartprod @ SV129 @ SV273 ) )
| ( iskpair @ SY1636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(821,plain,
! [SV274: $i,SV130: $i] :
( ( ( SV130 != SV274 )
| ! [SY1637: $i > $o,SY1638: $i > $o] :
( ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV130 )
| ! [SY1640: $i] :
( ~ ( in @ SY1640 @ SV274 )
| ( SY1639 != SY1640 )
| ~ ( ~ ( ~ ( SY1637 @ SY1639 )
| ( SY1638 @ SY1640 ) )
| ~ ( ~ ( SY1638 @ SY1640 )
| ( SY1637 @ SY1639 ) ) ) ) )
| ( ( dsetconstr @ SV130
@ ^ [SX4: $i] : ( SY1637 @ SX4 ) )
= ( dsetconstr @ SV274
@ ^ [SX4: $i] : ( SY1638 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(822,plain,
! [SV275: $i,SV131: $i] :
( ( ! [SY1643: $i] :
( ~ ( subset @ SV131 @ SY1643 )
| ( subset @ SV131 @ ( setadjoin @ SV275 @ SY1643 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(823,plain,
! [SV132: $i] :
( ( ( ~ ( iskpair @ SV132 ) )
= $true )
| ( ( ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) )
| ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
!= ( setadjoin @ SY1396 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(824,plain,
! [SV276: $i,SV133: $i] :
( ( ( ( binintersect @ SV133 @ SV276 )
!= SV133 )
| ( subset @ SV133 @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(825,plain,
! [SV277: $i,SV134: $i] :
( ( ! [SY1644: $i] :
( ~ ( in @ SY1644 @ ( setadjoin @ SV134 @ SV277 ) )
| ( SY1644 = SV134 )
| ( in @ SY1644 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(826,plain,
! [SV278: $i > $o,SV135: $i] :
( ( ~ ~ ! [SY1645: $i] :
~ ~ ( ~ ( in @ SY1645 @ SV135 )
| ~ ~ ( SV278 @ SY1645 ) )
| ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(827,plain,
! [SV279: $i > $o,SV136: $i] :
( ( ~ ~ ! [SY1647: $i] :
~ ~ ( ~ ( in @ SY1647 @ SV136 )
| ~ ( SV279 @ SY1647 ) )
| ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(828,plain,
! [SV280: $i,SV137: $i] :
( ( ! [SY1649: $i] :
( ~ ( in @ SY1649 @ SV137 )
| ! [SY1650: $i] :
( ~ ( in @ SY1650 @ SV280 )
| ( subset @ ( setadjoin @ SY1649 @ ( setadjoin @ SY1650 @ emptyset ) ) @ ( binunion @ SV137 @ SV280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(829,plain,
! [SV281: $i,SV138: $i] :
( ( ~ ( subset @ SV138 @ SV281 )
| ( in @ SV138 @ ( powerset @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(830,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ~ ! [SY1651: $i,SY1652: $i] :
( ( SY1651 != SY1652 )
| ~ ( ~ ( ~ ( SV139 @ SY1651 )
| ( SV282 @ SY1652 ) )
| ~ ( ~ ( SV282 @ SY1652 )
| ( SV139 @ SY1651 ) ) ) )
| ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(831,plain,
! [SV283: $i,SV140: $i] :
( ( ~ ! [SY1659: $i] :
~ ( ~ ( ~ ( in @ SY1659 @ SV140 )
| ( in @ SY1659 @ SV283 ) )
| ~ ( ~ ( in @ SY1659 @ SV283 )
| ( in @ SY1659 @ SV140 ) ) )
| ( SV140 = SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(832,plain,
! [SV141: $i] :
( ( ! [SY1423: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1424: $i] :
( ~ ( in @ SY1424 @ SY1423 )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1424 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1426: $i,SY1427: $i] :
( ~ ~ ( ~ ( in @ SY1426 @ SV141 )
| ~ ( in @ SY1427 @ SV141 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1423 )
| ~ ( ~ ( ~ ( in @ SY1426 @ SX4 )
| ( in @ SY1427 @ SX4 ) )
| ~ ( ~ ( in @ SY1427 @ SX4 )
| ( in @ SY1426 @ SX4 ) ) ) )
| ( SY1426 = SY1427 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY1423 )
| ~ ( in @ SX3 @ SY1423 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY1433: $i] :
( ~ ~ ( ~ ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SY1433 )
| ( in @ SY1434 @ SV141 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1433 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY1423 )
| ~ ( in @ SX4 @ SY1433 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY1433 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY1423 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(833,plain,
! [SV284: $i,SV142: $i] :
( ( ! [SY1660: $i] :
( ~ ( in @ SY1660 @ SV142 )
| ! [SY1661: $i] :
( ~ ( in @ SY1661 @ SV284 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1660 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1660 @ ( setadjoin @ SY1661 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV142 @ SV284 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(834,plain,
! [SV143: $i] :
( ( ( ~ ( in @ SV143 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV143 @ SV143 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(835,plain,
! [SV144: $i,SV285: $i] :
( ( ~ ( subset @ SV285 @ SV144 )
| ( ( binintersect @ SV144 @ SV285 )
= SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(836,plain,
! [SV145: $i,SV286: $i] :
( ( ! [SY1662: $i] :
( ~ ( in @ SY1662 @ SV286 )
| ~ ( in @ SY1662 @ ( setminus @ SV145 @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(837,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ~ ! [SY1663: $i] :
( ~ ( in @ SY1663 @ SV146 )
| ! [SY1664: $i] :
( ~ ( in @ SY1664 @ SV146 )
| ~ ( SV287 @ SY1663 )
| ~ ( SV287 @ SY1664 )
| ( SY1663 = SY1664 ) ) )
| ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(838,plain,
! [SV288: $i,SV147: $i] :
( ( ! [SY1669: $i] :
( ~ ( in @ SY1669 @ ( setadjoin @ SV147 @ SV288 ) )
| ! [SY1670: $o] :
( ~ ( ( SY1669 != SV147 )
| SY1670 )
| ~ ( ~ ( in @ SY1669 @ SV288 )
| SY1670 )
| SY1670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(839,plain,
! [SV289: $i,SV148: $i] :
( ( ( SV148 != SV289 )
| ( subset @ SV289 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(840,plain,
! [SV290: $i,SV149: $i] :
( ( ! [SY1671: $i] :
( ~ ( in @ SY1671 @ SV149 )
| ! [SY1672: $i] :
( ~ ( in @ SY1672 @ SV290 )
| ( ( kfst @ ( kpair @ SY1671 @ SY1672 ) )
= SY1671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(841,plain,
! [SV291: $i > $o,SV150: $i] :
( ( ! [SY1673: $i] :
( ~ ( in @ SY1673 @ SV150 )
| ~ ( SV291 @ SY1673 )
| ( in @ SY1673
@ ( dsetconstr @ SV150
@ ^ [SY1674: $i] : ( SV291 @ SY1674 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(842,plain,
! [SV151: $i,SV292: $i] :
( ( ! [SY1675: $i] :
( ~ ( in @ SV292 @ ( powerset @ SV151 ) )
| ~ ( in @ SY1675 @ SV292 )
| ( in @ SY1675 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(843,plain,
! [SV293: $i,SV152: $i] :
( ( ( SV152 != SV293 )
| ( ( setunion @ SV152 )
= ( setunion @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(844,plain,
! [SV294: $i,SV153: $i] :
( ( ! [SY1676: $i,SY1677: $o] :
( ~ ( in @ SY1676 @ ( binunion @ SV153 @ SV294 ) )
| ~ ( ~ ( in @ SY1676 @ SV153 )
| SY1677 )
| ~ ( ~ ( in @ SY1676 @ SV294 )
| SY1677 )
| SY1677 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(845,plain,
! [SV295: $i,SV154: $i] :
( ( ( SV154 != SV295 )
| ( ( setadjoin @ ( setadjoin @ SV154 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV154 @ ( setadjoin @ SV295 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV154 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(846,plain,
! [SV296: $i > $o,SV155: $i] :
( ( ~ ~ ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV155 )
| ( SV296 @ SY1678 ) )
| ~ ! [SY1679: $i] :
~ ~ ( ~ ( in @ SY1679 @ SV155 )
| ~ ~ ( SV296 @ SY1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(847,plain,
! [SV297: $i,SV156: $i] :
( ( ! [SY1680: $i] :
( ~ ( in @ SY1680 @ SV156 )
| ( in @ ( setadjoin @ SY1680 @ emptyset ) @ ( powerset @ ( binunion @ SV156 @ SV297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(848,plain,
! [SV157: $o,SV298: $i] :
( ( ~ ( in @ SV298 @ ( prop2set @ SV157 ) )
| SV157 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(849,plain,
! [SV299: $i] :
( ( ~ ( in @ SV299 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(850,plain,
! [SV300: $i] :
( ( ~ ( in @ SV300 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(851,plain,
! [SV158: $i,SV301: $i] :
( ( ~ ( in @ SV301 @ ( setunion @ SV158 ) )
| ! [SY1681: $o] :
( ~ ! [SY1682: $i] :
( ~ ( in @ SV301 @ SY1682 )
| ~ ( in @ SY1682 @ SV158 )
| SY1681 )
| SY1681 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(852,plain,
! [SV302: $i > $o,SV159: $i] :
( ( ~ ~ ! [SY1683: $i] :
~ ~ ( ~ ( in @ SY1683
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SY1683 @ emptyset ) ) )
| ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(853,plain,
! [SV303: $i,SV160: $i] :
( ( ( SV160 != SV303 )
| ! [SY1687: $i,SY1688: $i] :
( ( SY1687 != SY1688 )
| ( ( setadjoin @ SV160 @ SY1687 )
= ( setadjoin @ SV303 @ SY1688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(854,plain,
! [SV161: $i > $i > $o,SV304: $i] :
( ( ~ ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV304 )
| ~ ! [SY1490: $i] :
~ ~ ( ~ ( SV161 @ SY1689 @ SY1490 )
| ~ ! [SY1491: $i] :
( ~ ( SV161 @ SY1689 @ SY1491 )
| ( SY1490 = SY1491 ) ) ) )
| ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(855,plain,
! [SV305: $i,SV162: $i] :
( ( ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV162 )
| ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV305 )
| ( ( ksnd @ ( kpair @ SY1696 @ SY1697 ) )
= SY1697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(856,plain,
! [SV306: $i,SV163: $i] :
( ( ! [SY1698: $i] :
( ~ ( subset @ SV163 @ SV306 )
| ~ ( subset @ SV306 @ SY1698 )
| ( subset @ SV163 @ SY1698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(857,plain,
! [SV307: $i,SV164: $i] :
( ( ! [SY1699: $i] :
( ~ ( in @ SY1699 @ ( setminus @ SV164 @ SV307 ) )
| ( in @ SY1699 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(858,plain,
! [SV308: $i,SV165: $i] :
( ( ! [SY1700: $i] :
( ~ ( in @ SY1700 @ SV165 )
| ~ ~ ( in @ SY1700 @ SV308 )
| ( in @ SY1700 @ ( symdiff @ SV165 @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(859,plain,
! [SV309: $i,SV166: $i] :
( ( ! [SY1701: $i] :
( ~ ~ ( in @ SY1701 @ SV166 )
| ~ ( in @ SY1701 @ ( setminus @ SV166 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(860,plain,
! [SV167: $i > $o] :
( ( ( ~ ~ ! [SY1507: $i] :
~ ~ ( ~ ( SV167 @ SY1507 )
| ~ ! [SY1508: $i] :
( ~ ( SV167 @ SY1508 )
| ( SY1507 = SY1508 ) ) ) )
= $true )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(861,plain,
! [SV310: $i,SV168: $i] :
( ( ! [SY1702: $i] :
( ~ ( in @ SY1702 @ ( setminus @ SV168 @ SV310 ) )
| ~ ( in @ SY1702 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(862,plain,
! [SV311: $i,SV169: $i] :
( ( ! [SY1703: $i] :
( ~ ( in @ SY1703 @ SV169 )
| ~ ( in @ SY1703 @ SV311 )
| ~ ( in @ SY1703 @ ( symdiff @ SV169 @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(863,plain,
! [SV170: $i] :
( ( ( ~ ~ ! [SY1515: $i] :
~ ~ ( ~ ( in @ SY1515 @ SV170 )
| ( SV170
!= ( setadjoin @ SY1515 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(864,plain,
! [SV312: $i,SV171: $i] :
( ( ! [SY1704: $i] :
( ~ ( in @ SY1704 @ SV171 )
| ! [SY1705: $i] :
( ~ ( in @ SY1705 @ SV312 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1704 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1704 @ ( setadjoin @ SY1705 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV171 @ SV312 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(865,plain,
! [SV172: $i,SV313: $i] :
( ( ~ ( in @ SV313 @ ( powerset @ SV172 ) )
| ( subset @ SV313 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(866,plain,
! [SV314: $i,SV173: $i] :
( ( ! [SY1706: $i] :
( ~ ( in @ SY1706 @ SV173 )
| ! [SY1707: $i] :
( ~ ( in @ SY1707 @ SV314 )
| ( in @ ( kpair @ SY1706 @ SY1707 ) @ ( cartprod @ SV173 @ SV314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(867,plain,
! [SV315: $i,SV174: $i] :
( ( ! [SY1708: $i] :
( ~ ( in @ SY1708 @ SV174 )
| ! [SY1709: $i] :
( ~ ( in @ SY1709 @ SV315 )
| ( ( kpair @ SY1708 @ SY1709 )
= ( kpair @ SY1708 @ SY1709 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(868,plain,
! [SV175: $i > $o] :
( ( ( ~ ~ ! [SY1526: $i] :
~ ~ ( ~ ( SV175 @ SY1526 )
| ~ ! [SY1527: $i] :
( ~ ( SV175 @ SY1527 )
| ( SY1526 = SY1527 ) ) ) )
= $true )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(869,plain,
! [SV316: $i,SV176: $i] :
( ( ( SV176 != SV316 )
| ! [SY1710: $i,SY1711: $i] :
( ( SY1710 != SY1711 )
| ~ ( in @ SY1710 @ SV176 )
| ( in @ SY1711 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(870,plain,
! [SV317: $i,SV185: $i,SV12: $i] :
( ( ( binintersect @ SV12 @ ( binunion @ SV185 @ SV317 ) )
= ( binunion @ ( binintersect @ SV12 @ SV185 ) @ ( binintersect @ SV12 @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(871,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ~ ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
| ! [SY1712: $o] :
( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| SY1712 )
| ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SY1712 )
| SY1712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(872,plain,
! [SV198: $i,SV33: $i,SV319: $i] :
( ( ~ ( in @ SV319 @ ( binunion @ SV33 @ SV198 ) )
| ( in @ SV319 @ SV33 )
| ( in @ SV319 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(873,plain,
! [SV199: $i,SV34: $i] :
( ( ( ~ ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV34 )
| ( in @ SY1538 @ SV199 ) ) )
= $true )
| ( ( subset @ SV34 @ SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(874,plain,
! [SV200: $i,SV35: $i] :
( ( ( ~ ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV35 )
| ( in @ SY1539 @ SV200 ) ) )
= $true )
| ( ( subset @ SV35 @ SV200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(875,plain,
! [SV320: $i,SV201: $i,SV36: $i] :
( ( ! [SY1713: $i] :
( ( ( setadjoin @ ( setadjoin @ SV36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV36 @ ( setadjoin @ SV201 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV320 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV320 @ ( setadjoin @ SY1713 @ emptyset ) ) @ emptyset ) ) )
| ( SV320 != SY1713 )
| ( SV201 = SY1713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(876,plain,
! [SV37: $i,SV321: $i,SV202: $i] :
( ( ~ ( in @ SV202 @ SV321 )
| ~ ( in @ SV321 @ SV37 )
| ( in @ SV202 @ ( setunion @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(877,plain,
! [SV203: $i,SV38: $i,SV322: $i] :
( ( ~ ( in @ SV322 @ SV38 )
| ~ ~ ( in @ SV322 @ SV203 )
| ( in @ SV322 @ ( setminus @ SV38 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(878,plain,
! [SV39: $i,SV204: $i,SV323: $i] :
( ( ~ ( in @ SV323 @ SV204 )
| ( in @ SV323 @ ( binunion @ SV39 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(879,plain,
! [SV205: $i,SV40: $i] :
( ( ( ~ ~ ( subset @ SV40 @ SV205 ) )
= $true )
| ( ( SV40 != SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(880,plain,
! [SV206: $i > $o,SV41: $i] :
( ( ( ~ ~ ~ ! [SY1545: $i] :
~ ~ ( ~ ( in @ SY1545 @ SV41 )
| ~ ( SV206 @ SY1545 ) ) )
= $true )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(881,plain,
! [SV207: $i,SV42: $i,SV324: $i] :
( ( ~ ( in @ SV324 @ ( cartprod @ SV42 @ SV207 ) )
| ( in @ ( ksnd @ SV324 ) @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(882,plain,
! [SV208: $i,SV43: $i,SV325: $i] :
( ( ~ ( in @ SV325 @ SV43 )
| ~ ( in @ SV325 @ SV208 )
| ( in @ SV325 @ ( binintersect @ SV43 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(883,plain,
! [SV209: $i,SV44: $i,SV326: $i] :
( ( ~ ( in @ SV326 @ SV44 )
| ( in @ SV326 @ ( binunion @ SV44 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(884,plain,
! [SV210: $i,SV45: $i] :
( ( ( ( binintersect @ SV45 @ SV210 )
!= SV210 )
= $true )
| ( ( subset @ SV210 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(885,plain,
! [SV46: $i > $o] :
( ( ( ~ ! [SY1197: $i] :
~ ~ ( ~ ( SV46 @ SY1197 )
| ~ ! [SY1198: $i] :
( ~ ( SV46 @ SY1198 )
| ( SY1197 = SY1198 ) ) ) )
= $false )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(886,plain,
! [SV211: $i,SV47: $i,SV327: $i] :
( ( ~ ( in @ SV327 @ SV47 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV211 )
| ( in @ ( setadjoin @ SV327 @ ( setadjoin @ SY1714 @ emptyset ) ) @ ( powerset @ ( binunion @ SV47 @ SV211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(887,plain,
! [SV212: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( setadjoin @ SV212 @ emptyset ) ) )
= $true )
| ( ( SV48 = SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(888,plain,
! [SV49: $i > $o] :
( ( ( ~ ! [SY1205: $i] :
~ ( SV49 @ SY1205 ) )
= $false )
| ( ( ~ ! [SY1206: $i,SY1207: $i] :
( ~ ( SV49 @ SY1206 )
| ~ ( SV49 @ SY1207 )
| ( SY1206 = SY1207 ) )
| ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(889,plain,
! [SV50: $i] :
( ( ( in @ SV50 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(890,plain,
! [SV213: $i > $o,SV51: $i] :
( ( ( ~ ! [SY1552: $i] :
( ~ ( in @ SY1552 @ SV51 )
| ~ ( SV213 @ SY1552 ) ) )
= $true )
| ( ( ~ ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(891,plain,
! [SV214: $i,SV52: $i,SV328: $i] :
( ( ~ ( in @ SV328 @ SV52 )
| ! [SY1715: $i] :
( ~ ( in @ SY1715 @ SV214 )
| ( in @ ( kpair @ SV328 @ SY1715 ) @ ( powerset @ ( powerset @ ( binunion @ SV52 @ SV214 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(892,plain,
! [SV329: $i,SV215: $i,SV53: $i] :
( ( ! [SY1716: $i] :
( ( ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV215 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV329 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV329 @ ( setadjoin @ SY1716 @ emptyset ) ) @ emptyset ) ) )
| ( SV53 = SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(893,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ! [SY1558: $i,SY1559: $i] :
( ( SY1558 != SY1559 )
| ~ ( ~ ( ~ ( SV54 @ SY1558 )
| ( SV216 @ SY1559 ) )
| ~ ( ~ ( SV216 @ SY1559 )
| ( SV54 @ SY1558 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(894,plain,
! [SV330: $i,SV217: $i,SV55: $i] :
( ( ( ( setadjoin @ SV55 @ ( setadjoin @ SV217 @ emptyset ) )
!= ( setadjoin @ SV330 @ emptyset ) )
| ( SV55 = SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(895,plain,
! [SV218: $i,SV56: $i,SV331: $i] :
( ( ! [SY1717: $i] :
( ~ ( in @ ( kpair @ SV331 @ SY1717 ) @ ( cartprod @ SV56 @ SV218 ) )
| ( in @ SV331 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(896,plain,
! [SV219: $i > $o,SV57: $i,SV332: $i] :
( ( ~ ( in @ SV332
@ ( dsetconstr @ SV57
@ ^ [SY1572: $i] : ( SV219 @ SY1572 ) ) )
| ( SV219 @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(897,plain,
! [SV220: $i,SV58: $i,SV333: $i] :
( ( ~ ~ ( in @ SV333 @ SV58 )
| ~ ( in @ SV333 @ SV220 )
| ( in @ SV333 @ ( symdiff @ SV58 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(898,plain,
! [SV221: $i,SV59: $i] :
( ( ( SV59 != SV221 )
= $true )
| ( ( subset @ SV59 @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(899,plain,
! [SV222: $i,SV60: $i,SV334: $i] :
( ( ~ ( in @ SV334 @ ( cartprod @ SV60 @ SV222 ) )
| ( in @ ( kfst @ SV334 ) @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(900,plain,
! [SV335: $i,SV223: $i,SV61: $i] :
( ( ! [SY1719: $i] :
( ( ( kpair @ SV61 @ SV223 )
!= ( kpair @ SV335 @ SY1719 ) )
| ( SV61 = SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(901,plain,
! [SV224: $i > $o,SV62: $i,SV336: $i] :
( ( ~ ( in @ SV336 @ SV62 )
| ~ ( ~ ( ~ ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) )
| ( SV224 @ SV336 ) )
| ~ ( ~ ( SV224 @ SV336 )
| ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(902,plain,
! [SV337: $i,SV225: $i,SV63: $i] :
( ( ~ ( subset @ SV63 @ SV225 )
| ~ ~ ( in @ SV337 @ SV225 )
| ~ ( in @ SV337 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(903,plain,
! [SV226: $i,SV64: $i] :
( ( ( SV64 != SV226 )
= $true )
| ( ( ( setadjoin @ SV64 @ ( setadjoin @ SV226 @ emptyset ) )
= ( setadjoin @ SV64 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(904,plain,
! [SV65: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV65 )
| ~ ! [SY1253: $i] :
( ~ ~ ( ~ ( in @ SY1253 @ omega )
| ~ ( in @ SY1253 @ SV65 ) )
| ( in @ ( setadjoin @ SY1253 @ SY1253 ) @ SV65 ) ) ) )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(905,plain,
! [SV227: $i > $o,SV66: $i,SV338: $i] :
( ( ~ ( in @ SV338
@ ( dsetconstr @ SV66
@ ^ [SY1582: $i] : ( SV227 @ SY1582 ) ) )
| ( in @ SV338 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(906,plain,
! [SV67: $i > $o] :
( ( ( ~ ! [SY1258: $i] :
~ ~ ( ~ ( SV67 @ SY1258 )
| ~ ! [SY1259: $i] :
( ~ ( SV67 @ SY1259 )
| ( SY1258 = SY1259 ) ) ) )
= $false )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(907,plain,
! [SV228: $i,SV68: $i,SV339: $i] :
( ( ~ ( in @ ( setadjoin @ SV339 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ ( setadjoin @ SV228 @ emptyset ) ) @ emptyset ) ) )
| ( SV68 = SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(908,plain,
! [SV229: $i,SV69: $i,SV340: $i] :
( ( ~ ( in @ SV340 @ ( binintersect @ SV69 @ SV229 ) )
| ( in @ SV340 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(909,plain,
! [SV70: $i,SV230: $i] :
( ( ~ ( ~ ( in @ SV230 @ ( setunion @ SV70 ) )
| ~ ! [SY1585: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1585 )
| ~ ( in @ SY1585 @ SV70 ) ) )
| ~ ( ~ ~ ! [SY1586: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1586 )
| ~ ( in @ SY1586 @ SV70 ) )
| ( in @ SV230 @ ( setunion @ SV70 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(910,plain,
! [SV71: $o] :
( ( SV71 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(911,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(912,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(913,plain,
! [SV72: $i] :
( ( ( ~ ! [SY1269: $i] :
~ ( in @ SY1269 @ SV72 ) )
= $false )
| ( ( SV72 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(914,plain,
! [SV73: $i,SV231: $i] :
( ( ( ~ ( in @ SV231 @ SV73 ) )
= $true )
| ( ( in @ SV231 @ ( powerset @ ( setunion @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(915,plain,
! [SV232: $i,SV74: $i,SV341: $i] :
( ( ~ ( in @ SV341 @ SV74 )
| ~ ~ ( in @ SV341 @ SV232 )
| ( SV74 != SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(916,plain,
! [SV75: $i] :
( ( ( subset @ SV75 @ emptyset )
= $false )
| ( ( SV75 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(917,plain,
! [SV233: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( setadjoin @ SV233 @ emptyset ) ) )
= $true )
| ( ( in @ SV233 @ ( setadjoin @ SV76 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(918,plain,
! [SV77: $i] :
( ( ( iskpair @ SV77 )
= $false )
| ( ( ~ ! [SY1274: $i] :
~ ~ ( ~ ( in @ SY1274
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
!= ( setadjoin @ SY1274 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(919,plain,
! [SV234: $i,SV78: $i,SV342: $i] :
( ( ~ ~ ( in @ SV342 @ ( setminus @ SV78 @ SV234 ) )
| ~ ~ ( in @ SV342 @ SV234 )
| ~ ( in @ SV342 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(920,plain,
! [SV235: $i,SV79: $i,SV343: $i] :
( ( ~ ~ ( in @ SV343 @ ( setminus @ SV79 @ SV235 ) )
| ~ ( in @ SV343 @ SV79 )
| ( in @ SV343 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(921,plain,
! [SV236: $i,SV80: $i] :
( ( ( ( setadjoin @ SV80 @ emptyset )
!= ( setadjoin @ SV236 @ emptyset ) )
= $true )
| ( ( SV80 = SV236 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(922,plain,
! [SV81: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ SV81 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV237 @ emptyset ) @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(923,plain,
! [SV82: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV82 ) )
= $true )
| ( ( in @ ( setadjoin @ SV238 @ emptyset ) @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(924,plain,
! [SV239: $i,SV83: $i] :
( ( ( SV83 != SV239 )
= $true )
| ( ( in @ SV83 @ ( setadjoin @ SV239 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(925,plain,
! [SV240: $i,SV84: $i,SV344: $i] :
( ( ~ ( subset @ SV344 @ SV84 )
| ~ ( subset @ SV344 @ SV240 )
| ( subset @ SV344 @ ( binintersect @ SV84 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(926,plain,
! [SV85: $i] :
( ( ( iskpair @ SV85 )
= $false )
| ( ( ( kpair @ ( kfst @ SV85 ) @ ( ksnd @ SV85 ) )
= SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(927,plain,
! [SV241: $i > $o,SV86: $i] :
( ( ( ~ ~ ~ ! [SY1591: $i] :
~ ~ ( ~ ( in @ SY1591 @ SV86 )
| ~ ( SV241 @ SY1591 ) ) )
= $true )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(928,plain,
! [SV242: $i,SV87: $i,SV345: $i] :
( ( ~ ( in @ SV345 @ ( setadjoin @ SV87 @ ( setadjoin @ SV242 @ emptyset ) ) )
| ( SV345 = SV87 )
| ( SV345 = SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(929,plain,
! [SV243: $i,SV88: $i] :
( ( ( SV88 != SV243 )
= $true )
| ( ( ( powerset @ SV88 )
= ( powerset @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(930,plain,
! [SV244: $i > $o,SV89: $i] :
( ( ( ~ ~ ! [SY1594: $i] :
( ~ ( in @ SY1594 @ SV89 )
| ( SV244 @ SY1594 ) ) )
= $true )
| ( ( ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV89 )
| ~ ~ ( SV244 @ SY1595 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(931,plain,
! [SV90: $i] :
( ( ( SV90 != emptyset )
= $false )
| ( ( ~ ! [SY1296: $i] :
~ ~ ( ~ ( in @ SY1296 @ SV90 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(932,plain,
! [SV91: $i] :
( ( ( ! [SY1297: $i] :
~ ( in @ SY1297 @ SV91 ) )
= $false )
| ( ( SV91 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(933,plain,
! [SV346: $i,SV245: $i,SV92: $i] :
( ( ! [SY1723: $i] :
( ( ( kpair @ SV92 @ SV245 )
!= ( kpair @ SV346 @ SY1723 ) )
| ( SV245 = SY1723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(934,plain,
! [SV93: $i,SV246: $i,SV347: $i] :
( ( ~ ( in @ SV347 @ SV246 )
| ( in @ SV347 @ ( setadjoin @ SV93 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(935,plain,
! [SV94: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ ( setunion @ SV94 ) ) )
= $true )
| ( ( ~ ! [SY1599: $i] :
~ ~ ( ~ ( in @ SY1599 @ SV94 )
| ~ ( in @ SV247 @ SY1599 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(936,plain,
! [SV248: $i,SV95: $i] :
( ( ( ~ ( subset @ SV95 @ SV248 ) )
= $true )
| ( ( ~ ( subset @ SV248 @ SV95 )
| ( SV95 = SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(937,plain,
! [SV249: $i,SV96: $i,SV348: $i] :
( ( ! [SY1724: $i] :
( ~ ( in @ ( kpair @ SV348 @ SY1724 ) @ ( cartprod @ SV96 @ SV249 ) )
| ( in @ SY1724 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(938,plain,
! [SV250: $i,SV97: $i,SV349: $i] :
( ( ~ ( in @ SV349 @ ( binintersect @ SV97 @ SV250 ) )
| ( in @ SV349 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(939,plain,
! [SV251: $i,SV98: $i] :
( ( ( SV98 != SV251 )
= $true )
| ( ( ! [SY1603: $i,SY1604: $i] :
( ( SY1603 != SY1604 )
| ~ ( ~ ( ~ ( in @ SY1603 @ SV98 )
| ( in @ SY1604 @ SV251 ) )
| ~ ( ~ ( in @ SY1604 @ SV251 )
| ( in @ SY1603 @ SV98 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(940,plain,
! [SV252: $i,SV99: $i,SV350: $i] :
( ( ~ ( in @ SV350 @ ( setadjoin @ SV99 @ ( setadjoin @ SV252 @ emptyset ) ) )
| ( SV350 = SV99 )
| ( SV350 = SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(941,plain,
! [SV253: $i,SV100: $i] :
( ( ( ( setminus @ SV100 @ SV253 )
!= emptyset )
= $true )
| ( ( subset @ SV100 @ SV253 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(942,plain,
! [SV101: $i] :
( ( ( SV101 != emptyset )
= $false )
| ( ( ~ ! [SY1317: $i] :
~ ( in @ SY1317 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(943,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ~ ( ~ ( ~ ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
| ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
| ~ ( ~ ( ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
| ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(944,plain,
! [SV103: $i > $o] :
( ( ( ~ ! [SY1320: $i] :
~ ~ ( ~ ( SV103 @ SY1320 )
| ~ ! [SY1321: $i] :
( ~ ( SV103 @ SY1321 )
| ( SY1320 = SY1321 ) ) ) )
= $false )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(945,plain,
! [SV255: $i,SV104: $i] :
( ( ( ~ ~ ~ ! [SY1607: $i] :
~ ~ ( ~ ( in @ SY1607 @ SV104 )
| ~ ( in @ SY1607 @ SV255 ) ) )
= $true )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(946,plain,
! [SV256: $i,SV105: $i,SV352: $i] :
( ( ~ ( in @ SV352 @ SV105 )
| ~ ~ ( in @ SV352 @ SV256 )
| ~ ( subset @ SV105 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(947,plain,
! [SV257: $i,SV106: $i,SV353: $i] :
( ( ~ ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
| ~ ! [SY1725: $i] :
~ ~ ( ~ ( in @ SY1725 @ SV106 )
| ~ ~ ! [SY1726: $i] :
~ ~ ( ~ ( in @ SY1726 @ SV257 )
| ( SV353
!= ( kpair @ SY1725 @ SY1726 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(948,plain,
! [SV107: $i > $o] :
( ( ( ~ ! [SY1332: $i] :
~ ~ ( ~ ( SV107 @ SY1332 )
| ~ ! [SY1333: $i] :
( ~ ( SV107 @ SY1333 )
| ( SY1332 = SY1333 ) ) ) )
= $false )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(949,plain,
! [SV258: $i,SV108: $i,SV354: $i] :
( ( ~ ~ ( in @ SV354 @ SV108 )
| ~ ~ ( in @ SV354 @ SV258 )
| ~ ( in @ SV354 @ ( symdiff @ SV108 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(950,plain,
! [SV109: $i,SV259: $i] :
( ( ~ ( ~ ( in @ SV259 @ ( powerset @ SV109 ) )
| ! [SY1613: $i] :
( ~ ( in @ SY1613 @ SV259 )
| ( in @ SY1613 @ SV109 ) ) )
| ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ SV259 )
| ( in @ SY1614 @ SV109 ) )
| ( in @ SV259 @ ( powerset @ SV109 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(951,plain,
! [SV260: $i,SV110: $i] :
( ( ( ~ ( subset @ SV110 @ SV260 ) )
= $true )
| ( ( ( binintersect @ SV110 @ SV260 )
= SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(952,plain,
! [SV111: $i] :
( ( ( in @ SV111 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(953,plain,
! [SV112: $i] :
( ( ( ! [SY1343: $i] :
~ ( in @ SY1343 @ SV112 ) )
= $false )
| ( ( SV112 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(954,plain,
! [SV113: $o] :
( ( SV113 = $false )
| ( ( set2prop @ ( prop2set @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(955,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(956,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(957,plain,
! [SV114: $i > $o,SV261: $i] :
( ( ( ~ ( in @ SV261 @ emptyset ) )
= $true )
| ( ( SV114 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(958,plain,
! [SV355: $i,SV262: $i,SV115: $i] :
( ( ! [SY1727: $i] :
( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV262 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SY1727 @ emptyset ) ) @ emptyset ) ) )
| ( SV262 = SY1727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(959,plain,
! [SV263: $i,SV116: $i] :
( ( ( ~ ( ( SV116 != SV263 ) ) )
= $true )
| ( ( ~ ( in @ SV263 @ ( setadjoin @ SV116 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(960,plain,
! [SV117: $i > $o] :
( ( ( ~ ! [SY1349: $i] :
~ ~ ( ~ ( SV117 @ SY1349 )
| ~ ! [SY1350: $i] :
( ~ ( SV117 @ SY1350 )
| ( SY1349 = SY1350 ) ) ) )
= $false )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(961,plain,
! [SV264: $i > $o,SV118: $i,SV356: $i] :
( ( ~ ( in @ SV356 @ SV118 )
| ~ ( SV264 @ SV356 )
| ( ( dsetconstr @ SV118
@ ^ [SY1618: $i] : ( SV264 @ SY1618 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(962,plain,
! [SV265: $i > $o,SV119: $i,SV357: $i] :
( ( ~ ( in @ SV357 @ SV119 )
| ~ ( SV265 @ SV357 )
| ~ ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV119 )
| ~ ( SV265 @ SY1729 )
| ( SY1729 = SV357 ) )
| ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(963,plain,
! [SV120: $i,SV266: $i] :
( ( ( ~ ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV266 )
| ( in @ SY1624 @ SV120 ) ) )
= $true )
| ( ( in @ SV266 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(964,plain,
! [SV267: $i,SV121: $i] :
( ( ( ~ ! [SY1625: $i] :
( ~ ( in @ SY1625 @ SV121 )
| ( in @ SY1625 @ SV267 ) ) )
= $true )
| ( ( ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) )
| ( SV121 = SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(965,plain,
! [SV268: $i,SV122: $i] :
( ( ( ~ ( subset @ SV122 @ SV268 ) )
= $true )
| ( ( ( setminus @ SV122 @ SV268 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(966,plain,
! [SV123: $i,SV269: $i] :
( ( ( ~ ( subset @ SV269 @ SV123 ) )
= $true )
| ( ( in @ SV269 @ ( powerset @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(967,plain,
! [SV358: $i,SV270: $i,SV124: $i] :
( ( ~ ( subset @ SV124 @ SV270 )
| ~ ( in @ SV358 @ SV124 )
| ( in @ SV358 @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(968,plain,
! [SV125: $i] :
( ( ( ~ ! [SY1370: $i] :
~ ( in @ SY1370 @ SV125 ) )
= $false )
| ( ( ~ ! [SY1371: $i] :
~ ~ ( ~ ( in @ SY1371 @ SV125 )
| ~ ~ ~ ! [SY1372: $i] :
~ ~ ( ~ ( in @ SY1372 @ SY1371 )
| ~ ( in @ SY1372 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(969,plain,
! [SV126: $i > $o] :
( ( ( ~ ! [SY1373: $i] :
~ ! [SY1374: $i] :
~ ( ~ ( ~ ( SV126 @ SY1374 )
| ( SY1374 = SY1373 ) )
| ~ ( ( SY1374 != SY1373 )
| ( SV126 @ SY1374 ) ) ) )
= $false )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(970,plain,
( ( ! [SY1733: $i] :
( ~ ( in @ SY1733 @ ( cartprod @ sK1_SX0 @ sK2_SY1628 ) )
| ( ( kpair @ ( kfst @ SY1733 ) @ ( ksnd @ SY1733 ) )
= SY1733 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[817]) ).
thf(971,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ! [SY1630: $i] :
( ~ ( in @ SY1630 @ SV127 )
| ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV127 )
| ~ ( SV271 @ SY1630 )
| ~ ( SV271 @ SY1631 )
| ( SY1630 = SY1631 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(972,plain,
! [SV272: $i,SV128: $i] :
( ( ( ~ ( subset @ SV128 @ SV272 ) )
= $true )
| ( ( subset @ ( powerset @ SV128 ) @ ( powerset @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(973,plain,
! [SV273: $i,SV129: $i,SV359: $i] :
( ( ~ ( in @ SV359 @ ( cartprod @ SV129 @ SV273 ) )
| ( iskpair @ SV359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(974,plain,
! [SV274: $i,SV130: $i] :
( ( ( SV130 != SV274 )
= $true )
| ( ( ! [SY1637: $i > $o,SY1638: $i > $o] :
( ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV130 )
| ! [SY1640: $i] :
( ~ ( in @ SY1640 @ SV274 )
| ( SY1639 != SY1640 )
| ~ ( ~ ( ~ ( SY1637 @ SY1639 )
| ( SY1638 @ SY1640 ) )
| ~ ( ~ ( SY1638 @ SY1640 )
| ( SY1637 @ SY1639 ) ) ) ) )
| ( ( dsetconstr @ SV130
@ ^ [SX4: $i] : ( SY1637 @ SX4 ) )
= ( dsetconstr @ SV274
@ ^ [SX4: $i] : ( SY1638 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(975,plain,
! [SV275: $i,SV360: $i,SV131: $i] :
( ( ~ ( subset @ SV131 @ SV360 )
| ( subset @ SV131 @ ( setadjoin @ SV275 @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(976,plain,
! [SV132: $i] :
( ( ( iskpair @ SV132 )
= $false )
| ( ( ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) )
| ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
!= ( setadjoin @ SY1396 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(977,plain,
! [SV276: $i,SV133: $i] :
( ( ( ( binintersect @ SV133 @ SV276 )
!= SV133 )
= $true )
| ( ( subset @ SV133 @ SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(978,plain,
! [SV277: $i,SV134: $i,SV361: $i] :
( ( ~ ( in @ SV361 @ ( setadjoin @ SV134 @ SV277 ) )
| ( SV361 = SV134 )
| ( in @ SV361 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(979,plain,
! [SV278: $i > $o,SV135: $i] :
( ( ( ~ ~ ! [SY1645: $i] :
~ ~ ( ~ ( in @ SY1645 @ SV135 )
| ~ ~ ( SV278 @ SY1645 ) ) )
= $true )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(980,plain,
! [SV279: $i > $o,SV136: $i] :
( ( ( ~ ~ ! [SY1647: $i] :
~ ~ ( ~ ( in @ SY1647 @ SV136 )
| ~ ( SV279 @ SY1647 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(981,plain,
! [SV280: $i,SV137: $i,SV362: $i] :
( ( ~ ( in @ SV362 @ SV137 )
| ! [SY1734: $i] :
( ~ ( in @ SY1734 @ SV280 )
| ( subset @ ( setadjoin @ SV362 @ ( setadjoin @ SY1734 @ emptyset ) ) @ ( binunion @ SV137 @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(982,plain,
! [SV281: $i,SV138: $i] :
( ( ( ~ ( subset @ SV138 @ SV281 ) )
= $true )
| ( ( in @ SV138 @ ( powerset @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(983,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ! [SY1651: $i,SY1652: $i] :
( ( SY1651 != SY1652 )
| ~ ( ~ ( ~ ( SV139 @ SY1651 )
| ( SV282 @ SY1652 ) )
| ~ ( ~ ( SV282 @ SY1652 )
| ( SV139 @ SY1651 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(984,plain,
! [SV283: $i,SV140: $i] :
( ( ( ~ ! [SY1659: $i] :
~ ( ~ ( ~ ( in @ SY1659 @ SV140 )
| ( in @ SY1659 @ SV283 ) )
| ~ ( ~ ( in @ SY1659 @ SV283 )
| ( in @ SY1659 @ SV140 ) ) ) )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(985,plain,
! [SV141: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
| ~ ! [SY1740: $i,SY1741: $i] :
( ~ ~ ( ~ ( in @ SY1740 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1741 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1740 )
| ( in @ SX4 @ SY1741 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1741 )
| ( in @ SX4 @ SY1740 ) ) ) )
| ~ ! [SY1744: $i] :
( ~ ~ ( ~ ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SY1744 )
| ( in @ SY1434 @ SV141 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1744 ) )
| ~ ! [SY1747: $i] :
~ ~ ! [SY1748: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1747 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1748 @ SY1744 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1747 )
| ~ ( in @ SX5 @ SY1744 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1747 ) )
| ( in @ SY1748 @ SY1750 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[832]) ).
thf(986,plain,
! [SV284: $i,SV142: $i,SV363: $i] :
( ( ~ ( in @ SV363 @ SV142 )
| ! [SY1752: $i] :
( ~ ( in @ SY1752 @ SV284 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV363 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV363 @ ( setadjoin @ SY1752 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV142 @ SV284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(987,plain,
! [SV143: $i] :
( ( ( in @ SV143 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV143 @ SV143 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(988,plain,
! [SV144: $i,SV285: $i] :
( ( ( ~ ( subset @ SV285 @ SV144 ) )
= $true )
| ( ( ( binintersect @ SV144 @ SV285 )
= SV285 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(989,plain,
! [SV145: $i,SV286: $i,SV364: $i] :
( ( ~ ( in @ SV364 @ SV286 )
| ~ ( in @ SV364 @ ( setminus @ SV145 @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(990,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ! [SY1663: $i] :
( ~ ( in @ SY1663 @ SV146 )
| ! [SY1664: $i] :
( ~ ( in @ SY1664 @ SV146 )
| ~ ( SV287 @ SY1663 )
| ~ ( SV287 @ SY1664 )
| ( SY1663 = SY1664 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(991,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ~ ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
| ! [SY1753: $o] :
( ~ ( ( SV365 != SV147 )
| SY1753 )
| ~ ( ~ ( in @ SV365 @ SV288 )
| SY1753 )
| SY1753 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(992,plain,
! [SV289: $i,SV148: $i] :
( ( ( SV148 != SV289 )
= $true )
| ( ( subset @ SV289 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(993,plain,
! [SV290: $i,SV149: $i,SV366: $i] :
( ( ~ ( in @ SV366 @ SV149 )
| ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV290 )
| ( ( kfst @ ( kpair @ SV366 @ SY1754 ) )
= SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(994,plain,
! [SV291: $i > $o,SV150: $i,SV367: $i] :
( ( ~ ( in @ SV367 @ SV150 )
| ~ ( SV291 @ SV367 )
| ( in @ SV367
@ ( dsetconstr @ SV150
@ ^ [SY1674: $i] : ( SV291 @ SY1674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(995,plain,
! [SV368: $i,SV151: $i,SV292: $i] :
( ( ~ ( in @ SV292 @ ( powerset @ SV151 ) )
| ~ ( in @ SV368 @ SV292 )
| ( in @ SV368 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(996,plain,
! [SV293: $i,SV152: $i] :
( ( ( SV152 != SV293 )
= $true )
| ( ( ( setunion @ SV152 )
= ( setunion @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(997,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ! [SY1756: $o] :
( ~ ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
| ~ ( ~ ( in @ SV369 @ SV153 )
| SY1756 )
| ~ ( ~ ( in @ SV369 @ SV294 )
| SY1756 )
| SY1756 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(998,plain,
! [SV295: $i,SV154: $i] :
( ( ( SV154 != SV295 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV154 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV154 @ ( setadjoin @ SV295 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV154 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(999,plain,
! [SV296: $i > $o,SV155: $i] :
( ( ( ~ ~ ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV155 )
| ( SV296 @ SY1678 ) ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ( ~ ( in @ SY1679 @ SV155 )
| ~ ~ ( SV296 @ SY1679 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(1000,plain,
! [SV297: $i,SV156: $i,SV370: $i] :
( ( ~ ( in @ SV370 @ SV156 )
| ( in @ ( setadjoin @ SV370 @ emptyset ) @ ( powerset @ ( binunion @ SV156 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1001,plain,
! [SV157: $o,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( prop2set @ SV157 ) ) )
= $true )
| ( SV157 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(1002,plain,
! [SV299: $i] :
( ( ( ~ ( in @ SV299 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(1003,plain,
! [SV300: $i] :
( ( ( ~ ( in @ SV300 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(1004,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( setunion @ SV158 ) ) )
= $true )
| ( ( ! [SY1681: $o] :
( ~ ! [SY1682: $i] :
( ~ ( in @ SV301 @ SY1682 )
| ~ ( in @ SY1682 @ SV158 )
| SY1681 )
| SY1681 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(1005,plain,
! [SV302: $i > $o,SV159: $i] :
( ( ( ~ ~ ! [SY1683: $i] :
~ ~ ( ~ ( in @ SY1683
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SY1683 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(1006,plain,
! [SV303: $i,SV160: $i] :
( ( ( SV160 != SV303 )
= $true )
| ( ( ! [SY1687: $i,SY1688: $i] :
( ( SY1687 != SY1688 )
| ( ( setadjoin @ SV160 @ SY1687 )
= ( setadjoin @ SV303 @ SY1688 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(1007,plain,
! [SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV304 )
| ~ ! [SY1490: $i] :
~ ~ ( ~ ( SV161 @ SY1689 @ SY1490 )
| ~ ! [SY1491: $i] :
( ~ ( SV161 @ SY1689 @ SY1491 )
| ( SY1490 = SY1491 ) ) ) ) )
= $true )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(1008,plain,
! [SV305: $i,SV162: $i,SV371: $i] :
( ( ~ ( in @ SV371 @ SV162 )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SV305 )
| ( ( ksnd @ ( kpair @ SV371 @ SY1757 ) )
= SY1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1009,plain,
! [SV372: $i,SV306: $i,SV163: $i] :
( ( ~ ( subset @ SV163 @ SV306 )
| ~ ( subset @ SV306 @ SV372 )
| ( subset @ SV163 @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1010,plain,
! [SV307: $i,SV164: $i,SV373: $i] :
( ( ~ ( in @ SV373 @ ( setminus @ SV164 @ SV307 ) )
| ( in @ SV373 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1011,plain,
! [SV308: $i,SV165: $i,SV374: $i] :
( ( ~ ( in @ SV374 @ SV165 )
| ~ ~ ( in @ SV374 @ SV308 )
| ( in @ SV374 @ ( symdiff @ SV165 @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1012,plain,
! [SV309: $i,SV166: $i,SV375: $i] :
( ( ~ ~ ( in @ SV375 @ SV166 )
| ~ ( in @ SV375 @ ( setminus @ SV166 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1013,plain,
! [SV167: $i > $o] :
( ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( SV167 @ SY1507 )
| ~ ! [SY1508: $i] :
( ~ ( SV167 @ SY1508 )
| ( SY1507 = SY1508 ) ) ) )
= $false )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(1014,plain,
! [SV310: $i,SV168: $i,SV376: $i] :
( ( ~ ( in @ SV376 @ ( setminus @ SV168 @ SV310 ) )
| ~ ( in @ SV376 @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1015,plain,
! [SV311: $i,SV169: $i,SV377: $i] :
( ( ~ ( in @ SV377 @ SV169 )
| ~ ( in @ SV377 @ SV311 )
| ~ ( in @ SV377 @ ( symdiff @ SV169 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1016,plain,
! [SV170: $i] :
( ( ( ~ ! [SY1515: $i] :
~ ~ ( ~ ( in @ SY1515 @ SV170 )
| ( SV170
!= ( setadjoin @ SY1515 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(1017,plain,
! [SV312: $i,SV171: $i,SV378: $i] :
( ( ~ ( in @ SV378 @ SV171 )
| ! [SY1758: $i] :
( ~ ( in @ SY1758 @ SV312 )
| ( in @ ( setadjoin @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV378 @ ( setadjoin @ SY1758 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV171 @ SV312 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1018,plain,
! [SV172: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ ( powerset @ SV172 ) ) )
= $true )
| ( ( subset @ SV313 @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(1019,plain,
! [SV314: $i,SV173: $i,SV379: $i] :
( ( ~ ( in @ SV379 @ SV173 )
| ! [SY1759: $i] :
( ~ ( in @ SY1759 @ SV314 )
| ( in @ ( kpair @ SV379 @ SY1759 ) @ ( cartprod @ SV173 @ SV314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1020,plain,
! [SV315: $i,SV174: $i,SV380: $i] :
( ( ~ ( in @ SV380 @ SV174 )
| ! [SY1760: $i] :
( ~ ( in @ SY1760 @ SV315 )
| ( ( kpair @ SV380 @ SY1760 )
= ( kpair @ SV380 @ SY1760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1021,plain,
! [SV175: $i > $o] :
( ( ( ~ ! [SY1526: $i] :
~ ~ ( ~ ( SV175 @ SY1526 )
| ~ ! [SY1527: $i] :
( ~ ( SV175 @ SY1527 )
| ( SY1526 = SY1527 ) ) ) )
= $false )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(1022,plain,
! [SV316: $i,SV176: $i] :
( ( ( SV176 != SV316 )
= $true )
| ( ( ! [SY1710: $i,SY1711: $i] :
( ( SY1710 != SY1711 )
| ~ ( in @ SY1710 @ SV176 )
| ( in @ SY1711 @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(1023,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) ) )
= $true )
| ( ( ! [SY1712: $o] :
( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| SY1712 )
| ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SY1712 )
| SY1712 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(1024,plain,
! [SV198: $i,SV33: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ ( binunion @ SV33 @ SV198 ) ) )
= $true )
| ( ( ( in @ SV319 @ SV33 )
| ( in @ SV319 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1025,plain,
! [SV199: $i,SV34: $i] :
( ( ( ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV34 )
| ( in @ SY1538 @ SV199 ) ) )
= $false )
| ( ( subset @ SV34 @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(1026,plain,
! [SV200: $i,SV35: $i] :
( ( ( ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV35 )
| ( in @ SY1539 @ SV200 ) ) )
= $false )
| ( ( subset @ SV35 @ SV200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(1027,plain,
! [SV381: $i,SV320: $i,SV201: $i,SV36: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV36 @ ( setadjoin @ SV201 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV320 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV320 @ ( setadjoin @ SV381 @ emptyset ) ) @ emptyset ) ) )
| ( SV320 != SV381 )
| ( SV201 = SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1028,plain,
! [SV37: $i,SV321: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV321 ) )
= $true )
| ( ( ~ ( in @ SV321 @ SV37 )
| ( in @ SV202 @ ( setunion @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(1029,plain,
! [SV203: $i,SV38: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ SV38 ) )
= $true )
| ( ( ~ ~ ( in @ SV322 @ SV203 )
| ( in @ SV322 @ ( setminus @ SV38 @ SV203 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(1030,plain,
! [SV39: $i,SV204: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV204 ) )
= $true )
| ( ( in @ SV323 @ ( binunion @ SV39 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(1031,plain,
! [SV205: $i,SV40: $i] :
( ( ( ~ ( subset @ SV40 @ SV205 ) )
= $false )
| ( ( SV40 != SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(1032,plain,
! [SV206: $i > $o,SV41: $i] :
( ( ( ~ ~ ! [SY1545: $i] :
~ ~ ( ~ ( in @ SY1545 @ SV41 )
| ~ ( SV206 @ SY1545 ) ) )
= $false )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(1033,plain,
! [SV207: $i,SV42: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( cartprod @ SV42 @ SV207 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV324 ) @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(1034,plain,
! [SV208: $i,SV43: $i,SV325: $i] :
( ( ( ~ ( in @ SV325 @ SV43 ) )
= $true )
| ( ( ~ ( in @ SV325 @ SV208 )
| ( in @ SV325 @ ( binintersect @ SV43 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(1035,plain,
! [SV209: $i,SV44: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ SV44 ) )
= $true )
| ( ( in @ SV326 @ ( binunion @ SV44 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(1036,plain,
! [SV210: $i,SV45: $i] :
( ( ( ( binintersect @ SV45 @ SV210 )
= SV210 )
= $false )
| ( ( subset @ SV210 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(1037,plain,
! [SV46: $i > $o] :
( ( ( ! [SY1197: $i] :
~ ~ ( ~ ( SV46 @ SY1197 )
| ~ ! [SY1198: $i] :
( ~ ( SV46 @ SY1198 )
| ( SY1197 = SY1198 ) ) ) )
= $true )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(1038,plain,
! [SV211: $i,SV47: $i,SV327: $i] :
( ( ( ~ ( in @ SV327 @ SV47 ) )
= $true )
| ( ( ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV211 )
| ( in @ ( setadjoin @ SV327 @ ( setadjoin @ SY1714 @ emptyset ) ) @ ( powerset @ ( binunion @ SV47 @ SV211 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(1039,plain,
! [SV212: $i,SV48: $i] :
( ( ( in @ SV48 @ ( setadjoin @ SV212 @ emptyset ) )
= $false )
| ( ( SV48 = SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(1040,plain,
! [SV49: $i > $o] :
( ( ( ! [SY1205: $i] :
~ ( SV49 @ SY1205 ) )
= $true )
| ( ( ~ ! [SY1206: $i,SY1207: $i] :
( ~ ( SV49 @ SY1206 )
| ~ ( SV49 @ SY1207 )
| ( SY1206 = SY1207 ) )
| ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(1041,plain,
! [SV213: $i > $o,SV51: $i] :
( ( ( ! [SY1552: $i] :
( ~ ( in @ SY1552 @ SV51 )
| ~ ( SV213 @ SY1552 ) ) )
= $false )
| ( ( ~ ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(1042,plain,
! [SV214: $i,SV52: $i,SV328: $i] :
( ( ( ~ ( in @ SV328 @ SV52 ) )
= $true )
| ( ( ! [SY1715: $i] :
( ~ ( in @ SY1715 @ SV214 )
| ( in @ ( kpair @ SV328 @ SY1715 ) @ ( powerset @ ( powerset @ ( binunion @ SV52 @ SV214 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(1043,plain,
! [SV382: $i,SV329: $i,SV215: $i,SV53: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV215 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV329 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV329 @ ( setadjoin @ SV382 @ emptyset ) ) @ emptyset ) ) )
| ( SV53 = SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1044,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1558: $i,SY1559: $i] :
( ( SY1558 != SY1559 )
| ~ ( ~ ( ~ ( SV54 @ SY1558 )
| ( SV216 @ SY1559 ) )
| ~ ( ~ ( SV216 @ SY1559 )
| ( SV54 @ SY1558 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(1045,plain,
! [SV330: $i,SV217: $i,SV55: $i] :
( ( ( ( setadjoin @ SV55 @ ( setadjoin @ SV217 @ emptyset ) )
!= ( setadjoin @ SV330 @ emptyset ) )
= $true )
| ( ( SV55 = SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(1046,plain,
! [SV218: $i,SV56: $i,SV383: $i,SV331: $i] :
( ( ~ ( in @ ( kpair @ SV331 @ SV383 ) @ ( cartprod @ SV56 @ SV218 ) )
| ( in @ SV331 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1047,plain,
! [SV219: $i > $o,SV57: $i,SV332: $i] :
( ( ( ~ ( in @ SV332
@ ( dsetconstr @ SV57
@ ^ [SY1572: $i] : ( SV219 @ SY1572 ) ) ) )
= $true )
| ( ( SV219 @ SV332 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(1048,plain,
! [SV220: $i,SV58: $i,SV333: $i] :
( ( ( ~ ~ ( in @ SV333 @ SV58 ) )
= $true )
| ( ( ~ ( in @ SV333 @ SV220 )
| ( in @ SV333 @ ( symdiff @ SV58 @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(1049,plain,
! [SV221: $i,SV59: $i] :
( ( ( SV59 = SV221 )
= $false )
| ( ( subset @ SV59 @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(1050,plain,
! [SV222: $i,SV60: $i,SV334: $i] :
( ( ( ~ ( in @ SV334 @ ( cartprod @ SV60 @ SV222 ) ) )
= $true )
| ( ( in @ ( kfst @ SV334 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(1051,plain,
! [SV384: $i,SV335: $i,SV223: $i,SV61: $i] :
( ( ( ( kpair @ SV61 @ SV223 )
!= ( kpair @ SV335 @ SV384 ) )
| ( SV61 = SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1052,plain,
! [SV224: $i > $o,SV62: $i,SV336: $i] :
( ( ( ~ ( in @ SV336 @ SV62 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) )
| ( SV224 @ SV336 ) )
| ~ ( ~ ( SV224 @ SV336 )
| ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(1053,plain,
! [SV337: $i,SV225: $i,SV63: $i] :
( ( ( ~ ( subset @ SV63 @ SV225 ) )
= $true )
| ( ( ~ ~ ( in @ SV337 @ SV225 )
| ~ ( in @ SV337 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1054,plain,
! [SV226: $i,SV64: $i] :
( ( ( SV64 = SV226 )
= $false )
| ( ( ( setadjoin @ SV64 @ ( setadjoin @ SV226 @ emptyset ) )
= ( setadjoin @ SV64 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1055,plain,
! [SV65: $i] :
( ( ( ~ ( in @ emptyset @ SV65 )
| ~ ! [SY1253: $i] :
( ~ ~ ( ~ ( in @ SY1253 @ omega )
| ~ ( in @ SY1253 @ SV65 ) )
| ( in @ ( setadjoin @ SY1253 @ SY1253 ) @ SV65 ) ) )
= $true )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(1056,plain,
! [SV227: $i > $o,SV66: $i,SV338: $i] :
( ( ( ~ ( in @ SV338
@ ( dsetconstr @ SV66
@ ^ [SY1582: $i] : ( SV227 @ SY1582 ) ) ) )
= $true )
| ( ( in @ SV338 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(1057,plain,
! [SV67: $i > $o] :
( ( ( ! [SY1258: $i] :
~ ~ ( ~ ( SV67 @ SY1258 )
| ~ ! [SY1259: $i] :
( ~ ( SV67 @ SY1259 )
| ( SY1258 = SY1259 ) ) ) )
= $true )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(1058,plain,
! [SV228: $i,SV68: $i,SV339: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV339 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ ( setadjoin @ SV228 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV68 = SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1059,plain,
! [SV229: $i,SV69: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ ( binintersect @ SV69 @ SV229 ) ) )
= $true )
| ( ( in @ SV340 @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1060,plain,
! [SV70: $i,SV230: $i] :
( ( ~ ( ~ ( in @ SV230 @ ( setunion @ SV70 ) )
| ~ ! [SY1585: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1585 )
| ~ ( in @ SY1585 @ SV70 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(1061,plain,
! [SV70: $i,SV230: $i] :
( ( ~ ( ~ ~ ! [SY1586: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1586 )
| ~ ( in @ SY1586 @ SV70 ) )
| ( in @ SV230 @ ( setunion @ SV70 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(1062,plain,
! [SV72: $i] :
( ( ( ! [SY1269: $i] :
~ ( in @ SY1269 @ SV72 ) )
= $true )
| ( ( SV72 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(1063,plain,
! [SV73: $i,SV231: $i] :
( ( ( in @ SV231 @ SV73 )
= $false )
| ( ( in @ SV231 @ ( powerset @ ( setunion @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1064,plain,
! [SV232: $i,SV74: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV74 ) )
= $true )
| ( ( ~ ~ ( in @ SV341 @ SV232 )
| ( SV74 != SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1065,plain,
! [SV233: $i,SV76: $i] :
( ( ( in @ SV76 @ ( setadjoin @ SV233 @ emptyset ) )
= $false )
| ( ( in @ SV233 @ ( setadjoin @ SV76 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1066,plain,
! [SV77: $i] :
( ( ( ! [SY1274: $i] :
~ ~ ( ~ ( in @ SY1274
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
!= ( setadjoin @ SY1274 @ emptyset ) ) ) )
= $false )
| ( ( iskpair @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(1067,plain,
! [SV234: $i,SV78: $i,SV342: $i] :
( ( ( ~ ~ ( in @ SV342 @ ( setminus @ SV78 @ SV234 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV342 @ SV234 )
| ~ ( in @ SV342 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1068,plain,
! [SV235: $i,SV79: $i,SV343: $i] :
( ( ( ~ ~ ( in @ SV343 @ ( setminus @ SV79 @ SV235 ) ) )
= $true )
| ( ( ~ ( in @ SV343 @ SV79 )
| ( in @ SV343 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1069,plain,
! [SV236: $i,SV80: $i] :
( ( ( ( setadjoin @ SV80 @ emptyset )
= ( setadjoin @ SV236 @ emptyset ) )
= $false )
| ( ( SV80 = SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1070,plain,
! [SV81: $i,SV237: $i] :
( ( ( in @ SV237 @ SV81 )
= $false )
| ( ( subset @ ( setadjoin @ SV237 @ emptyset ) @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1071,plain,
! [SV82: $i,SV238: $i] :
( ( ( in @ SV238 @ SV82 )
= $false )
| ( ( in @ ( setadjoin @ SV238 @ emptyset ) @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1072,plain,
! [SV239: $i,SV83: $i] :
( ( ( SV83 = SV239 )
= $false )
| ( ( in @ SV83 @ ( setadjoin @ SV239 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(1073,plain,
! [SV240: $i,SV84: $i,SV344: $i] :
( ( ( ~ ( subset @ SV344 @ SV84 ) )
= $true )
| ( ( ~ ( subset @ SV344 @ SV240 )
| ( subset @ SV344 @ ( binintersect @ SV84 @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1074,plain,
! [SV241: $i > $o,SV86: $i] :
( ( ( ~ ~ ! [SY1591: $i] :
~ ~ ( ~ ( in @ SY1591 @ SV86 )
| ~ ( SV241 @ SY1591 ) ) )
= $false )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1075,plain,
! [SV242: $i,SV87: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ ( setadjoin @ SV87 @ ( setadjoin @ SV242 @ emptyset ) ) ) )
= $true )
| ( ( ( SV345 = SV87 )
| ( SV345 = SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1076,plain,
! [SV243: $i,SV88: $i] :
( ( ( SV88 = SV243 )
= $false )
| ( ( ( powerset @ SV88 )
= ( powerset @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(1077,plain,
! [SV244: $i > $o,SV89: $i] :
( ( ( ~ ! [SY1594: $i] :
( ~ ( in @ SY1594 @ SV89 )
| ( SV244 @ SY1594 ) ) )
= $false )
| ( ( ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV89 )
| ~ ~ ( SV244 @ SY1595 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1078,plain,
! [SV90: $i] :
( ( ( SV90 = emptyset )
= $true )
| ( ( ~ ! [SY1296: $i] :
~ ~ ( ~ ( in @ SY1296 @ SV90 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(1079,plain,
! [SV91: $i] :
( ( ( ~ ( in @ ( sK4_SY1297 @ SV91 ) @ SV91 ) )
= $false )
| ( ( SV91 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[932]) ).
thf(1080,plain,
! [SV385: $i,SV346: $i,SV245: $i,SV92: $i] :
( ( ( ( kpair @ SV92 @ SV245 )
!= ( kpair @ SV346 @ SV385 ) )
| ( SV245 = SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1081,plain,
! [SV93: $i,SV246: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ SV246 ) )
= $true )
| ( ( in @ SV347 @ ( setadjoin @ SV93 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1082,plain,
! [SV94: $i,SV247: $i] :
( ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false )
| ( ( ~ ! [SY1599: $i] :
~ ~ ( ~ ( in @ SY1599 @ SV94 )
| ~ ( in @ SV247 @ SY1599 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1083,plain,
! [SV248: $i,SV95: $i] :
( ( ( subset @ SV95 @ SV248 )
= $false )
| ( ( ~ ( subset @ SV248 @ SV95 )
| ( SV95 = SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1084,plain,
! [SV249: $i,SV96: $i,SV386: $i,SV348: $i] :
( ( ~ ( in @ ( kpair @ SV348 @ SV386 ) @ ( cartprod @ SV96 @ SV249 ) )
| ( in @ SV386 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1085,plain,
! [SV250: $i,SV97: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ ( binintersect @ SV97 @ SV250 ) ) )
= $true )
| ( ( in @ SV349 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1086,plain,
! [SV251: $i,SV98: $i] :
( ( ( SV98 = SV251 )
= $false )
| ( ( ! [SY1603: $i,SY1604: $i] :
( ( SY1603 != SY1604 )
| ~ ( ~ ( ~ ( in @ SY1603 @ SV98 )
| ( in @ SY1604 @ SV251 ) )
| ~ ( ~ ( in @ SY1604 @ SV251 )
| ( in @ SY1603 @ SV98 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1087,plain,
! [SV252: $i,SV99: $i,SV350: $i] :
( ( ( ~ ( in @ SV350 @ ( setadjoin @ SV99 @ ( setadjoin @ SV252 @ emptyset ) ) ) )
= $true )
| ( ( ( SV350 = SV99 )
| ( SV350 = SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1088,plain,
! [SV253: $i,SV100: $i] :
( ( ( ( setminus @ SV100 @ SV253 )
= emptyset )
= $false )
| ( ( subset @ SV100 @ SV253 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(1089,plain,
! [SV101: $i] :
( ( ( SV101 = emptyset )
= $true )
| ( ( ~ ! [SY1317: $i] :
~ ( in @ SY1317 @ SV101 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1090,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ~ ( ~ ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
| ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
| ~ ( ~ ( ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
| ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1091,plain,
! [SV103: $i > $o] :
( ( ( ! [SY1320: $i] :
~ ~ ( ~ ( SV103 @ SY1320 )
| ~ ! [SY1321: $i] :
( ~ ( SV103 @ SY1321 )
| ( SY1320 = SY1321 ) ) ) )
= $true )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(1092,plain,
! [SV255: $i,SV104: $i] :
( ( ( ~ ~ ! [SY1607: $i] :
~ ~ ( ~ ( in @ SY1607 @ SV104 )
| ~ ( in @ SY1607 @ SV255 ) ) )
= $false )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1093,plain,
! [SV256: $i,SV105: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ SV105 ) )
= $true )
| ( ( ~ ~ ( in @ SV352 @ SV256 )
| ~ ( subset @ SV105 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1094,plain,
! [SV257: $i,SV106: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) ) )
= $true )
| ( ( ~ ! [SY1725: $i] :
~ ~ ( ~ ( in @ SY1725 @ SV106 )
| ~ ~ ! [SY1726: $i] :
~ ~ ( ~ ( in @ SY1726 @ SV257 )
| ( SV353
!= ( kpair @ SY1725 @ SY1726 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1095,plain,
! [SV107: $i > $o] :
( ( ( ! [SY1332: $i] :
~ ~ ( ~ ( SV107 @ SY1332 )
| ~ ! [SY1333: $i] :
( ~ ( SV107 @ SY1333 )
| ( SY1332 = SY1333 ) ) ) )
= $true )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1096,plain,
! [SV258: $i,SV108: $i,SV354: $i] :
( ( ( ~ ~ ( in @ SV354 @ SV108 ) )
= $true )
| ( ( ~ ~ ( in @ SV354 @ SV258 )
| ~ ( in @ SV354 @ ( symdiff @ SV108 @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1097,plain,
! [SV109: $i,SV259: $i] :
( ( ~ ( ~ ( in @ SV259 @ ( powerset @ SV109 ) )
| ! [SY1613: $i] :
( ~ ( in @ SY1613 @ SV259 )
| ( in @ SY1613 @ SV109 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1098,plain,
! [SV109: $i,SV259: $i] :
( ( ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ SV259 )
| ( in @ SY1614 @ SV109 ) )
| ( in @ SV259 @ ( powerset @ SV109 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1099,plain,
! [SV260: $i,SV110: $i] :
( ( ( subset @ SV110 @ SV260 )
= $false )
| ( ( ( binintersect @ SV110 @ SV260 )
= SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1100,plain,
! [SV111: $i,SV387: $o] :
( ( SV387 = $true )
| ( ( in @ SV111 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[952]) ).
thf(1101,plain,
! [SV111: $i] :
( ( $true = $true )
| ( ( in @ SV111 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[952]) ).
thf(1102,plain,
! [SV111: $i] :
( ( $false = $true )
| ( ( in @ SV111 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[952]) ).
thf(1103,plain,
! [SV112: $i] :
( ( ( ~ ( in @ ( sK5_SY1343 @ SV112 ) @ SV112 ) )
= $false )
| ( ( SV112 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[953]) ).
thf(1104,plain,
! [SV114: $i > $o,SV261: $i] :
( ( ( in @ SV261 @ emptyset )
= $false )
| ( ( SV114 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1105,plain,
! [SV388: $i,SV355: $i,SV262: $i,SV115: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV262 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SV388 @ emptyset ) ) @ emptyset ) ) )
| ( SV262 = SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1106,plain,
! [SV263: $i,SV116: $i] :
( ( ( SV116 != SV263 )
= $false )
| ( ( ~ ( in @ SV263 @ ( setadjoin @ SV116 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1107,plain,
! [SV117: $i > $o] :
( ( ( ! [SY1349: $i] :
~ ~ ( ~ ( SV117 @ SY1349 )
| ~ ! [SY1350: $i] :
( ~ ( SV117 @ SY1350 )
| ( SY1349 = SY1350 ) ) ) )
= $true )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(1108,plain,
! [SV264: $i > $o,SV118: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ SV118 ) )
= $true )
| ( ( ~ ( SV264 @ SV356 )
| ( ( dsetconstr @ SV118
@ ^ [SY1618: $i] : ( SV264 @ SY1618 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1109,plain,
! [SV265: $i > $o,SV119: $i,SV357: $i] :
( ( ( ~ ( in @ SV357 @ SV119 ) )
= $true )
| ( ( ~ ( SV265 @ SV357 )
| ~ ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV119 )
| ~ ( SV265 @ SY1729 )
| ( SY1729 = SV357 ) )
| ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1110,plain,
! [SV120: $i,SV266: $i] :
( ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV266 )
| ( in @ SY1624 @ SV120 ) ) )
= $false )
| ( ( in @ SV266 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1111,plain,
! [SV267: $i,SV121: $i] :
( ( ( ! [SY1625: $i] :
( ~ ( in @ SY1625 @ SV121 )
| ( in @ SY1625 @ SV267 ) ) )
= $false )
| ( ( ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) )
| ( SV121 = SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1112,plain,
! [SV268: $i,SV122: $i] :
( ( ( subset @ SV122 @ SV268 )
= $false )
| ( ( ( setminus @ SV122 @ SV268 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1113,plain,
! [SV123: $i,SV269: $i] :
( ( ( subset @ SV269 @ SV123 )
= $false )
| ( ( in @ SV269 @ ( powerset @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1114,plain,
! [SV358: $i,SV270: $i,SV124: $i] :
( ( ( ~ ( subset @ SV124 @ SV270 ) )
= $true )
| ( ( ~ ( in @ SV358 @ SV124 )
| ( in @ SV358 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1115,plain,
! [SV125: $i] :
( ( ( ! [SY1370: $i] :
~ ( in @ SY1370 @ SV125 ) )
= $true )
| ( ( ~ ! [SY1371: $i] :
~ ~ ( ~ ( in @ SY1371 @ SV125 )
| ~ ~ ~ ! [SY1372: $i] :
~ ~ ( ~ ( in @ SY1372 @ SY1371 )
| ~ ( in @ SY1372 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1116,plain,
! [SV126: $i > $o] :
( ( ( ! [SY1373: $i] :
~ ! [SY1374: $i] :
~ ( ~ ( ~ ( SV126 @ SY1374 )
| ( SY1374 = SY1373 ) )
| ~ ( ( SY1374 != SY1373 )
| ( SV126 @ SY1374 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1117,plain,
( ( ~ ( in @ sK6_SY1733 @ ( cartprod @ sK1_SX0 @ sK2_SY1628 ) )
| ( ( kpair @ ( kfst @ sK6_SY1733 ) @ ( ksnd @ sK6_SY1733 ) )
= sK6_SY1733 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[970]) ).
thf(1118,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1630: $i] :
( ~ ( in @ SY1630 @ SV127 )
| ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV127 )
| ~ ( SV271 @ SY1630 )
| ~ ( SV271 @ SY1631 )
| ( SY1630 = SY1631 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1119,plain,
! [SV272: $i,SV128: $i] :
( ( ( subset @ SV128 @ SV272 )
= $false )
| ( ( subset @ ( powerset @ SV128 ) @ ( powerset @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1120,plain,
! [SV273: $i,SV129: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ ( cartprod @ SV129 @ SV273 ) ) )
= $true )
| ( ( iskpair @ SV359 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1121,plain,
! [SV274: $i,SV130: $i] :
( ( ( SV130 = SV274 )
= $false )
| ( ( ! [SY1637: $i > $o,SY1638: $i > $o] :
( ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV130 )
| ! [SY1640: $i] :
( ~ ( in @ SY1640 @ SV274 )
| ( SY1639 != SY1640 )
| ~ ( ~ ( ~ ( SY1637 @ SY1639 )
| ( SY1638 @ SY1640 ) )
| ~ ( ~ ( SY1638 @ SY1640 )
| ( SY1637 @ SY1639 ) ) ) ) )
| ( ( dsetconstr @ SV130
@ ^ [SX4: $i] : ( SY1637 @ SX4 ) )
= ( dsetconstr @ SV274
@ ^ [SX4: $i] : ( SY1638 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1122,plain,
! [SV275: $i,SV360: $i,SV131: $i] :
( ( ( ~ ( subset @ SV131 @ SV360 ) )
= $true )
| ( ( subset @ SV131 @ ( setadjoin @ SV275 @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1123,plain,
! [SV132: $i] :
( ( ( ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) )
| ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
!= ( setadjoin @ SY1396 @ emptyset ) ) ) )
= $false )
| ( ( iskpair @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1124,plain,
! [SV276: $i,SV133: $i] :
( ( ( ( binintersect @ SV133 @ SV276 )
= SV133 )
= $false )
| ( ( subset @ SV133 @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1125,plain,
! [SV277: $i,SV134: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ ( setadjoin @ SV134 @ SV277 ) ) )
= $true )
| ( ( ( SV361 = SV134 )
| ( in @ SV361 @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1126,plain,
! [SV278: $i > $o,SV135: $i] :
( ( ( ~ ! [SY1645: $i] :
~ ~ ( ~ ( in @ SY1645 @ SV135 )
| ~ ~ ( SV278 @ SY1645 ) ) )
= $false )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1127,plain,
! [SV279: $i > $o,SV136: $i] :
( ( ( ~ ! [SY1647: $i] :
~ ~ ( ~ ( in @ SY1647 @ SV136 )
| ~ ( SV279 @ SY1647 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1128,plain,
! [SV280: $i,SV137: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV137 ) )
= $true )
| ( ( ! [SY1734: $i] :
( ~ ( in @ SY1734 @ SV280 )
| ( subset @ ( setadjoin @ SV362 @ ( setadjoin @ SY1734 @ emptyset ) ) @ ( binunion @ SV137 @ SV280 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1129,plain,
! [SV281: $i,SV138: $i] :
( ( ( subset @ SV138 @ SV281 )
= $false )
| ( ( in @ SV138 @ ( powerset @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1130,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ! [SY1651: $i,SY1652: $i] :
( ( SY1651 != SY1652 )
| ~ ( ~ ( ~ ( SV139 @ SY1651 )
| ( SV282 @ SY1652 ) )
| ~ ( ~ ( SV282 @ SY1652 )
| ( SV139 @ SY1651 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1131,plain,
! [SV283: $i,SV140: $i] :
( ( ( ! [SY1659: $i] :
~ ( ~ ( ~ ( in @ SY1659 @ SV140 )
| ( in @ SY1659 @ SV283 ) )
| ~ ( ~ ( in @ SY1659 @ SV283 )
| ( in @ SY1659 @ SV140 ) ) ) )
= $false )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1132,plain,
! [SV141: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
| ~ ! [SY1740: $i,SY1741: $i] :
( ~ ~ ( ~ ( in @ SY1740 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1741 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1740 )
| ( in @ SX4 @ SY1741 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1741 )
| ( in @ SX4 @ SY1740 ) ) ) )
| ~ ! [SY1744: $i] :
( ~ ~ ( ~ ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SY1744 )
| ( in @ SY1434 @ SV141 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1744 ) )
| ~ ! [SY1747: $i] :
~ ~ ! [SY1748: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1747 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1748 @ SY1744 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1747 )
| ~ ( in @ SX5 @ SY1744 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1747 ) )
| ( in @ SY1748 @ SY1750 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1133,plain,
! [SV284: $i,SV142: $i,SV363: $i] :
( ( ( ~ ( in @ SV363 @ SV142 ) )
= $true )
| ( ( ! [SY1752: $i] :
( ~ ( in @ SY1752 @ SV284 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV363 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV363 @ ( setadjoin @ SY1752 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV142 @ SV284 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1134,plain,
! [SV144: $i,SV285: $i] :
( ( ( subset @ SV285 @ SV144 )
= $false )
| ( ( ( binintersect @ SV144 @ SV285 )
= SV285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1135,plain,
! [SV145: $i,SV286: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ SV286 ) )
= $true )
| ( ( ~ ( in @ SV364 @ ( setminus @ SV145 @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1136,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1663: $i] :
( ~ ( in @ SY1663 @ SV146 )
| ! [SY1664: $i] :
( ~ ( in @ SY1664 @ SV146 )
| ~ ( SV287 @ SY1663 )
| ~ ( SV287 @ SY1664 )
| ( SY1663 = SY1664 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1137,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) ) )
= $true )
| ( ( ! [SY1753: $o] :
( ~ ( ( SV365 != SV147 )
| SY1753 )
| ~ ( ~ ( in @ SV365 @ SV288 )
| SY1753 )
| SY1753 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1138,plain,
! [SV289: $i,SV148: $i] :
( ( ( SV148 = SV289 )
= $false )
| ( ( subset @ SV289 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1139,plain,
! [SV290: $i,SV149: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV149 ) )
= $true )
| ( ( ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV290 )
| ( ( kfst @ ( kpair @ SV366 @ SY1754 ) )
= SV366 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1140,plain,
! [SV291: $i > $o,SV150: $i,SV367: $i] :
( ( ( ~ ( in @ SV367 @ SV150 ) )
= $true )
| ( ( ~ ( SV291 @ SV367 )
| ( in @ SV367
@ ( dsetconstr @ SV150
@ ^ [SY1674: $i] : ( SV291 @ SY1674 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1141,plain,
! [SV368: $i,SV151: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ ( powerset @ SV151 ) ) )
= $true )
| ( ( ~ ( in @ SV368 @ SV292 )
| ( in @ SV368 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1142,plain,
! [SV293: $i,SV152: $i] :
( ( ( SV152 = SV293 )
= $false )
| ( ( ( setunion @ SV152 )
= ( setunion @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1143,plain,
! [SV389: $o,SV294: $i,SV153: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
| ~ ( ~ ( in @ SV369 @ SV153 )
| SV389 )
| ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 )
| SV389 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[997]) ).
thf(1144,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
| ~ ( ~ ( in @ SV369 @ SV153 )
| $true )
| ~ ( ~ ( in @ SV369 @ SV294 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[997]) ).
thf(1145,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
| ~ ( ~ ( in @ SV369 @ SV153 )
| $false )
| ~ ( ~ ( in @ SV369 @ SV294 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[997]) ).
thf(1146,plain,
! [SV295: $i,SV154: $i] :
( ( ( SV154 = SV295 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV154 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV154 @ ( setadjoin @ SV295 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV154 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1147,plain,
! [SV296: $i > $o,SV155: $i] :
( ( ( ~ ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV155 )
| ( SV296 @ SY1678 ) ) )
= $false )
| ( ( ~ ! [SY1679: $i] :
~ ~ ( ~ ( in @ SY1679 @ SV155 )
| ~ ~ ( SV296 @ SY1679 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1148,plain,
! [SV297: $i,SV156: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV156 ) )
= $true )
| ( ( in @ ( setadjoin @ SV370 @ emptyset ) @ ( powerset @ ( binunion @ SV156 @ SV297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1149,plain,
! [SV157: $o,SV298: $i] :
( ( ( in @ SV298 @ ( prop2set @ SV157 ) )
= $false )
| ( SV157 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1150,plain,
! [SV299: $i] :
( ( ( in @ SV299 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1151,plain,
! [SV300: $i] :
( ( ( in @ SV300 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1152,plain,
! [SV158: $i,SV301: $i] :
( ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false )
| ( ( ! [SY1681: $o] :
( ~ ! [SY1682: $i] :
( ~ ( in @ SV301 @ SY1682 )
| ~ ( in @ SY1682 @ SV158 )
| SY1681 )
| SY1681 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1153,plain,
! [SV302: $i > $o,SV159: $i] :
( ( ( ~ ! [SY1683: $i] :
~ ~ ( ~ ( in @ SY1683
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SY1683 @ emptyset ) ) ) )
= $false )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1154,plain,
! [SV303: $i,SV160: $i] :
( ( ( SV160 = SV303 )
= $false )
| ( ( ! [SY1687: $i,SY1688: $i] :
( ( SY1687 != SY1688 )
| ( ( setadjoin @ SV160 @ SY1687 )
= ( setadjoin @ SV303 @ SY1688 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1155,plain,
! [SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV304 )
| ~ ! [SY1490: $i] :
~ ~ ( ~ ( SV161 @ SY1689 @ SY1490 )
| ~ ! [SY1491: $i] :
( ~ ( SV161 @ SY1689 @ SY1491 )
| ( SY1490 = SY1491 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1156,plain,
! [SV305: $i,SV162: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV162 ) )
= $true )
| ( ( ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SV305 )
| ( ( ksnd @ ( kpair @ SV371 @ SY1757 ) )
= SY1757 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1157,plain,
! [SV372: $i,SV306: $i,SV163: $i] :
( ( ( ~ ( subset @ SV163 @ SV306 ) )
= $true )
| ( ( ~ ( subset @ SV306 @ SV372 )
| ( subset @ SV163 @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1158,plain,
! [SV307: $i,SV164: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ ( setminus @ SV164 @ SV307 ) ) )
= $true )
| ( ( in @ SV373 @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1159,plain,
! [SV308: $i,SV165: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ SV165 ) )
= $true )
| ( ( ~ ~ ( in @ SV374 @ SV308 )
| ( in @ SV374 @ ( symdiff @ SV165 @ SV308 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1160,plain,
! [SV309: $i,SV166: $i,SV375: $i] :
( ( ( ~ ~ ( in @ SV375 @ SV166 ) )
= $true )
| ( ( ~ ( in @ SV375 @ ( setminus @ SV166 @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1161,plain,
! [SV167: $i > $o] :
( ( ( ! [SY1507: $i] :
~ ~ ( ~ ( SV167 @ SY1507 )
| ~ ! [SY1508: $i] :
( ~ ( SV167 @ SY1508 )
| ( SY1507 = SY1508 ) ) ) )
= $true )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1162,plain,
! [SV310: $i,SV168: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ ( setminus @ SV168 @ SV310 ) ) )
= $true )
| ( ( ~ ( in @ SV376 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1163,plain,
! [SV311: $i,SV169: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV169 ) )
= $true )
| ( ( ~ ( in @ SV377 @ SV311 )
| ~ ( in @ SV377 @ ( symdiff @ SV169 @ SV311 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1164,plain,
! [SV170: $i] :
( ( ( ! [SY1515: $i] :
~ ~ ( ~ ( in @ SY1515 @ SV170 )
| ( SV170
!= ( setadjoin @ SY1515 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1165,plain,
! [SV312: $i,SV171: $i,SV378: $i] :
( ( ( ~ ( in @ SV378 @ SV171 ) )
= $true )
| ( ( ! [SY1758: $i] :
( ~ ( in @ SY1758 @ SV312 )
| ( in @ ( setadjoin @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV378 @ ( setadjoin @ SY1758 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV171 @ SV312 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1166,plain,
! [SV172: $i,SV313: $i] :
( ( ( in @ SV313 @ ( powerset @ SV172 ) )
= $false )
| ( ( subset @ SV313 @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1167,plain,
! [SV314: $i,SV173: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV173 ) )
= $true )
| ( ( ! [SY1759: $i] :
( ~ ( in @ SY1759 @ SV314 )
| ( in @ ( kpair @ SV379 @ SY1759 ) @ ( cartprod @ SV173 @ SV314 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1168,plain,
! [SV315: $i,SV174: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ SV174 ) )
= $true )
| ( ( ! [SY1760: $i] :
( ~ ( in @ SY1760 @ SV315 )
| ( ( kpair @ SV380 @ SY1760 )
= ( kpair @ SV380 @ SY1760 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1169,plain,
! [SV175: $i > $o] :
( ( ( ! [SY1526: $i] :
~ ~ ( ~ ( SV175 @ SY1526 )
| ~ ! [SY1527: $i] :
( ~ ( SV175 @ SY1527 )
| ( SY1526 = SY1527 ) ) ) )
= $true )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1170,plain,
! [SV316: $i,SV176: $i] :
( ( ( SV176 = SV316 )
= $false )
| ( ( ! [SY1710: $i,SY1711: $i] :
( ( SY1710 != SY1711 )
| ~ ( in @ SY1710 @ SV176 )
| ( in @ SY1711 @ SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1171,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false )
| ( ( ! [SY1712: $o] :
( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| SY1712 )
| ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SY1712 )
| SY1712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1172,plain,
! [SV198: $i,SV33: $i,SV319: $i] :
( ( ( in @ SV319 @ ( binunion @ SV33 @ SV198 ) )
= $false )
| ( ( ( in @ SV319 @ SV33 )
| ( in @ SV319 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1173,plain,
! [SV34: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK7_SY1538 @ SV199 @ SV34 ) @ SV34 )
| ( in @ ( sK7_SY1538 @ SV199 @ SV34 ) @ SV199 ) )
= $false )
| ( ( subset @ SV34 @ SV199 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1025]) ).
thf(1174,plain,
! [SV35: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK8_SY1539 @ SV200 @ SV35 ) @ SV35 )
| ( in @ ( sK8_SY1539 @ SV200 @ SV35 ) @ SV200 ) )
= $false )
| ( ( subset @ SV35 @ SV200 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1026]) ).
thf(1175,plain,
! [SV381: $i,SV320: $i,SV201: $i,SV36: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV36 @ ( setadjoin @ SV201 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV320 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV320 @ ( setadjoin @ SV381 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV320 != SV381 )
| ( SV201 = SV381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1176,plain,
! [SV37: $i,SV321: $i,SV202: $i] :
( ( ( in @ SV202 @ SV321 )
= $false )
| ( ( ~ ( in @ SV321 @ SV37 )
| ( in @ SV202 @ ( setunion @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1177,plain,
! [SV203: $i,SV38: $i,SV322: $i] :
( ( ( in @ SV322 @ SV38 )
= $false )
| ( ( ~ ~ ( in @ SV322 @ SV203 )
| ( in @ SV322 @ ( setminus @ SV38 @ SV203 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1178,plain,
! [SV39: $i,SV204: $i,SV323: $i] :
( ( ( in @ SV323 @ SV204 )
= $false )
| ( ( in @ SV323 @ ( binunion @ SV39 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1179,plain,
! [SV205: $i,SV40: $i] :
( ( ( subset @ SV40 @ SV205 )
= $true )
| ( ( SV40 != SV205 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1180,plain,
! [SV206: $i > $o,SV41: $i] :
( ( ( ~ ! [SY1545: $i] :
~ ~ ( ~ ( in @ SY1545 @ SV41 )
| ~ ( SV206 @ SY1545 ) ) )
= $true )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1181,plain,
! [SV207: $i,SV42: $i,SV324: $i] :
( ( ( in @ SV324 @ ( cartprod @ SV42 @ SV207 ) )
= $false )
| ( ( in @ ( ksnd @ SV324 ) @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1182,plain,
! [SV208: $i,SV43: $i,SV325: $i] :
( ( ( in @ SV325 @ SV43 )
= $false )
| ( ( ~ ( in @ SV325 @ SV208 )
| ( in @ SV325 @ ( binintersect @ SV43 @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1183,plain,
! [SV209: $i,SV44: $i,SV326: $i] :
( ( ( in @ SV326 @ SV44 )
= $false )
| ( ( in @ SV326 @ ( binunion @ SV44 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1184,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( ~ ~ ( ~ ( SV46 @ SV390 )
| ~ ! [SY1761: $i] :
( ~ ( SV46 @ SY1761 )
| ( SV390 = SY1761 ) ) ) )
= $true )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1185,plain,
! [SV211: $i,SV47: $i,SV327: $i] :
( ( ( in @ SV327 @ SV47 )
= $false )
| ( ( ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV211 )
| ( in @ ( setadjoin @ SV327 @ ( setadjoin @ SY1714 @ emptyset ) ) @ ( powerset @ ( binunion @ SV47 @ SV211 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1186,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV391 ) )
= $true )
| ( ( ~ ! [SY1206: $i,SY1207: $i] :
( ~ ( SV49 @ SY1206 )
| ~ ( SV49 @ SY1207 )
| ( SY1206 = SY1207 ) )
| ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1187,plain,
! [SV51: $i,SV213: $i > $o] :
( ( ( ~ ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
| ~ ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) ) )
= $false )
| ( ( ~ ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1041]) ).
thf(1188,plain,
! [SV214: $i,SV52: $i,SV328: $i] :
( ( ( in @ SV328 @ SV52 )
= $false )
| ( ( ! [SY1715: $i] :
( ~ ( in @ SY1715 @ SV214 )
| ( in @ ( kpair @ SV328 @ SY1715 ) @ ( powerset @ ( powerset @ ( binunion @ SV52 @ SV214 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1189,plain,
! [SV382: $i,SV329: $i,SV215: $i,SV53: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV215 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV329 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV329 @ ( setadjoin @ SV382 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV53 = SV329 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1190,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1762: $i] :
( ( ( sK10_SY1558 @ SV216 @ SV54 )
!= SY1762 )
| ~ ( ~ ( ~ ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
| ( SV216 @ SY1762 ) )
| ~ ( ~ ( SV216 @ SY1762 )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1044]) ).
thf(1191,plain,
! [SV330: $i,SV217: $i,SV55: $i] :
( ( ( ( setadjoin @ SV55 @ ( setadjoin @ SV217 @ emptyset ) )
= ( setadjoin @ SV330 @ emptyset ) )
= $false )
| ( ( SV55 = SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1192,plain,
! [SV218: $i,SV56: $i,SV383: $i,SV331: $i] :
( ( ( ~ ( in @ ( kpair @ SV331 @ SV383 ) @ ( cartprod @ SV56 @ SV218 ) ) )
= $true )
| ( ( in @ SV331 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1193,plain,
! [SV219: $i > $o,SV57: $i,SV332: $i] :
( ( ( in @ SV332
@ ( dsetconstr @ SV57
@ ^ [SY1572: $i] : ( SV219 @ SY1572 ) ) )
= $false )
| ( ( SV219 @ SV332 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1194,plain,
! [SV220: $i,SV58: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV58 ) )
= $false )
| ( ( ~ ( in @ SV333 @ SV220 )
| ( in @ SV333 @ ( symdiff @ SV58 @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1195,plain,
! [SV222: $i,SV60: $i,SV334: $i] :
( ( ( in @ SV334 @ ( cartprod @ SV60 @ SV222 ) )
= $false )
| ( ( in @ ( kfst @ SV334 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1196,plain,
! [SV384: $i,SV335: $i,SV223: $i,SV61: $i] :
( ( ( ( kpair @ SV61 @ SV223 )
!= ( kpair @ SV335 @ SV384 ) )
= $true )
| ( ( SV61 = SV335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1197,plain,
! [SV224: $i > $o,SV62: $i,SV336: $i] :
( ( ( in @ SV336 @ SV62 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) )
| ( SV224 @ SV336 ) )
| ~ ( ~ ( SV224 @ SV336 )
| ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1198,plain,
! [SV337: $i,SV225: $i,SV63: $i] :
( ( ( subset @ SV63 @ SV225 )
= $false )
| ( ( ~ ~ ( in @ SV337 @ SV225 )
| ~ ( in @ SV337 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1199,plain,
! [SV65: $i] :
( ( ( ~ ( in @ emptyset @ SV65 ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
( ~ ~ ( ~ ( in @ SY1253 @ omega )
| ~ ( in @ SY1253 @ SV65 ) )
| ( in @ ( setadjoin @ SY1253 @ SY1253 ) @ SV65 ) ) )
= $true )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1200,plain,
! [SV227: $i > $o,SV66: $i,SV338: $i] :
( ( ( in @ SV338
@ ( dsetconstr @ SV66
@ ^ [SY1582: $i] : ( SV227 @ SY1582 ) ) )
= $false )
| ( ( in @ SV338 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1201,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ~ ( ~ ( SV67 @ SV392 )
| ~ ! [SY1763: $i] :
( ~ ( SV67 @ SY1763 )
| ( SV392 = SY1763 ) ) ) )
= $true )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1202,plain,
! [SV228: $i,SV68: $i,SV339: $i] :
( ( ( in @ ( setadjoin @ SV339 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV68 @ ( setadjoin @ SV228 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV68 = SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1203,plain,
! [SV229: $i,SV69: $i,SV340: $i] :
( ( ( in @ SV340 @ ( binintersect @ SV69 @ SV229 ) )
= $false )
| ( ( in @ SV340 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1204,plain,
! [SV70: $i,SV230: $i] :
( ( ~ ( in @ SV230 @ ( setunion @ SV70 ) )
| ~ ! [SY1585: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1585 )
| ~ ( in @ SY1585 @ SV70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1205,plain,
! [SV70: $i,SV230: $i] :
( ( ~ ~ ! [SY1586: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1586 )
| ~ ( in @ SY1586 @ SV70 ) )
| ( in @ SV230 @ ( setunion @ SV70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1206,plain,
! [SV72: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ SV72 ) )
= $true )
| ( ( SV72 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1207,plain,
! [SV232: $i,SV74: $i,SV341: $i] :
( ( ( in @ SV341 @ SV74 )
= $false )
| ( ( ~ ~ ( in @ SV341 @ SV232 )
| ( SV74 != SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1208,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY1274 @ SV77 )
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
!= ( setadjoin @ ( sK11_SY1274 @ SV77 ) @ emptyset ) ) ) )
= $false )
| ( ( iskpair @ SV77 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1066]) ).
thf(1209,plain,
! [SV234: $i,SV78: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ ( setminus @ SV78 @ SV234 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV342 @ SV234 )
| ~ ( in @ SV342 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1210,plain,
! [SV235: $i,SV79: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ ( setminus @ SV79 @ SV235 ) ) )
= $false )
| ( ( ~ ( in @ SV343 @ SV79 )
| ( in @ SV343 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1211,plain,
! [SV240: $i,SV84: $i,SV344: $i] :
( ( ( subset @ SV344 @ SV84 )
= $false )
| ( ( ~ ( subset @ SV344 @ SV240 )
| ( subset @ SV344 @ ( binintersect @ SV84 @ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1212,plain,
! [SV241: $i > $o,SV86: $i] :
( ( ( ~ ! [SY1591: $i] :
~ ~ ( ~ ( in @ SY1591 @ SV86 )
| ~ ( SV241 @ SY1591 ) ) )
= $true )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1213,plain,
! [SV242: $i,SV87: $i,SV345: $i] :
( ( ( in @ SV345 @ ( setadjoin @ SV87 @ ( setadjoin @ SV242 @ emptyset ) ) )
= $false )
| ( ( ( SV345 = SV87 )
| ( SV345 = SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1214,plain,
! [SV244: $i > $o,SV89: $i] :
( ( ( ! [SY1594: $i] :
( ~ ( in @ SY1594 @ SV89 )
| ( SV244 @ SY1594 ) ) )
= $true )
| ( ( ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV89 )
| ~ ~ ( SV244 @ SY1595 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1215,plain,
! [SV90: $i] :
( ( ( ! [SY1296: $i] :
~ ~ ( ~ ( in @ SY1296 @ SV90 )
| ~ $true ) )
= $false )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1216,plain,
! [SV91: $i] :
( ( ( in @ ( sK4_SY1297 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1217,plain,
! [SV385: $i,SV346: $i,SV245: $i,SV92: $i] :
( ( ( ( kpair @ SV92 @ SV245 )
!= ( kpair @ SV346 @ SV385 ) )
= $true )
| ( ( SV245 = SV385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1218,plain,
! [SV93: $i,SV246: $i,SV347: $i] :
( ( ( in @ SV347 @ SV246 )
= $false )
| ( ( in @ SV347 @ ( setadjoin @ SV93 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1219,plain,
! [SV247: $i,SV94: $i] :
( ( ( ! [SY1599: $i] :
~ ~ ( ~ ( in @ SY1599 @ SV94 )
| ~ ( in @ SV247 @ SY1599 ) ) )
= $false )
| ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1220,plain,
! [SV95: $i,SV248: $i] :
( ( ( ~ ( subset @ SV248 @ SV95 ) )
= $true )
| ( ( SV95 = SV248 )
= $true )
| ( ( subset @ SV95 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1221,plain,
! [SV249: $i,SV96: $i,SV386: $i,SV348: $i] :
( ( ( ~ ( in @ ( kpair @ SV348 @ SV386 ) @ ( cartprod @ SV96 @ SV249 ) ) )
= $true )
| ( ( in @ SV386 @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1222,plain,
! [SV250: $i,SV97: $i,SV349: $i] :
( ( ( in @ SV349 @ ( binintersect @ SV97 @ SV250 ) )
= $false )
| ( ( in @ SV349 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1223,plain,
! [SV251: $i,SV98: $i,SV394: $i] :
( ( ( ! [SY1766: $i] :
( ( SV394 != SY1766 )
| ~ ( ~ ( ~ ( in @ SV394 @ SV98 )
| ( in @ SY1766 @ SV251 ) )
| ~ ( ~ ( in @ SY1766 @ SV251 )
| ( in @ SV394 @ SV98 ) ) ) ) )
= $true )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1224,plain,
! [SV252: $i,SV99: $i,SV350: $i] :
( ( ( in @ SV350 @ ( setadjoin @ SV99 @ ( setadjoin @ SV252 @ emptyset ) ) )
= $false )
| ( ( ( SV350 = SV99 )
| ( SV350 = SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1225,plain,
! [SV101: $i] :
( ( ( ! [SY1317: $i] :
~ ( in @ SY1317 @ SV101 ) )
= $false )
| ( ( SV101 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1226,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ~ ( ~ ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
| ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1227,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ~ ( ~ ( ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
| ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1228,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ~ ~ ( ~ ( SV103 @ SV395 )
| ~ ! [SY1767: $i] :
( ~ ( SV103 @ SY1767 )
| ( SV395 = SY1767 ) ) ) )
= $true )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1229,plain,
! [SV255: $i,SV104: $i] :
( ( ( ~ ! [SY1607: $i] :
~ ~ ( ~ ( in @ SY1607 @ SV104 )
| ~ ( in @ SY1607 @ SV255 ) ) )
= $true )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1230,plain,
! [SV256: $i,SV105: $i,SV352: $i] :
( ( ( in @ SV352 @ SV105 )
= $false )
| ( ( ~ ~ ( in @ SV352 @ SV256 )
| ~ ( subset @ SV105 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1231,plain,
! [SV257: $i,SV106: $i,SV353: $i] :
( ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false )
| ( ( ~ ! [SY1725: $i] :
~ ~ ( ~ ( in @ SY1725 @ SV106 )
| ~ ~ ! [SY1726: $i] :
~ ~ ( ~ ( in @ SY1726 @ SV257 )
| ( SV353
!= ( kpair @ SY1725 @ SY1726 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1232,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ SV396 )
| ~ ! [SY1768: $i] :
( ~ ( SV107 @ SY1768 )
| ( SV396 = SY1768 ) ) ) )
= $true )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1233,plain,
! [SV258: $i,SV108: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ SV108 ) )
= $false )
| ( ( ~ ~ ( in @ SV354 @ SV258 )
| ~ ( in @ SV354 @ ( symdiff @ SV108 @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1234,plain,
! [SV109: $i,SV259: $i] :
( ( ~ ( in @ SV259 @ ( powerset @ SV109 ) )
| ! [SY1613: $i] :
( ~ ( in @ SY1613 @ SV259 )
| ( in @ SY1613 @ SV109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1235,plain,
! [SV109: $i,SV259: $i] :
( ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ SV259 )
| ( in @ SY1614 @ SV109 ) )
| ( in @ SV259 @ ( powerset @ SV109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1236,plain,
! [SV112: $i] :
( ( ( in @ ( sK5_SY1343 @ SV112 ) @ SV112 )
= $true )
| ( ( SV112 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1237,plain,
! [SV388: $i,SV355: $i,SV262: $i,SV115: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV262 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SV388 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV262 = SV388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1238,plain,
! [SV263: $i,SV116: $i] :
( ( ( SV116 = SV263 )
= $true )
| ( ( ~ ( in @ SV263 @ ( setadjoin @ SV116 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1239,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ~ ~ ( ~ ( SV117 @ SV397 )
| ~ ! [SY1769: $i] :
( ~ ( SV117 @ SY1769 )
| ( SV397 = SY1769 ) ) ) )
= $true )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1240,plain,
! [SV264: $i > $o,SV118: $i,SV356: $i] :
( ( ( in @ SV356 @ SV118 )
= $false )
| ( ( ~ ( SV264 @ SV356 )
| ( ( dsetconstr @ SV118
@ ^ [SY1618: $i] : ( SV264 @ SY1618 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1241,plain,
! [SV265: $i > $o,SV119: $i,SV357: $i] :
( ( ( in @ SV357 @ SV119 )
= $false )
| ( ( ~ ( SV265 @ SV357 )
| ~ ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV119 )
| ~ ( SV265 @ SY1729 )
| ( SY1729 = SV357 ) )
| ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1242,plain,
! [SV266: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK12_SY1624 @ SV120 @ SV266 ) @ SV266 )
| ( in @ ( sK12_SY1624 @ SV120 @ SV266 ) @ SV120 ) )
= $false )
| ( ( in @ SV266 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1110]) ).
thf(1243,plain,
! [SV121: $i,SV267: $i] :
( ( ( ~ ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 )
| ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV267 ) )
= $false )
| ( ( ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) )
| ( SV121 = SV267 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1111]) ).
thf(1244,plain,
! [SV358: $i,SV270: $i,SV124: $i] :
( ( ( subset @ SV124 @ SV270 )
= $false )
| ( ( ~ ( in @ SV358 @ SV124 )
| ( in @ SV358 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1245,plain,
! [SV125: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ SV125 ) )
= $true )
| ( ( ~ ! [SY1371: $i] :
~ ~ ( ~ ( in @ SY1371 @ SV125 )
| ~ ~ ~ ! [SY1372: $i] :
~ ~ ( ~ ( in @ SY1372 @ SY1371 )
| ~ ( in @ SY1372 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1246,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ! [SY1770: $i] :
~ ( ~ ( ~ ( SV126 @ SY1770 )
| ( SY1770 = SV399 ) )
| ~ ( ( SY1770 != SV399 )
| ( SV126 @ SY1770 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1247,plain,
( ( ~ ( in @ sK6_SY1733 @ ( cartprod @ sK1_SX0 @ sK2_SY1628 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1248,plain,
( ( ( kpair @ ( kfst @ sK6_SY1733 ) @ ( ksnd @ sK6_SY1733 ) )
= sK6_SY1733 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1249,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
| ! [SY1771: $i] :
( ~ ( in @ SY1771 @ SV127 )
| ~ ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
| ~ ( SV271 @ SY1771 )
| ( ( sK14_SY1630 @ SV271 @ SV127 )
= SY1771 ) ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1118]) ).
thf(1250,plain,
! [SV273: $i,SV129: $i,SV359: $i] :
( ( ( in @ SV359 @ ( cartprod @ SV129 @ SV273 ) )
= $false )
| ( ( iskpair @ SV359 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1251,plain,
! [SV400: $i > $o,SV274: $i,SV130: $i] :
( ( ( ! [SY1772: $i > $o] :
( ~ ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SV130 )
| ! [SY1774: $i] :
( ~ ( in @ SY1774 @ SV274 )
| ( SY1773 != SY1774 )
| ~ ( ~ ( ~ ( SV400 @ SY1773 )
| ( SY1772 @ SY1774 ) )
| ~ ( ~ ( SY1772 @ SY1774 )
| ( SV400 @ SY1773 ) ) ) ) )
| ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SX4: $i] : ( SY1772 @ SX4 ) ) ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1252,plain,
! [SV275: $i,SV360: $i,SV131: $i] :
( ( ( subset @ SV131 @ SV360 )
= $false )
| ( ( subset @ SV131 @ ( setadjoin @ SV275 @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1253,plain,
! [SV132: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY1396 @ SV132 )
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) )
| ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
!= ( setadjoin @ ( sK15_SY1396 @ SV132 ) @ emptyset ) ) ) )
= $false )
| ( ( iskpair @ SV132 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1123]) ).
thf(1254,plain,
! [SV277: $i,SV134: $i,SV361: $i] :
( ( ( in @ SV361 @ ( setadjoin @ SV134 @ SV277 ) )
= $false )
| ( ( ( SV361 = SV134 )
| ( in @ SV361 @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1255,plain,
! [SV278: $i > $o,SV135: $i] :
( ( ( ! [SY1645: $i] :
~ ~ ( ~ ( in @ SY1645 @ SV135 )
| ~ ~ ( SV278 @ SY1645 ) ) )
= $true )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1256,plain,
! [SV279: $i > $o,SV136: $i] :
( ( ( ! [SY1647: $i] :
~ ~ ( ~ ( in @ SY1647 @ SV136 )
| ~ ( SV279 @ SY1647 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1257,plain,
! [SV280: $i,SV137: $i,SV362: $i] :
( ( ( in @ SV362 @ SV137 )
= $false )
| ( ( ! [SY1734: $i] :
( ~ ( in @ SY1734 @ SV280 )
| ( subset @ ( setadjoin @ SV362 @ ( setadjoin @ SY1734 @ emptyset ) ) @ ( binunion @ SV137 @ SV280 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1258,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1779: $i] :
( ( ( sK16_SY1651 @ SV282 @ SV139 )
!= SY1779 )
| ~ ( ~ ( ~ ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
| ( SV282 @ SY1779 ) )
| ~ ( ~ ( SV282 @ SY1779 )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1130]) ).
thf(1259,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 ) )
| ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) ) ) )
= $false )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1131]) ).
thf(1260,plain,
! [SV141: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
| ~ ! [SY1740: $i,SY1741: $i] :
( ~ ~ ( ~ ( in @ SY1740 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1741 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1740 )
| ( in @ SX4 @ SY1741 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1741 )
| ( in @ SX4 @ SY1740 ) ) ) )
| ~ ! [SY1744: $i] :
( ~ ~ ( ~ ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SY1744 )
| ( in @ SY1434 @ SV141 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1744 ) )
| ~ ! [SY1747: $i] :
~ ~ ! [SY1748: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1747 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1748 @ SY1744 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1747 )
| ~ ( in @ SX5 @ SY1744 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1747 ) )
| ( in @ SY1748 @ SY1750 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1261,plain,
! [SV284: $i,SV142: $i,SV363: $i] :
( ( ( in @ SV363 @ SV142 )
= $false )
| ( ( ! [SY1752: $i] :
( ~ ( in @ SY1752 @ SV284 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV363 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV363 @ ( setadjoin @ SY1752 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV142 @ SV284 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1262,plain,
! [SV145: $i,SV286: $i,SV364: $i] :
( ( ( in @ SV364 @ SV286 )
= $false )
| ( ( ~ ( in @ SV364 @ ( setminus @ SV145 @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1263,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ~ ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
| ! [SY1780: $i] :
( ~ ( in @ SY1780 @ SV146 )
| ~ ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
| ~ ( SV287 @ SY1780 )
| ( ( sK18_SY1663 @ SV287 @ SV146 )
= SY1780 ) ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1136]) ).
thf(1264,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false )
| ( ( ! [SY1753: $o] :
( ~ ( ( SV365 != SV147 )
| SY1753 )
| ~ ( ~ ( in @ SV365 @ SV288 )
| SY1753 )
| SY1753 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1265,plain,
! [SV290: $i,SV149: $i,SV366: $i] :
( ( ( in @ SV366 @ SV149 )
= $false )
| ( ( ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV290 )
| ( ( kfst @ ( kpair @ SV366 @ SY1754 ) )
= SV366 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1266,plain,
! [SV291: $i > $o,SV150: $i,SV367: $i] :
( ( ( in @ SV367 @ SV150 )
= $false )
| ( ( ~ ( SV291 @ SV367 )
| ( in @ SV367
@ ( dsetconstr @ SV150
@ ^ [SY1674: $i] : ( SV291 @ SY1674 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1267,plain,
! [SV368: $i,SV151: $i,SV292: $i] :
( ( ( in @ SV292 @ ( powerset @ SV151 ) )
= $false )
| ( ( ~ ( in @ SV368 @ SV292 )
| ( in @ SV368 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1268,plain,
! [SV389: $o,SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| SV389 )
| ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 )
| SV389 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1269,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| $true )
| ~ ( ~ ( in @ SV369 @ SV294 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1270,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| $false )
| ~ ( ~ ( in @ SV369 @ SV294 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1271,plain,
! [SV296: $i > $o,SV155: $i] :
( ( ( ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV155 )
| ( SV296 @ SY1678 ) ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ( ~ ( in @ SY1679 @ SV155 )
| ~ ~ ( SV296 @ SY1679 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1147]) ).
thf(1272,plain,
! [SV297: $i,SV156: $i,SV370: $i] :
( ( ( in @ SV370 @ SV156 )
= $false )
| ( ( in @ ( setadjoin @ SV370 @ emptyset ) @ ( powerset @ ( binunion @ SV156 @ SV297 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1273,plain,
! [SV401: $o,SV158: $i,SV301: $i] :
( ( ( ~ ! [SY1781: $i] :
( ~ ( in @ SV301 @ SY1781 )
| ~ ( in @ SY1781 @ SV158 )
| SV401 )
| SV401 )
= $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1152]) ).
thf(1274,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV301 @ SX0 )
| ~ ( in @ SX0 @ SV158 )
| $true )
| $true )
= $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1152]) ).
thf(1275,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV301 @ SX0 )
| ~ ( in @ SX0 @ SV158 )
| $false )
| $false )
= $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1152]) ).
thf(1276,plain,
! [SV302: $i > $o,SV159: $i] :
( ( ( ! [SY1683: $i] :
~ ~ ( ~ ( in @ SY1683
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SY1683 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1277,plain,
! [SV303: $i,SV160: $i,SV402: $i] :
( ( ( ! [SY1782: $i] :
( ( SV402 != SY1782 )
| ( ( setadjoin @ SV160 @ SV402 )
= ( setadjoin @ SV303 @ SY1782 ) ) ) )
= $true )
| ( ( SV160 = SV303 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1278,plain,
! [SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
| ~ ! [SY1783: $i] :
~ ~ ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1783 )
| ~ ! [SY1784: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1784 )
| ( SY1783 = SY1784 ) ) ) )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1155]) ).
thf(1279,plain,
! [SV305: $i,SV162: $i,SV371: $i] :
( ( ( in @ SV371 @ SV162 )
= $false )
| ( ( ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SV305 )
| ( ( ksnd @ ( kpair @ SV371 @ SY1757 ) )
= SY1757 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1280,plain,
! [SV372: $i,SV306: $i,SV163: $i] :
( ( ( subset @ SV163 @ SV306 )
= $false )
| ( ( ~ ( subset @ SV306 @ SV372 )
| ( subset @ SV163 @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1281,plain,
! [SV307: $i,SV164: $i,SV373: $i] :
( ( ( in @ SV373 @ ( setminus @ SV164 @ SV307 ) )
= $false )
| ( ( in @ SV373 @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1282,plain,
! [SV308: $i,SV165: $i,SV374: $i] :
( ( ( in @ SV374 @ SV165 )
= $false )
| ( ( ~ ~ ( in @ SV374 @ SV308 )
| ( in @ SV374 @ ( symdiff @ SV165 @ SV308 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1283,plain,
! [SV309: $i,SV166: $i,SV375: $i] :
( ( ( ~ ( in @ SV375 @ SV166 ) )
= $false )
| ( ( ~ ( in @ SV375 @ ( setminus @ SV166 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1284,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ~ ( ~ ( SV167 @ SV403 )
| ~ ! [SY1785: $i] :
( ~ ( SV167 @ SY1785 )
| ( SV403 = SY1785 ) ) ) )
= $true )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1285,plain,
! [SV310: $i,SV168: $i,SV376: $i] :
( ( ( in @ SV376 @ ( setminus @ SV168 @ SV310 ) )
= $false )
| ( ( ~ ( in @ SV376 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1286,plain,
! [SV311: $i,SV169: $i,SV377: $i] :
( ( ( in @ SV377 @ SV169 )
= $false )
| ( ( ~ ( in @ SV377 @ SV311 )
| ~ ( in @ SV377 @ ( symdiff @ SV169 @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1287,plain,
! [SV170: $i,SV404: $i] :
( ( ( ~ ~ ( ~ ( in @ SV404 @ SV170 )
| ( SV170
!= ( setadjoin @ SV404 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1288,plain,
! [SV312: $i,SV171: $i,SV378: $i] :
( ( ( in @ SV378 @ SV171 )
= $false )
| ( ( ! [SY1758: $i] :
( ~ ( in @ SY1758 @ SV312 )
| ( in @ ( setadjoin @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV378 @ ( setadjoin @ SY1758 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV171 @ SV312 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1289,plain,
! [SV314: $i,SV173: $i,SV379: $i] :
( ( ( in @ SV379 @ SV173 )
= $false )
| ( ( ! [SY1759: $i] :
( ~ ( in @ SY1759 @ SV314 )
| ( in @ ( kpair @ SV379 @ SY1759 ) @ ( cartprod @ SV173 @ SV314 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1290,plain,
! [SV315: $i,SV174: $i,SV380: $i] :
( ( ( in @ SV380 @ SV174 )
= $false )
| ( ( ! [SY1760: $i] :
( ~ ( in @ SY1760 @ SV315 )
| ( ( kpair @ SV380 @ SY1760 )
= ( kpair @ SV380 @ SY1760 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1291,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( ~ ~ ( ~ ( SV175 @ SV405 )
| ~ ! [SY1786: $i] :
( ~ ( SV175 @ SY1786 )
| ( SV405 = SY1786 ) ) ) )
= $true )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1292,plain,
! [SV316: $i,SV176: $i,SV406: $i] :
( ( ( ! [SY1787: $i] :
( ( SV406 != SY1787 )
| ~ ( in @ SV406 @ SV176 )
| ( in @ SY1787 @ SV316 ) ) )
= $true )
| ( ( SV176 = SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1293,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| SV407 )
| ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1171]) ).
thf(1294,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| $true )
| ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1171]) ).
thf(1295,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| $false )
| ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1171]) ).
thf(1296,plain,
! [SV198: $i,SV33: $i,SV319: $i] :
( ( ( in @ SV319 @ SV33 )
= $true )
| ( ( in @ SV319 @ SV198 )
= $true )
| ( ( in @ SV319 @ ( binunion @ SV33 @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1297,plain,
! [SV34: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK7_SY1538 @ SV199 @ SV34 ) @ SV34 ) )
= $false )
| ( ( subset @ SV34 @ SV199 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1298,plain,
! [SV34: $i,SV199: $i] :
( ( ( in @ ( sK7_SY1538 @ SV199 @ SV34 ) @ SV199 )
= $false )
| ( ( subset @ SV34 @ SV199 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1299,plain,
! [SV35: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK8_SY1539 @ SV200 @ SV35 ) @ SV35 ) )
= $false )
| ( ( subset @ SV35 @ SV200 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1300,plain,
! [SV35: $i,SV200: $i] :
( ( ( in @ ( sK8_SY1539 @ SV200 @ SV35 ) @ SV200 )
= $false )
| ( ( subset @ SV35 @ SV200 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1301,plain,
! [SV381: $i,SV320: $i,SV201: $i,SV36: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV36 @ ( setadjoin @ SV201 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV320 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV320 @ ( setadjoin @ SV381 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV320 != SV381 )
| ( SV201 = SV381 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1302,plain,
! [SV202: $i,SV37: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ SV37 ) )
= $true )
| ( ( in @ SV202 @ ( setunion @ SV37 ) )
= $true )
| ( ( in @ SV202 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1303,plain,
! [SV38: $i,SV203: $i,SV322: $i] :
( ( ( ~ ~ ( in @ SV322 @ SV203 ) )
= $true )
| ( ( in @ SV322 @ ( setminus @ SV38 @ SV203 ) )
= $true )
| ( ( in @ SV322 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1304,plain,
! [SV205: $i,SV40: $i] :
( ( ( SV40 = SV205 )
= $false )
| ( ( subset @ SV40 @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1305,plain,
! [SV206: $i > $o,SV41: $i] :
( ( ( ! [SY1545: $i] :
~ ~ ( ~ ( in @ SY1545 @ SV41 )
| ~ ( SV206 @ SY1545 ) ) )
= $false )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1306,plain,
! [SV43: $i,SV208: $i,SV325: $i] :
( ( ( ~ ( in @ SV325 @ SV208 ) )
= $true )
| ( ( in @ SV325 @ ( binintersect @ SV43 @ SV208 ) )
= $true )
| ( ( in @ SV325 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1307,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( ~ ( ~ ( SV46 @ SV390 )
| ~ ! [SY1761: $i] :
( ~ ( SV46 @ SY1761 )
| ( SV390 = SY1761 ) ) ) )
= $false )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1308,plain,
! [SV47: $i,SV327: $i,SV211: $i,SV408: $i] :
( ( ( ~ ( in @ SV408 @ SV211 )
| ( in @ ( setadjoin @ SV327 @ ( setadjoin @ SV408 @ emptyset ) ) @ ( powerset @ ( binunion @ SV47 @ SV211 ) ) ) )
= $true )
| ( ( in @ SV327 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1309,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( SV49 @ SV391 )
= $false )
| ( ( ~ ! [SY1206: $i,SY1207: $i] :
( ~ ( SV49 @ SY1206 )
| ~ ( SV49 @ SY1207 )
| ( SY1206 = SY1207 ) )
| ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1310,plain,
! [SV51: $i,SV213: $i > $o] :
( ( ( ~ ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 ) )
= $false )
| ( ( ~ ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1187]) ).
thf(1311,plain,
! [SV51: $i,SV213: $i > $o] :
( ( ( ~ ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) ) )
= $false )
| ( ( ~ ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1187]) ).
thf(1312,plain,
! [SV52: $i,SV328: $i,SV214: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ SV214 )
| ( in @ ( kpair @ SV328 @ SV409 ) @ ( powerset @ ( powerset @ ( binunion @ SV52 @ SV214 ) ) ) ) )
= $true )
| ( ( in @ SV328 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1313,plain,
! [SV382: $i,SV329: $i,SV215: $i,SV53: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV215 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV329 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV329 @ ( setadjoin @ SV382 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV53 = SV329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1314,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ( ( sK10_SY1558 @ SV216 @ SV54 )
!= ( sK20_SY1762 @ SV54 @ SV216 ) )
| ~ ( ~ ( ~ ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
| ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) ) )
| ~ ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1190]) ).
thf(1315,plain,
! [SV218: $i,SV56: $i,SV383: $i,SV331: $i] :
( ( ( in @ ( kpair @ SV331 @ SV383 ) @ ( cartprod @ SV56 @ SV218 ) )
= $false )
| ( ( in @ SV331 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1316,plain,
! [SV220: $i,SV58: $i,SV333: $i] :
( ( ( in @ SV333 @ SV58 )
= $true )
| ( ( ~ ( in @ SV333 @ SV220 )
| ( in @ SV333 @ ( symdiff @ SV58 @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1317,plain,
! [SV384: $i,SV335: $i,SV223: $i,SV61: $i] :
( ( ( ( kpair @ SV61 @ SV223 )
= ( kpair @ SV335 @ SV384 ) )
= $false )
| ( ( SV61 = SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1318,plain,
! [SV224: $i > $o,SV62: $i,SV336: $i] :
( ( ( ~ ( ~ ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) )
| ( SV224 @ SV336 ) )
| ~ ( ~ ( SV224 @ SV336 )
| ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) ) ) )
= $false )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1319,plain,
! [SV63: $i,SV225: $i,SV337: $i] :
( ( ( ~ ~ ( in @ SV337 @ SV225 ) )
= $true )
| ( ( ~ ( in @ SV337 @ SV63 ) )
= $true )
| ( ( subset @ SV63 @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1320,plain,
! [SV65: $i] :
( ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ~ ! [SY1253: $i] :
( ~ ~ ( ~ ( in @ SY1253 @ omega )
| ~ ( in @ SY1253 @ SV65 ) )
| ( in @ ( setadjoin @ SY1253 @ SY1253 ) @ SV65 ) ) )
= $true )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1321,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( ~ ( SV67 @ SV392 )
| ~ ! [SY1763: $i] :
( ~ ( SV67 @ SY1763 )
| ( SV392 = SY1763 ) ) ) )
= $false )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1322,plain,
! [SV70: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ ( setunion @ SV70 ) ) )
= $true )
| ( ( ~ ! [SY1585: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1585 )
| ~ ( in @ SY1585 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1323,plain,
! [SV70: $i,SV230: $i] :
( ( ( ~ ~ ! [SY1586: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1586 )
| ~ ( in @ SY1586 @ SV70 ) ) )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1324,plain,
! [SV72: $i,SV393: $i] :
( ( ( in @ SV393 @ SV72 )
= $false )
| ( ( SV72 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1325,plain,
! [SV74: $i,SV232: $i,SV341: $i] :
( ( ( ~ ~ ( in @ SV341 @ SV232 ) )
= $true )
| ( ( SV74 != SV232 )
= $true )
| ( ( in @ SV341 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1326,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY1274 @ SV77 )
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
!= ( setadjoin @ ( sK11_SY1274 @ SV77 ) @ emptyset ) ) ) )
= $true )
| ( ( iskpair @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1327,plain,
! [SV234: $i,SV78: $i,SV342: $i] :
( ( ( in @ SV342 @ ( setminus @ SV78 @ SV234 ) )
= $true )
| ( ( ~ ~ ( in @ SV342 @ SV234 )
| ~ ( in @ SV342 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1328,plain,
! [SV235: $i,SV79: $i,SV343: $i] :
( ( ( in @ SV343 @ ( setminus @ SV79 @ SV235 ) )
= $true )
| ( ( ~ ( in @ SV343 @ SV79 )
| ( in @ SV343 @ SV235 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1329,plain,
! [SV84: $i,SV240: $i,SV344: $i] :
( ( ( ~ ( subset @ SV344 @ SV240 ) )
= $true )
| ( ( subset @ SV344 @ ( binintersect @ SV84 @ SV240 ) )
= $true )
| ( ( subset @ SV344 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1330,plain,
! [SV241: $i > $o,SV86: $i] :
( ( ( ! [SY1591: $i] :
~ ~ ( ~ ( in @ SY1591 @ SV86 )
| ~ ( SV241 @ SY1591 ) ) )
= $false )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1331,plain,
! [SV242: $i,SV87: $i,SV345: $i] :
( ( ( SV345 = SV87 )
= $true )
| ( ( SV345 = SV242 )
= $true )
| ( ( in @ SV345 @ ( setadjoin @ SV87 @ ( setadjoin @ SV242 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1332,plain,
! [SV244: $i > $o,SV89: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ SV89 )
| ( SV244 @ SV410 ) )
= $true )
| ( ( ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV89 )
| ~ ~ ( SV244 @ SY1595 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1333,plain,
! [SV90: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_SY1296 @ SV90 ) @ SV90 )
| ~ $true ) )
= $false )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1215]) ).
thf(1334,plain,
! [SV385: $i,SV346: $i,SV245: $i,SV92: $i] :
( ( ( ( kpair @ SV92 @ SV245 )
= ( kpair @ SV346 @ SV385 ) )
= $false )
| ( ( SV245 = SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1335,plain,
! [SV94: $i,SV247: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY1599 @ SV247 @ SV94 ) @ SV94 )
| ~ ( in @ SV247 @ ( sK22_SY1599 @ SV247 @ SV94 ) ) ) )
= $false )
| ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1219]) ).
thf(1336,plain,
! [SV95: $i,SV248: $i] :
( ( ( subset @ SV248 @ SV95 )
= $false )
| ( ( SV95 = SV248 )
= $true )
| ( ( subset @ SV95 @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1337,plain,
! [SV249: $i,SV96: $i,SV386: $i,SV348: $i] :
( ( ( in @ ( kpair @ SV348 @ SV386 ) @ ( cartprod @ SV96 @ SV249 ) )
= $false )
| ( ( in @ SV386 @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1338,plain,
! [SV251: $i,SV98: $i,SV411: $i,SV394: $i] :
( ( ( ( SV394 != SV411 )
| ~ ( ~ ( ~ ( in @ SV394 @ SV98 )
| ( in @ SV411 @ SV251 ) )
| ~ ( ~ ( in @ SV411 @ SV251 )
| ( in @ SV394 @ SV98 ) ) ) )
= $true )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1339,plain,
! [SV252: $i,SV99: $i,SV350: $i] :
( ( ( SV350 = SV99 )
= $true )
| ( ( SV350 = SV252 )
= $true )
| ( ( in @ SV350 @ ( setadjoin @ SV99 @ ( setadjoin @ SV252 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1340,plain,
! [SV101: $i] :
( ( ( ~ ( in @ ( sK23_SY1317 @ SV101 ) @ SV101 ) )
= $false )
| ( ( SV101 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1225]) ).
thf(1341,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ~ ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
| ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1342,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ~ ( ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
| ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1343,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( SV103 @ SV395 )
| ~ ! [SY1767: $i] :
( ~ ( SV103 @ SY1767 )
| ( SV395 = SY1767 ) ) ) )
= $false )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1344,plain,
! [SV255: $i,SV104: $i] :
( ( ( ! [SY1607: $i] :
~ ~ ( ~ ( in @ SY1607 @ SV104 )
| ~ ( in @ SY1607 @ SV255 ) ) )
= $false )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1345,plain,
! [SV105: $i,SV256: $i,SV352: $i] :
( ( ( ~ ~ ( in @ SV352 @ SV256 ) )
= $true )
| ( ( ~ ( subset @ SV105 @ SV256 ) )
= $true )
| ( ( in @ SV352 @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1346,plain,
! [SV353: $i,SV257: $i,SV106: $i] :
( ( ( ! [SY1725: $i] :
~ ~ ( ~ ( in @ SY1725 @ SV106 )
| ~ ~ ! [SY1726: $i] :
~ ~ ( ~ ( in @ SY1726 @ SV257 )
| ( SV353
!= ( kpair @ SY1725 @ SY1726 ) ) ) ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1347,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ SV396 )
| ~ ! [SY1768: $i] :
( ~ ( SV107 @ SY1768 )
| ( SV396 = SY1768 ) ) ) )
= $false )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1348,plain,
! [SV258: $i,SV108: $i,SV354: $i] :
( ( ( in @ SV354 @ SV108 )
= $true )
| ( ( ~ ~ ( in @ SV354 @ SV258 )
| ~ ( in @ SV354 @ ( symdiff @ SV108 @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1349,plain,
! [SV109: $i,SV259: $i] :
( ( ( ~ ( in @ SV259 @ ( powerset @ SV109 ) ) )
= $true )
| ( ( ! [SY1613: $i] :
( ~ ( in @ SY1613 @ SV259 )
| ( in @ SY1613 @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1350,plain,
! [SV109: $i,SV259: $i] :
( ( ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ SV259 )
| ( in @ SY1614 @ SV109 ) ) )
= $true )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1351,plain,
! [SV388: $i,SV355: $i,SV262: $i,SV115: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV262 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SV388 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV262 = SV388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1352,plain,
! [SV116: $i,SV263: $i] :
( ( ( in @ SV263 @ ( setadjoin @ SV116 @ emptyset ) )
= $false )
| ( ( SV116 = SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1353,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ~ ( ~ ( SV117 @ SV397 )
| ~ ! [SY1769: $i] :
( ~ ( SV117 @ SY1769 )
| ( SV397 = SY1769 ) ) ) )
= $false )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1354,plain,
! [SV118: $i,SV356: $i,SV264: $i > $o] :
( ( ( ~ ( SV264 @ SV356 ) )
= $true )
| ( ( ( dsetconstr @ SV118
@ ^ [SY1618: $i] : ( SV264 @ SY1618 ) )
!= emptyset )
= $true )
| ( ( in @ SV356 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1355,plain,
! [SV119: $i,SV357: $i,SV265: $i > $o] :
( ( ( ~ ( SV265 @ SV357 ) )
= $true )
| ( ( ~ ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV119 )
| ~ ( SV265 @ SY1729 )
| ( SY1729 = SV357 ) )
| ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1356,plain,
! [SV266: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK12_SY1624 @ SV120 @ SV266 ) @ SV266 ) )
= $false )
| ( ( in @ SV266 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1357,plain,
! [SV266: $i,SV120: $i] :
( ( ( in @ ( sK12_SY1624 @ SV120 @ SV266 ) @ SV120 )
= $false )
| ( ( in @ SV266 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1358,plain,
! [SV121: $i,SV267: $i] :
( ( ( ~ ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) )
| ( SV121 = SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1359,plain,
! [SV121: $i,SV267: $i] :
( ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV267 )
= $false )
| ( ( ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) )
| ( SV121 = SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1360,plain,
! [SV270: $i,SV124: $i,SV358: $i] :
( ( ( ~ ( in @ SV358 @ SV124 ) )
= $true )
| ( ( in @ SV358 @ SV270 )
= $true )
| ( ( subset @ SV124 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1361,plain,
! [SV125: $i,SV398: $i] :
( ( ( in @ SV398 @ SV125 )
= $false )
| ( ( ~ ! [SY1371: $i] :
~ ~ ( ~ ( in @ SY1371 @ SV125 )
| ~ ~ ~ ! [SY1372: $i] :
~ ~ ( ~ ( in @ SY1372 @ SY1371 )
| ~ ( in @ SY1372 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1362,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1770: $i] :
~ ( ~ ( ~ ( SV126 @ SY1770 )
| ( SY1770 = SV399 ) )
| ~ ( ( SY1770 != SV399 )
| ( SV126 @ SY1770 ) ) ) )
= $false )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1363,plain,
( ( in @ sK6_SY1733 @ ( cartprod @ sK1_SX0 @ sK2_SY1628 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1364,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1365,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1771: $i] :
( ~ ( in @ SY1771 @ SV127 )
| ~ ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
| ~ ( SV271 @ SY1771 )
| ( ( sK14_SY1630 @ SV271 @ SV127 )
= SY1771 ) ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1366,plain,
! [SV412: $i > $o,SV400: $i > $o,SV274: $i,SV130: $i] :
( ( ( ~ ! [SY1788: $i] :
( ~ ( in @ SY1788 @ SV130 )
| ! [SY1789: $i] :
( ~ ( in @ SY1789 @ SV274 )
| ( SY1788 != SY1789 )
| ~ ( ~ ( ~ ( SV400 @ SY1788 )
| ( SV412 @ SY1789 ) )
| ~ ( ~ ( SV412 @ SY1789 )
| ( SV400 @ SY1788 ) ) ) ) )
| ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1367,plain,
! [SV132: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY1396 @ SV132 )
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) )
| ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
!= ( setadjoin @ ( sK15_SY1396 @ SV132 ) @ emptyset ) ) ) )
= $true )
| ( ( iskpair @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1253]) ).
thf(1368,plain,
! [SV277: $i,SV134: $i,SV361: $i] :
( ( ( SV361 = SV134 )
= $true )
| ( ( in @ SV361 @ SV277 )
= $true )
| ( ( in @ SV361 @ ( setadjoin @ SV134 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1369,plain,
! [SV278: $i > $o,SV135: $i,SV413: $i] :
( ( ( ~ ~ ( ~ ( in @ SV413 @ SV135 )
| ~ ~ ( SV278 @ SV413 ) ) )
= $true )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1370,plain,
! [SV279: $i > $o,SV136: $i,SV414: $i] :
( ( ( ~ ~ ( ~ ( in @ SV414 @ SV136 )
| ~ ( SV279 @ SV414 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1371,plain,
! [SV137: $i,SV362: $i,SV280: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ SV280 )
| ( subset @ ( setadjoin @ SV362 @ ( setadjoin @ SV415 @ emptyset ) ) @ ( binunion @ SV137 @ SV280 ) ) )
= $true )
| ( ( in @ SV362 @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1372,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( ( ( sK16_SY1651 @ SV282 @ SV139 )
!= ( sK24_SY1779 @ SV139 @ SV282 ) )
| ~ ( ~ ( ~ ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
| ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) ) )
| ~ ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1258]) ).
thf(1373,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 ) )
| ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) ) )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1374,plain,
! [SV141: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
| ~ ! [SY1740: $i,SY1741: $i] :
( ~ ~ ( ~ ( in @ SY1740 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1741 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1740 )
| ( in @ SX4 @ SY1741 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1741 )
| ( in @ SX4 @ SY1740 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1375,plain,
! [SV141: $i] :
( ( ~ ! [SY1744: $i] :
( ~ ~ ( ~ ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SY1744 )
| ( in @ SY1434 @ SV141 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1744 ) )
| ~ ! [SY1747: $i] :
~ ~ ! [SY1748: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1747 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1748 @ SY1744 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1747 )
| ~ ( in @ SX5 @ SY1744 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1747 ) )
| ( in @ SY1748 @ SY1750 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1376,plain,
! [SV142: $i,SV363: $i,SV284: $i,SV416: $i] :
( ( ( ~ ( in @ SV416 @ SV284 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV363 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV363 @ ( setadjoin @ SV416 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV142 @ SV284 ) ) ) )
= $true )
| ( ( in @ SV363 @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1377,plain,
! [SV286: $i,SV145: $i,SV364: $i] :
( ( ( in @ SV364 @ ( setminus @ SV145 @ SV286 ) )
= $false )
| ( ( in @ SV364 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1378,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ~ ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1379,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1780: $i] :
( ~ ( in @ SY1780 @ SV146 )
| ~ ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
| ~ ( SV287 @ SY1780 )
| ( ( sK18_SY1663 @ SV287 @ SV146 )
= SY1780 ) ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1380,plain,
! [SV288: $i,SV417: $o,SV147: $i,SV365: $i] :
( ( ( ~ ( ( SV365 != SV147 )
| SV417 )
| ~ ( ~ ( in @ SV365 @ SV288 )
| SV417 )
| SV417 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1264]) ).
thf(1381,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( ~ ( ( SV365 != SV147 )
| $true )
| ~ ( ~ ( in @ SV365 @ SV288 )
| $true )
| $true )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1264]) ).
thf(1382,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( ~ ( ( SV365 != SV147 )
| $false )
| ~ ( ~ ( in @ SV365 @ SV288 )
| $false )
| $false )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1264]) ).
thf(1383,plain,
! [SV149: $i,SV366: $i,SV290: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ SV290 )
| ( ( kfst @ ( kpair @ SV366 @ SV418 ) )
= SV366 ) )
= $true )
| ( ( in @ SV366 @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1384,plain,
! [SV150: $i,SV367: $i,SV291: $i > $o] :
( ( ( ~ ( SV291 @ SV367 ) )
= $true )
| ( ( in @ SV367
@ ( dsetconstr @ SV150
@ ^ [SY1674: $i] : ( SV291 @ SY1674 ) ) )
= $true )
| ( ( in @ SV367 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1385,plain,
! [SV151: $i,SV292: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV292 ) )
= $true )
| ( ( in @ SV368 @ SV151 )
= $true )
| ( ( in @ SV292 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1386,plain,
! [SV389: $o,SV294: $i,SV153: $i,SV369: $i] :
( ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| SV389 )
| ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 )
| SV389 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1387,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| $true )
| ~ ( ~ ( in @ SV369 @ SV294 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1388,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| $false )
| ~ ( ~ ( in @ SV369 @ SV294 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1389,plain,
! [SV296: $i > $o,SV155: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ SV155 )
| ( SV296 @ SV419 ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ( ~ ( in @ SY1679 @ SV155 )
| ~ ~ ( SV296 @ SY1679 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1390,plain,
! [SV401: $o,SV158: $i,SV301: $i] :
( ( ( ~ ! [SY1781: $i] :
( ~ ( in @ SV301 @ SY1781 )
| ~ ( in @ SY1781 @ SV158 )
| SV401 ) )
= $true )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1391,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV301 @ SX0 )
| ~ ( in @ SX0 @ SV158 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1392,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV301 @ SX0 )
| ~ ( in @ SX0 @ SV158 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1393,plain,
! [SV302: $i > $o,SV159: $i,SV420: $i] :
( ( ( ~ ~ ( ~ ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SV420 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1394,plain,
! [SV303: $i,SV160: $i,SV421: $i,SV402: $i] :
( ( ( ( SV402 != SV421 )
| ( ( setadjoin @ SV160 @ SV402 )
= ( setadjoin @ SV303 @ SV421 ) ) )
= $true )
| ( ( SV160 = SV303 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1395,plain,
! [SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 ) )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1278]) ).
thf(1396,plain,
! [SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ! [SY1783: $i] :
~ ~ ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1783 )
| ~ ! [SY1784: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1784 )
| ( SY1783 = SY1784 ) ) ) )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1278]) ).
thf(1397,plain,
! [SV162: $i,SV371: $i,SV305: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV305 )
| ( ( ksnd @ ( kpair @ SV371 @ SV422 ) )
= SV422 ) )
= $true )
| ( ( in @ SV371 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1398,plain,
! [SV163: $i,SV372: $i,SV306: $i] :
( ( ( ~ ( subset @ SV306 @ SV372 ) )
= $true )
| ( ( subset @ SV163 @ SV372 )
= $true )
| ( ( subset @ SV163 @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1399,plain,
! [SV165: $i,SV308: $i,SV374: $i] :
( ( ( ~ ~ ( in @ SV374 @ SV308 ) )
= $true )
| ( ( in @ SV374 @ ( symdiff @ SV165 @ SV308 ) )
= $true )
| ( ( in @ SV374 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1400,plain,
! [SV309: $i,SV166: $i,SV375: $i] :
( ( ( in @ SV375 @ SV166 )
= $true )
| ( ( ~ ( in @ SV375 @ ( setminus @ SV166 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1283]) ).
thf(1401,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ SV403 )
| ~ ! [SY1785: $i] :
( ~ ( SV167 @ SY1785 )
| ( SV403 = SY1785 ) ) ) )
= $false )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1402,plain,
! [SV168: $i,SV310: $i,SV376: $i] :
( ( ( in @ SV376 @ SV310 )
= $false )
| ( ( in @ SV376 @ ( setminus @ SV168 @ SV310 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1403,plain,
! [SV169: $i,SV311: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV311 ) )
= $true )
| ( ( ~ ( in @ SV377 @ ( symdiff @ SV169 @ SV311 ) ) )
= $true )
| ( ( in @ SV377 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1404,plain,
! [SV170: $i,SV404: $i] :
( ( ( ~ ( ~ ( in @ SV404 @ SV170 )
| ( SV170
!= ( setadjoin @ SV404 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1405,plain,
! [SV171: $i,SV378: $i,SV312: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV312 )
| ( in @ ( setadjoin @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV378 @ ( setadjoin @ SV423 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV171 @ SV312 ) ) ) ) )
= $true )
| ( ( in @ SV378 @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1406,plain,
! [SV173: $i,SV379: $i,SV314: $i,SV424: $i] :
( ( ( ~ ( in @ SV424 @ SV314 )
| ( in @ ( kpair @ SV379 @ SV424 ) @ ( cartprod @ SV173 @ SV314 ) ) )
= $true )
| ( ( in @ SV379 @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1407,plain,
! [SV174: $i,SV380: $i,SV315: $i,SV425: $i] :
( ( ( ~ ( in @ SV425 @ SV315 )
| ( ( kpair @ SV380 @ SV425 )
= ( kpair @ SV380 @ SV425 ) ) )
= $true )
| ( ( in @ SV380 @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1408,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( ~ ( ~ ( SV175 @ SV405 )
| ~ ! [SY1786: $i] :
( ~ ( SV175 @ SY1786 )
| ( SV405 = SY1786 ) ) ) )
= $false )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1409,plain,
! [SV316: $i,SV176: $i,SV426: $i,SV406: $i] :
( ( ( ( SV406 != SV426 )
| ~ ( in @ SV406 @ SV176 )
| ( in @ SV426 @ SV316 ) )
= $true )
| ( ( SV176 = SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1410,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| SV407 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1411,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1412,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1413,plain,
! [SV34: $i,SV199: $i] :
( ( ( in @ ( sK7_SY1538 @ SV199 @ SV34 ) @ SV34 )
= $true )
| ( ( subset @ SV34 @ SV199 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1297]) ).
thf(1414,plain,
! [SV35: $i,SV200: $i] :
( ( ( in @ ( sK8_SY1539 @ SV200 @ SV35 ) @ SV35 )
= $true )
| ( ( subset @ SV35 @ SV200 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1415,plain,
! [SV36: $i,SV201: $i,SV381: $i,SV320: $i] :
( ( ( SV320 != SV381 )
= $true )
| ( ( SV201 = SV381 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV36 @ ( setadjoin @ SV201 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV320 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV320 @ ( setadjoin @ SV381 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1416,plain,
! [SV202: $i,SV37: $i,SV321: $i] :
( ( ( in @ SV321 @ SV37 )
= $false )
| ( ( in @ SV202 @ ( setunion @ SV37 ) )
= $true )
| ( ( in @ SV202 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1417,plain,
! [SV38: $i,SV203: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ SV203 ) )
= $false )
| ( ( in @ SV322 @ ( setminus @ SV38 @ SV203 ) )
= $true )
| ( ( in @ SV322 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1418,plain,
! [SV41: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 )
| ~ ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) ) ) )
= $false )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1305]) ).
thf(1419,plain,
! [SV43: $i,SV208: $i,SV325: $i] :
( ( ( in @ SV325 @ SV208 )
= $false )
| ( ( in @ SV325 @ ( binintersect @ SV43 @ SV208 ) )
= $true )
| ( ( in @ SV325 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1420,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV390 )
| ~ ! [SY1761: $i] :
( ~ ( SV46 @ SY1761 )
| ( SV390 = SY1761 ) ) )
= $true )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1307]) ).
thf(1421,plain,
! [SV47: $i,SV327: $i,SV211: $i,SV408: $i] :
( ( ( ~ ( in @ SV408 @ SV211 ) )
= $true )
| ( ( in @ ( setadjoin @ SV327 @ ( setadjoin @ SV408 @ emptyset ) ) @ ( powerset @ ( binunion @ SV47 @ SV211 ) ) )
= $true )
| ( ( in @ SV327 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1422,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ! [SY1206: $i,SY1207: $i] :
( ~ ( SV49 @ SY1206 )
| ~ ( SV49 @ SY1207 )
| ( SY1206 = SY1207 ) ) )
= $true )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1423,plain,
! [SV51: $i,SV213: $i > $o] :
( ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true )
| ( ( ~ ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1310]) ).
thf(1424,plain,
! [SV51: $i,SV213: $i > $o] :
( ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true )
| ( ( ~ ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1311]) ).
thf(1425,plain,
! [SV52: $i,SV328: $i,SV214: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ SV214 ) )
= $true )
| ( ( in @ ( kpair @ SV328 @ SV409 ) @ ( powerset @ ( powerset @ ( binunion @ SV52 @ SV214 ) ) ) )
= $true )
| ( ( in @ SV328 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1426,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ( sK10_SY1558 @ SV216 @ SV54 )
!= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1314]) ).
thf(1427,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
| ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) ) )
| ~ ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1314]) ).
thf(1428,plain,
! [SV58: $i,SV220: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV220 ) )
= $true )
| ( ( in @ SV333 @ ( symdiff @ SV58 @ SV220 ) )
= $true )
| ( ( in @ SV333 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1429,plain,
! [SV224: $i > $o,SV62: $i,SV336: $i] :
( ( ( ~ ( ~ ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) )
| ( SV224 @ SV336 ) ) )
= $false )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1430,plain,
! [SV62: $i,SV336: $i,SV224: $i > $o] :
( ( ( ~ ( ~ ( SV224 @ SV336 )
| ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) ) ) )
= $false )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1431,plain,
! [SV63: $i,SV225: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ SV225 ) )
= $false )
| ( ( ~ ( in @ SV337 @ SV63 ) )
= $true )
| ( ( subset @ SV63 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1432,plain,
! [SV65: $i] :
( ( ( ! [SY1253: $i] :
( ~ ~ ( ~ ( in @ SY1253 @ omega )
| ~ ( in @ SY1253 @ SV65 ) )
| ( in @ ( setadjoin @ SY1253 @ SY1253 ) @ SV65 ) ) )
= $false )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1433,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ SV392 )
| ~ ! [SY1763: $i] :
( ~ ( SV67 @ SY1763 )
| ( SV392 = SY1763 ) ) )
= $true )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1434,plain,
! [SV70: $i,SV230: $i] :
( ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false )
| ( ( ~ ! [SY1585: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1585 )
| ~ ( in @ SY1585 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1435,plain,
! [SV70: $i,SV230: $i] :
( ( ( ~ ! [SY1586: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1586 )
| ~ ( in @ SY1586 @ SV70 ) ) )
= $false )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1436,plain,
! [SV393: $i,SV72: $i] :
( ( ( SV72 = emptyset )
= $false )
| ( ( in @ SV393 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1437,plain,
! [SV74: $i,SV232: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV232 ) )
= $false )
| ( ( SV74 != SV232 )
= $true )
| ( ( in @ SV341 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1438,plain,
! [SV77: $i] :
( ( ( ~ ( in @ ( sK11_SY1274 @ SV77 )
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
!= ( setadjoin @ ( sK11_SY1274 @ SV77 ) @ emptyset ) ) )
= $false )
| ( ( iskpair @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1439,plain,
! [SV78: $i,SV234: $i,SV342: $i] :
( ( ( ~ ~ ( in @ SV342 @ SV234 ) )
= $true )
| ( ( ~ ( in @ SV342 @ SV78 ) )
= $true )
| ( ( in @ SV342 @ ( setminus @ SV78 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1440,plain,
! [SV235: $i,SV79: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ SV79 ) )
= $true )
| ( ( in @ SV343 @ SV235 )
= $true )
| ( ( in @ SV343 @ ( setminus @ SV79 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1441,plain,
! [SV84: $i,SV240: $i,SV344: $i] :
( ( ( subset @ SV344 @ SV240 )
= $false )
| ( ( subset @ SV344 @ ( binintersect @ SV84 @ SV240 ) )
= $true )
| ( ( subset @ SV344 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1442,plain,
! [SV86: $i,SV241: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 )
| ~ ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) ) ) )
= $false )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1330]) ).
thf(1443,plain,
! [SV244: $i > $o,SV89: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ SV89 ) )
= $true )
| ( ( SV244 @ SV410 )
= $true )
| ( ( ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV89 )
| ~ ~ ( SV244 @ SY1595 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1444,plain,
! [SV90: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY1296 @ SV90 ) @ SV90 )
| ~ $true ) )
= $true )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1445,plain,
! [SV94: $i,SV247: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY1599 @ SV247 @ SV94 ) @ SV94 )
| ~ ( in @ SV247 @ ( sK22_SY1599 @ SV247 @ SV94 ) ) ) )
= $true )
| ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1446,plain,
! [SV251: $i,SV98: $i,SV411: $i,SV394: $i] :
( ( ( SV394 != SV411 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV394 @ SV98 )
| ( in @ SV411 @ SV251 ) )
| ~ ( ~ ( in @ SV411 @ SV251 )
| ( in @ SV394 @ SV98 ) ) ) )
= $true )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1447,plain,
! [SV101: $i] :
( ( ( in @ ( sK23_SY1317 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1448,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ( ~ ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) ) )
= $true )
| ( ( ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1449,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ( ~ ( ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) ) )
= $true )
| ( ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1450,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ SV395 )
| ~ ! [SY1767: $i] :
( ~ ( SV103 @ SY1767 )
| ( SV395 = SY1767 ) ) )
= $true )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1451,plain,
! [SV104: $i,SV255: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV104 )
| ~ ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV255 ) ) )
= $false )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1344]) ).
thf(1452,plain,
! [SV105: $i,SV256: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ SV256 ) )
= $false )
| ( ( ~ ( subset @ SV105 @ SV256 ) )
= $true )
| ( ( in @ SV352 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1453,plain,
! [SV106: $i,SV257: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SV106 )
| ~ ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SY1794 ) ) ) ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1346]) ).
thf(1454,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV396 )
| ~ ! [SY1768: $i] :
( ~ ( SV107 @ SY1768 )
| ( SV396 = SY1768 ) ) )
= $true )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1455,plain,
! [SV108: $i,SV258: $i,SV354: $i] :
( ( ( ~ ~ ( in @ SV354 @ SV258 ) )
= $true )
| ( ( ~ ( in @ SV354 @ ( symdiff @ SV108 @ SV258 ) ) )
= $true )
| ( ( in @ SV354 @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1456,plain,
! [SV109: $i,SV259: $i] :
( ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $false )
| ( ( ! [SY1613: $i] :
( ~ ( in @ SY1613 @ SV259 )
| ( in @ SY1613 @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1457,plain,
! [SV109: $i,SV259: $i] :
( ( ( ! [SY1614: $i] :
( ~ ( in @ SY1614 @ SV259 )
| ( in @ SY1614 @ SV109 ) ) )
= $false )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1458,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ SV397 )
| ~ ! [SY1769: $i] :
( ~ ( SV117 @ SY1769 )
| ( SV397 = SY1769 ) ) )
= $true )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1459,plain,
! [SV118: $i,SV356: $i,SV264: $i > $o] :
( ( ( SV264 @ SV356 )
= $false )
| ( ( ( dsetconstr @ SV118
@ ^ [SY1618: $i] : ( SV264 @ SY1618 ) )
!= emptyset )
= $true )
| ( ( in @ SV356 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1460,plain,
! [SV119: $i,SV357: $i,SV265: $i > $o] :
( ( ( SV265 @ SV357 )
= $false )
| ( ( ~ ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV119 )
| ~ ( SV265 @ SY1729 )
| ( SY1729 = SV357 ) )
| ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1461,plain,
! [SV266: $i,SV120: $i] :
( ( ( in @ ( sK12_SY1624 @ SV120 @ SV266 ) @ SV266 )
= $true )
| ( ( in @ SV266 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1462,plain,
! [SV121: $i,SV267: $i] :
( ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 )
= $true )
| ( ( ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) )
| ( SV121 = SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1463,plain,
! [SV121: $i,SV267: $i] :
( ( ( ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) ) )
= $true )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1464,plain,
! [SV270: $i,SV124: $i,SV358: $i] :
( ( ( in @ SV358 @ SV124 )
= $false )
| ( ( in @ SV358 @ SV270 )
= $true )
| ( ( subset @ SV124 @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1465,plain,
! [SV398: $i,SV125: $i] :
( ( ( ! [SY1371: $i] :
~ ~ ( ~ ( in @ SY1371 @ SV125 )
| ~ ~ ~ ! [SY1372: $i] :
~ ~ ( ~ ( in @ SY1372 @ SY1371 )
| ~ ( in @ SY1372 @ SV125 ) ) ) )
= $false )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1466,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
| ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 ) )
| ~ ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1362]) ).
thf(1467,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1468,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
| ~ ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
| ~ ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
| ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1365]) ).
thf(1469,plain,
! [SV412: $i > $o,SV400: $i > $o,SV274: $i,SV130: $i] :
( ( ( ~ ! [SY1788: $i] :
( ~ ( in @ SY1788 @ SV130 )
| ! [SY1789: $i] :
( ~ ( in @ SY1789 @ SV274 )
| ( SY1788 != SY1789 )
| ~ ( ~ ( ~ ( SV400 @ SY1788 )
| ( SV412 @ SY1789 ) )
| ~ ( ~ ( SV412 @ SY1789 )
| ( SV400 @ SY1788 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1470,plain,
! [SV132: $i] :
( ( ( ~ ( in @ ( sK15_SY1396 @ SV132 )
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) )
| ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
!= ( setadjoin @ ( sK15_SY1396 @ SV132 ) @ emptyset ) ) )
= $false )
| ( ( iskpair @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1471,plain,
! [SV278: $i > $o,SV135: $i,SV413: $i] :
( ( ( ~ ( ~ ( in @ SV413 @ SV135 )
| ~ ~ ( SV278 @ SV413 ) ) )
= $false )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1472,plain,
! [SV279: $i > $o,SV136: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ SV136 )
| ~ ( SV279 @ SV414 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1473,plain,
! [SV137: $i,SV362: $i,SV280: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ SV280 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV362 @ ( setadjoin @ SV415 @ emptyset ) ) @ ( binunion @ SV137 @ SV280 ) )
= $true )
| ( ( in @ SV362 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1474,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( ( sK16_SY1651 @ SV282 @ SV139 )
!= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1475,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
| ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) ) )
| ~ ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1476,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) ) )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1477,plain,
! [SV141: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
| ~ ! [SY1740: $i,SY1741: $i] :
( ~ ~ ( ~ ( in @ SY1740 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1741 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1740 )
| ( in @ SX4 @ SY1741 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1741 )
| ( in @ SX4 @ SY1740 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1374]) ).
thf(1478,plain,
! [SV141: $i] :
( ( ! [SY1744: $i] :
( ~ ~ ( ~ ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SY1744 )
| ( in @ SY1434 @ SV141 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1744 ) )
| ~ ! [SY1747: $i] :
~ ~ ! [SY1748: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1747 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1748 @ SY1744 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1747 )
| ~ ( in @ SX5 @ SY1744 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1747 ) )
| ( in @ SY1748 @ SY1750 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1479,plain,
! [SV142: $i,SV363: $i,SV284: $i,SV416: $i] :
( ( ( ~ ( in @ SV416 @ SV284 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV363 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV363 @ ( setadjoin @ SV416 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV142 @ SV284 ) ) )
= $true )
| ( ( in @ SV363 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1480,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1481,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
| ~ ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
| ~ ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
| ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1379]) ).
thf(1482,plain,
! [SV288: $i,SV417: $o,SV147: $i,SV365: $i] :
( ( ( ~ ( ( SV365 != SV147 )
| SV417 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| SV417 )
| SV417 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1483,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( ~ ( ( SV365 != SV147 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $true )
| $true )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1484,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( ~ ( ( SV365 != SV147 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $false )
| $false )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1485,plain,
! [SV149: $i,SV366: $i,SV290: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ SV290 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV366 @ SV418 ) )
= SV366 )
= $true )
| ( ( in @ SV366 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1486,plain,
! [SV150: $i,SV367: $i,SV291: $i > $o] :
( ( ( SV291 @ SV367 )
= $false )
| ( ( in @ SV367
@ ( dsetconstr @ SV150
@ ^ [SY1674: $i] : ( SV291 @ SY1674 ) ) )
= $true )
| ( ( in @ SV367 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1487,plain,
! [SV151: $i,SV292: $i,SV368: $i] :
( ( ( in @ SV368 @ SV292 )
= $false )
| ( ( in @ SV368 @ SV151 )
= $true )
| ( ( in @ SV292 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1488,plain,
! [SV294: $i,SV389: $o,SV153: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| SV389 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 )
| SV389 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1489,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $true )
| $true )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1490,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV153 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $false )
| $false )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1491,plain,
! [SV296: $i > $o,SV155: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ SV155 ) )
= $true )
| ( ( SV296 @ SV419 )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ( ~ ( in @ SY1679 @ SV155 )
| ~ ~ ( SV296 @ SY1679 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1492,plain,
! [SV401: $o,SV158: $i,SV301: $i] :
( ( ( ! [SY1781: $i] :
( ~ ( in @ SV301 @ SY1781 )
| ~ ( in @ SY1781 @ SV158 )
| SV401 ) )
= $false )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1493,plain,
! [SV158: $i,SV301: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV301 @ SX0 )
| ~ ( in @ SX0 @ SV158 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1494,plain,
! [SV158: $i,SV301: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV301 @ SX0 )
| ~ ( in @ SX0 @ SV158 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1495,plain,
! [SV302: $i > $o,SV159: $i,SV420: $i] :
( ( ( ~ ( ~ ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SV420 @ emptyset ) ) ) )
= $false )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1496,plain,
! [SV303: $i,SV160: $i,SV421: $i,SV402: $i] :
( ( ( SV402 != SV421 )
= $true )
| ( ( ( setadjoin @ SV160 @ SV402 )
= ( setadjoin @ SV303 @ SV421 ) )
= $true )
| ( ( SV160 = SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1497,plain,
! [SV304: $i,SV161: $i > $i > $o] :
( ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1498,plain,
! [SV304: $i,SV161: $i > $i > $o] :
( ( ( ! [SY1783: $i] :
~ ~ ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1783 )
| ~ ! [SY1784: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1784 )
| ( SY1783 = SY1784 ) ) ) )
= $true )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1499,plain,
! [SV162: $i,SV371: $i,SV305: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV305 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV371 @ SV422 ) )
= SV422 )
= $true )
| ( ( in @ SV371 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1500,plain,
! [SV163: $i,SV372: $i,SV306: $i] :
( ( ( subset @ SV306 @ SV372 )
= $false )
| ( ( subset @ SV163 @ SV372 )
= $true )
| ( ( subset @ SV163 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1501,plain,
! [SV165: $i,SV308: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ SV308 ) )
= $false )
| ( ( in @ SV374 @ ( symdiff @ SV165 @ SV308 ) )
= $true )
| ( ( in @ SV374 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1502,plain,
! [SV309: $i,SV166: $i,SV375: $i] :
( ( ( in @ SV375 @ ( setminus @ SV166 @ SV309 ) )
= $false )
| ( ( in @ SV375 @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1503,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV403 )
| ~ ! [SY1785: $i] :
( ~ ( SV167 @ SY1785 )
| ( SV403 = SY1785 ) ) )
= $true )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1504,plain,
! [SV169: $i,SV311: $i,SV377: $i] :
( ( ( in @ SV377 @ SV311 )
= $false )
| ( ( ~ ( in @ SV377 @ ( symdiff @ SV169 @ SV311 ) ) )
= $true )
| ( ( in @ SV377 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1505,plain,
! [SV170: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV170 )
| ( SV170
!= ( setadjoin @ SV404 @ emptyset ) ) )
= $true )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1506,plain,
! [SV171: $i,SV378: $i,SV312: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV312 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV378 @ ( setadjoin @ SV423 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV171 @ SV312 ) ) ) )
= $true )
| ( ( in @ SV378 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1507,plain,
! [SV173: $i,SV379: $i,SV314: $i,SV424: $i] :
( ( ( ~ ( in @ SV424 @ SV314 ) )
= $true )
| ( ( in @ ( kpair @ SV379 @ SV424 ) @ ( cartprod @ SV173 @ SV314 ) )
= $true )
| ( ( in @ SV379 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1508,plain,
! [SV174: $i,SV380: $i,SV315: $i,SV425: $i] :
( ( ( ~ ( in @ SV425 @ SV315 ) )
= $true )
| ( ( ( kpair @ SV380 @ SV425 )
= ( kpair @ SV380 @ SV425 ) )
= $true )
| ( ( in @ SV380 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1509,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ SV405 )
| ~ ! [SY1786: $i] :
( ~ ( SV175 @ SY1786 )
| ( SV405 = SY1786 ) ) )
= $true )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1510,plain,
! [SV316: $i,SV176: $i,SV426: $i,SV406: $i] :
( ( ( SV406 != SV426 )
= $true )
| ( ( ~ ( in @ SV406 @ SV176 )
| ( in @ SV426 @ SV316 ) )
= $true )
| ( ( SV176 = SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1511,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| SV407 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1512,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1513,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 )
| ~ ~ ( in @ SV318 @ SV197 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1514,plain,
! [SV36: $i,SV201: $i,SV381: $i,SV320: $i] :
( ( ( SV320 = SV381 )
= $false )
| ( ( SV201 = SV381 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV36 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV36 @ ( setadjoin @ SV201 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV320 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV320 @ ( setadjoin @ SV381 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1515,plain,
! [SV38: $i,SV203: $i,SV322: $i] :
( ( ( in @ SV322 @ SV203 )
= $true )
| ( ( in @ SV322 @ ( setminus @ SV38 @ SV203 ) )
= $true )
| ( ( in @ SV322 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1516,plain,
! [SV41: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 )
| ~ ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) ) ) )
= $true )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1517,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV390 ) )
= $true )
| ( ( ~ ! [SY1761: $i] :
( ~ ( SV46 @ SY1761 )
| ( SV390 = SY1761 ) ) )
= $true )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1518,plain,
! [SV47: $i,SV327: $i,SV211: $i,SV408: $i] :
( ( ( in @ SV408 @ SV211 )
= $false )
| ( ( in @ ( setadjoin @ SV327 @ ( setadjoin @ SV408 @ emptyset ) ) @ ( powerset @ ( binunion @ SV47 @ SV211 ) ) )
= $true )
| ( ( in @ SV327 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1519,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ! [SY1206: $i,SY1207: $i] :
( ~ ( SV49 @ SY1206 )
| ~ ( SV49 @ SY1207 )
| ( SY1206 = SY1207 ) ) )
= $false )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1520,plain,
! [SV213: $i > $o,SV51: $i] :
( ( ( ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $false )
| ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1521,plain,
! [SV213: $i > $o,SV51: $i] :
( ( ( ~ ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $false )
| ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1522,plain,
! [SV52: $i,SV328: $i,SV214: $i,SV409: $i] :
( ( ( in @ SV409 @ SV214 )
= $false )
| ( ( in @ ( kpair @ SV328 @ SV409 ) @ ( powerset @ ( powerset @ ( binunion @ SV52 @ SV214 ) ) ) )
= $true )
| ( ( in @ SV328 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1523,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1426]) ).
thf(1524,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
| ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) ) )
| ~ ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1427]) ).
thf(1525,plain,
! [SV58: $i,SV220: $i,SV333: $i] :
( ( ( in @ SV333 @ SV220 )
= $false )
| ( ( in @ SV333 @ ( symdiff @ SV58 @ SV220 ) )
= $true )
| ( ( in @ SV333 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1526,plain,
! [SV224: $i > $o,SV62: $i,SV336: $i] :
( ( ( ~ ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) )
| ( SV224 @ SV336 ) )
= $true )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1527,plain,
! [SV62: $i,SV336: $i,SV224: $i > $o] :
( ( ( ~ ( SV224 @ SV336 )
| ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) ) )
= $true )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1528,plain,
! [SV63: $i,SV225: $i,SV337: $i] :
( ( ( in @ SV337 @ SV225 )
= $true )
| ( ( ~ ( in @ SV337 @ SV63 ) )
= $true )
| ( ( subset @ SV63 @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1529,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY1253 @ SV65 ) @ omega )
| ~ ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 ) )
| ( in @ ( setadjoin @ ( sK32_SY1253 @ SV65 ) @ ( sK32_SY1253 @ SV65 ) ) @ SV65 ) )
= $false )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1432]) ).
thf(1530,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ SV392 ) )
= $true )
| ( ( ~ ! [SY1763: $i] :
( ~ ( SV67 @ SY1763 )
| ( SV392 = SY1763 ) ) )
= $true )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1531,plain,
! [SV70: $i,SV230: $i] :
( ( ( ! [SY1585: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1585 )
| ~ ( in @ SY1585 @ SV70 ) ) )
= $false )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1532,plain,
! [SV70: $i,SV230: $i] :
( ( ( ! [SY1586: $i] :
~ ~ ( ~ ( in @ SV230 @ SY1586 )
| ~ ( in @ SY1586 @ SV70 ) ) )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1533,plain,
! [SV74: $i,SV232: $i,SV341: $i] :
( ( ( in @ SV341 @ SV232 )
= $true )
| ( ( SV74 != SV232 )
= $true )
| ( ( in @ SV341 @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1534,plain,
! [SV77: $i] :
( ( ( ~ ( in @ ( sK11_SY1274 @ SV77 )
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) ) )
= $false )
| ( ( iskpair @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1535,plain,
! [SV77: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
!= ( setadjoin @ ( sK11_SY1274 @ SV77 ) @ emptyset ) )
= $false )
| ( ( iskpair @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1536,plain,
! [SV78: $i,SV234: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ SV234 ) )
= $false )
| ( ( ~ ( in @ SV342 @ SV78 ) )
= $true )
| ( ( in @ SV342 @ ( setminus @ SV78 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1537,plain,
! [SV235: $i,SV79: $i,SV343: $i] :
( ( ( in @ SV343 @ SV79 )
= $false )
| ( ( in @ SV343 @ SV235 )
= $true )
| ( ( in @ SV343 @ ( setminus @ SV79 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1538,plain,
! [SV86: $i,SV241: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 )
| ~ ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) ) ) )
= $true )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1442]) ).
thf(1539,plain,
! [SV244: $i > $o,SV89: $i,SV410: $i] :
( ( ( in @ SV410 @ SV89 )
= $false )
| ( ( SV244 @ SV410 )
= $true )
| ( ( ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV89 )
| ~ ~ ( SV244 @ SY1595 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1540,plain,
! [SV90: $i] :
( ( ( ~ ( in @ ( sK21_SY1296 @ SV90 ) @ SV90 )
| ~ $true )
= $false )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1541,plain,
! [SV94: $i,SV247: $i] :
( ( ( ~ ( in @ ( sK22_SY1599 @ SV247 @ SV94 ) @ SV94 )
| ~ ( in @ SV247 @ ( sK22_SY1599 @ SV247 @ SV94 ) ) )
= $false )
| ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1542,plain,
! [SV251: $i,SV98: $i,SV411: $i,SV394: $i] :
( ( ( SV394 = SV411 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV394 @ SV98 )
| ( in @ SV411 @ SV251 ) )
| ~ ( ~ ( in @ SV411 @ SV251 )
| ( in @ SV394 @ SV98 ) ) ) )
= $true )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1543,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
= $false )
| ( ( ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1544,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ( ( SV351 = SV102 )
| ( in @ SV351 @ SV254 ) )
= $false )
| ( ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1545,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ SV395 ) )
= $true )
| ( ( ~ ! [SY1767: $i] :
( ~ ( SV103 @ SY1767 )
| ( SV395 = SY1767 ) ) )
= $true )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1546,plain,
! [SV104: $i,SV255: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV104 )
| ~ ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV255 ) ) )
= $true )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1547,plain,
! [SV105: $i,SV256: $i,SV352: $i] :
( ( ( in @ SV352 @ SV256 )
= $true )
| ( ( ~ ( subset @ SV105 @ SV256 ) )
= $true )
| ( ( in @ SV352 @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1548,plain,
! [SV106: $i,SV257: $i,SV353: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SV106 )
| ~ ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SY1794 ) ) ) ) )
= $true )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1549,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV396 ) )
= $true )
| ( ( ~ ! [SY1768: $i] :
( ~ ( SV107 @ SY1768 )
| ( SV396 = SY1768 ) ) )
= $true )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1550,plain,
! [SV108: $i,SV258: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ SV258 ) )
= $false )
| ( ( ~ ( in @ SV354 @ ( symdiff @ SV108 @ SV258 ) ) )
= $true )
| ( ( in @ SV354 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1551,plain,
! [SV109: $i,SV259: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV259 )
| ( in @ SV427 @ SV109 ) )
= $true )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1552,plain,
! [SV259: $i,SV109: $i] :
( ( ( ~ ( in @ ( sK33_SY1614 @ SV109 @ SV259 ) @ SV259 )
| ( in @ ( sK33_SY1614 @ SV109 @ SV259 ) @ SV109 ) )
= $false )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1457]) ).
thf(1553,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ SV397 ) )
= $true )
| ( ( ~ ! [SY1769: $i] :
( ~ ( SV117 @ SY1769 )
| ( SV397 = SY1769 ) ) )
= $true )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1554,plain,
! [SV356: $i,SV264: $i > $o,SV118: $i] :
( ( ( ( dsetconstr @ SV118
@ ^ [SY1618: $i] : ( SV264 @ SY1618 ) )
= emptyset )
= $false )
| ( ( SV264 @ SV356 )
= $false )
| ( ( in @ SV356 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1555,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ~ ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV119 )
| ~ ( SV265 @ SY1729 )
| ( SY1729 = SV357 ) ) )
= $true )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1460]) ).
thf(1556,plain,
! [SV121: $i,SV267: $i] :
( ( ( ~ ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) ) )
= $true )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1557,plain,
! [SV121: $i,SV267: $i] :
( ( ( ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) ) )
= $false )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1558,plain,
! [SV125: $i,SV398: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY1371 @ SV398 @ SV125 ) @ SV125 )
| ~ ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SY1795 @ SV125 ) ) ) )
= $false )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1465]) ).
thf(1559,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
| ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 ) )
| ~ ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1560,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1561,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1562,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ~ ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
| ~ ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
| ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1563,plain,
! [SV412: $i > $o,SV400: $i > $o,SV274: $i,SV130: $i] :
( ( ( ! [SY1788: $i] :
( ~ ( in @ SY1788 @ SV130 )
| ! [SY1789: $i] :
( ~ ( in @ SY1789 @ SV274 )
| ( SY1788 != SY1789 )
| ~ ( ~ ( ~ ( SV400 @ SY1788 )
| ( SV412 @ SY1789 ) )
| ~ ( ~ ( SV412 @ SY1789 )
| ( SV400 @ SY1788 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1564,plain,
! [SV132: $i] :
( ( ( ~ ( in @ ( sK15_SY1396 @ SV132 )
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) ) )
= $false )
| ( ( iskpair @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1565,plain,
! [SV132: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
!= ( setadjoin @ ( sK15_SY1396 @ SV132 ) @ emptyset ) )
= $false )
| ( ( iskpair @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1566,plain,
! [SV278: $i > $o,SV135: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV135 )
| ~ ~ ( SV278 @ SV413 ) )
= $true )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1567,plain,
! [SV279: $i > $o,SV136: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV136 )
| ~ ( SV279 @ SV414 ) )
= $true )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1472]) ).
thf(1568,plain,
! [SV137: $i,SV362: $i,SV280: $i,SV415: $i] :
( ( ( in @ SV415 @ SV280 )
= $false )
| ( ( subset @ ( setadjoin @ SV362 @ ( setadjoin @ SV415 @ emptyset ) ) @ ( binunion @ SV137 @ SV280 ) )
= $true )
| ( ( in @ SV362 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1569,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1570,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( ~ ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
| ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) ) )
| ~ ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1571,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) ) )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1572,plain,
! [SV141: $i] :
( ( ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
| ~ ! [SY1740: $i,SY1741: $i] :
( ~ ~ ( ~ ( in @ SY1740 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1741 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1740 )
| ( in @ SX4 @ SY1741 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1741 )
| ( in @ SX4 @ SY1740 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1573,plain,
! [SV141: $i,SV428: $i] :
( ( ~ ~ ( ~ ! [SY1796: $i] :
( ~ ( in @ SY1796 @ SV428 )
| ( in @ SY1796 @ SV141 ) )
| ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
| ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1574,plain,
! [SV142: $i,SV363: $i,SV284: $i,SV416: $i] :
( ( ( in @ SV416 @ SV284 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV363 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV363 @ ( setadjoin @ SV416 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV142 @ SV284 ) ) )
= $true )
| ( ( in @ SV363 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1575,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1576,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1577,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
| ~ ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
| ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1578,plain,
! [SV288: $i,SV417: $o,SV147: $i,SV365: $i] :
( ( ( ( SV365 != SV147 )
| SV417 )
= $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| SV417 )
| SV417 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1579,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( ( SV365 != SV147 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $true )
| $true )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1580,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( ( SV365 != SV147 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $false )
| $false )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1581,plain,
! [SV149: $i,SV366: $i,SV290: $i,SV418: $i] :
( ( ( in @ SV418 @ SV290 )
= $false )
| ( ( ( kfst @ ( kpair @ SV366 @ SV418 ) )
= SV366 )
= $true )
| ( ( in @ SV366 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1582,plain,
! [SV294: $i,SV389: $o,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV153 )
| SV389 )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 )
| SV389 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1583,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV153 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $true )
| $true )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1584,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV153 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $false )
| $false )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1585,plain,
! [SV296: $i > $o,SV155: $i,SV419: $i] :
( ( ( in @ SV419 @ SV155 )
= $false )
| ( ( SV296 @ SV419 )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ( ~ ( in @ SY1679 @ SV155 )
| ~ ~ ( SV296 @ SY1679 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1586,plain,
! [SV158: $i,SV401: $o,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( sK35_SY1781 @ SV401 @ SV158 @ SV301 ) )
| ~ ( in @ ( sK35_SY1781 @ SV401 @ SV158 @ SV301 ) @ SV158 )
| SV401 )
= $false )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1492]) ).
thf(1587,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( sK36_SX0 @ SV158 @ SV301 ) )
| ~ ( in @ ( sK36_SX0 @ SV158 @ SV301 ) @ SV158 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1493]) ).
thf(1588,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( sK37_SX0 @ SV158 @ SV301 ) )
| ~ ( in @ ( sK37_SX0 @ SV158 @ SV301 ) @ SV158 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1494]) ).
thf(1589,plain,
! [SV302: $i > $o,SV159: $i,SV420: $i] :
( ( ( ~ ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SV420 @ emptyset ) ) )
= $true )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1590,plain,
! [SV303: $i,SV160: $i,SV421: $i,SV402: $i] :
( ( ( SV402 = SV421 )
= $false )
| ( ( ( setadjoin @ SV160 @ SV402 )
= ( setadjoin @ SV303 @ SV421 ) )
= $true )
| ( ( SV160 = SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1591,plain,
! [SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1592,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
| ~ ! [SY1803: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1803 )
| ( SV429 = SY1803 ) ) ) )
= $true )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1593,plain,
! [SV162: $i,SV371: $i,SV305: $i,SV422: $i] :
( ( ( in @ SV422 @ SV305 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV371 @ SV422 ) )
= SV422 )
= $true )
| ( ( in @ SV371 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1594,plain,
! [SV165: $i,SV308: $i,SV374: $i] :
( ( ( in @ SV374 @ SV308 )
= $true )
| ( ( in @ SV374 @ ( symdiff @ SV165 @ SV308 ) )
= $true )
| ( ( in @ SV374 @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1595,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV403 ) )
= $true )
| ( ( ~ ! [SY1785: $i] :
( ~ ( SV167 @ SY1785 )
| ( SV403 = SY1785 ) ) )
= $true )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1596,plain,
! [SV311: $i,SV169: $i,SV377: $i] :
( ( ( in @ SV377 @ ( symdiff @ SV169 @ SV311 ) )
= $false )
| ( ( in @ SV377 @ SV311 )
= $false )
| ( ( in @ SV377 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1597,plain,
! [SV170: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV170 ) )
= $true )
| ( ( SV170
!= ( setadjoin @ SV404 @ emptyset ) )
= $true )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1598,plain,
! [SV171: $i,SV378: $i,SV312: $i,SV423: $i] :
( ( ( in @ SV423 @ SV312 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV378 @ ( setadjoin @ SV423 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV171 @ SV312 ) ) ) )
= $true )
| ( ( in @ SV378 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1599,plain,
! [SV173: $i,SV379: $i,SV314: $i,SV424: $i] :
( ( ( in @ SV424 @ SV314 )
= $false )
| ( ( in @ ( kpair @ SV379 @ SV424 ) @ ( cartprod @ SV173 @ SV314 ) )
= $true )
| ( ( in @ SV379 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1600,plain,
! [SV174: $i,SV380: $i,SV315: $i,SV425: $i] :
( ( ( in @ SV425 @ SV315 )
= $false )
| ( ( ( kpair @ SV380 @ SV425 )
= ( kpair @ SV380 @ SV425 ) )
= $true )
| ( ( in @ SV380 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1601,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ SV405 ) )
= $true )
| ( ( ~ ! [SY1786: $i] :
( ~ ( SV175 @ SY1786 )
| ( SV405 = SY1786 ) ) )
= $true )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1602,plain,
! [SV316: $i,SV176: $i,SV426: $i,SV406: $i] :
( ( ( SV406 = SV426 )
= $false )
| ( ( ~ ( in @ SV406 @ SV176 )
| ( in @ SV426 @ SV316 ) )
= $true )
| ( ( SV176 = SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1603,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1604,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV197 )
| SV407 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1605,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1512]) ).
thf(1606,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV197 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1512]) ).
thf(1607,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1608,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV197 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1609,plain,
! [SV41: $i,SV206: $i > $o] :
( ( ( ~ ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 )
| ~ ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) ) )
= $false )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1610,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( SV46 @ SV390 )
= $false )
| ( ( ~ ! [SY1761: $i] :
( ~ ( SV46 @ SY1761 )
| ( SV390 = SY1761 ) ) )
= $true )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1611,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ! [SY1804: $i] :
( ~ ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
| ~ ( SV49 @ SY1804 )
| ( ( sK38_SY1206 @ SV391 @ SV49 )
= SY1804 ) ) )
= $false )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1519]) ).
thf(1612,plain,
! [SV213: $i > $o,SV51: $i] :
( ( ( ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true )
| ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1613,plain,
! [SV213: $i > $o,SV51: $i] :
( ( ( ! [SY1553: $i] :
~ ~ ( ~ ( in @ SY1553 @ SV51 )
| ~ ( SV213 @ SY1553 ) ) )
= $true )
| ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1521]) ).
thf(1614,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1615,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
| ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1616,plain,
! [SV224: $i > $o,SV62: $i,SV336: $i] :
( ( ( ~ ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) ) )
= $true )
| ( ( SV224 @ SV336 )
= $true )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1617,plain,
! [SV62: $i,SV336: $i,SV224: $i > $o] :
( ( ( ~ ( SV224 @ SV336 ) )
= $true )
| ( ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) )
= $true )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1618,plain,
! [SV225: $i,SV63: $i,SV337: $i] :
( ( ( in @ SV337 @ SV63 )
= $false )
| ( ( in @ SV337 @ SV225 )
= $true )
| ( ( subset @ SV63 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1619,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY1253 @ SV65 ) @ omega )
| ~ ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 ) ) )
= $false )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1620,plain,
! [SV65: $i] :
( ( ( in @ ( setadjoin @ ( sK32_SY1253 @ SV65 ) @ ( sK32_SY1253 @ SV65 ) ) @ SV65 )
= $false )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1621,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( SV67 @ SV392 )
= $false )
| ( ( ~ ! [SY1763: $i] :
( ~ ( SV67 @ SY1763 )
| ( SV392 = SY1763 ) ) )
= $true )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1622,plain,
! [SV70: $i,SV230: $i] :
( ( ( ~ ~ ( ~ ( in @ SV230 @ ( sK39_SY1585 @ SV70 @ SV230 ) )
| ~ ( in @ ( sK39_SY1585 @ SV70 @ SV230 ) @ SV70 ) ) )
= $false )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1531]) ).
thf(1623,plain,
! [SV70: $i,SV430: $i,SV230: $i] :
( ( ( ~ ~ ( ~ ( in @ SV230 @ SV430 )
| ~ ( in @ SV430 @ SV70 ) ) )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1624,plain,
! [SV341: $i,SV232: $i,SV74: $i] :
( ( ( SV74 = SV232 )
= $false )
| ( ( in @ SV341 @ SV232 )
= $true )
| ( ( in @ SV341 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1625,plain,
! [SV77: $i] :
( ( ( in @ ( sK11_SY1274 @ SV77 )
@ ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1275: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1275 ) ) ) )
= $true )
| ( ( iskpair @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1626,plain,
! [SV77: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV77 )
@ ^ [SY1276: $i] :
( SV77
= ( kpair @ ( kfst @ SV77 ) @ SY1276 ) ) )
= ( setadjoin @ ( sK11_SY1274 @ SV77 ) @ emptyset ) )
= $true )
| ( ( iskpair @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1627,plain,
! [SV78: $i,SV234: $i,SV342: $i] :
( ( ( in @ SV342 @ SV234 )
= $true )
| ( ( ~ ( in @ SV342 @ SV78 ) )
= $true )
| ( ( in @ SV342 @ ( setminus @ SV78 @ SV234 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1628,plain,
! [SV86: $i,SV241: $i > $o] :
( ( ( ~ ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 )
| ~ ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) ) )
= $false )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1629,plain,
! [SV410: $i,SV244: $i > $o,SV89: $i] :
( ( ( ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV89 )
| ~ ~ ( SV244 @ SY1595 ) ) )
= $false )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1630,plain,
! [SV90: $i] :
( ( ( ~ ( in @ ( sK21_SY1296 @ SV90 ) @ SV90 ) )
= $false )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1631,plain,
! [SV90: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1540]) ).
thf(1632,plain,
! [SV94: $i,SV247: $i] :
( ( ( ~ ( in @ ( sK22_SY1599 @ SV247 @ SV94 ) @ SV94 ) )
= $false )
| ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1633,plain,
! [SV94: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ ( sK22_SY1599 @ SV247 @ SV94 ) ) )
= $false )
| ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1634,plain,
! [SV251: $i,SV411: $i,SV98: $i,SV394: $i] :
( ( ( ~ ( ~ ( in @ SV394 @ SV98 )
| ( in @ SV411 @ SV251 ) )
| ~ ( ~ ( in @ SV411 @ SV251 )
| ( in @ SV394 @ SV98 ) ) )
= $false )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1635,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ( SV351 = SV102 )
= $true )
| ( ( in @ SV351 @ SV254 )
= $true )
| ( ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1636,plain,
! [SV254: $i,SV102: $i,SV351: $i] :
( ( ( SV351 = SV102 )
= $false )
| ( ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1637,plain,
! [SV102: $i,SV254: $i,SV351: $i] :
( ( ( in @ SV351 @ SV254 )
= $false )
| ( ( in @ SV351 @ ( setadjoin @ SV102 @ SV254 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1638,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( SV103 @ SV395 )
= $false )
| ( ( ~ ! [SY1767: $i] :
( ~ ( SV103 @ SY1767 )
| ( SV395 = SY1767 ) ) )
= $true )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1639,plain,
! [SV104: $i,SV255: $i] :
( ( ( ~ ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV104 )
| ~ ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV255 ) )
= $false )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1640,plain,
! [SV352: $i,SV256: $i,SV105: $i] :
( ( ( subset @ SV105 @ SV256 )
= $false )
| ( ( in @ SV352 @ SV256 )
= $true )
| ( ( in @ SV352 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1641,plain,
! [SV106: $i,SV257: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SV106 )
| ~ ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SY1794 ) ) ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1642,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( SV107 @ SV396 )
= $false )
| ( ( ~ ! [SY1768: $i] :
( ~ ( SV107 @ SY1768 )
| ( SV396 = SY1768 ) ) )
= $true )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1643,plain,
! [SV108: $i,SV258: $i,SV354: $i] :
( ( ( in @ SV354 @ SV258 )
= $true )
| ( ( ~ ( in @ SV354 @ ( symdiff @ SV108 @ SV258 ) ) )
= $true )
| ( ( in @ SV354 @ SV108 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1644,plain,
! [SV109: $i,SV259: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV259 ) )
= $true )
| ( ( in @ SV427 @ SV109 )
= $true )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1645,plain,
! [SV259: $i,SV109: $i] :
( ( ( ~ ( in @ ( sK33_SY1614 @ SV109 @ SV259 ) @ SV259 ) )
= $false )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1646,plain,
! [SV259: $i,SV109: $i] :
( ( ( in @ ( sK33_SY1614 @ SV109 @ SV259 ) @ SV109 )
= $false )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1647,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( SV117 @ SV397 )
= $false )
| ( ( ~ ! [SY1769: $i] :
( ~ ( SV117 @ SY1769 )
| ( SV397 = SY1769 ) ) )
= $true )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1648,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV119 )
| ~ ( SV265 @ SY1729 )
| ( SY1729 = SV357 ) ) )
= $false )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1649,plain,
! [SV121: $i,SV267: $i] :
( ( ( ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV267 )
| ( in @ SY1626 @ SV121 ) ) )
= $false )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1650,plain,
! [SV267: $i,SV121: $i] :
( ( ( ~ ( in @ ( sK40_SY1626 @ SV121 @ SV267 ) @ SV267 )
| ( in @ ( sK40_SY1626 @ SV121 @ SV267 ) @ SV121 ) )
= $false )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV267 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1557]) ).
thf(1651,plain,
! [SV125: $i,SV398: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY1371 @ SV398 @ SV125 ) @ SV125 )
| ~ ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SY1795 @ SV125 ) ) ) )
= $true )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1652,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
| ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 ) ) )
= $true )
| ( ( ~ ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1653,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1654,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1655,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ~ ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1562]) ).
thf(1656,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ~ ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
| ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1562]) ).
thf(1657,plain,
! [SV130: $i,SV274: $i,SV400: $i > $o,SV412: $i > $o] :
( ( ( ~ ( in @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) @ SV130 )
| ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV274 )
| ( ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 )
!= SY1805 )
| ~ ( ~ ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
| ( SV412 @ SY1805 ) )
| ~ ( ~ ( SV412 @ SY1805 )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1563]) ).
thf(1658,plain,
! [SV132: $i] :
( ( ( in @ ( sK15_SY1396 @ SV132 )
@ ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1397: $i] : ( in @ ( setadjoin @ SY1397 @ emptyset ) @ SV132 ) ) )
= $true )
| ( ( iskpair @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1659,plain,
! [SV132: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV132 )
@ ^ [SY1398: $i] : ( in @ ( setadjoin @ SY1398 @ emptyset ) @ SV132 ) )
= ( setadjoin @ ( sK15_SY1396 @ SV132 ) @ emptyset ) )
= $true )
| ( ( iskpair @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1660,plain,
! [SV278: $i > $o,SV135: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV135 ) )
= $true )
| ( ( ~ ~ ( SV278 @ SV413 ) )
= $true )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1661,plain,
! [SV279: $i > $o,SV136: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV136 ) )
= $true )
| ( ( ~ ( SV279 @ SV414 ) )
= $true )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1662,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1663,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( ~ ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
| ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1664,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) ) )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1571]) ).
thf(1665,plain,
! [SV140: $i,SV283: $i] :
( ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) ) )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1571]) ).
thf(1666,plain,
! [SV141: $i] :
( ( ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1667,plain,
! [SV141: $i] :
( ( ~ ! [SY1740: $i,SY1741: $i] :
( ~ ~ ( ~ ( in @ SY1740 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1741 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1740 )
| ( in @ SX4 @ SY1741 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1741 )
| ( in @ SX4 @ SY1740 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1668,plain,
! [SV141: $i,SV428: $i] :
( ( ( ~ ~ ( ~ ! [SY1796: $i] :
( ~ ( in @ SY1796 @ SV428 )
| ( in @ SY1796 @ SV141 ) )
| ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1669,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1670,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1671,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1672,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
| ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1673,plain,
! [SV417: $o,SV288: $i,SV147: $i,SV365: $i] :
( ( ( SV365 != SV147 )
= $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| SV417 )
| SV417 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1674,plain,
! [SV147: $i,SV288: $i,SV365: $i,SV417: $o] :
( ( SV417 = $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| SV417 )
| SV417 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1675,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( SV365 != SV147 )
= $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $true )
| $true )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1676,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $true )
| $true )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1677,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( SV365 != SV147 )
= $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $false )
| $false )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1678,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $false )
| $false )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1580]) ).
thf(1679,plain,
! [SV389: $o,SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV153 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 )
| SV389 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1680,plain,
! [SV153: $i,SV294: $i,SV369: $i,SV389: $o] :
( ( SV389 = $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 )
| SV389 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1681,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV153 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $true )
| $true )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1682,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $true )
| $true )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1683,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV153 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $false )
| $false )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1584]) ).
thf(1684,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $false )
| $false )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1584]) ).
thf(1685,plain,
! [SV419: $i,SV296: $i > $o,SV155: $i] :
( ( ( ! [SY1679: $i] :
~ ~ ( ~ ( in @ SY1679 @ SV155 )
| ~ ~ ( SV296 @ SY1679 ) ) )
= $false )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1686,plain,
! [SV158: $i,SV401: $o,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( sK35_SY1781 @ SV401 @ SV158 @ SV301 ) ) )
= $false )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1687,plain,
! [SV301: $i,SV158: $i,SV401: $o] :
( ( ( ~ ( in @ ( sK35_SY1781 @ SV401 @ SV158 @ SV301 ) @ SV158 )
| SV401 )
= $false )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1688,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( sK36_SX0 @ SV158 @ SV301 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1689,plain,
! [SV301: $i,SV158: $i] :
( ( ( ~ ( in @ ( sK36_SX0 @ SV158 @ SV301 ) @ SV158 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1690,plain,
! [SV158: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( sK37_SX0 @ SV158 @ SV301 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1691,plain,
! [SV301: $i,SV158: $i] :
( ( ( ~ ( in @ ( sK37_SX0 @ SV158 @ SV301 ) @ SV158 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1692,plain,
! [SV302: $i > $o,SV159: $i,SV420: $i] :
( ( ( ~ ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SV420 @ emptyset ) )
= $true )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1693,plain,
! [SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ! [SY1806: $i] :
~ ( ~ ( ~ ( in @ SY1806 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1806 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1806 ) )
| ( in @ SY1806 @ ( sK42_SY1692 @ SV161 @ SV304 ) ) ) ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1591]) ).
thf(1694,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
| ~ ! [SY1803: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1803 )
| ( SV429 = SY1803 ) ) ) )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1695,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( SV167 @ SV403 )
= $false )
| ( ( ~ ! [SY1785: $i] :
( ~ ( SV167 @ SY1785 )
| ( SV403 = SY1785 ) ) )
= $true )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1696,plain,
! [SV170: $i,SV404: $i] :
( ( ( in @ SV404 @ SV170 )
= $false )
| ( ( SV170
!= ( setadjoin @ SV404 @ emptyset ) )
= $true )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1697,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( SV175 @ SV405 )
= $false )
| ( ( ~ ! [SY1786: $i] :
( ~ ( SV175 @ SY1786 )
| ( SV405 = SY1786 ) ) )
= $true )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1698,plain,
! [SV316: $i,SV426: $i,SV176: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ SV176 ) )
= $true )
| ( ( in @ SV426 @ SV316 )
= $true )
| ( ( SV406 = SV426 )
= $false )
| ( ( SV176 = SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1699,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1700,plain,
! [SV407: $o,SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1701,plain,
! [SV197: $i,SV32: $i,SV318: $i,SV407: $o] :
( ( SV407 = $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1702,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1703,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1606]) ).
thf(1704,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1606]) ).
thf(1705,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1706,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1608]) ).
thf(1707,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1608]) ).
thf(1708,plain,
! [SV41: $i,SV206: $i > $o] :
( ( ( ~ ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 ) )
= $false )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1709,plain,
! [SV41: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) ) )
= $false )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1710,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( ! [SY1761: $i] :
( ~ ( SV46 @ SY1761 )
| ( SV390 = SY1761 ) ) )
= $false )
| ( ( SV46 @ SV390 )
= $false )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1711,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
| ~ ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
| ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) ) )
= $false )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1611]) ).
thf(1712,plain,
! [SV213: $i > $o,SV51: $i,SV431: $i] :
( ( ( ~ ~ ( ~ ( in @ SV431 @ SV51 )
| ~ ( SV213 @ SV431 ) ) )
= $true )
| ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1713,plain,
! [SV213: $i > $o,SV51: $i,SV432: $i] :
( ( ( ~ ~ ( ~ ( in @ SV432 @ SV51 )
| ~ ( SV213 @ SV432 ) ) )
= $true )
| ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1714,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1715,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1614]) ).
thf(1716,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
| ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) ) )
= $false )
| ( ( ~ ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1717,plain,
! [SV224: $i > $o,SV62: $i,SV336: $i] :
( ( ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1578: $i] : ( SV224 @ SY1578 ) ) )
= $false )
| ( ( SV224 @ SV336 )
= $true )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1718,plain,
! [SV62: $i,SV336: $i,SV224: $i > $o] :
( ( ( SV224 @ SV336 )
= $false )
| ( ( in @ SV336
@ ( dsetconstr @ SV62
@ ^ [SY1579: $i] : ( SV224 @ SY1579 ) ) )
= $true )
| ( ( in @ SV336 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1719,plain,
! [SV65: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_SY1253 @ SV65 ) @ omega )
| ~ ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 ) ) )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1720,plain,
! [SV65: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ omega )
| ( in @ SV433 @ SV65 ) )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( setadjoin @ ( sK32_SY1253 @ SV65 ) @ ( sK32_SY1253 @ SV65 ) ) @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1721,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ! [SY1763: $i] :
( ~ ( SV67 @ SY1763 )
| ( SV392 = SY1763 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1722,plain,
! [SV70: $i,SV230: $i] :
( ( ( ~ ( ~ ( in @ SV230 @ ( sK39_SY1585 @ SV70 @ SV230 ) )
| ~ ( in @ ( sK39_SY1585 @ SV70 @ SV230 ) @ SV70 ) ) )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1723,plain,
! [SV70: $i,SV430: $i,SV230: $i] :
( ( ( ~ ( ~ ( in @ SV230 @ SV430 )
| ~ ( in @ SV430 @ SV70 ) ) )
= $false )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1724,plain,
! [SV234: $i,SV78: $i,SV342: $i] :
( ( ( in @ SV342 @ SV78 )
= $false )
| ( ( in @ SV342 @ SV234 )
= $true )
| ( ( in @ SV342 @ ( setminus @ SV78 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1725,plain,
! [SV86: $i,SV241: $i > $o] :
( ( ( ~ ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 ) )
= $false )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1726,plain,
! [SV86: $i,SV241: $i > $o] :
( ( ( ~ ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) ) )
= $false )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1727,plain,
! [SV89: $i,SV244: $i > $o,SV410: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) @ SV89 )
| ~ ~ ( SV244 @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) ) ) )
= $false )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1629]) ).
thf(1728,plain,
! [SV90: $i] :
( ( ( in @ ( sK21_SY1296 @ SV90 ) @ SV90 )
= $true )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1729,plain,
! [SV90: $i] :
( ( $true = $true )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1730,plain,
! [SV94: $i,SV247: $i] :
( ( ( in @ ( sK22_SY1599 @ SV247 @ SV94 ) @ SV94 )
= $true )
| ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1731,plain,
! [SV94: $i,SV247: $i] :
( ( ( in @ SV247 @ ( sK22_SY1599 @ SV247 @ SV94 ) )
= $true )
| ( ( in @ SV247 @ ( setunion @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1732,plain,
! [SV251: $i,SV411: $i,SV98: $i,SV394: $i] :
( ( ( ~ ( ~ ( in @ SV394 @ SV98 )
| ( in @ SV411 @ SV251 ) ) )
= $false )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1733,plain,
! [SV98: $i,SV394: $i,SV251: $i,SV411: $i] :
( ( ( ~ ( ~ ( in @ SV411 @ SV251 )
| ( in @ SV394 @ SV98 ) ) )
= $false )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1734,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ! [SY1767: $i] :
( ~ ( SV103 @ SY1767 )
| ( SV395 = SY1767 ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1735,plain,
! [SV104: $i,SV255: $i] :
( ( ( ~ ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV104 ) )
= $false )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1736,plain,
! [SV104: $i,SV255: $i] :
( ( ( ~ ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV255 ) )
= $false )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1737,plain,
! [SV106: $i,SV257: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SV106 ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1738,plain,
! [SV106: $i,SV353: $i,SV257: $i] :
( ( ( ~ ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SY1794 ) ) ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1739,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( ! [SY1768: $i] :
( ~ ( SV107 @ SY1768 )
| ( SV396 = SY1768 ) ) )
= $false )
| ( ( SV107 @ SV396 )
= $false )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1740,plain,
! [SV258: $i,SV108: $i,SV354: $i] :
( ( ( in @ SV354 @ ( symdiff @ SV108 @ SV258 ) )
= $false )
| ( ( in @ SV354 @ SV258 )
= $true )
| ( ( in @ SV354 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1741,plain,
! [SV109: $i,SV259: $i,SV427: $i] :
( ( ( in @ SV427 @ SV259 )
= $false )
| ( ( in @ SV427 @ SV109 )
= $true )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1742,plain,
! [SV259: $i,SV109: $i] :
( ( ( in @ ( sK33_SY1614 @ SV109 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV259 @ ( powerset @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1743,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ! [SY1769: $i] :
( ~ ( SV117 @ SY1769 )
| ( SV397 = SY1769 ) ) )
= $false )
| ( ( SV117 @ SV397 )
= $false )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1744,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
| ~ ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
| ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 ) )
= $false )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1648]) ).
thf(1745,plain,
! [SV267: $i,SV121: $i] :
( ( ( ~ ( in @ ( sK46_SY1626 @ SV121 @ SV267 ) @ SV267 )
| ( in @ ( sK46_SY1626 @ SV121 @ SV267 ) @ SV121 ) )
= $false )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1649]) ).
thf(1746,plain,
! [SV267: $i,SV121: $i] :
( ( ( ~ ( in @ ( sK40_SY1626 @ SV121 @ SV267 ) @ SV267 ) )
= $false )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1747,plain,
! [SV267: $i,SV121: $i] :
( ( ( in @ ( sK40_SY1626 @ SV121 @ SV267 ) @ SV121 )
= $false )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV267 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1748,plain,
! [SV125: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK34_SY1371 @ SV398 @ SV125 ) @ SV125 )
| ~ ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SY1795 @ SV125 ) ) )
= $false )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1749,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
| ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 ) )
= $false )
| ( ( ~ ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1750,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1751,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1752,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1753,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ~ ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1754,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1755,plain,
! [SV130: $i,SV274: $i,SV400: $i > $o,SV412: $i > $o] :
( ( ( ~ ( in @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) @ SV130 ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1756,plain,
! [SV130: $i,SV400: $i > $o,SV412: $i > $o,SV274: $i] :
( ( ( ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV274 )
| ( ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 )
!= SY1805 )
| ~ ( ~ ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
| ( SV412 @ SY1805 ) )
| ~ ( ~ ( SV412 @ SY1805 )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1757,plain,
! [SV278: $i > $o,SV135: $i,SV413: $i] :
( ( ( in @ SV413 @ SV135 )
= $false )
| ( ( ~ ~ ( SV278 @ SV413 ) )
= $true )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1758,plain,
! [SV279: $i > $o,SV136: $i,SV414: $i] :
( ( ( in @ SV414 @ SV136 )
= $false )
| ( ( ~ ( SV279 @ SV414 ) )
= $true )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1759,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1760,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
| ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) ) )
= $false )
| ( ( ~ ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1761,plain,
! [SV140: $i,SV283: $i] :
( ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) ) )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1762,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) )
= $false )
| ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
= $false )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1763,plain,
! [SV141: $i] :
( ( ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1764,plain,
! [SV141: $i] :
( ( ! [SY1740: $i,SY1741: $i] :
( ~ ~ ( ~ ( in @ SY1740 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1741 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1740 )
| ( in @ SX4 @ SY1741 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1741 )
| ( in @ SX4 @ SY1740 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1765,plain,
! [SV141: $i,SV428: $i] :
( ( ( ~ ( ~ ! [SY1796: $i] :
( ~ ( in @ SY1796 @ SV428 )
| ( in @ SY1796 @ SV141 ) )
| ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) ) )
= $false )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1766,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1767,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1768,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1769,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(1770,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(1771,plain,
! [SV417: $o,SV288: $i,SV147: $i,SV365: $i] :
( ( ( SV365 = SV147 )
= $true )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| SV417 )
| SV417 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1772,plain,
! [SV147: $i,SV417: $o,SV288: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| SV417 ) )
= $true )
| ( SV417 = $true )
| ( SV417 = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1773,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( SV365 = SV147 )
= $true )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $true )
| $true )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1774,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1775,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( ( SV365 = SV147 )
= $true )
| ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $false )
| $false )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1776,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1777,plain,
! [SV389: $o,SV294: $i,SV153: $i,SV369: $i] :
( ( ( in @ SV369 @ SV153 )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 )
| SV389 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1778,plain,
! [SV153: $i,SV389: $o,SV294: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 ) )
= $true )
| ( SV389 = $true )
| ( SV389 = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1779,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( in @ SV369 @ SV153 )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $true )
| $true )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1780,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1781,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( ( in @ SV369 @ SV153 )
= $true )
| ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $false )
| $false )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1683]) ).
thf(1782,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1783,plain,
! [SV155: $i,SV296: $i > $o,SV419: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) @ SV155 )
| ~ ~ ( SV296 @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) ) ) )
= $false )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1685]) ).
thf(1784,plain,
! [SV158: $i,SV401: $o,SV301: $i] :
( ( ( in @ SV301 @ ( sK35_SY1781 @ SV401 @ SV158 @ SV301 ) )
= $true )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1785,plain,
! [SV301: $i,SV158: $i,SV401: $o] :
( ( ( ~ ( in @ ( sK35_SY1781 @ SV401 @ SV158 @ SV301 ) @ SV158 ) )
= $false )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1786,plain,
! [SV158: $i,SV301: $i,SV401: $o] :
( ( SV401 = $false )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1787,plain,
! [SV158: $i,SV301: $i] :
( ( ( in @ SV301 @ ( sK36_SX0 @ SV158 @ SV301 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1788,plain,
! [SV301: $i,SV158: $i] :
( ( ( ~ ( in @ ( sK36_SX0 @ SV158 @ SV301 ) @ SV158 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1789,plain,
! [SV158: $i,SV301: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1790,plain,
! [SV158: $i,SV301: $i] :
( ( ( in @ SV301 @ ( sK37_SX0 @ SV158 @ SV301 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1791,plain,
! [SV301: $i,SV158: $i] :
( ( ( ~ ( in @ ( sK37_SX0 @ SV158 @ SV301 ) @ SV158 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1792,plain,
! [SV158: $i,SV301: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1793,plain,
! [SV302: $i > $o,SV159: $i,SV420: $i] :
( ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
!= ( setadjoin @ SV420 @ emptyset ) )
= $true )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1794,plain,
! [SV304: $i,SV161: $i > $i > $o] :
( ( ( ! [SY1806: $i] :
~ ( ~ ( ~ ( in @ SY1806 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1806 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1806 ) )
| ( in @ SY1806 @ ( sK42_SY1692 @ SV161 @ SV304 ) ) ) ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1795,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
| ~ ! [SY1803: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1803 )
| ( SV429 = SY1803 ) ) )
= $true )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1796,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ! [SY1785: $i] :
( ~ ( SV167 @ SY1785 )
| ( SV403 = SY1785 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1797,plain,
! [SV404: $i,SV170: $i] :
( ( ( SV170
= ( setadjoin @ SV404 @ emptyset ) )
= $false )
| ( ( in @ SV404 @ SV170 )
= $false )
| ( ( in @ ( setunion @ SV170 ) @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1798,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( ! [SY1786: $i] :
( ~ ( SV175 @ SY1786 )
| ( SV405 = SY1786 ) ) )
= $false )
| ( ( SV175 @ SV405 )
= $false )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1799,plain,
! [SV316: $i,SV426: $i,SV176: $i,SV406: $i] :
( ( ( in @ SV406 @ SV176 )
= $false )
| ( ( in @ SV426 @ SV316 )
= $true )
| ( ( SV406 = SV426 )
= $false )
| ( ( SV176 = SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1800,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 ) )
= $true )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1801,plain,
! [SV407: $o,SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1802,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 ) )
= $true )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1803,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1804,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1805,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1806,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1807,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1808,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1809,plain,
! [SV41: $i,SV206: $i > $o] :
( ( ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 )
= $true )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1810,plain,
! [SV41: $i,SV206: $i > $o] :
( ( ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) )
= $true )
| ( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV41 )
| ~ ( SV206 @ SY1546 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1811,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) )
| ( SV390
= ( sK48_SY1761 @ SV390 @ SV46 ) ) )
= $false )
| ( ( SV46 @ SV390 )
= $false )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1710]) ).
thf(1812,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) ) )
= $false )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1813,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
| ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) ) )
= $false )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1814,plain,
! [SV213: $i > $o,SV51: $i,SV431: $i] :
( ( ( ~ ( ~ ( in @ SV431 @ SV51 )
| ~ ( SV213 @ SV431 ) ) )
= $false )
| ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1815,plain,
! [SV213: $i > $o,SV51: $i,SV432: $i] :
( ( ( ~ ( ~ ( in @ SV432 @ SV51 )
| ~ ( SV213 @ SV432 ) ) )
= $false )
| ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1816,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1817,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1818,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) )
= $false )
| ( ( ~ ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1716]) ).
thf(1819,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1716]) ).
thf(1820,plain,
! [SV65: $i] :
( ( ( ~ ( in @ ( sK32_SY1253 @ SV65 ) @ omega )
| ~ ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 ) )
= $false )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1821,plain,
! [SV65: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ omega ) )
= $true )
| ( ( in @ SV433 @ SV65 )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( setadjoin @ ( sK32_SY1253 @ SV65 ) @ ( sK32_SY1253 @ SV65 ) ) @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1822,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
| ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1721]) ).
thf(1823,plain,
! [SV70: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ ( sK39_SY1585 @ SV70 @ SV230 ) )
| ~ ( in @ ( sK39_SY1585 @ SV70 @ SV230 ) @ SV70 ) )
= $false )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1824,plain,
! [SV70: $i,SV430: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV430 )
| ~ ( in @ SV430 @ SV70 ) )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1825,plain,
! [SV86: $i,SV241: $i > $o] :
( ( ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 )
= $true )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1826,plain,
! [SV86: $i,SV241: $i > $o] :
( ( ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) )
= $true )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV86 )
| ~ ( SV241 @ SY1592 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1827,plain,
! [SV89: $i,SV244: $i > $o,SV410: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) @ SV89 )
| ~ ~ ( SV244 @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) ) ) )
= $true )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1828,plain,
! [SV251: $i,SV411: $i,SV98: $i,SV394: $i] :
( ( ( ~ ( in @ SV394 @ SV98 )
| ( in @ SV411 @ SV251 ) )
= $true )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1732]) ).
thf(1829,plain,
! [SV98: $i,SV394: $i,SV251: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ SV251 )
| ( in @ SV394 @ SV98 ) )
= $true )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1733]) ).
thf(1830,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
| ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1734]) ).
thf(1831,plain,
! [SV104: $i,SV255: $i] :
( ( ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV104 )
= $true )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1832,plain,
! [SV104: $i,SV255: $i] :
( ( ( in @ ( sK27_SY1607 @ SV255 @ SV104 ) @ SV255 )
= $true )
| ( ( ( binintersect @ SV104 @ SV255 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1833,plain,
! [SV106: $i,SV257: $i,SV353: $i] :
( ( ( in @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SV106 )
= $true )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1834,plain,
! [SV106: $i,SV353: $i,SV257: $i] :
( ( ( ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SY1794 ) ) ) )
= $true )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1738]) ).
thf(1835,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) )
| ( SV396
= ( sK51_SY1768 @ SV396 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV396 )
= $false )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1739]) ).
thf(1836,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ ( sK52_SY1769 @ SV397 @ SV117 ) )
| ( SV397
= ( sK52_SY1769 @ SV397 @ SV117 ) ) )
= $false )
| ( ( SV117 @ SV397 )
= $false )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1743]) ).
thf(1837,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 ) )
= $false )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1744]) ).
thf(1838,plain,
! [SV119: $i,SV357: $i,SV265: $i > $o] :
( ( ( ~ ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
| ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 ) )
= $false )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1744]) ).
thf(1839,plain,
! [SV267: $i,SV121: $i] :
( ( ( ~ ( in @ ( sK46_SY1626 @ SV121 @ SV267 ) @ SV267 ) )
= $false )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1840,plain,
! [SV267: $i,SV121: $i] :
( ( ( in @ ( sK46_SY1626 @ SV121 @ SV267 ) @ SV121 )
= $false )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1841,plain,
! [SV267: $i,SV121: $i] :
( ( ( in @ ( sK40_SY1626 @ SV121 @ SV267 ) @ SV267 )
= $true )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV267 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1842,plain,
! [SV125: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK34_SY1371 @ SV398 @ SV125 ) @ SV125 ) )
= $false )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1843,plain,
! [SV125: $i,SV398: $i] :
( ( ( ~ ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SY1795 @ SV125 ) ) )
= $false )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1844,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) )
= $false )
| ( ( ~ ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1845,plain,
! [SV126: $i > $o,SV399: $i] :
( ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ~ ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1846,plain,
! [SV271: $i > $o,SV127: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ( in @ SV434 @ SV127 )
| ~ ( SV271 @ SV434 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1847,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1848,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1849,plain,
! [SV127: $i,SV271: $i > $o] :
( ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true )
| ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1850,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1851,plain,
! [SV130: $i,SV274: $i,SV400: $i > $o,SV412: $i > $o] :
( ( ( in @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) @ SV130 )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1755]) ).
thf(1852,plain,
! [SV274: $i,SV412: $i > $o,SV400: $i > $o,SV130: $i] :
( ( ( ~ ( in @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) @ SV274 )
| ( ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 )
!= ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ~ ( ~ ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
| ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) ) )
| ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1756]) ).
thf(1853,plain,
! [SV135: $i,SV413: $i,SV278: $i > $o] :
( ( ( ~ ( SV278 @ SV413 ) )
= $false )
| ( ( in @ SV413 @ SV135 )
= $false )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1854,plain,
! [SV136: $i,SV414: $i,SV279: $i > $o] :
( ( ( SV279 @ SV414 )
= $false )
| ( ( in @ SV414 @ SV136 )
= $false )
| ( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1855,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1856,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) )
= $false )
| ( ( ~ ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1857,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( ~ ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1858,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
| ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 ) )
= $false )
| ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1859,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 ) )
= $false )
| ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
= $false )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1762]) ).
thf(1860,plain,
! [SV140: $i,SV283: $i] :
( ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
= $false )
| ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
= $false )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1762]) ).
thf(1861,plain,
! [SV141: $i] :
( ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) )
| ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1862,plain,
! [SV141: $i,SV435: $i] :
( ( ! [SY1809: $i] :
( ~ ~ ( ~ ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1809 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SY1810: $i] :
( ~ ( in @ SY1810 @ SV435 )
| ( in @ SY1810 @ SY1809 ) )
| ! [SY1811: $i] :
( ~ ( in @ SY1811 @ SY1809 )
| ( in @ SY1811 @ SV435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(1863,plain,
! [SV141: $i,SV428: $i] :
( ( ( ~ ! [SY1796: $i] :
( ~ ( in @ SY1796 @ SV428 )
| ( in @ SY1796 @ SV141 ) )
| ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1864,plain,
! [SV287: $i > $o,SV146: $i,SV436: $i] :
( ( ( ~ ~ ( ~ ( in @ SV436 @ SV146 )
| ~ ( SV287 @ SV436 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(1865,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1866,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1867,plain,
! [SV146: $i,SV287: $i > $o] :
( ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true )
| ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) )
| ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1868,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1869,plain,
! [SV147: $i,SV417: $o,SV288: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| SV417 ) )
= $true )
| ( SV417 = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1870,plain,
! [SV147: $i,SV417: $o,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 )
| SV417 )
= $false )
| ( SV417 = $true )
| ( SV417 = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1871,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1872,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1873,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( ~ ( in @ SV365 @ SV288 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1874,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1875,plain,
! [SV153: $i,SV389: $o,SV294: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| SV389 ) )
= $true )
| ( SV389 = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1876,plain,
! [SV153: $i,SV389: $o,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 )
| SV389 )
= $false )
| ( SV389 = $true )
| ( SV389 = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1877,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1878,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1879,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV294 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(1880,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1881,plain,
! [SV155: $i,SV296: $i > $o,SV419: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) @ SV155 )
| ~ ~ ( SV296 @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) ) ) )
= $true )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1783]) ).
thf(1882,plain,
! [SV301: $i,SV158: $i,SV401: $o] :
( ( ( in @ ( sK35_SY1781 @ SV401 @ SV158 @ SV301 ) @ SV158 )
= $true )
| ( SV401 = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1883,plain,
! [SV301: $i,SV158: $i] :
( ( ( in @ ( sK36_SX0 @ SV158 @ SV301 ) @ SV158 )
= $true )
| ( $true = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1884,plain,
! [SV301: $i,SV158: $i] :
( ( ( in @ ( sK37_SX0 @ SV158 @ SV301 ) @ SV158 )
= $true )
| ( $false = $true )
| ( ( in @ SV301 @ ( setunion @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1885,plain,
! [SV420: $i,SV302: $i > $o,SV159: $i] :
( ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ~ ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1886,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
| ~ ! [SY1812: $i] :
~ ~ ( ~ ( in @ SY1812 @ SV304 )
| ~ ( SV161 @ SY1812 @ SV437 ) ) )
| ~ ( ~ ~ ! [SY1813: $i] :
~ ~ ( ~ ( in @ SY1813 @ SV304 )
| ~ ( SV161 @ SY1813 @ SV437 ) )
| ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) ) ) ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(1887,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 ) )
= $true )
| ( ( ~ ! [SY1803: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1803 )
| ( SV429 = SY1803 ) ) )
= $true )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(1888,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
| ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1796]) ).
thf(1889,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ ( sK55_SY1786 @ SV405 @ SV175 ) )
| ( SV405
= ( sK55_SY1786 @ SV405 @ SV175 ) ) )
= $false )
| ( ( SV175 @ SV405 )
= $false )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1798]) ).
thf(1890,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1891,plain,
! [SV407: $o,SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
| SV407 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1892,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
= $false )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1893,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1894,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
| $true )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1895,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1896,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1897,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
| $false )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1898,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1899,plain,
! [SV206: $i > $o,SV41: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV41 )
| ~ ( SV206 @ SV438 ) )
= $true )
| ( ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(1900,plain,
! [SV206: $i > $o,SV41: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ SV41 )
| ~ ( SV206 @ SV439 ) )
= $true )
| ( ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(1901,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) ) )
= $false )
| ( ( SV46 @ SV390 )
= $false )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1902,plain,
! [SV46: $i > $o,SV390: $i] :
( ( ( SV390
= ( sK48_SY1761 @ SV390 @ SV46 ) )
= $false )
| ( ( SV46 @ SV390 )
= $false )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1903,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1904,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) ) )
= $false )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1813]) ).
thf(1905,plain,
! [SV49: $i > $o,SV391: $i] :
( ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1813]) ).
thf(1906,plain,
! [SV213: $i > $o,SV51: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV51 )
| ~ ( SV213 @ SV431 ) )
= $true )
| ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1907,plain,
! [SV213: $i > $o,SV51: $i,SV432: $i] :
( ( ( ~ ( in @ SV432 @ SV51 )
| ~ ( SV213 @ SV432 ) )
= $true )
| ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1908,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1909,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(1910,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( ~ ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1911,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1912,plain,
! [SV65: $i] :
( ( ( ~ ( in @ ( sK32_SY1253 @ SV65 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1820]) ).
thf(1913,plain,
! [SV65: $i] :
( ( ( ~ ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 ) )
= $false )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1820]) ).
thf(1914,plain,
! [SV65: $i,SV433: $i] :
( ( ( in @ SV433 @ omega )
= $false )
| ( ( in @ SV433 @ SV65 )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( setadjoin @ ( sK32_SY1253 @ SV65 ) @ ( sK32_SY1253 @ SV65 ) ) @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1915,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1822]) ).
thf(1916,plain,
! [SV67: $i > $o,SV392: $i] :
( ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1822]) ).
thf(1917,plain,
! [SV70: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ ( sK39_SY1585 @ SV70 @ SV230 ) ) )
= $false )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1918,plain,
! [SV230: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK39_SY1585 @ SV70 @ SV230 ) @ SV70 ) )
= $false )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1919,plain,
! [SV70: $i,SV430: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV430 ) )
= $true )
| ( ( ~ ( in @ SV430 @ SV70 ) )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(1920,plain,
! [SV241: $i > $o,SV86: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV86 )
| ~ ( SV241 @ SV440 ) )
= $true )
| ( ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(1921,plain,
! [SV241: $i > $o,SV86: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ SV86 )
| ~ ( SV241 @ SV441 ) )
= $true )
| ( ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(1922,plain,
! [SV89: $i,SV244: $i > $o,SV410: $i] :
( ( ( ~ ( in @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) @ SV89 )
| ~ ~ ( SV244 @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) ) )
= $false )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1923,plain,
! [SV251: $i,SV411: $i,SV98: $i,SV394: $i] :
( ( ( ~ ( in @ SV394 @ SV98 ) )
= $true )
| ( ( in @ SV411 @ SV251 )
= $true )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1924,plain,
! [SV98: $i,SV394: $i,SV251: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ SV251 ) )
= $true )
| ( ( in @ SV394 @ SV98 )
= $true )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1925,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1926,plain,
! [SV103: $i > $o,SV395: $i] :
( ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1830]) ).
thf(1927,plain,
! [SV106: $i,SV353: $i,SV257: $i] :
( ( ( ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ SY1794 ) ) ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1928,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV396 )
= $false )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1929,plain,
! [SV107: $i > $o,SV396: $i] :
( ( ( SV396
= ( sK51_SY1768 @ SV396 @ SV107 ) )
= $false )
| ( ( SV107 @ SV396 )
= $false )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1930,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ ( sK52_SY1769 @ SV397 @ SV117 ) ) )
= $false )
| ( ( SV117 @ SV397 )
= $false )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1931,plain,
! [SV117: $i > $o,SV397: $i] :
( ( ( SV397
= ( sK52_SY1769 @ SV397 @ SV117 ) )
= $false )
| ( ( SV117 @ SV397 )
= $false )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1932,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1933,plain,
! [SV119: $i,SV357: $i,SV265: $i > $o] :
( ( ( ~ ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) ) )
= $false )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1934,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1935,plain,
! [SV267: $i,SV121: $i] :
( ( ( in @ ( sK46_SY1626 @ SV121 @ SV267 ) @ SV267 )
= $true )
| ( ( SV121 = SV267 )
= $true )
| ( ( in @ ( sK13_SY1625 @ SV267 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1936,plain,
! [SV125: $i,SV398: $i] :
( ( ( in @ ( sK34_SY1371 @ SV398 @ SV125 ) @ SV125 )
= $true )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(1937,plain,
! [SV125: $i,SV398: $i] :
( ( ( ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SY1795 @ SV125 ) ) )
= $true )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1843]) ).
thf(1938,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ~ ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(1939,plain,
! [SV126: $i > $o,SV399: $i] :
( ( ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1940,plain,
! [SV271: $i > $o,SV127: $i,SV434: $i] :
( ( ( ~ ( ~ ( in @ SV434 @ SV127 )
| ~ ( SV271 @ SV434 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1941,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1847]) ).
thf(1942,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(1943,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(1944,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1945,plain,
! [SV274: $i,SV412: $i > $o,SV400: $i > $o,SV130: $i] :
( ( ( ~ ( in @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) @ SV274 ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(1946,plain,
! [SV130: $i,SV274: $i,SV400: $i > $o,SV412: $i > $o] :
( ( ( ( ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 )
!= ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ~ ( ~ ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
| ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) ) )
| ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(1947,plain,
! [SV135: $i,SV413: $i,SV278: $i > $o] :
( ( ( SV278 @ SV413 )
= $true )
| ( ( in @ SV413 @ SV135 )
= $false )
| ( ( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1948,plain,
! [SV414: $i,SV279: $i > $o,SV136: $i] :
( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV414 @ SV136 )
= $false )
| ( ( SV279 @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(1949,plain,
! [SV282: $i > $o,SV442: $i,SV139: $i > $o] :
( ( ( ~ ~ ( ~ ( SV139 @ SV442 )
| ~ ! [SY1814: $i] :
( ~ ( SV139 @ SY1814 )
| ( SV442 = SY1814 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(1950,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( ~ ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1951,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1952,plain,
! [SV140: $i,SV283: $i] :
( ( ( ~ ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 ) )
= $false )
| ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1953,plain,
! [SV140: $i,SV283: $i] :
( ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
= $false )
| ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1954,plain,
! [SV140: $i,SV283: $i] :
( ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
= $true )
| ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
= $false )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(1955,plain,
! [SV141: $i] :
( ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1861]) ).
thf(1956,plain,
! [SV141: $i] :
( ( ~ ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1861]) ).
thf(1957,plain,
! [SV443: $i,SV141: $i,SV435: $i] :
( ( ~ ~ ( ~ ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) ) )
| ! [SY1815: $i] :
( ~ ( in @ SY1815 @ SV435 )
| ( in @ SY1815 @ SV443 ) )
| ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1958,plain,
! [SV141: $i,SV428: $i] :
( ( ( ~ ! [SY1796: $i] :
( ~ ( in @ SY1796 @ SV428 )
| ( in @ SY1796 @ SV141 ) ) )
= $true )
| ( ( ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(1959,plain,
! [SV287: $i > $o,SV146: $i,SV436: $i] :
( ( ( ~ ( ~ ( in @ SV436 @ SV146 )
| ~ ( SV287 @ SV436 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(1960,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(1961,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1962,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(1963,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1964,plain,
! [SV147: $i,SV417: $o,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 )
| SV417 )
= $false )
| ( SV417 = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1965,plain,
! [SV147: $i,SV417: $o,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 ) )
= $false )
| ( SV417 = $true )
| ( SV417 = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1966,plain,
! [SV288: $i,SV147: $i,SV365: $i,SV417: $o] :
( ( SV417 = $false )
| ( SV417 = $true )
| ( SV417 = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1967,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1968,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1969,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1970,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1971,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1972,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1973,plain,
! [SV153: $i,SV389: $o,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 )
| SV389 )
= $false )
| ( SV389 = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(1974,plain,
! [SV153: $i,SV389: $o,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 ) )
= $false )
| ( SV389 = $true )
| ( SV389 = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1975,plain,
! [SV294: $i,SV153: $i,SV369: $i,SV389: $o] :
( ( SV389 = $false )
| ( SV389 = $true )
| ( SV389 = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1976,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(1977,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1878]) ).
thf(1978,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1878]) ).
thf(1979,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1980,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(1981,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(1982,plain,
! [SV155: $i,SV296: $i > $o,SV419: $i] :
( ( ( ~ ( in @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) @ SV155 )
| ~ ~ ( SV296 @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) ) )
= $false )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(1983,plain,
! [SV420: $i,SV302: $i > $o,SV159: $i] :
( ( ( ! [SY1686: $i] :
~ ~ ( ~ ( in @ SY1686 @ SV159 )
| ~ ( SV302 @ SY1686 ) ) )
= $false )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1984,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ( ~ ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
| ~ ! [SY1812: $i] :
~ ~ ( ~ ( in @ SY1812 @ SV304 )
| ~ ( SV161 @ SY1812 @ SV437 ) ) )
| ~ ( ~ ~ ! [SY1813: $i] :
~ ~ ( ~ ( in @ SY1813 @ SV304 )
| ~ ( SV161 @ SY1813 @ SV437 ) )
| ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(1985,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( ~ ! [SY1803: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1803 )
| ( SV429 = SY1803 ) ) )
= $true )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1986,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(1987,plain,
! [SV167: $i > $o,SV403: $i] :
( ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(1988,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ ( sK55_SY1786 @ SV405 @ SV175 ) ) )
= $false )
| ( ( SV175 @ SV405 )
= $false )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1889]) ).
thf(1989,plain,
! [SV175: $i > $o,SV405: $i] :
( ( ( SV405
= ( sK55_SY1786 @ SV405 @ SV175 ) )
= $false )
| ( ( SV175 @ SV405 )
= $false )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1889]) ).
thf(1990,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1991,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| SV407 )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1992,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 ) )
= $true )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(1993,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1994,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| SV407 )
= $false )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(1995,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1893]) ).
thf(1996,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1893]) ).
thf(1997,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(1998,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(1999,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(2000,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2001,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2002,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2003,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(2004,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(2005,plain,
! [SV206: $i > $o,SV41: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV41 ) )
= $true )
| ( ( ~ ( SV206 @ SV438 ) )
= $true )
| ( ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2006,plain,
! [SV206: $i > $o,SV41: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ SV41 ) )
= $true )
| ( ( ~ ( SV206 @ SV439 ) )
= $true )
| ( ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2007,plain,
! [SV390: $i,SV46: $i > $o] :
( ( ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( ! [SY1199: $i,SY1200: $i] :
( ~ ( SV46 @ SY1199 )
| ~ ( SV46 @ SY1200 )
| ( SY1199 = SY1200 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(2008,plain,
! [SV390: $i,SV444: $i,SV46: $i > $o] :
( ( ( ! [SY1817: $i] :
( ~ ( SV46 @ SV444 )
| ~ ( SV46 @ SY1817 )
| ( SV444 = SY1817 ) ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV390
= ( sK48_SY1761 @ SV390 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2009,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $false )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2010,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( ~ ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(2011,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $false )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(2012,plain,
! [SV213: $i > $o,SV51: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV51 ) )
= $true )
| ( ( ~ ( SV213 @ SV431 ) )
= $true )
| ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2013,plain,
! [SV213: $i > $o,SV51: $i,SV432: $i] :
( ( ( ~ ( in @ SV432 @ SV51 ) )
= $true )
| ( ( ~ ( SV213 @ SV432 ) )
= $true )
| ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2014,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2015,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2016,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
| ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(2017,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1911]) ).
thf(2018,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1911]) ).
thf(2019,plain,
! [SV65: $i] :
( ( ( in @ ( sK32_SY1253 @ SV65 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(2020,plain,
! [SV65: $i] :
( ( ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( ! [SY1254: $i] :
( ~ ( in @ SY1254 @ omega )
| ( in @ SY1254 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(2021,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( ~ ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(2022,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2023,plain,
! [SV70: $i,SV230: $i] :
( ( ( in @ SV230 @ ( sK39_SY1585 @ SV70 @ SV230 ) )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(2024,plain,
! [SV230: $i,SV70: $i] :
( ( ( in @ ( sK39_SY1585 @ SV70 @ SV230 ) @ SV70 )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(2025,plain,
! [SV70: $i,SV430: $i,SV230: $i] :
( ( ( in @ SV230 @ SV430 )
= $false )
| ( ( ~ ( in @ SV430 @ SV70 ) )
= $true )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2026,plain,
! [SV241: $i > $o,SV86: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ SV86 ) )
= $true )
| ( ( ~ ( SV241 @ SV440 ) )
= $true )
| ( ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(2027,plain,
! [SV241: $i > $o,SV86: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ SV86 ) )
= $true )
| ( ( ~ ( SV241 @ SV441 ) )
= $true )
| ( ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1921]) ).
thf(2028,plain,
! [SV89: $i,SV244: $i > $o,SV410: $i] :
( ( ( ~ ( in @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) @ SV89 ) )
= $false )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2029,plain,
! [SV89: $i,SV410: $i,SV244: $i > $o] :
( ( ( ~ ~ ( SV244 @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) ) )
= $false )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2030,plain,
! [SV251: $i,SV411: $i,SV98: $i,SV394: $i] :
( ( ( in @ SV394 @ SV98 )
= $false )
| ( ( in @ SV411 @ SV251 )
= $true )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2031,plain,
! [SV98: $i,SV394: $i,SV251: $i,SV411: $i] :
( ( ( in @ SV411 @ SV251 )
= $false )
| ( ( in @ SV394 @ SV98 )
= $true )
| ( ( SV394 = SV411 )
= $false )
| ( ( SV98 = SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2032,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( ~ ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(2033,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2034,plain,
! [SV257: $i,SV353: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) ) ) ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1927]) ).
thf(2035,plain,
! [SV396: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( ! [SY1334: $i,SY1335: $i] :
( ~ ( SV107 @ SY1334 )
| ~ ( SV107 @ SY1335 )
| ( SY1334 = SY1335 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(2036,plain,
! [SV396: $i,SV445: $i,SV107: $i > $o] :
( ( ( ! [SY1818: $i] :
( ~ ( SV107 @ SV445 )
| ~ ( SV107 @ SY1818 )
| ( SV445 = SY1818 ) ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV396
= ( sK51_SY1768 @ SV396 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2037,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( SV117 @ ( sK52_SY1769 @ SV397 @ SV117 ) )
= $true )
| ( ( SV117 @ SV397 )
= $false )
| ( ( ~ ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(2038,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $false )
| ( ( SV117 @ SV397 )
= $false )
| ( ( SV397
= ( sK52_SY1769 @ SV397 @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2039,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2040,plain,
! [SV119: $i,SV357: $i,SV265: $i > $o] :
( ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( ~ ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1933]) ).
thf(2041,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $false )
| ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2042,plain,
! [SV125: $i,SV398: $i] :
( ( ( ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SY1795 @ SV125 ) ) )
= $false )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2043,plain,
! [SV126: $i > $o,SV399: $i] :
( ( ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
| ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2044,plain,
! [SV126: $i > $o,SV399: $i] :
( ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2045,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2046,plain,
! [SV271: $i > $o,SV127: $i,SV434: $i] :
( ( ( ~ ( in @ SV434 @ SV127 )
| ~ ( SV271 @ SV434 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(2047,plain,
! [SV271: $i > $o,SV127: $i,SV446: $i] :
( ( ( ~ ~ ( ~ ( in @ SV446 @ SV127 )
| ~ ( SV271 @ SV446 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2048,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(2049,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2050,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2051,plain,
! [SV274: $i,SV412: $i > $o,SV400: $i > $o,SV130: $i] :
( ( ( in @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) @ SV274 )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2052,plain,
! [SV130: $i,SV274: $i,SV400: $i > $o,SV412: $i > $o] :
( ( ( ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 )
!= ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2053,plain,
! [SV130: $i,SV274: $i,SV412: $i > $o,SV400: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
| ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) ) )
| ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2054,plain,
! [SV413: $i,SV278: $i > $o,SV135: $i] :
( ( ( ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV135 )
| ( SV278 @ SY1646 ) ) )
= $false )
| ( ( in @ SV413 @ SV135 )
= $false )
| ( ( SV278 @ SV413 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2055,plain,
! [SV414: $i,SV279: $i > $o,SV136: $i] :
( ( ( ( dsetconstr @ SV136
@ ^ [SY1648: $i] : ( SV279 @ SY1648 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV136 )
= $false )
| ( ( SV279 @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2056,plain,
! [SV282: $i > $o,SV442: $i,SV139: $i > $o] :
( ( ( ~ ( ~ ( SV139 @ SV442 )
| ~ ! [SY1814: $i] :
( ~ ( SV139 @ SY1814 )
| ( SV442 = SY1814 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2057,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
| ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2058,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1951]) ).
thf(2059,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1951]) ).
thf(2060,plain,
! [SV140: $i,SV283: $i] :
( ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV283 )
= $true )
| ( ( in @ ( sK17_SY1659 @ SV283 @ SV140 ) @ SV140 )
= $true )
| ( ( SV140 = SV283 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2061,plain,
! [SV141: $i] :
( ( ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SY1735 )
| ( in @ SY1425 @ SV141 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(2062,plain,
! [SV141: $i] :
( ( ! [SY1737: $i,SY1738: $i] :
( ~ ~ ( ~ ( in @ SY1737 @ SV141 )
| ~ ( in @ SY1738 @ SV141 ) )
| ~ ! [SY1739: $i] :
( ~ ( in @ SY1739 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SY1737 @ SY1739 )
| ( in @ SY1738 @ SY1739 ) )
| ~ ( ~ ( in @ SY1738 @ SY1739 )
| ( in @ SY1737 @ SY1739 ) ) ) )
| ( SY1737 = SY1738 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(2063,plain,
! [SV443: $i,SV141: $i,SV435: $i] :
( ( ( ~ ~ ( ~ ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) ) ) )
= $true )
| ( ( ! [SY1815: $i] :
( ~ ( in @ SY1815 @ SV435 )
| ( in @ SY1815 @ SV443 ) )
| ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2064,plain,
! [SV141: $i,SV428: $i] :
( ( ( ! [SY1796: $i] :
( ~ ( in @ SY1796 @ SV428 )
| ( in @ SY1796 @ SV141 ) ) )
= $false )
| ( ( ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2065,plain,
! [SV287: $i > $o,SV146: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ SV146 )
| ~ ( SV287 @ SV436 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2066,plain,
! [SV287: $i > $o,SV146: $i,SV447: $i] :
( ( ( ~ ~ ( ~ ( in @ SV447 @ SV146 )
| ~ ( SV287 @ SV447 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2067,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(2068,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ~ ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2069,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(2070,plain,
! [SV147: $i,SV417: $o,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 ) )
= $false )
| ( SV417 = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1964]) ).
thf(2071,plain,
! [SV288: $i,SV147: $i,SV365: $i,SV417: $o] :
( ( SV417 = $false )
| ( SV417 = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1964]) ).
thf(2072,plain,
! [SV147: $i,SV417: $o,SV288: $i,SV365: $i] :
( ( ( in @ SV365 @ SV288 )
= $true )
| ( SV417 = $true )
| ( SV417 = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2073,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 ) )
= $false )
| ( $true = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1967]) ).
thf(2074,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1967]) ).
thf(2075,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( in @ SV365 @ SV288 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1968]) ).
thf(2076,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV288 ) )
= $false )
| ( $false = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1970]) ).
thf(2077,plain,
! [SV288: $i,SV147: $i,SV365: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1970]) ).
thf(2078,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( in @ SV365 @ SV288 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2079,plain,
! [SV153: $i,SV389: $o,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 ) )
= $false )
| ( SV389 = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(2080,plain,
! [SV294: $i,SV153: $i,SV369: $i,SV389: $o] :
( ( SV389 = $false )
| ( SV389 = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(2081,plain,
! [SV153: $i,SV389: $o,SV294: $i,SV369: $i] :
( ( ( in @ SV369 @ SV294 )
= $true )
| ( SV389 = $true )
| ( SV389 = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2082,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2083,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2084,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( in @ SV369 @ SV294 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2085,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV294 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2086,plain,
! [SV294: $i,SV153: $i,SV369: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2087,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( in @ SV369 @ SV294 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1980]) ).
thf(2088,plain,
! [SV155: $i,SV296: $i > $o,SV419: $i] :
( ( ( ~ ( in @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) @ SV155 ) )
= $false )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2089,plain,
! [SV155: $i,SV419: $i,SV296: $i > $o] :
( ( ( ~ ~ ( SV296 @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) ) )
= $false )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2090,plain,
! [SV159: $i,SV302: $i > $o,SV420: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) @ SV159 )
| ~ ( SV302 @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) ) ) )
= $false )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1983]) ).
thf(2091,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ( ~ ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
| ~ ! [SY1812: $i] :
~ ~ ( ~ ( in @ SY1812 @ SV304 )
| ~ ( SV161 @ SY1812 @ SV437 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2092,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ( ~ ~ ! [SY1813: $i] :
~ ~ ( ~ ( in @ SY1813 @ SV304 )
| ~ ( SV161 @ SY1813 @ SV437 ) )
| ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) ) ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2093,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( ! [SY1803: $i] :
( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SY1803 )
| ( SV429 = SY1803 ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2094,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( ~ ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2095,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2096,plain,
! [SV405: $i,SV175: $i > $o] :
( ( ( SV175 @ ( sK55_SY1786 @ SV405 @ SV175 ) )
= $true )
| ( ( SV175 @ SV405 )
= $false )
| ( ( SV175
@ ( descr
@ ^ [SY1528: $i] : ( SV175 @ SY1528 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2097,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2098,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2099,plain,
! [SV197: $i,SV32: $i,SV318: $i,SV407: $o] :
( ( SV407 = $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2100,plain,
! [SV407: $o,SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| SV407 )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2101,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2102,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2103,plain,
! [SV197: $i,SV32: $i,SV318: $i,SV407: $o] :
( ( SV407 = $false )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2104,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2105,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2106,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2107,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2108,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2109,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2110,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2111,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2112,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2113,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2114,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 )
| ~ ( in @ SV318 @ SV197 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2115,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2116,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2117,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2118,plain,
! [SV206: $i > $o,SV41: $i,SV438: $i] :
( ( ( in @ SV438 @ SV41 )
= $false )
| ( ( ~ ( SV206 @ SV438 ) )
= $true )
| ( ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2119,plain,
! [SV206: $i > $o,SV41: $i,SV439: $i] :
( ( ( in @ SV439 @ SV41 )
= $false )
| ( ( ~ ( SV206 @ SV439 ) )
= $true )
| ( ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2120,plain,
! [SV390: $i,SV448: $i,SV46: $i > $o] :
( ( ( ! [SY1819: $i] :
( ~ ( SV46 @ SV448 )
| ~ ( SV46 @ SY1819 )
| ( SV448 = SY1819 ) ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2121,plain,
! [SV390: $i,SV449: $i,SV444: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV444 )
| ~ ( SV46 @ SV449 )
| ( SV444 = SV449 ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV390
= ( sK48_SY1761 @ SV390 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2122,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ ( sK58_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1820: $i] :
( ~ ( SV49 @ SY1820 )
| ( ( sK58_SY1208 @ SV391 @ SV49 )
= SY1820 ) ) ) )
= $false )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2009]) ).
thf(2123,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ! [SY1208: $i] :
~ ~ ( ~ ( SV49 @ SY1208 )
| ~ ! [SY1209: $i] :
( ~ ( SV49 @ SY1209 )
| ( SY1208 = SY1209 ) ) ) )
= $false )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2124,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ ( sK59_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1821: $i] :
( ~ ( SV49 @ SY1821 )
| ( ( sK59_SY1208 @ SV391 @ SV49 )
= SY1821 ) ) ) )
= $false )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2011]) ).
thf(2125,plain,
! [SV213: $i > $o,SV51: $i,SV431: $i] :
( ( ( in @ SV431 @ SV51 )
= $false )
| ( ( ~ ( SV213 @ SV431 ) )
= $true )
| ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2126,plain,
! [SV213: $i > $o,SV51: $i,SV432: $i] :
( ( ( in @ SV432 @ SV51 )
= $false )
| ( ( ~ ( SV213 @ SV432 ) )
= $true )
| ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2127,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2128,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2129,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2130,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2131,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2132,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2133,plain,
! [SV65: $i,SV450: $i] :
( ( ( ~ ( in @ SV450 @ omega )
| ( in @ SV450 @ SV65 ) )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( sK32_SY1253 @ SV65 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2134,plain,
! [SV65: $i,SV451: $i] :
( ( ( ~ ( in @ SV451 @ omega )
| ( in @ SV451 @ SV65 ) )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2135,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ! [SY1260: $i] :
~ ~ ( ~ ( SV67 @ SY1260 )
| ~ ! [SY1261: $i] :
( ~ ( SV67 @ SY1261 )
| ( SY1260 = SY1261 ) ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2136,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ~ ( ~ ( SV67 @ ( sK60_SY1260 @ SV392 @ SV67 ) )
| ~ ! [SY1822: $i] :
( ~ ( SV67 @ SY1822 )
| ( ( sK60_SY1260 @ SV392 @ SV67 )
= SY1822 ) ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2022]) ).
thf(2137,plain,
! [SV230: $i,SV70: $i,SV430: $i] :
( ( ( in @ SV430 @ SV70 )
= $false )
| ( ( in @ SV230 @ SV430 )
= $false )
| ( ( in @ SV230 @ ( setunion @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2138,plain,
! [SV241: $i > $o,SV86: $i,SV440: $i] :
( ( ( in @ SV440 @ SV86 )
= $false )
| ( ( ~ ( SV241 @ SV440 ) )
= $true )
| ( ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2139,plain,
! [SV241: $i > $o,SV86: $i,SV441: $i] :
( ( ( in @ SV441 @ SV86 )
= $false )
| ( ( ~ ( SV241 @ SV441 ) )
= $true )
| ( ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2140,plain,
! [SV89: $i,SV244: $i > $o,SV410: $i] :
( ( ( in @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) @ SV89 )
= $true )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2028]) ).
thf(2141,plain,
! [SV89: $i,SV410: $i,SV244: $i > $o] :
( ( ( ~ ( SV244 @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) ) )
= $true )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2029]) ).
thf(2142,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ! [SY1322: $i] :
~ ! [SY1323: $i] :
~ ( ~ ( ~ ( SV103 @ SY1323 )
| ( SY1323 = SY1322 ) )
| ~ ( ( SY1323 != SY1322 )
| ( SV103 @ SY1323 ) ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2143,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ~ ! [SY1823: $i] :
~ ( ~ ( ~ ( SV103 @ SY1823 )
| ( SY1823
= ( sK61_SY1322 @ SV395 @ SV103 ) ) )
| ~ ( ( SY1823
!= ( sK61_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SY1823 ) ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2033]) ).
thf(2144,plain,
! [SV257: $i,SV353: $i,SV106: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) ) ) ) )
= $true )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2145,plain,
! [SV396: $i,SV452: $i,SV107: $i > $o] :
( ( ( ! [SY1824: $i] :
( ~ ( SV107 @ SV452 )
| ~ ( SV107 @ SY1824 )
| ( SV452 = SY1824 ) ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2146,plain,
! [SV396: $i,SV453: $i,SV445: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV445 )
| ~ ( SV107 @ SV453 )
| ( SV445 = SV453 ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV396
= ( sK51_SY1768 @ SV396 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2147,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ! [SY1351: $i] :
~ ( SV117 @ SY1351 ) )
= $false )
| ( ( SV117 @ SV397 )
= $false )
| ( ( SV117 @ ( sK52_SY1769 @ SV397 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2148,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ ( sK62_SY1351 @ SV397 @ SV117 ) ) )
= $false )
| ( ( SV117 @ SV397 )
= $false )
| ( ( SV397
= ( sK52_SY1769 @ SV397 @ SV117 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2038]) ).
thf(2149,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2039]) ).
thf(2150,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ! [SY1621: $i] :
~ ~ ( ~ ( in @ SY1621
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ SY1621 @ emptyset ) ) ) )
= $false )
| ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2151,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) ) )
= $false )
| ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2041]) ).
thf(2152,plain,
! [SV125: $i,SV398: $i] :
( ( ( ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SY1795 @ SV125 ) ) )
= $true )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2153,plain,
! [SV126: $i > $o,SV399: $i] :
( ( ( ( sK29_SY1770 @ SV399 @ SV126 )
!= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2043]) ).
thf(2154,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2043]) ).
thf(2155,plain,
! [SV126: $i > $o,SV399: $i] :
( ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2044]) ).
thf(2156,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2157,plain,
! [SV271: $i > $o,SV127: $i,SV434: $i] :
( ( ( ~ ( in @ SV434 @ SV127 ) )
= $true )
| ( ( ~ ( SV271 @ SV434 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2158,plain,
! [SV271: $i > $o,SV127: $i,SV446: $i] :
( ( ( ~ ( ~ ( in @ SV446 @ SV127 )
| ~ ( SV271 @ SV446 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2159,plain,
! [SV271: $i > $o,SV127: $i,SV454: $i] :
( ( ( ~ ~ ( ~ ( in @ SV454 @ SV127 )
| ~ ( SV271 @ SV454 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2160,plain,
! [SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ SV127 )
| ~ ( SV271 @ SY1632 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2161,plain,
! [SV271: $i > $o,SV127: $i,SV455: $i] :
( ( ( ~ ~ ( ~ ( in @ SV455 @ SV127 )
| ~ ( SV271 @ SV455 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2162,plain,
! [SV130: $i,SV274: $i,SV400: $i > $o,SV412: $i > $o] :
( ( ( ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 )
= ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2163,plain,
! [SV130: $i,SV274: $i,SV412: $i > $o,SV400: $i > $o] :
( ( ( ~ ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
| ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) ) )
| ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2164,plain,
! [SV135: $i,SV278: $i > $o,SV413: $i] :
( ( ( ~ ( in @ ( sK65_SY1646 @ SV413 @ SV278 @ SV135 ) @ SV135 )
| ( SV278 @ ( sK65_SY1646 @ SV413 @ SV278 @ SV135 ) ) )
= $false )
| ( ( in @ SV413 @ SV135 )
= $false )
| ( ( SV278 @ SV413 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2054]) ).
thf(2165,plain,
! [SV282: $i > $o,SV442: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV442 )
| ~ ! [SY1814: $i] :
( ~ ( SV139 @ SY1814 )
| ( SV442 = SY1814 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2056]) ).
thf(2166,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2167,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2168,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2169,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2170,plain,
! [SV141: $i,SV456: $i] :
( ( ~ ( in @ SV456 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1829: $i] :
( ~ ( in @ SY1829 @ SV456 )
| ( in @ SY1829 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2171,plain,
! [SV141: $i,SV457: $i] :
( ( ! [SY1830: $i] :
( ~ ~ ( ~ ( in @ SV457 @ SV141 )
| ~ ( in @ SY1830 @ SV141 ) )
| ~ ! [SY1831: $i] :
( ~ ( in @ SY1831 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1831 )
| ( in @ SY1830 @ SY1831 ) )
| ~ ( ~ ( in @ SY1830 @ SY1831 )
| ( in @ SV457 @ SY1831 ) ) ) )
| ( SV457 = SY1830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2172,plain,
! [SV443: $i,SV141: $i,SV435: $i] :
( ( ( ~ ( ~ ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) ) ) )
= $false )
| ( ( ! [SY1815: $i] :
( ~ ( in @ SY1815 @ SV435 )
| ( in @ SY1815 @ SV443 ) )
| ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2173,plain,
! [SV428: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
| ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 ) )
= $false )
| ( ( ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2064]) ).
thf(2174,plain,
! [SV287: $i > $o,SV146: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ SV146 ) )
= $true )
| ( ( ~ ( SV287 @ SV436 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2065]) ).
thf(2175,plain,
! [SV287: $i > $o,SV146: $i,SV447: $i] :
( ( ( ~ ( ~ ( in @ SV447 @ SV146 )
| ~ ( SV287 @ SV447 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2176,plain,
! [SV287: $i > $o,SV146: $i,SV458: $i] :
( ( ( ~ ~ ( ~ ( in @ SV458 @ SV146 )
| ~ ( SV287 @ SV458 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2177,plain,
! [SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1665: $i] :
~ ~ ( ~ ( in @ SY1665 @ SV146 )
| ~ ( SV287 @ SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2178,plain,
! [SV287: $i > $o,SV146: $i,SV459: $i] :
( ( ( ~ ~ ( ~ ( in @ SV459 @ SV146 )
| ~ ( SV287 @ SV459 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2179,plain,
! [SV147: $i,SV417: $o,SV288: $i,SV365: $i] :
( ( ( in @ SV365 @ SV288 )
= $true )
| ( SV417 = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2180,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( in @ SV365 @ SV288 )
= $true )
| ( $true = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2181,plain,
! [SV147: $i,SV288: $i,SV365: $i] :
( ( ( in @ SV365 @ SV288 )
= $true )
| ( $false = $true )
| ( ( SV365 = SV147 )
= $true )
| ( ( in @ SV365 @ ( setadjoin @ SV147 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2182,plain,
! [SV153: $i,SV389: $o,SV294: $i,SV369: $i] :
( ( ( in @ SV369 @ SV294 )
= $true )
| ( SV389 = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2183,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( in @ SV369 @ SV294 )
= $true )
| ( $true = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2184,plain,
! [SV153: $i,SV294: $i,SV369: $i] :
( ( ( in @ SV369 @ SV294 )
= $true )
| ( $false = $true )
| ( ( in @ SV369 @ SV153 )
= $true )
| ( ( in @ SV369 @ ( binunion @ SV153 @ SV294 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2085]) ).
thf(2185,plain,
! [SV155: $i,SV296: $i > $o,SV419: $i] :
( ( ( in @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) @ SV155 )
= $true )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2186,plain,
! [SV155: $i,SV419: $i,SV296: $i > $o] :
( ( ( ~ ( SV296 @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) ) )
= $true )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2187,plain,
! [SV159: $i,SV302: $i > $o,SV420: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) @ SV159 )
| ~ ( SV302 @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) ) ) )
= $true )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2090]) ).
thf(2188,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
| ~ ! [SY1812: $i] :
~ ~ ( ~ ( in @ SY1812 @ SV304 )
| ~ ( SV161 @ SY1812 @ SV437 ) ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2189,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ~ ! [SY1813: $i] :
~ ~ ( ~ ( in @ SY1813 @ SV304 )
| ~ ( SV161 @ SY1813 @ SV437 ) )
| ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2190,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
| ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2093]) ).
thf(2191,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ! [SY1509: $i] :
~ ~ ( ~ ( SV167 @ SY1509 )
| ~ ! [SY1510: $i] :
( ~ ( SV167 @ SY1510 )
| ( SY1509 = SY1510 ) ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2192,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ~ ( ~ ( SV167 @ ( sK68_SY1509 @ SV403 @ SV167 ) )
| ~ ! [SY1832: $i] :
( ~ ( SV167 @ SY1832 )
| ( ( sK68_SY1509 @ SV403 @ SV167 )
= SY1832 ) ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2095]) ).
thf(2193,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2194,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2195,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2196,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| SV407 )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2197,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2198,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( SV407 = $true )
| ( SV407 = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2102]) ).
thf(2199,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2200,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( $true = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2201,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2107]) ).
thf(2202,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2107]) ).
thf(2203,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2204,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2109]) ).
thf(2205,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2206,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( $false = $true )
| ( ( in @ SV318 @ SV32 )
= $true )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2207,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ~ ( in @ SV318 @ SV32 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2208,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2114]) ).
thf(2209,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2210,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2116]) ).
thf(2211,plain,
! [SV41: $i,SV438: $i,SV206: $i > $o] :
( ( ( SV206 @ SV438 )
= $false )
| ( ( in @ SV438 @ SV41 )
= $false )
| ( ( in @ ( sK25_SY1545 @ SV206 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2212,plain,
! [SV41: $i,SV439: $i,SV206: $i > $o] :
( ( ( SV206 @ SV439 )
= $false )
| ( ( in @ SV439 @ SV41 )
= $false )
| ( ( SV206 @ ( sK25_SY1545 @ SV206 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2213,plain,
! [SV390: $i,SV460: $i,SV448: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV448 )
| ~ ( SV46 @ SV460 )
| ( SV448 = SV460 ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2214,plain,
! [SV390: $i,SV449: $i,SV444: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV444 ) )
= $true )
| ( ( ~ ( SV46 @ SV449 )
| ( SV444 = SV449 ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV390
= ( sK48_SY1761 @ SV390 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2121]) ).
thf(2215,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ ( sK58_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1820: $i] :
( ~ ( SV49 @ SY1820 )
| ( ( sK58_SY1208 @ SV391 @ SV49 )
= SY1820 ) ) ) )
= $true )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2216,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ ( sK69_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1833: $i] :
( ~ ( SV49 @ SY1833 )
| ( ( sK69_SY1208 @ SV391 @ SV49 )
= SY1833 ) ) ) )
= $false )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2123]) ).
thf(2217,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ ( sK59_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1821: $i] :
( ~ ( SV49 @ SY1821 )
| ( ( sK59_SY1208 @ SV391 @ SV49 )
= SY1821 ) ) ) )
= $true )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2218,plain,
! [SV51: $i,SV431: $i,SV213: $i > $o] :
( ( ( SV213 @ SV431 )
= $false )
| ( ( in @ SV431 @ SV51 )
= $false )
| ( ( in @ ( sK9_SY1552 @ SV213 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2219,plain,
! [SV51: $i,SV432: $i,SV213: $i > $o] :
( ( ( SV213 @ SV432 )
= $false )
| ( ( in @ SV432 @ SV51 )
= $false )
| ( ( SV213 @ ( sK9_SY1552 @ SV213 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2220,plain,
! [SV216: $i > $o,SV461: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ SV461 )
| ~ ! [SY1834: $i] :
( ~ ( SV54 @ SY1834 )
| ( SV461 = SY1834 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2221,plain,
! [SV54: $i > $o,SV462: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ SV462 )
| ~ ! [SY1835: $i] :
( ~ ( SV216 @ SY1835 )
| ( SV462 = SY1835 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2222,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2129]) ).
thf(2223,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2224,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2225,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2226,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2227,plain,
! [SV65: $i,SV450: $i] :
( ( ( ~ ( in @ SV450 @ omega ) )
= $true )
| ( ( in @ SV450 @ SV65 )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( sK32_SY1253 @ SV65 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2228,plain,
! [SV65: $i,SV451: $i] :
( ( ( ~ ( in @ SV451 @ omega ) )
= $true )
| ( ( in @ SV451 @ SV65 )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2229,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ~ ( ~ ( SV67 @ ( sK70_SY1260 @ SV392 @ SV67 ) )
| ~ ! [SY1836: $i] :
( ~ ( SV67 @ SY1836 )
| ( ( sK70_SY1260 @ SV392 @ SV67 )
= SY1836 ) ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2135]) ).
thf(2230,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( ~ ( SV67 @ ( sK60_SY1260 @ SV392 @ SV67 ) )
| ~ ! [SY1822: $i] :
( ~ ( SV67 @ SY1822 )
| ( ( sK60_SY1260 @ SV392 @ SV67 )
= SY1822 ) ) ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2231,plain,
! [SV86: $i,SV440: $i,SV241: $i > $o] :
( ( ( SV241 @ SV440 )
= $false )
| ( ( in @ SV440 @ SV86 )
= $false )
| ( ( in @ ( sK26_SY1591 @ SV241 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2232,plain,
! [SV86: $i,SV441: $i,SV241: $i > $o] :
( ( ( SV241 @ SV441 )
= $false )
| ( ( in @ SV441 @ SV86 )
= $false )
| ( ( SV241 @ ( sK26_SY1591 @ SV241 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2233,plain,
! [SV89: $i,SV410: $i,SV244: $i > $o] :
( ( ( SV244 @ ( sK44_SY1595 @ SV410 @ SV244 @ SV89 ) )
= $false )
| ( ( SV244 @ SV410 )
= $true )
| ( ( in @ SV410 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2234,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ~ ! [SY1837: $i] :
~ ( ~ ( ~ ( SV103 @ SY1837 )
| ( SY1837
= ( sK71_SY1322 @ SV395 @ SV103 ) ) )
| ~ ( ( SY1837
!= ( sK71_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SY1837 ) ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2142]) ).
thf(2235,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ! [SY1823: $i] :
~ ( ~ ( ~ ( SV103 @ SY1823 )
| ( SY1823
= ( sK61_SY1322 @ SV395 @ SV103 ) ) )
| ~ ( ( SY1823
!= ( sK61_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SY1823 ) ) ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2236,plain,
! [SV257: $i,SV353: $i,SV106: $i] :
( ( ( ~ ( in @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) @ SV257 )
| ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) ) ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2237,plain,
! [SV396: $i,SV463: $i,SV452: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV452 )
| ~ ( SV107 @ SV463 )
| ( SV452 = SV463 ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2238,plain,
! [SV396: $i,SV453: $i,SV445: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV445 ) )
= $true )
| ( ( ~ ( SV107 @ SV453 )
| ( SV445 = SV453 ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV396
= ( sK51_SY1768 @ SV396 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2239,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ ( sK72_SY1351 @ SV397 @ SV117 ) ) )
= $false )
| ( ( SV117 @ SV397 )
= $false )
| ( ( SV117 @ ( sK52_SY1769 @ SV397 @ SV117 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2147]) ).
thf(2240,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( SV117 @ ( sK62_SY1351 @ SV397 @ SV117 ) )
= $true )
| ( ( SV117 @ SV397 )
= $false )
| ( ( SV397
= ( sK52_SY1769 @ SV397 @ SV117 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2241,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2242,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) ) )
= $false )
| ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2150]) ).
thf(2243,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( ~ ( in @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) ) )
= $true )
| ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2244,plain,
! [SV125: $i,SV398: $i,SV464: $i] :
( ( ( ~ ~ ( ~ ( in @ SV464 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SV464 @ SV125 ) ) )
= $true )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2245,plain,
! [SV126: $i > $o,SV399: $i] :
( ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2153]) ).
thf(2246,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2247,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2248,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ~ ( ~ ( SV126 @ ( sK74_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1840: $i] :
( ~ ( SV126 @ SY1840 )
| ( ( sK74_SY1375 @ SV399 @ SV126 )
= SY1840 ) ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2156]) ).
thf(2249,plain,
! [SV271: $i > $o,SV127: $i,SV434: $i] :
( ( ( in @ SV434 @ SV127 )
= $false )
| ( ( ~ ( SV271 @ SV434 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2250,plain,
! [SV271: $i > $o,SV127: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ SV127 )
| ~ ( SV271 @ SV446 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2158]) ).
thf(2251,plain,
! [SV271: $i > $o,SV127: $i,SV454: $i] :
( ( ( ~ ( ~ ( in @ SV454 @ SV127 )
| ~ ( SV271 @ SV454 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2252,plain,
! [SV271: $i > $o,SV127: $i,SV465: $i] :
( ( ( ~ ~ ( ~ ( in @ SV465 @ SV127 )
| ~ ( SV271 @ SV465 ) ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2253,plain,
! [SV271: $i > $o,SV127: $i,SV455: $i] :
( ( ( ~ ( ~ ( in @ SV455 @ SV127 )
| ~ ( SV271 @ SV455 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2254,plain,
! [SV130: $i,SV274: $i,SV412: $i > $o,SV400: $i > $o] :
( ( ( ~ ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
| ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2255,plain,
! [SV135: $i,SV278: $i > $o,SV413: $i] :
( ( ( ~ ( in @ ( sK65_SY1646 @ SV413 @ SV278 @ SV135 ) @ SV135 ) )
= $false )
| ( ( in @ SV413 @ SV135 )
= $false )
| ( ( SV278 @ SV413 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2256,plain,
! [SV135: $i,SV413: $i,SV278: $i > $o] :
( ( ( SV278 @ ( sK65_SY1646 @ SV413 @ SV278 @ SV135 ) )
= $false )
| ( ( in @ SV413 @ SV135 )
= $false )
| ( ( SV278 @ SV413 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2164]) ).
thf(2257,plain,
! [SV282: $i > $o,SV442: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV442 ) )
= $true )
| ( ( ~ ! [SY1814: $i] :
( ~ ( SV139 @ SY1814 )
| ( SV442 = SY1814 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2258,plain,
! [SV139: $i > $o,SV282: $i > $o] :
( ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) )
| ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2166]) ).
thf(2259,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2260,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2261,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2262,plain,
! [SV141: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ ( sK3_SY1423 @ SV141 ) ) )
= $true )
| ( ( ! [SY1829: $i] :
( ~ ( in @ SY1829 @ SV456 )
| ( in @ SY1829 @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2263,plain,
! [SV466: $i,SV141: $i,SV457: $i] :
( ( ~ ~ ( ~ ( in @ SV457 @ SV141 )
| ~ ( in @ SV466 @ SV141 ) )
| ~ ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) )
| ( SV457 = SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2264,plain,
! [SV443: $i,SV141: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) ) )
= $true )
| ( ( ! [SY1815: $i] :
( ~ ( in @ SY1815 @ SV435 )
| ( in @ SY1815 @ SV443 ) )
| ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2172]) ).
thf(2265,plain,
! [SV428: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 ) )
= $false )
| ( ( ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2266,plain,
! [SV428: $i,SV141: $i] :
( ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2267,plain,
! [SV287: $i > $o,SV146: $i,SV436: $i] :
( ( ( in @ SV436 @ SV146 )
= $false )
| ( ( ~ ( SV287 @ SV436 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2268,plain,
! [SV287: $i > $o,SV146: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ SV146 )
| ~ ( SV287 @ SV447 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2269,plain,
! [SV287: $i > $o,SV146: $i,SV458: $i] :
( ( ( ~ ( ~ ( in @ SV458 @ SV146 )
| ~ ( SV287 @ SV458 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2270,plain,
! [SV287: $i > $o,SV146: $i,SV467: $i] :
( ( ( ~ ~ ( ~ ( in @ SV467 @ SV146 )
| ~ ( SV287 @ SV467 ) ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2271,plain,
! [SV287: $i > $o,SV146: $i,SV459: $i] :
( ( ( ~ ( ~ ( in @ SV459 @ SV146 )
| ~ ( SV287 @ SV459 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2272,plain,
! [SV155: $i,SV419: $i,SV296: $i > $o] :
( ( ( SV296 @ ( sK47_SY1679 @ SV419 @ SV296 @ SV155 ) )
= $false )
| ( ( SV296 @ SV419 )
= $true )
| ( ( in @ SV419 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2273,plain,
! [SV159: $i,SV302: $i > $o,SV420: $i] :
( ( ( ~ ( in @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) @ SV159 )
| ~ ( SV302 @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) ) )
= $false )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2274,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) ) )
= $true )
| ( ( ~ ! [SY1812: $i] :
~ ~ ( ~ ( in @ SY1812 @ SV304 )
| ~ ( SV161 @ SY1812 @ SV437 ) ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2188]) ).
thf(2275,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ~ ! [SY1813: $i] :
~ ~ ( ~ ( in @ SY1813 @ SV304 )
| ~ ( SV161 @ SY1813 @ SV437 ) ) )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2276,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( ~ ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2190]) ).
thf(2277,plain,
! [SV161: $i > $i > $o,SV304: $i,SV429: $i] :
( ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2190]) ).
thf(2278,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ~ ( ~ ( SV167 @ ( sK75_SY1509 @ SV403 @ SV167 ) )
| ~ ! [SY1842: $i] :
( ~ ( SV167 @ SY1842 )
| ( ( sK75_SY1509 @ SV403 @ SV167 )
= SY1842 ) ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2191]) ).
thf(2279,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ ( sK68_SY1509 @ SV403 @ SV167 ) )
| ~ ! [SY1832: $i] :
( ~ ( SV167 @ SY1832 )
| ( ( sK68_SY1509 @ SV403 @ SV167 )
= SY1832 ) ) ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2192]) ).
thf(2280,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2281,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2282,plain,
! [SV32: $i,SV197: $i,SV318: $i,SV407: $o] :
( ( SV407 = $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2283,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2284,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2202]) ).
thf(2285,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2202]) ).
thf(2286,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV32 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2287,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV197 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2288,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2208]) ).
thf(2289,plain,
! [SV390: $i,SV460: $i,SV448: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV448 ) )
= $true )
| ( ( ~ ( SV46 @ SV460 )
| ( SV448 = SV460 ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2290,plain,
! [SV390: $i,SV449: $i,SV444: $i,SV46: $i > $o] :
( ( ( SV46 @ SV444 )
= $false )
| ( ( ~ ( SV46 @ SV449 )
| ( SV444 = SV449 ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV390
= ( sK48_SY1761 @ SV390 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2291,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK58_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1820: $i] :
( ~ ( SV49 @ SY1820 )
| ( ( sK58_SY1208 @ SV391 @ SV49 )
= SY1820 ) ) )
= $false )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2292,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ ( sK69_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1833: $i] :
( ~ ( SV49 @ SY1833 )
| ( ( sK69_SY1208 @ SV391 @ SV49 )
= SY1833 ) ) ) )
= $true )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2293,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK59_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1821: $i] :
( ~ ( SV49 @ SY1821 )
| ( ( sK59_SY1208 @ SV391 @ SV49 )
= SY1821 ) ) )
= $false )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2294,plain,
! [SV216: $i > $o,SV461: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ SV461 )
| ~ ! [SY1834: $i] :
( ~ ( SV54 @ SY1834 )
| ( SV461 = SY1834 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2295,plain,
! [SV54: $i > $o,SV462: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ SV462 )
| ~ ! [SY1835: $i] :
( ~ ( SV216 @ SY1835 )
| ( SV462 = SY1835 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2296,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
| ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2297,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2223]) ).
thf(2298,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2223]) ).
thf(2299,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2300,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2301,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2302,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2226]) ).
thf(2303,plain,
! [SV65: $i,SV450: $i] :
( ( ( in @ SV450 @ omega )
= $false )
| ( ( in @ SV450 @ SV65 )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( sK32_SY1253 @ SV65 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2304,plain,
! [SV65: $i,SV451: $i] :
( ( ( in @ SV451 @ omega )
= $false )
| ( ( in @ SV451 @ SV65 )
= $true )
| ( ( in @ emptyset @ SV65 )
= $false )
| ( ( in @ ( sK32_SY1253 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2305,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( ~ ( SV67 @ ( sK70_SY1260 @ SV392 @ SV67 ) )
| ~ ! [SY1836: $i] :
( ~ ( SV67 @ SY1836 )
| ( ( sK70_SY1260 @ SV392 @ SV67 )
= SY1836 ) ) ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2229]) ).
thf(2306,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ ( sK60_SY1260 @ SV392 @ SV67 ) )
| ~ ! [SY1822: $i] :
( ~ ( SV67 @ SY1822 )
| ( ( sK60_SY1260 @ SV392 @ SV67 )
= SY1822 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2307,plain,
! [SV395: $i,SV103: $i > $o] :
( ( ( ! [SY1837: $i] :
~ ( ~ ( ~ ( SV103 @ SY1837 )
| ( SY1837
= ( sK71_SY1322 @ SV395 @ SV103 ) ) )
| ~ ( ( SY1837
!= ( sK71_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SY1837 ) ) ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2308,plain,
! [SV395: $i,SV468: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV103 @ SV468 )
| ( SV468
= ( sK61_SY1322 @ SV395 @ SV103 ) ) )
| ~ ( ( SV468
!= ( sK61_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SV468 ) ) ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2309,plain,
! [SV257: $i,SV353: $i,SV106: $i] :
( ( ( ~ ( in @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) @ SV257 ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2236]) ).
thf(2310,plain,
! [SV106: $i,SV257: $i,SV353: $i] :
( ( ( SV353
!= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) ) )
= $false )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2236]) ).
thf(2311,plain,
! [SV396: $i,SV463: $i,SV452: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV452 ) )
= $true )
| ( ( ~ ( SV107 @ SV463 )
| ( SV452 = SV463 ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2312,plain,
! [SV396: $i,SV453: $i,SV445: $i,SV107: $i > $o] :
( ( ( SV107 @ SV445 )
= $false )
| ( ( ~ ( SV107 @ SV453 )
| ( SV445 = SV453 ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV396
= ( sK51_SY1768 @ SV396 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2313,plain,
! [SV397: $i,SV117: $i > $o] :
( ( ( SV117 @ ( sK72_SY1351 @ SV397 @ SV117 ) )
= $true )
| ( ( SV117 @ SV397 )
= $false )
| ( ( SV117 @ ( sK52_SY1769 @ SV397 @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2239]) ).
thf(2314,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( in @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) )
= $false )
| ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2315,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( ~ ( in @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) ) )
= $true )
| ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2316,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( in @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) )
= $false )
| ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2317,plain,
! [SV125: $i,SV398: $i,SV464: $i] :
( ( ( ~ ( ~ ( in @ SV464 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SV464 @ SV125 ) ) )
= $false )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2318,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1375: $i] :
~ ~ ( ~ ( SV126 @ SY1375 )
| ~ ! [SY1376: $i] :
( ~ ( SV126 @ SY1376 )
| ( SY1375 = SY1376 ) ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2319,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ~ ( ~ ( SV126 @ ( sK76_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1843: $i] :
( ~ ( SV126 @ SY1843 )
| ( ( sK76_SY1375 @ SV399 @ SV126 )
= SY1843 ) ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2246]) ).
thf(2320,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ~ ( ~ ( SV126 @ ( sK77_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1844: $i] :
( ~ ( SV126 @ SY1844 )
| ( ( sK77_SY1375 @ SV399 @ SV126 )
= SY1844 ) ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2247]) ).
thf(2321,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK74_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1840: $i] :
( ~ ( SV126 @ SY1840 )
| ( ( sK74_SY1375 @ SV399 @ SV126 )
= SY1840 ) ) ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2322,plain,
! [SV127: $i,SV434: $i,SV271: $i > $o] :
( ( ( SV271 @ SV434 )
= $false )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2323,plain,
! [SV271: $i > $o,SV127: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ SV127 ) )
= $true )
| ( ( ~ ( SV271 @ SV446 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2324,plain,
! [SV271: $i > $o,SV127: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ SV127 )
| ~ ( SV271 @ SV454 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2325,plain,
! [SV271: $i > $o,SV127: $i,SV465: $i] :
( ( ( ~ ( ~ ( in @ SV465 @ SV127 )
| ~ ( SV271 @ SV465 ) ) )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2326,plain,
! [SV271: $i > $o,SV127: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV127 )
| ~ ( SV271 @ SV455 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2253]) ).
thf(2327,plain,
! [SV130: $i,SV274: $i,SV412: $i > $o,SV400: $i > $o] :
( ( ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
| ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) ) )
= $false )
| ( ( ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2328,plain,
! [SV135: $i,SV278: $i > $o,SV413: $i] :
( ( ( in @ ( sK65_SY1646 @ SV413 @ SV278 @ SV135 ) @ SV135 )
= $true )
| ( ( in @ SV413 @ SV135 )
= $false )
| ( ( SV278 @ SV413 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2255]) ).
thf(2329,plain,
! [SV282: $i > $o,SV442: $i,SV139: $i > $o] :
( ( ( SV139 @ SV442 )
= $false )
| ( ( ~ ! [SY1814: $i] :
( ~ ( SV139 @ SY1814 )
| ( SV442 = SY1814 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2330,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2331,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2332,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2333,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2261]) ).
thf(2334,plain,
! [SV141: $i,SV456: $i] :
( ( ( in @ SV456 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( ! [SY1829: $i] :
( ~ ( in @ SY1829 @ SV456 )
| ( in @ SY1829 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2335,plain,
! [SV466: $i,SV141: $i,SV457: $i] :
( ( ( ~ ~ ( ~ ( in @ SV457 @ SV141 )
| ~ ( in @ SV466 @ SV141 ) ) )
= $true )
| ( ( ~ ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) )
| ( SV457 = SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2336,plain,
! [SV443: $i,SV141: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) ) )
= $true )
| ( ( ~ ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) ) )
= $true )
| ( ( ! [SY1815: $i] :
( ~ ( in @ SY1815 @ SV435 )
| ( in @ SY1815 @ SV443 ) )
| ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2337,plain,
! [SV428: $i,SV141: $i] :
( ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( ~ ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2338,plain,
! [SV141: $i,SV428: $i] :
( ( ( ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2339,plain,
! [SV146: $i,SV436: $i,SV287: $i > $o] :
( ( ( SV287 @ SV436 )
= $false )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2340,plain,
! [SV287: $i > $o,SV146: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ SV146 ) )
= $true )
| ( ( ~ ( SV287 @ SV447 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2341,plain,
! [SV287: $i > $o,SV146: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ SV146 )
| ~ ( SV287 @ SV458 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2269]) ).
thf(2342,plain,
! [SV287: $i > $o,SV146: $i,SV467: $i] :
( ( ( ~ ( ~ ( in @ SV467 @ SV146 )
| ~ ( SV287 @ SV467 ) ) )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2343,plain,
! [SV287: $i > $o,SV146: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV146 )
| ~ ( SV287 @ SV459 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2344,plain,
! [SV159: $i,SV302: $i > $o,SV420: $i] :
( ( ( ~ ( in @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) @ SV159 ) )
= $false )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2273]) ).
thf(2345,plain,
! [SV159: $i,SV420: $i,SV302: $i > $o] :
( ( ( ~ ( SV302 @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) ) )
= $false )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2273]) ).
thf(2346,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( ~ ! [SY1812: $i] :
~ ~ ( ~ ( in @ SY1812 @ SV304 )
| ~ ( SV161 @ SY1812 @ SV437 ) ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2347,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ! [SY1813: $i] :
~ ~ ( ~ ( in @ SY1813 @ SV304 )
| ~ ( SV161 @ SY1813 @ SV437 ) ) )
= $false )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2348,plain,
! [SV429: $i,SV304: $i,SV161: $i > $i > $o] :
( ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( ~ ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2276]) ).
thf(2349,plain,
! [SV429: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2350,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ ( sK75_SY1509 @ SV403 @ SV167 ) )
| ~ ! [SY1842: $i] :
( ~ ( SV167 @ SY1842 )
| ( ( sK75_SY1509 @ SV403 @ SV167 )
= SY1842 ) ) ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2278]) ).
thf(2351,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK68_SY1509 @ SV403 @ SV167 ) )
| ~ ! [SY1832: $i] :
( ~ ( SV167 @ SY1832 )
| ( ( sK68_SY1509 @ SV403 @ SV167 )
= SY1832 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2352,plain,
! [SV197: $i,SV407: $o,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2280]) ).
thf(2353,plain,
! [SV32: $i,SV407: $o,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( SV407 = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2354,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2355,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( $true = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2284]) ).
thf(2356,plain,
! [SV197: $i,SV32: $i,SV318: $i] :
( ( ( in @ SV318 @ SV32 )
= $false )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2357,plain,
! [SV32: $i,SV197: $i,SV318: $i] :
( ( ( in @ SV318 @ SV197 )
= $true )
| ( $false = $true )
| ( ( in @ SV318 @ SV197 )
= $false )
| ( ( in @ SV318 @ ( symdiff @ SV32 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2287]) ).
thf(2358,plain,
! [SV390: $i,SV460: $i,SV448: $i,SV46: $i > $o] :
( ( ( SV46 @ SV448 )
= $false )
| ( ( ~ ( SV46 @ SV460 )
| ( SV448 = SV460 ) )
= $true )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2359,plain,
! [SV390: $i,SV444: $i,SV449: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV449 ) )
= $true )
| ( ( SV444 = SV449 )
= $true )
| ( ( SV46 @ SV444 )
= $false )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV390
= ( sK48_SY1761 @ SV390 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2360,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK58_SY1208 @ SV391 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2291]) ).
thf(2361,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ! [SY1820: $i] :
( ~ ( SV49 @ SY1820 )
| ( ( sK58_SY1208 @ SV391 @ SV49 )
= SY1820 ) ) )
= $false )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2291]) ).
thf(2362,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK69_SY1208 @ SV391 @ SV49 ) )
| ~ ! [SY1833: $i] :
( ~ ( SV49 @ SY1833 )
| ( ( sK69_SY1208 @ SV391 @ SV49 )
= SY1833 ) ) )
= $false )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2363,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK59_SY1208 @ SV391 @ SV49 ) ) )
= $false )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2364,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ! [SY1821: $i] :
( ~ ( SV49 @ SY1821 )
| ( ( sK59_SY1208 @ SV391 @ SV49 )
= SY1821 ) ) )
= $false )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2365,plain,
! [SV216: $i > $o,SV461: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV461 )
| ~ ! [SY1834: $i] :
( ~ ( SV54 @ SY1834 )
| ( SV461 = SY1834 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2366,plain,
! [SV54: $i > $o,SV462: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV462 )
| ~ ! [SY1835: $i] :
( ~ ( SV216 @ SY1835 )
| ( SV462 = SY1835 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2295]) ).
thf(2367,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2296]) ).
thf(2368,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2296]) ).
thf(2369,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2370,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2298]) ).
thf(2371,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2299]) ).
thf(2372,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2300]) ).
thf(2373,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2374,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2375,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ ( sK70_SY1260 @ SV392 @ SV67 ) )
| ~ ! [SY1836: $i] :
( ~ ( SV67 @ SY1836 )
| ( ( sK70_SY1260 @ SV392 @ SV67 )
= SY1836 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2376,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ ( sK60_SY1260 @ SV392 @ SV67 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2306]) ).
thf(2377,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ! [SY1822: $i] :
( ~ ( SV67 @ SY1822 )
| ( ( sK60_SY1260 @ SV392 @ SV67 )
= SY1822 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2306]) ).
thf(2378,plain,
! [SV395: $i,SV469: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV103 @ SV469 )
| ( SV469
= ( sK71_SY1322 @ SV395 @ SV103 ) ) )
| ~ ( ( SV469
!= ( sK71_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SV469 ) ) ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2379,plain,
! [SV395: $i,SV468: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( SV103 @ SV468 )
| ( SV468
= ( sK61_SY1322 @ SV395 @ SV103 ) ) )
| ~ ( ( SV468
!= ( sK61_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SV468 ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2380,plain,
! [SV257: $i,SV353: $i,SV106: $i] :
( ( ( in @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) @ SV257 )
= $true )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2381,plain,
! [SV106: $i,SV257: $i,SV353: $i] :
( ( ( SV353
= ( kpair @ ( sK28_SY1725 @ SV353 @ SV257 @ SV106 ) @ ( sK56_SY1794 @ SV106 @ SV353 @ SV257 ) ) )
= $true )
| ( ( in @ SV353 @ ( cartprod @ SV106 @ SV257 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2310]) ).
thf(2382,plain,
! [SV396: $i,SV463: $i,SV452: $i,SV107: $i > $o] :
( ( ( SV107 @ SV452 )
= $false )
| ( ( ~ ( SV107 @ SV463 )
| ( SV452 = SV463 ) )
= $true )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2383,plain,
! [SV396: $i,SV445: $i,SV453: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV453 ) )
= $true )
| ( ( SV445 = SV453 )
= $true )
| ( ( SV107 @ SV445 )
= $false )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV396
= ( sK51_SY1768 @ SV396 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2312]) ).
thf(2384,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( in @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) ) )
= $false )
| ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2385,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) )
= $false )
| ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2386,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( in @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
| ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) ) )
= $false )
| ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2387,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( in @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) ) )
= $false )
| ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2388,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) )
= $false )
| ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2389,plain,
! [SV125: $i,SV398: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
| ~ ( in @ SV464 @ SV125 ) )
= $true )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2317]) ).
thf(2390,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ~ ( ~ ( SV126 @ ( sK78_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1845: $i] :
( ~ ( SV126 @ SY1845 )
| ( ( sK78_SY1375 @ SV399 @ SV126 )
= SY1845 ) ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2318]) ).
thf(2391,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK76_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1843: $i] :
( ~ ( SV126 @ SY1843 )
| ( ( sK76_SY1375 @ SV399 @ SV126 )
= SY1843 ) ) ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2319]) ).
thf(2392,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK77_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1844: $i] :
( ~ ( SV126 @ SY1844 )
| ( ( sK77_SY1375 @ SV399 @ SV126 )
= SY1844 ) ) ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2320]) ).
thf(2393,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK74_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1840: $i] :
( ~ ( SV126 @ SY1840 )
| ( ( sK74_SY1375 @ SV399 @ SV126 )
= SY1840 ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2394,plain,
! [SV434: $i,SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( SV271 @ SV434 )
= $false )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2395,plain,
! [SV271: $i > $o,SV127: $i,SV446: $i] :
( ( ( in @ SV446 @ SV127 )
= $false )
| ( ( ~ ( SV271 @ SV446 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2396,plain,
! [SV271: $i > $o,SV127: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ SV127 ) )
= $true )
| ( ( ~ ( SV271 @ SV454 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2397,plain,
! [SV271: $i > $o,SV127: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ SV127 )
| ~ ( SV271 @ SV465 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2325]) ).
thf(2398,plain,
! [SV271: $i > $o,SV127: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV127 ) )
= $true )
| ( ( ~ ( SV271 @ SV455 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2399,plain,
! [SV130: $i,SV274: $i,SV412: $i > $o,SV400: $i > $o] :
( ( ( ~ ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2327]) ).
thf(2400,plain,
! [SV274: $i,SV400: $i > $o,SV130: $i,SV412: $i > $o] :
( ( ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $false )
| ( ( ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2327]) ).
thf(2401,plain,
! [SV282: $i > $o,SV442: $i,SV139: $i > $o] :
( ( ( ! [SY1814: $i] :
( ~ ( SV139 @ SY1814 )
| ( SV442 = SY1814 ) ) )
= $false )
| ( ( SV139 @ SV442 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2402,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2403,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2331]) ).
thf(2404,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2332]) ).
thf(2405,plain,
! [SV282: $i > $o,SV470: $i,SV139: $i > $o] :
( ( ( ~ ~ ( ~ ( SV139 @ SV470 )
| ~ ! [SY1846: $i] :
( ~ ( SV139 @ SY1846 )
| ( SV470 = SY1846 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2406,plain,
! [SV141: $i,SV456: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ SV456 )
| ( in @ SV471 @ SV141 ) )
= $true )
| ( ( in @ SV456 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2407,plain,
! [SV466: $i,SV141: $i,SV457: $i] :
( ( ( ~ ( ~ ( in @ SV457 @ SV141 )
| ~ ( in @ SV466 @ SV141 ) ) )
= $false )
| ( ( ~ ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) )
| ( SV457 = SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2408,plain,
! [SV443: $i,SV141: $i,SV435: $i] :
( ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( ~ ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) ) )
= $true )
| ( ( ! [SY1815: $i] :
( ~ ( in @ SY1815 @ SV435 )
| ( in @ SY1815 @ SV443 ) )
| ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2409,plain,
! [SV141: $i,SV428: $i] :
( ( ( ~ ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2410,plain,
! [SV141: $i,SV428: $i] :
( ( ( ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2411,plain,
! [SV436: $i,SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( SV287 @ SV436 )
= $false )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2412,plain,
! [SV287: $i > $o,SV146: $i,SV447: $i] :
( ( ( in @ SV447 @ SV146 )
= $false )
| ( ( ~ ( SV287 @ SV447 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2413,plain,
! [SV287: $i > $o,SV146: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ SV146 ) )
= $true )
| ( ( ~ ( SV287 @ SV458 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2414,plain,
! [SV287: $i > $o,SV146: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ SV146 )
| ~ ( SV287 @ SV467 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2415,plain,
! [SV287: $i > $o,SV146: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV146 ) )
= $true )
| ( ( ~ ( SV287 @ SV459 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2416,plain,
! [SV159: $i,SV302: $i > $o,SV420: $i] :
( ( ( in @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) @ SV159 )
= $true )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2344]) ).
thf(2417,plain,
! [SV159: $i,SV420: $i,SV302: $i > $o] :
( ( ( SV302 @ ( sK57_SY1686 @ SV420 @ SV302 @ SV159 ) )
= $true )
| ( ( in @ SV420
@ ( dsetconstr @ SV159
@ ^ [SY1684: $i] : ( SV302 @ SY1684 ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY1685: $i] : ( SV302 @ SY1685 ) )
= ( setadjoin @ SV420 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2418,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1812: $i] :
~ ~ ( ~ ( in @ SY1812 @ SV304 )
| ~ ( SV161 @ SY1812 @ SV437 ) ) )
= $false )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2419,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1813: $i] :
~ ~ ( ~ ( in @ SY1813 @ SV304 )
| ~ ( SV161 @ SY1813 @ SV437 ) ) )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2347]) ).
thf(2420,plain,
! [SV429: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1692: $i] :
~ ! [SY1693: $i] :
~ ( ~ ( ~ ( in @ SY1693 @ SY1692 )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1693 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1693 ) )
| ( in @ SY1693 @ SY1692 ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2421,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i] :
( ( ( ~ ! [SY1847: $i] :
~ ( ~ ( ~ ( in @ SY1847 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1847 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1847 ) )
| ( in @ SY1847 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2349]) ).
thf(2422,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK75_SY1509 @ SV403 @ SV167 ) )
| ~ ! [SY1842: $i] :
( ~ ( SV167 @ SY1842 )
| ( ( sK75_SY1509 @ SV403 @ SV167 )
= SY1842 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2423,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK68_SY1509 @ SV403 @ SV167 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2424,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ! [SY1832: $i] :
( ~ ( SV167 @ SY1832 )
| ( ( sK68_SY1509 @ SV403 @ SV167 )
= SY1832 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2425,plain,
! [SV390: $i,SV448: $i,SV460: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV460 ) )
= $true )
| ( ( SV448 = SV460 )
= $true )
| ( ( SV46 @ SV448 )
= $false )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2426,plain,
! [SV390: $i,SV444: $i,SV449: $i,SV46: $i > $o] :
( ( ( SV46 @ SV449 )
= $false )
| ( ( SV444 = SV449 )
= $true )
| ( ( SV46 @ SV444 )
= $false )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV390
= ( sK48_SY1761 @ SV390 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2427,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( SV49 @ ( sK58_SY1208 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2428,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ! [SY1820: $i] :
( ~ ( SV49 @ SY1820 )
| ( ( sK58_SY1208 @ SV391 @ SV49 )
= SY1820 ) ) )
= $true )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2361]) ).
thf(2429,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK69_SY1208 @ SV391 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2362]) ).
thf(2430,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ~ ! [SY1833: $i] :
( ~ ( SV49 @ SY1833 )
| ( ( sK69_SY1208 @ SV391 @ SV49 )
= SY1833 ) ) )
= $false )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2362]) ).
thf(2431,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( SV49 @ ( sK59_SY1208 @ SV391 @ SV49 ) )
= $true )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2432,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ! [SY1821: $i] :
( ~ ( SV49 @ SY1821 )
| ( ( sK59_SY1208 @ SV391 @ SV49 )
= SY1821 ) ) )
= $true )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2364]) ).
thf(2433,plain,
! [SV216: $i > $o,SV461: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV461 ) )
= $true )
| ( ( ~ ! [SY1834: $i] :
( ~ ( SV54 @ SY1834 )
| ( SV461 = SY1834 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2434,plain,
! [SV54: $i > $o,SV462: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV462 ) )
= $true )
| ( ( ~ ! [SY1835: $i] :
( ~ ( SV216 @ SY1835 )
| ( SV462 = SY1835 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2435,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) )
| ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2367]) ).
thf(2436,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) )
| ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2437,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2438,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2439,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2440,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2441,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2442,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2443,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ ( sK70_SY1260 @ SV392 @ SV67 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2444,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ~ ! [SY1836: $i] :
( ~ ( SV67 @ SY1836 )
| ( ( sK70_SY1260 @ SV392 @ SV67 )
= SY1836 ) ) )
= $false )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2445,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( SV67 @ ( sK60_SY1260 @ SV392 @ SV67 ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2376]) ).
thf(2446,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ! [SY1822: $i] :
( ~ ( SV67 @ SY1822 )
| ( ( sK60_SY1260 @ SV392 @ SV67 )
= SY1822 ) ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2377]) ).
thf(2447,plain,
! [SV395: $i,SV469: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( SV103 @ SV469 )
| ( SV469
= ( sK71_SY1322 @ SV395 @ SV103 ) ) )
| ~ ( ( SV469
!= ( sK71_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SV469 ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2448,plain,
! [SV395: $i,SV468: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( SV103 @ SV468 )
| ( SV468
= ( sK61_SY1322 @ SV395 @ SV103 ) ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2449,plain,
! [SV103: $i > $o,SV395: $i,SV468: $i] :
( ( ( ~ ( ( SV468
!= ( sK61_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SV468 ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2450,plain,
! [SV396: $i,SV452: $i,SV463: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV463 ) )
= $true )
| ( ( SV452 = SV463 )
= $true )
| ( ( SV107 @ SV452 )
= $false )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2451,plain,
! [SV396: $i,SV445: $i,SV453: $i,SV107: $i > $o] :
( ( ( SV107 @ SV453 )
= $false )
| ( ( SV445 = SV453 )
= $true )
| ( ( SV107 @ SV445 )
= $false )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV396
= ( sK51_SY1768 @ SV396 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2452,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( in @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
= $true )
| ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2384]) ).
thf(2453,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
= ( setadjoin @ ( sK63_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) )
= $true )
| ( ( in @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) @ SV119 )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2385]) ).
thf(2454,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( ~ ( in @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) ) )
= $false )
| ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2386]) ).
thf(2455,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
!= ( setadjoin @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) )
= $false )
| ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2386]) ).
thf(2456,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( in @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
= $true )
| ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2387]) ).
thf(2457,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
= ( setadjoin @ ( sK64_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) )
= $true )
| ( ( ( sK45_SY1729 @ SV357 @ SV265 @ SV119 )
= SV357 )
= $false )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2388]) ).
thf(2458,plain,
! [SV125: $i,SV398: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ ( sK34_SY1371 @ SV398 @ SV125 ) ) )
= $true )
| ( ( ~ ( in @ SV464 @ SV125 ) )
= $true )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2459,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK78_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1845: $i] :
( ~ ( SV126 @ SY1845 )
| ( ( sK78_SY1375 @ SV399 @ SV126 )
= SY1845 ) ) ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2390]) ).
thf(2460,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK76_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1843: $i] :
( ~ ( SV126 @ SY1843 )
| ( ( sK76_SY1375 @ SV399 @ SV126 )
= SY1843 ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2461,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK77_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1844: $i] :
( ~ ( SV126 @ SY1844 )
| ( ( sK77_SY1375 @ SV399 @ SV126 )
= SY1844 ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2462,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK74_SY1375 @ SV399 @ SV126 ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2393]) ).
thf(2463,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ! [SY1840: $i] :
( ~ ( SV126 @ SY1840 )
| ( ( sK74_SY1375 @ SV399 @ SV126 )
= SY1840 ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2393]) ).
thf(2464,plain,
! [SV127: $i,SV271: $i > $o,SV434: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( SV271 @ SV434 )
= $false )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2394]) ).
thf(2465,plain,
! [SV127: $i,SV446: $i,SV271: $i > $o] :
( ( ( SV271 @ SV446 )
= $false )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2466,plain,
! [SV271: $i > $o,SV127: $i,SV454: $i] :
( ( ( in @ SV454 @ SV127 )
= $false )
| ( ( ~ ( SV271 @ SV454 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2467,plain,
! [SV271: $i > $o,SV127: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ SV127 ) )
= $true )
| ( ( ~ ( SV271 @ SV465 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(2468,plain,
! [SV271: $i > $o,SV127: $i,SV455: $i] :
( ( ( in @ SV455 @ SV127 )
= $false )
| ( ( ~ ( SV271 @ SV455 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2469,plain,
! [SV130: $i,SV274: $i,SV412: $i > $o,SV400: $i > $o] :
( ( ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
= $true )
| ( ( ~ ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2470,plain,
! [SV274: $i,SV400: $i > $o,SV130: $i,SV412: $i > $o] :
( ( ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) )
= $false )
| ( ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2471,plain,
! [SV442: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
| ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV442 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2401]) ).
thf(2472,plain,
! [SV282: $i > $o,SV139: $i > $o] :
( ( ( ! [SY1415: $i] :
~ ~ ( ~ ( SV139 @ SY1415 )
| ~ ! [SY1416: $i] :
( ~ ( SV139 @ SY1416 )
| ( SY1415 = SY1416 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2402]) ).
thf(2473,plain,
! [SV282: $i > $o,SV472: $i,SV139: $i > $o] :
( ( ( ~ ~ ( ~ ( SV139 @ SV472 )
| ~ ! [SY1852: $i] :
( ~ ( SV139 @ SY1852 )
| ( SV472 = SY1852 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2474,plain,
! [SV282: $i > $o,SV473: $i,SV139: $i > $o] :
( ( ( ~ ~ ( ~ ( SV139 @ SV473 )
| ~ ! [SY1853: $i] :
( ~ ( SV139 @ SY1853 )
| ( SV473 = SY1853 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2475,plain,
! [SV282: $i > $o,SV470: $i,SV139: $i > $o] :
( ( ( ~ ( ~ ( SV139 @ SV470 )
| ~ ! [SY1846: $i] :
( ~ ( SV139 @ SY1846 )
| ( SV470 = SY1846 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2476,plain,
! [SV141: $i,SV456: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ SV456 ) )
= $true )
| ( ( in @ SV471 @ SV141 )
= $true )
| ( ( in @ SV456 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2477,plain,
! [SV466: $i,SV141: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ SV141 )
| ~ ( in @ SV466 @ SV141 ) )
= $true )
| ( ( ~ ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) )
| ( SV457 = SV466 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2407]) ).
thf(2478,plain,
! [SV435: $i,SV141: $i,SV443: $i] :
( ( ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( ! [SY1815: $i] :
( ~ ( in @ SY1815 @ SV435 )
| ( in @ SY1815 @ SV443 ) )
| ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2479,plain,
! [SV141: $i,SV428: $i] :
( ( ( ! [SY1797: $i] :
~ ( in @ SY1797 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2480,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2481,plain,
! [SV146: $i,SV287: $i > $o,SV436: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( SV287 @ SV436 )
= $false )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2411]) ).
thf(2482,plain,
! [SV146: $i,SV447: $i,SV287: $i > $o] :
( ( ( SV287 @ SV447 )
= $false )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2483,plain,
! [SV287: $i > $o,SV146: $i,SV458: $i] :
( ( ( in @ SV458 @ SV146 )
= $false )
| ( ( ~ ( SV287 @ SV458 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2484,plain,
! [SV287: $i > $o,SV146: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ SV146 ) )
= $true )
| ( ( ~ ( SV287 @ SV467 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2485,plain,
! [SV287: $i > $o,SV146: $i,SV459: $i] :
( ( ( in @ SV459 @ SV146 )
= $false )
| ( ( ~ ( SV287 @ SV459 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2486,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV437 ) ) )
= $false )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2418]) ).
thf(2487,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i,SV475: $i] :
( ( ( ~ ~ ( ~ ( in @ SV475 @ SV304 )
| ~ ( SV161 @ SV475 @ SV437 ) ) )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2488,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i] :
( ( ( ~ ! [SY1856: $i] :
~ ( ~ ( ~ ( in @ SY1856 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1856 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1856 ) )
| ( in @ SY1856 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2420]) ).
thf(2489,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i] :
( ( ( ! [SY1847: $i] :
~ ( ~ ( ~ ( in @ SY1847 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1847 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1847 ) )
| ( in @ SY1847 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2421]) ).
thf(2490,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK75_SY1509 @ SV403 @ SV167 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2422]) ).
thf(2491,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ~ ! [SY1842: $i] :
( ~ ( SV167 @ SY1842 )
| ( ( sK75_SY1509 @ SV403 @ SV167 )
= SY1842 ) ) )
= $false )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2422]) ).
thf(2492,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( SV167 @ ( sK68_SY1509 @ SV403 @ SV167 ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2423]) ).
thf(2493,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ! [SY1832: $i] :
( ~ ( SV167 @ SY1832 )
| ( ( sK68_SY1509 @ SV403 @ SV167 )
= SY1832 ) ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2424]) ).
thf(2494,plain,
! [SV390: $i,SV448: $i,SV460: $i,SV46: $i > $o] :
( ( ( SV46 @ SV460 )
= $false )
| ( ( SV448 = SV460 )
= $true )
| ( ( SV46 @ SV448 )
= $false )
| ( ( SV46 @ SV390 )
= $false )
| ( ( SV46 @ ( sK48_SY1761 @ SV390 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2495,plain,
! [SV391: $i,SV476: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV476 )
| ( ( sK58_SY1208 @ SV391 @ SV49 )
= SV476 ) )
= $true )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2496,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( SV49 @ ( sK69_SY1208 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2429]) ).
thf(2497,plain,
! [SV391: $i,SV49: $i > $o] :
( ( ( ! [SY1833: $i] :
( ~ ( SV49 @ SY1833 )
| ( ( sK69_SY1208 @ SV391 @ SV49 )
= SY1833 ) ) )
= $true )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2430]) ).
thf(2498,plain,
! [SV391: $i,SV477: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV477 )
| ( ( sK59_SY1208 @ SV391 @ SV49 )
= SV477 ) )
= $true )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2499,plain,
! [SV216: $i > $o,SV461: $i,SV54: $i > $o] :
( ( ( SV54 @ SV461 )
= $false )
| ( ( ~ ! [SY1834: $i] :
( ~ ( SV54 @ SY1834 )
| ( SV461 = SY1834 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2500,plain,
! [SV54: $i > $o,SV462: $i,SV216: $i > $o] :
( ( ( SV216 @ SV462 )
= $false )
| ( ( ~ ! [SY1835: $i] :
( ~ ( SV216 @ SY1835 )
| ( SV462 = SY1835 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2501,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2502,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2503,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2504,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2505,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2506,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2507,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2441]) ).
thf(2508,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2442]) ).
thf(2509,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( SV67 @ ( sK70_SY1260 @ SV392 @ SV67 ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2510,plain,
! [SV392: $i,SV67: $i > $o] :
( ( ( ! [SY1836: $i] :
( ~ ( SV67 @ SY1836 )
| ( ( sK70_SY1260 @ SV392 @ SV67 )
= SY1836 ) ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2444]) ).
thf(2511,plain,
! [SV392: $i,SV478: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ SV478 )
| ( ( sK60_SY1260 @ SV392 @ SV67 )
= SV478 ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2512,plain,
! [SV395: $i,SV469: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( SV103 @ SV469 )
| ( SV469
= ( sK71_SY1322 @ SV395 @ SV103 ) ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2447]) ).
thf(2513,plain,
! [SV103: $i > $o,SV395: $i,SV469: $i] :
( ( ( ~ ( ( SV469
!= ( sK71_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SV469 ) ) )
= $false )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2447]) ).
thf(2514,plain,
! [SV395: $i,SV468: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ SV468 )
| ( SV468
= ( sK61_SY1322 @ SV395 @ SV103 ) ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2448]) ).
thf(2515,plain,
! [SV103: $i > $o,SV395: $i,SV468: $i] :
( ( ( ( SV468
!= ( sK61_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SV468 ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2516,plain,
! [SV396: $i,SV452: $i,SV463: $i,SV107: $i > $o] :
( ( ( SV107 @ SV463 )
= $false )
| ( ( SV452 = SV463 )
= $true )
| ( ( SV107 @ SV452 )
= $false )
| ( ( SV107 @ SV396 )
= $false )
| ( ( SV107 @ ( sK51_SY1768 @ SV396 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2517,plain,
! [SV119: $i,SV265: $i > $o,SV357: $i] :
( ( ( in @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1622: $i] : ( SV265 @ SY1622 ) ) )
= $true )
| ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2454]) ).
thf(2518,plain,
! [SV357: $i,SV265: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1623: $i] : ( SV265 @ SY1623 ) )
= ( setadjoin @ ( sK73_SY1621 @ SV357 @ SV265 @ SV119 ) @ emptyset ) )
= $true )
| ( ( SV265 @ ( sK45_SY1729 @ SV357 @ SV265 @ SV119 ) )
= $true )
| ( ( SV265 @ SV357 )
= $false )
| ( ( in @ SV357 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2455]) ).
thf(2519,plain,
! [SV125: $i,SV398: $i,SV464: $i] :
( ( ( in @ SV464 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
= $false )
| ( ( ~ ( in @ SV464 @ SV125 ) )
= $true )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2520,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK78_SY1375 @ SV399 @ SV126 ) )
| ~ ! [SY1845: $i] :
( ~ ( SV126 @ SY1845 )
| ( ( sK78_SY1375 @ SV399 @ SV126 )
= SY1845 ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2521,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK76_SY1375 @ SV399 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2460]) ).
thf(2522,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ! [SY1843: $i] :
( ~ ( SV126 @ SY1843 )
| ( ( sK76_SY1375 @ SV399 @ SV126 )
= SY1843 ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2460]) ).
thf(2523,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK77_SY1375 @ SV399 @ SV126 ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2461]) ).
thf(2524,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ! [SY1844: $i] :
( ~ ( SV126 @ SY1844 )
| ( ( sK77_SY1375 @ SV399 @ SV126 )
= SY1844 ) ) )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2461]) ).
thf(2525,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( SV126 @ ( sK74_SY1375 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2462]) ).
thf(2526,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1840: $i] :
( ~ ( SV126 @ SY1840 )
| ( ( sK74_SY1375 @ SV399 @ SV126 )
= SY1840 ) ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2463]) ).
thf(2527,plain,
! [SV127: $i,SV271: $i > $o,SV434: $i] :
( ( ( ~ ( ~ ( in @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( SV271 @ SV434 )
= $false )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2464]) ).
thf(2528,plain,
! [SV446: $i,SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( SV271 @ SV446 )
= $false )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2529,plain,
! [SV127: $i,SV454: $i,SV271: $i > $o] :
( ( ( SV271 @ SV454 )
= $false )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2530,plain,
! [SV271: $i > $o,SV127: $i,SV465: $i] :
( ( ( in @ SV465 @ SV127 )
= $false )
| ( ( ~ ( SV271 @ SV465 ) )
= $true )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2531,plain,
! [SV127: $i,SV455: $i,SV271: $i > $o] :
( ( ( SV271 @ SV455 )
= $false )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2532,plain,
! [SV274: $i,SV400: $i > $o,SV130: $i,SV412: $i > $o] :
( ( ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
| ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) ) )
= $false )
| ( ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2533,plain,
! [SV274: $i,SV400: $i > $o,SV130: $i,SV412: $i > $o] :
( ( ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) ) )
= $false )
| ( ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2534,plain,
! [SV130: $i,SV274: $i,SV412: $i > $o,SV400: $i > $o] :
( ( ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
= $false )
| ( ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2535,plain,
! [SV442: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV442 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2471]) ).
thf(2536,plain,
! [SV139: $i > $o,SV282: $i > $o,SV442: $i] :
( ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( SV139 @ SV442 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2471]) ).
thf(2537,plain,
! [SV282: $i > $o,SV479: $i,SV139: $i > $o] :
( ( ( ~ ~ ( ~ ( SV139 @ SV479 )
| ~ ! [SY1859: $i] :
( ~ ( SV139 @ SY1859 )
| ( SV479 = SY1859 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2538,plain,
! [SV282: $i > $o,SV472: $i,SV139: $i > $o] :
( ( ( ~ ( ~ ( SV139 @ SV472 )
| ~ ! [SY1852: $i] :
( ~ ( SV139 @ SY1852 )
| ( SV472 = SY1852 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2539,plain,
! [SV282: $i > $o,SV473: $i,SV139: $i > $o] :
( ( ( ~ ( ~ ( SV139 @ SV473 )
| ~ ! [SY1853: $i] :
( ~ ( SV139 @ SY1853 )
| ( SV473 = SY1853 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2540,plain,
! [SV282: $i > $o,SV470: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV470 )
| ~ ! [SY1846: $i] :
( ~ ( SV139 @ SY1846 )
| ( SV470 = SY1846 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2475]) ).
thf(2541,plain,
! [SV141: $i,SV456: $i,SV471: $i] :
( ( ( in @ SV471 @ SV456 )
= $false )
| ( ( in @ SV471 @ SV141 )
= $true )
| ( ( in @ SV456 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2542,plain,
! [SV466: $i,SV141: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ SV141 ) )
= $true )
| ( ( ~ ( in @ SV466 @ SV141 ) )
= $true )
| ( ( ~ ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) )
| ( SV457 = SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2543,plain,
! [SV141: $i,SV443: $i,SV435: $i] :
( ( ( ! [SY1815: $i] :
( ~ ( in @ SY1815 @ SV435 )
| ( in @ SY1815 @ SV443 ) ) )
= $true )
| ( ( ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true )
| ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2544,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2545,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( in @ SV474 @ SV428 )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2546,plain,
! [SV146: $i,SV287: $i > $o,SV436: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( SV287 @ SV436 )
= $false )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2547,plain,
! [SV447: $i,SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( SV287 @ SV447 )
= $false )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2548,plain,
! [SV146: $i,SV458: $i,SV287: $i > $o] :
( ( ( SV287 @ SV458 )
= $false )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2549,plain,
! [SV287: $i > $o,SV146: $i,SV467: $i] :
( ( ( in @ SV467 @ SV146 )
= $false )
| ( ( ~ ( SV287 @ SV467 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2550,plain,
! [SV146: $i,SV459: $i,SV287: $i > $o] :
( ( ( SV287 @ SV459 )
= $false )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(2551,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV437 ) ) )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2552,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i,SV475: $i] :
( ( ( ~ ( ~ ( in @ SV475 @ SV304 )
| ~ ( SV161 @ SV475 @ SV437 ) ) )
= $false )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2553,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i] :
( ( ( ! [SY1856: $i] :
~ ( ~ ( ~ ( in @ SY1856 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV304 )
| ~ ( SV161 @ SY1694 @ SY1856 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV304 )
| ~ ( SV161 @ SY1695 @ SY1856 ) )
| ( in @ SY1856 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2554,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV481: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV304 )
| ~ ( SV161 @ SY1860 @ SV481 ) ) )
| ~ ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV304 )
| ~ ( SV161 @ SY1861 @ SV481 ) )
| ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2555,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( SV167 @ ( sK75_SY1509 @ SV403 @ SV167 ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2490]) ).
thf(2556,plain,
! [SV403: $i,SV167: $i > $o] :
( ( ( ! [SY1842: $i] :
( ~ ( SV167 @ SY1842 )
| ( ( sK75_SY1509 @ SV403 @ SV167 )
= SY1842 ) ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2491]) ).
thf(2557,plain,
! [SV403: $i,SV482: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV482 )
| ( ( sK68_SY1509 @ SV403 @ SV167 )
= SV482 ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(2558,plain,
! [SV391: $i,SV476: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV476 ) )
= $true )
| ( ( ( sK58_SY1208 @ SV391 @ SV49 )
= SV476 )
= $true )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2559,plain,
! [SV391: $i,SV483: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV483 )
| ( ( sK69_SY1208 @ SV391 @ SV49 )
= SV483 ) )
= $true )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2560,plain,
! [SV391: $i,SV477: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV477 ) )
= $true )
| ( ( ( sK59_SY1208 @ SV391 @ SV49 )
= SV477 )
= $true )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2561,plain,
! [SV216: $i > $o,SV461: $i,SV54: $i > $o] :
( ( ( ! [SY1834: $i] :
( ~ ( SV54 @ SY1834 )
| ( SV461 = SY1834 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2562,plain,
! [SV54: $i > $o,SV462: $i,SV216: $i > $o] :
( ( ( ! [SY1835: $i] :
( ~ ( SV216 @ SY1835 )
| ( SV462 = SY1835 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2563,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2564,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2565,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2566,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2504]) ).
thf(2567,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2568,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2569,plain,
! [SV216: $i > $o,SV484: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ SV484 )
| ~ ! [SY1862: $i] :
( ~ ( SV54 @ SY1862 )
| ( SV484 = SY1862 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2570,plain,
! [SV54: $i > $o,SV485: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ SV485 )
| ~ ! [SY1863: $i] :
( ~ ( SV216 @ SY1863 )
| ( SV485 = SY1863 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(2571,plain,
! [SV392: $i,SV486: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ SV486 )
| ( ( sK70_SY1260 @ SV392 @ SV67 )
= SV486 ) )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2572,plain,
! [SV392: $i,SV478: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ SV478 ) )
= $true )
| ( ( ( sK60_SY1260 @ SV392 @ SV67 )
= SV478 )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2573,plain,
! [SV395: $i,SV469: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ SV469 )
| ( SV469
= ( sK71_SY1322 @ SV395 @ SV103 ) ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2512]) ).
thf(2574,plain,
! [SV103: $i > $o,SV395: $i,SV469: $i] :
( ( ( ( SV469
!= ( sK71_SY1322 @ SV395 @ SV103 ) )
| ( SV103 @ SV469 ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2513]) ).
thf(2575,plain,
! [SV395: $i,SV468: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ SV468 ) )
= $true )
| ( ( SV468
= ( sK61_SY1322 @ SV395 @ SV103 ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2576,plain,
! [SV103: $i > $o,SV395: $i,SV468: $i] :
( ( ( SV468
!= ( sK61_SY1322 @ SV395 @ SV103 ) )
= $true )
| ( ( SV103 @ SV468 )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2577,plain,
! [SV398: $i,SV125: $i,SV464: $i] :
( ( ( in @ SV464 @ SV125 )
= $false )
| ( ( in @ SV464 @ ( sK34_SY1371 @ SV398 @ SV125 ) )
= $false )
| ( ( in @ SV398 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2578,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ ( sK78_SY1375 @ SV399 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2579,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ~ ! [SY1845: $i] :
( ~ ( SV126 @ SY1845 )
| ( ( sK78_SY1375 @ SV399 @ SV126 )
= SY1845 ) ) )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2580,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( SV126 @ ( sK76_SY1375 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2521]) ).
thf(2581,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1843: $i] :
( ~ ( SV126 @ SY1843 )
| ( ( sK76_SY1375 @ SV399 @ SV126 )
= SY1843 ) ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2522]) ).
thf(2582,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( SV126 @ ( sK77_SY1375 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2523]) ).
thf(2583,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1844: $i] :
( ~ ( SV126 @ SY1844 )
| ( ( sK77_SY1375 @ SV399 @ SV126 )
= SY1844 ) ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2584,plain,
! [SV399: $i,SV487: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ SV487 )
| ( ( sK74_SY1375 @ SV399 @ SV126 )
= SV487 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(2585,plain,
! [SV127: $i,SV271: $i > $o,SV434: $i] :
( ( ( ~ ( in @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( SV271 @ SV434 )
= $false )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2586,plain,
! [SV127: $i,SV271: $i > $o,SV446: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( SV271 @ SV446 )
= $false )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2528]) ).
thf(2587,plain,
! [SV454: $i,SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( SV271 @ SV454 )
= $false )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2588,plain,
! [SV127: $i,SV465: $i,SV271: $i > $o] :
( ( ( SV271 @ SV465 )
= $false )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $true )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2530]) ).
thf(2589,plain,
! [SV455: $i,SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( SV271 @ SV455 )
= $false )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2590,plain,
! [SV274: $i,SV400: $i > $o,SV130: $i,SV412: $i > $o] :
( ( ( ~ ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) ) )
= $false )
| ( ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2532]) ).
thf(2591,plain,
! [SV130: $i,SV274: $i,SV412: $i > $o,SV400: $i > $o] :
( ( ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
= $false )
| ( ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2532]) ).
thf(2592,plain,
! [SV274: $i,SV400: $i > $o,SV130: $i,SV412: $i > $o] :
( ( ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $true )
| ( ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $false )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2533]) ).
thf(2593,plain,
! [SV442: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2535]) ).
thf(2594,plain,
! [SV442: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2595,plain,
! [SV282: $i > $o,SV479: $i,SV139: $i > $o] :
( ( ( ~ ( ~ ( SV139 @ SV479 )
| ~ ! [SY1859: $i] :
( ~ ( SV139 @ SY1859 )
| ( SV479 = SY1859 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2596,plain,
! [SV282: $i > $o,SV472: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV472 )
| ~ ! [SY1852: $i] :
( ~ ( SV139 @ SY1852 )
| ( SV472 = SY1852 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2538]) ).
thf(2597,plain,
! [SV282: $i > $o,SV473: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV473 )
| ~ ! [SY1853: $i] :
( ~ ( SV139 @ SY1853 )
| ( SV473 = SY1853 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2598,plain,
! [SV282: $i > $o,SV470: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV470 ) )
= $true )
| ( ( ~ ! [SY1846: $i] :
( ~ ( SV139 @ SY1846 )
| ( SV470 = SY1846 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2599,plain,
! [SV466: $i,SV141: $i,SV457: $i] :
( ( ( in @ SV457 @ SV141 )
= $false )
| ( ( ~ ( in @ SV466 @ SV141 ) )
= $true )
| ( ( ~ ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) )
| ( SV457 = SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2600,plain,
! [SV141: $i,SV443: $i,SV435: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV435 )
| ( in @ SV488 @ SV443 ) )
= $true )
| ( ( ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true )
| ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(2601,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( in @ SV480 @ SV428 )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( ~ ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2602,plain,
! [SV474: $i,SV428: $i,SV141: $i] :
( ( ( ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2603,plain,
! [SV146: $i,SV287: $i > $o,SV436: $i] :
( ( ( ~ ( in @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( SV287 @ SV436 )
= $false )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2604,plain,
! [SV146: $i,SV287: $i > $o,SV447: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( SV287 @ SV447 )
= $false )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2547]) ).
thf(2605,plain,
! [SV458: $i,SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( SV287 @ SV458 )
= $false )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2606,plain,
! [SV146: $i,SV467: $i,SV287: $i > $o] :
( ( ( SV287 @ SV467 )
= $false )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( ~ ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $true )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2607,plain,
! [SV459: $i,SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( SV287 @ SV459 )
= $false )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2608,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ( in @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV437 ) )
= $false )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2609,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV304 )
| ~ ( SV161 @ SV475 @ SV437 ) )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2610,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV489: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1868: $i] :
~ ~ ( ~ ( in @ SY1868 @ SV304 )
| ~ ( SV161 @ SY1868 @ SV489 ) ) )
| ~ ( ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ SV304 )
| ~ ( SV161 @ SY1869 @ SV489 ) )
| ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(2611,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV481: $i] :
( ( ( ~ ( ~ ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV304 )
| ~ ( SV161 @ SY1860 @ SV481 ) ) )
| ~ ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV304 )
| ~ ( SV161 @ SY1861 @ SV481 ) )
| ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2612,plain,
! [SV403: $i,SV490: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV490 )
| ( ( sK75_SY1509 @ SV403 @ SV167 )
= SV490 ) )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(2613,plain,
! [SV403: $i,SV482: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV482 ) )
= $true )
| ( ( ( sK68_SY1509 @ SV403 @ SV167 )
= SV482 )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2614,plain,
! [SV391: $i,SV476: $i,SV49: $i > $o] :
( ( ( SV49 @ SV476 )
= $false )
| ( ( ( sK58_SY1208 @ SV391 @ SV49 )
= SV476 )
= $true )
| ( ( SV49 @ ( sK38_SY1206 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2615,plain,
! [SV391: $i,SV483: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV483 ) )
= $true )
| ( ( ( sK69_SY1208 @ SV391 @ SV49 )
= SV483 )
= $true )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2616,plain,
! [SV391: $i,SV477: $i,SV49: $i > $o] :
( ( ( SV49 @ SV477 )
= $false )
| ( ( ( sK59_SY1208 @ SV391 @ SV49 )
= SV477 )
= $true )
| ( ( ( sK38_SY1206 @ SV391 @ SV49 )
= ( sK43_SY1804 @ SV391 @ SV49 ) )
= $false )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2617,plain,
! [SV461: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
| ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2561]) ).
thf(2618,plain,
! [SV462: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
| ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2562]) ).
thf(2619,plain,
! [SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1222: $i] :
~ ~ ( ~ ( SV54 @ SY1222 )
| ~ ! [SY1223: $i] :
( ~ ( SV54 @ SY1223 )
| ( SY1222 = SY1223 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2620,plain,
! [SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1564: $i] :
~ ~ ( ~ ( SV216 @ SY1564 )
| ~ ! [SY1565: $i] :
( ~ ( SV216 @ SY1565 )
| ( SY1564 = SY1565 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2621,plain,
! [SV216: $i > $o,SV491: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ SV491 )
| ~ ! [SY1870: $i] :
( ~ ( SV54 @ SY1870 )
| ( SV491 = SY1870 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2622,plain,
! [SV54: $i > $o,SV492: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ SV492 )
| ~ ! [SY1871: $i] :
( ~ ( SV216 @ SY1871 )
| ( SV492 = SY1871 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2623,plain,
! [SV216: $i > $o,SV493: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ SV493 )
| ~ ! [SY1872: $i] :
( ~ ( SV54 @ SY1872 )
| ( SV493 = SY1872 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2624,plain,
! [SV54: $i > $o,SV494: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ SV494 )
| ~ ! [SY1873: $i] :
( ~ ( SV216 @ SY1873 )
| ( SV494 = SY1873 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(2625,plain,
! [SV216: $i > $o,SV484: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ SV484 )
| ~ ! [SY1862: $i] :
( ~ ( SV54 @ SY1862 )
| ( SV484 = SY1862 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2626,plain,
! [SV54: $i > $o,SV485: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ SV485 )
| ~ ! [SY1863: $i] :
( ~ ( SV216 @ SY1863 )
| ( SV485 = SY1863 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2627,plain,
! [SV392: $i,SV486: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ SV486 ) )
= $true )
| ( ( ( sK70_SY1260 @ SV392 @ SV67 )
= SV486 )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2571]) ).
thf(2628,plain,
! [SV392: $i,SV478: $i,SV67: $i > $o] :
( ( ( SV67 @ SV478 )
= $false )
| ( ( ( sK60_SY1260 @ SV392 @ SV67 )
= SV478 )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV392
= ( sK49_SY1763 @ SV392 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2629,plain,
! [SV395: $i,SV469: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ SV469 ) )
= $true )
| ( ( SV469
= ( sK71_SY1322 @ SV395 @ SV103 ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2573]) ).
thf(2630,plain,
! [SV103: $i > $o,SV395: $i,SV469: $i] :
( ( ( SV469
!= ( sK71_SY1322 @ SV395 @ SV103 ) )
= $true )
| ( ( SV103 @ SV469 )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2631,plain,
! [SV395: $i,SV468: $i,SV103: $i > $o] :
( ( ( SV103 @ SV468 )
= $false )
| ( ( SV468
= ( sK61_SY1322 @ SV395 @ SV103 ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2632,plain,
! [SV103: $i > $o,SV395: $i,SV468: $i] :
( ( ( SV468
= ( sK61_SY1322 @ SV395 @ SV103 ) )
= $false )
| ( ( SV103 @ SV468 )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV395
= ( sK50_SY1767 @ SV395 @ SV103 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2633,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( SV126 @ ( sK78_SY1375 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2634,plain,
! [SV399: $i,SV126: $i > $o] :
( ( ( ! [SY1845: $i] :
( ~ ( SV126 @ SY1845 )
| ( ( sK78_SY1375 @ SV399 @ SV126 )
= SY1845 ) ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2635,plain,
! [SV399: $i,SV495: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ SV495 )
| ( ( sK76_SY1375 @ SV399 @ SV126 )
= SV495 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(2636,plain,
! [SV399: $i,SV496: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ SV496 )
| ( ( sK77_SY1375 @ SV399 @ SV126 )
= SV496 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(2637,plain,
! [SV399: $i,SV487: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ SV487 ) )
= $true )
| ( ( ( sK74_SY1375 @ SV399 @ SV126 )
= SV487 )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2638,plain,
! [SV127: $i,SV271: $i > $o,SV434: $i] :
( ( ( ~ ( in @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) ) )
= $false )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( SV271 @ SV434 )
= $false )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2639,plain,
! [SV434: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 ) @ emptyset ) )
= $false )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( SV271 @ SV434 )
= $false )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2585]) ).
thf(2640,plain,
! [SV127: $i,SV271: $i > $o,SV446: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( SV271 @ SV446 )
= $false )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2641,plain,
! [SV127: $i,SV271: $i > $o,SV454: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( SV271 @ SV454 )
= $false )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2587]) ).
thf(2642,plain,
! [SV465: $i,SV271: $i > $o,SV127: $i] :
( ( ( ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ SY1633 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( SV271 @ SV465 )
= $false )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2643,plain,
! [SV127: $i,SV271: $i > $o,SV455: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( SV271 @ SV455 )
= $false )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2589]) ).
thf(2644,plain,
! [SV274: $i,SV400: $i > $o,SV130: $i,SV412: $i > $o] :
( ( ( SV412 @ ( sK53_SY1805 @ SV130 @ SV400 @ SV412 @ SV274 ) )
= $true )
| ( ( SV400 @ ( sK41_SY1788 @ SV412 @ SV400 @ SV274 @ SV130 ) )
= $true )
| ( ( ( dsetconstr @ SV130
@ ^ [SY1775: $i] : ( SV400 @ SY1775 ) )
= ( dsetconstr @ SV274
@ ^ [SY1791: $i] : ( SV412 @ SY1791 ) ) )
= $true )
| ( ( SV130 = SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2590]) ).
thf(2645,plain,
! [SV442: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2646,plain,
! [SV442: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2647,plain,
! [SV282: $i > $o,SV479: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV479 )
| ~ ! [SY1859: $i] :
( ~ ( SV139 @ SY1859 )
| ( SV479 = SY1859 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2595]) ).
thf(2648,plain,
! [SV282: $i > $o,SV472: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV472 ) )
= $true )
| ( ( ~ ! [SY1852: $i] :
( ~ ( SV139 @ SY1852 )
| ( SV472 = SY1852 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2649,plain,
! [SV282: $i > $o,SV473: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV473 ) )
= $true )
| ( ( ~ ! [SY1853: $i] :
( ~ ( SV139 @ SY1853 )
| ( SV473 = SY1853 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2650,plain,
! [SV282: $i > $o,SV470: $i,SV139: $i > $o] :
( ( ( SV139 @ SV470 )
= $false )
| ( ( ~ ! [SY1846: $i] :
( ~ ( SV139 @ SY1846 )
| ( SV470 = SY1846 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2651,plain,
! [SV457: $i,SV141: $i,SV466: $i] :
( ( ( in @ SV466 @ SV141 )
= $false )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( ~ ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) )
| ( SV457 = SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2652,plain,
! [SV141: $i,SV443: $i,SV435: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV435 ) )
= $true )
| ( ( in @ SV488 @ SV443 )
= $true )
| ( ( ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true )
| ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2653,plain,
! [SV480: $i,SV428: $i,SV141: $i] :
( ( ( ! [SY1798: $i] :
~ ~ ! [SY1799: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1798 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1799 @ SV428 ) )
| ~ ~ ~ ! [SY1800: $i] :
~ ~ ( ~ ( in @ SY1800 @ SY1798 )
| ~ ( in @ SY1800 @ SV428 ) ) )
| ~ ! [SY1750: $i] :
( ~ ( in @ SY1750 @ ( sK3_SY1423 @ SV141 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1750 )
| ( in @ SX6 @ SY1798 ) )
| ( in @ SY1799 @ SY1750 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2654,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ~ ! [SY1878: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1878 @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
| ~ ! [SY1880: $i] :
( ~ ( in @ SY1880 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1881: $i] :
( ~ ( in @ SY1881 @ SY1880 )
| ( in @ SY1881 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ SY1878 @ SY1880 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2602]) ).
thf(2655,plain,
! [SV146: $i,SV287: $i > $o,SV436: $i] :
( ( ( ~ ( in @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) ) )
= $false )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( SV287 @ SV436 )
= $false )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2603]) ).
thf(2656,plain,
! [SV436: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 ) @ emptyset ) )
= $false )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( SV287 @ SV436 )
= $false )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2603]) ).
thf(2657,plain,
! [SV146: $i,SV287: $i > $o,SV447: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( SV287 @ SV447 )
= $false )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2604]) ).
thf(2658,plain,
! [SV146: $i,SV287: $i > $o,SV458: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( SV287 @ SV458 )
= $false )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2605]) ).
thf(2659,plain,
! [SV467: $i,SV287: $i > $o,SV146: $i] :
( ( ( ! [SY1666: $i] :
~ ~ ( ~ ( in @ SY1666
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ SY1666 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( SV287 @ SV467 )
= $false )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2660,plain,
! [SV146: $i,SV287: $i > $o,SV459: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( SV287 @ SV459 )
= $false )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2607]) ).
thf(2661,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( ~ ( in @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV304 ) )
= $false )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2608]) ).
thf(2662,plain,
! [SV304: $i,SV437: $i,SV161: $i > $i > $o] :
( ( ( ~ ( SV161 @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV437 ) )
= $false )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2608]) ).
thf(2663,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV304 ) )
= $true )
| ( ( ~ ( SV161 @ SV475 @ SV437 ) )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2664,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV489: $i] :
( ( ( ~ ( ~ ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1868: $i] :
~ ~ ( ~ ( in @ SY1868 @ SV304 )
| ~ ( SV161 @ SY1868 @ SV489 ) ) )
| ~ ( ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ SV304 )
| ~ ( SV161 @ SY1869 @ SV489 ) )
| ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2665,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV481: $i] :
( ( ( ~ ( ~ ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV304 )
| ~ ( SV161 @ SY1860 @ SV481 ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2611]) ).
thf(2666,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV304 )
| ~ ( SV161 @ SY1861 @ SV481 ) )
| ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2611]) ).
thf(2667,plain,
! [SV403: $i,SV490: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV490 ) )
= $true )
| ( ( ( sK75_SY1509 @ SV403 @ SV167 )
= SV490 )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2668,plain,
! [SV403: $i,SV482: $i,SV167: $i > $o] :
( ( ( SV167 @ SV482 )
= $false )
| ( ( ( sK68_SY1509 @ SV403 @ SV167 )
= SV482 )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV403
= ( sK54_SY1785 @ SV403 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2669,plain,
! [SV391: $i,SV483: $i,SV49: $i > $o] :
( ( ( SV49 @ SV483 )
= $false )
| ( ( ( sK69_SY1208 @ SV391 @ SV49 )
= SV483 )
= $true )
| ( ( SV49 @ ( sK43_SY1804 @ SV391 @ SV49 ) )
= $true )
| ( ( SV49 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2670,plain,
! [SV461: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2617]) ).
thf(2671,plain,
! [SV54: $i > $o,SV216: $i > $o,SV461: $i] :
( ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2617]) ).
thf(2672,plain,
! [SV462: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2673,plain,
! [SV216: $i > $o,SV54: $i > $o,SV462: $i] :
( ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2674,plain,
! [SV216: $i > $o,SV497: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ SV497 )
| ~ ! [SY1886: $i] :
( ~ ( SV54 @ SY1886 )
| ( SV497 = SY1886 ) ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2675,plain,
! [SV54: $i > $o,SV498: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ SV498 )
| ~ ! [SY1887: $i] :
( ~ ( SV216 @ SY1887 )
| ( SV498 = SY1887 ) ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(2676,plain,
! [SV216: $i > $o,SV491: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ SV491 )
| ~ ! [SY1870: $i] :
( ~ ( SV54 @ SY1870 )
| ( SV491 = SY1870 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2677,plain,
! [SV54: $i > $o,SV492: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ SV492 )
| ~ ! [SY1871: $i] :
( ~ ( SV216 @ SY1871 )
| ( SV492 = SY1871 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2678,plain,
! [SV216: $i > $o,SV493: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ SV493 )
| ~ ! [SY1872: $i] :
( ~ ( SV54 @ SY1872 )
| ( SV493 = SY1872 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2679,plain,
! [SV54: $i > $o,SV494: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ SV494 )
| ~ ! [SY1873: $i] :
( ~ ( SV216 @ SY1873 )
| ( SV494 = SY1873 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(2680,plain,
! [SV216: $i > $o,SV484: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV484 )
| ~ ! [SY1862: $i] :
( ~ ( SV54 @ SY1862 )
| ( SV484 = SY1862 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2625]) ).
thf(2681,plain,
! [SV54: $i > $o,SV485: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV485 )
| ~ ! [SY1863: $i] :
( ~ ( SV216 @ SY1863 )
| ( SV485 = SY1863 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2626]) ).
thf(2682,plain,
! [SV392: $i,SV486: $i,SV67: $i > $o] :
( ( ( SV67 @ SV486 )
= $false )
| ( ( ( sK70_SY1260 @ SV392 @ SV67 )
= SV486 )
= $true )
| ( ( SV67 @ SV392 )
= $false )
| ( ( SV67 @ ( sK49_SY1763 @ SV392 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2683,plain,
! [SV395: $i,SV469: $i,SV103: $i > $o] :
( ( ( SV103 @ SV469 )
= $false )
| ( ( SV469
= ( sK71_SY1322 @ SV395 @ SV103 ) )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2684,plain,
! [SV103: $i > $o,SV395: $i,SV469: $i] :
( ( ( SV469
= ( sK71_SY1322 @ SV395 @ SV103 ) )
= $false )
| ( ( SV103 @ SV469 )
= $true )
| ( ( SV103 @ SV395 )
= $false )
| ( ( SV103 @ ( sK50_SY1767 @ SV395 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2685,plain,
! [SV399: $i,SV499: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ SV499 )
| ( ( sK78_SY1375 @ SV399 @ SV126 )
= SV499 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(2686,plain,
! [SV399: $i,SV495: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ SV495 ) )
= $true )
| ( ( ( sK76_SY1375 @ SV399 @ SV126 )
= SV495 )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2687,plain,
! [SV399: $i,SV496: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ SV496 ) )
= $true )
| ( ( ( sK77_SY1375 @ SV399 @ SV126 )
= SV496 )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2688,plain,
! [SV399: $i,SV487: $i,SV126: $i > $o] :
( ( ( SV126 @ SV487 )
= $false )
| ( ( ( sK74_SY1375 @ SV399 @ SV126 )
= SV487 )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2689,plain,
! [SV127: $i,SV271: $i > $o,SV434: $i] :
( ( ( in @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
= $true )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( SV271 @ SV434 )
= $false )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2638]) ).
thf(2690,plain,
! [SV434: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
= ( setadjoin @ ( sK80_SY1633 @ SV434 @ SV271 @ SV127 ) @ emptyset ) )
= $true )
| ( ( in @ SV434 @ SV127 )
= $false )
| ( ( SV271 @ SV434 )
= $false )
| ( ( in @ ( sK14_SY1630 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2639]) ).
thf(2691,plain,
! [SV127: $i,SV271: $i > $o,SV446: $i] :
( ( ( ~ ( in @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( SV271 @ SV446 )
= $false )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2692,plain,
! [SV127: $i,SV271: $i > $o,SV454: $i] :
( ( ( ~ ( ~ ( in @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( SV271 @ SV454 )
= $false )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2641]) ).
thf(2693,plain,
! [SV127: $i,SV271: $i > $o,SV465: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( SV271 @ SV465 )
= $false )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2642]) ).
thf(2694,plain,
! [SV127: $i,SV271: $i > $o,SV455: $i] :
( ( ( ~ ( ~ ( in @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( SV271 @ SV455 )
= $false )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2643]) ).
thf(2695,plain,
! [SV442: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2696,plain,
! [SV442: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2697,plain,
! [SV282: $i > $o,SV479: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV479 ) )
= $true )
| ( ( ~ ! [SY1859: $i] :
( ~ ( SV139 @ SY1859 )
| ( SV479 = SY1859 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(2698,plain,
! [SV282: $i > $o,SV472: $i,SV139: $i > $o] :
( ( ( SV139 @ SV472 )
= $false )
| ( ( ~ ! [SY1852: $i] :
( ~ ( SV139 @ SY1852 )
| ( SV472 = SY1852 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2699,plain,
! [SV282: $i > $o,SV473: $i,SV139: $i > $o] :
( ( ( SV139 @ SV473 )
= $false )
| ( ( ~ ! [SY1853: $i] :
( ~ ( SV139 @ SY1853 )
| ( SV473 = SY1853 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2700,plain,
! [SV282: $i > $o,SV470: $i,SV139: $i > $o] :
( ( ( ! [SY1846: $i] :
( ~ ( SV139 @ SY1846 )
| ( SV470 = SY1846 ) ) )
= $false )
| ( ( SV139 @ SV470 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2701,plain,
! [SV466: $i,SV457: $i,SV141: $i] :
( ( ( ~ ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2702,plain,
! [SV141: $i,SV443: $i,SV435: $i,SV488: $i] :
( ( ( in @ SV488 @ SV435 )
= $false )
| ( ( in @ SV488 @ SV443 )
= $true )
| ( ( ! [SY1816: $i] :
( ~ ( in @ SY1816 @ SV443 )
| ( in @ SY1816 @ SV435 ) ) )
= $true )
| ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2703,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ~ ! [SY1890: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1890 @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
| ~ ! [SY1892: $i] :
( ~ ( in @ SY1892 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SY1892 )
| ( in @ SY1893 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ SY1890 @ SY1892 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2653]) ).
thf(2704,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ! [SY1878: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1878 @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
| ~ ! [SY1880: $i] :
( ~ ( in @ SY1880 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1881: $i] :
( ~ ( in @ SY1881 @ SY1880 )
| ( in @ SY1881 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ SY1878 @ SY1880 ) ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2654]) ).
thf(2705,plain,
! [SV146: $i,SV287: $i > $o,SV436: $i] :
( ( ( in @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
= $true )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( SV287 @ SV436 )
= $false )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2655]) ).
thf(2706,plain,
! [SV436: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
= ( setadjoin @ ( sK82_SY1666 @ SV436 @ SV287 @ SV146 ) @ emptyset ) )
= $true )
| ( ( in @ SV436 @ SV146 )
= $false )
| ( ( SV287 @ SV436 )
= $false )
| ( ( in @ ( sK18_SY1663 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2656]) ).
thf(2707,plain,
! [SV146: $i,SV287: $i > $o,SV447: $i] :
( ( ( ~ ( in @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( SV287 @ SV447 )
= $false )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2708,plain,
! [SV146: $i,SV287: $i > $o,SV458: $i] :
( ( ( ~ ( ~ ( in @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( SV287 @ SV458 )
= $false )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2658]) ).
thf(2709,plain,
! [SV146: $i,SV287: $i > $o,SV467: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( SV287 @ SV467 )
= $false )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2659]) ).
thf(2710,plain,
! [SV146: $i,SV287: $i > $o,SV459: $i] :
( ( ( ~ ( ~ ( in @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( SV287 @ SV459 )
= $false )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2660]) ).
thf(2711,plain,
! [SV304: $i,SV161: $i > $i > $o,SV437: $i] :
( ( ( in @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2661]) ).
thf(2712,plain,
! [SV304: $i,SV437: $i,SV161: $i > $i > $o] :
( ( ( SV161 @ ( sK83_SY1812 @ SV437 @ SV161 @ SV304 ) @ SV437 )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $false )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2662]) ).
thf(2713,plain,
! [SV437: $i,SV161: $i > $i > $o,SV304: $i,SV475: $i] :
( ( ( in @ SV475 @ SV304 )
= $false )
| ( ( ~ ( SV161 @ SV475 @ SV437 ) )
= $true )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2714,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV489: $i] :
( ( ( ~ ( ~ ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1868: $i] :
~ ~ ( ~ ( in @ SY1868 @ SV304 )
| ~ ( SV161 @ SY1868 @ SV489 ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2664]) ).
thf(2715,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ( ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ SV304 )
| ~ ( SV161 @ SY1869 @ SV489 ) )
| ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) ) ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2664]) ).
thf(2716,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV304 )
| ~ ( SV161 @ SY1860 @ SV481 ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2717,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV304 )
| ~ ( SV161 @ SY1861 @ SV481 ) )
| ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2666]) ).
thf(2718,plain,
! [SV403: $i,SV490: $i,SV167: $i > $o] :
( ( ( SV167 @ SV490 )
= $false )
| ( ( ( sK75_SY1509 @ SV403 @ SV167 )
= SV490 )
= $true )
| ( ( SV167 @ SV403 )
= $false )
| ( ( SV167 @ ( sK54_SY1785 @ SV403 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2719,plain,
! [SV461: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2670]) ).
thf(2720,plain,
! [SV461: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2721,plain,
! [SV462: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2672]) ).
thf(2722,plain,
! [SV462: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2723,plain,
! [SV216: $i > $o,SV497: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ SV497 )
| ~ ! [SY1886: $i] :
( ~ ( SV54 @ SY1886 )
| ( SV497 = SY1886 ) ) ) )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2724,plain,
! [SV54: $i > $o,SV498: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ SV498 )
| ~ ! [SY1887: $i] :
( ~ ( SV216 @ SY1887 )
| ( SV498 = SY1887 ) ) ) )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2725,plain,
! [SV216: $i > $o,SV491: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV491 )
| ~ ! [SY1870: $i] :
( ~ ( SV54 @ SY1870 )
| ( SV491 = SY1870 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2676]) ).
thf(2726,plain,
! [SV54: $i > $o,SV492: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV492 )
| ~ ! [SY1871: $i] :
( ~ ( SV216 @ SY1871 )
| ( SV492 = SY1871 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2677]) ).
thf(2727,plain,
! [SV216: $i > $o,SV493: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV493 )
| ~ ! [SY1872: $i] :
( ~ ( SV54 @ SY1872 )
| ( SV493 = SY1872 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2678]) ).
thf(2728,plain,
! [SV54: $i > $o,SV494: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV494 )
| ~ ! [SY1873: $i] :
( ~ ( SV216 @ SY1873 )
| ( SV494 = SY1873 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2679]) ).
thf(2729,plain,
! [SV216: $i > $o,SV484: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV484 ) )
= $true )
| ( ( ~ ! [SY1862: $i] :
( ~ ( SV54 @ SY1862 )
| ( SV484 = SY1862 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2730,plain,
! [SV54: $i > $o,SV485: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV485 ) )
= $true )
| ( ( ~ ! [SY1863: $i] :
( ~ ( SV216 @ SY1863 )
| ( SV485 = SY1863 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(2731,plain,
! [SV399: $i,SV499: $i,SV126: $i > $o] :
( ( ( ~ ( SV126 @ SV499 ) )
= $true )
| ( ( ( sK78_SY1375 @ SV399 @ SV126 )
= SV499 )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2685]) ).
thf(2732,plain,
! [SV399: $i,SV495: $i,SV126: $i > $o] :
( ( ( SV126 @ SV495 )
= $false )
| ( ( ( sK76_SY1375 @ SV399 @ SV126 )
= SV495 )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2733,plain,
! [SV399: $i,SV496: $i,SV126: $i > $o] :
( ( ( SV126 @ SV496 )
= $false )
| ( ( ( sK77_SY1375 @ SV399 @ SV126 )
= SV496 )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $false )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2734,plain,
! [SV127: $i,SV271: $i > $o,SV446: $i] :
( ( ( ~ ( in @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) ) )
= $false )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( SV271 @ SV446 )
= $false )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2691]) ).
thf(2735,plain,
! [SV446: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 ) @ emptyset ) )
= $false )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( SV271 @ SV446 )
= $false )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2691]) ).
thf(2736,plain,
! [SV127: $i,SV271: $i > $o,SV454: $i] :
( ( ( ~ ( in @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( SV271 @ SV454 )
= $false )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2737,plain,
! [SV127: $i,SV271: $i > $o,SV465: $i] :
( ( ( ~ ( ~ ( in @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( SV271 @ SV465 )
= $false )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2738,plain,
! [SV127: $i,SV271: $i > $o,SV455: $i] :
( ( ( ~ ( in @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( SV271 @ SV455 )
= $false )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2739,plain,
! [SV442: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2740,plain,
! [SV442: $i,SV139: $i > $o,SV500: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV500 )
| ~ ! [SY1896: $i] :
( ~ ( SV282 @ SY1896 )
| ( SV500 = SY1896 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(2741,plain,
! [SV282: $i > $o,SV479: $i,SV139: $i > $o] :
( ( ( SV139 @ SV479 )
= $false )
| ( ( ~ ! [SY1859: $i] :
( ~ ( SV139 @ SY1859 )
| ( SV479 = SY1859 ) ) )
= $true )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2742,plain,
! [SV282: $i > $o,SV472: $i,SV139: $i > $o] :
( ( ( ! [SY1852: $i] :
( ~ ( SV139 @ SY1852 )
| ( SV472 = SY1852 ) ) )
= $false )
| ( ( SV139 @ SV472 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2743,plain,
! [SV282: $i > $o,SV473: $i,SV139: $i > $o] :
( ( ( ! [SY1853: $i] :
( ~ ( SV139 @ SY1853 )
| ( SV473 = SY1853 ) ) )
= $false )
| ( ( SV139 @ SV473 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2744,plain,
! [SV470: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
| ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV470 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2700]) ).
thf(2745,plain,
! [SV466: $i,SV457: $i,SV141: $i] :
( ( ( ! [SY1841: $i] :
( ~ ( in @ SY1841 @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ SY1841 )
| ( in @ SV466 @ SY1841 ) )
| ~ ( ~ ( in @ SV466 @ SY1841 )
| ( in @ SV457 @ SY1841 ) ) ) ) )
= $false )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2746,plain,
! [SV141: $i,SV488: $i,SV435: $i,SV443: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV443 )
| ( in @ SV501 @ SV435 ) )
= $true )
| ( ( in @ SV488 @ SV443 )
= $true )
| ( ( in @ SV488 @ SV435 )
= $false )
| ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(2747,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ! [SY1890: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1890 @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
| ~ ! [SY1892: $i] :
( ~ ( in @ SY1892 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SY1892 )
| ( in @ SY1893 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ SY1890 @ SY1892 ) ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2703]) ).
thf(2748,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ! [SY1878: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1878 @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
| ~ ! [SY1880: $i] :
( ~ ( in @ SY1880 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1881: $i] :
( ~ ( in @ SY1881 @ SY1880 )
| ( in @ SY1881 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ SY1878 @ SY1880 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2749,plain,
! [SV146: $i,SV287: $i > $o,SV447: $i] :
( ( ( ~ ( in @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) ) )
= $false )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( SV287 @ SV447 )
= $false )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2707]) ).
thf(2750,plain,
! [SV447: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 ) @ emptyset ) )
= $false )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( SV287 @ SV447 )
= $false )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2707]) ).
thf(2751,plain,
! [SV146: $i,SV287: $i > $o,SV458: $i] :
( ( ( ~ ( in @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( SV287 @ SV458 )
= $false )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2752,plain,
! [SV146: $i,SV287: $i > $o,SV467: $i] :
( ( ( ~ ( ~ ( in @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( SV287 @ SV467 )
= $false )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2709]) ).
thf(2753,plain,
! [SV146: $i,SV287: $i > $o,SV459: $i] :
( ( ( ~ ( in @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( SV287 @ SV459 )
= $false )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2754,plain,
! [SV304: $i,SV437: $i,SV475: $i,SV161: $i > $i > $o] :
( ( ( SV161 @ SV475 @ SV437 )
= $false )
| ( ( in @ SV475 @ SV304 )
= $false )
| ( ( in @ SV437 @ ( sK42_SY1692 @ SV161 @ SV304 ) )
= $true )
| ( ( in @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2755,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
| ~ ! [SY1868: $i] :
~ ~ ( ~ ( in @ SY1868 @ SV304 )
| ~ ( SV161 @ SY1868 @ SV489 ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2756,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ SV304 )
| ~ ( SV161 @ SY1869 @ SV489 ) )
| ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2715]) ).
thf(2757,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) ) )
= $true )
| ( ( ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV304 )
| ~ ( SV161 @ SY1860 @ SV481 ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(2758,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV304 )
| ~ ( SV161 @ SY1861 @ SV481 ) ) )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2717]) ).
thf(2759,plain,
! [SV461: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2760,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK98_SY1562 @ SV461 @ SV54 @ SV216 ) )
| ~ ! [SY1897: $i] :
( ~ ( SV216 @ SY1897 )
| ( ( sK98_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1897 ) ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2720]) ).
thf(2761,plain,
! [SV462: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2762,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK99_SY1228 @ SV462 @ SV216 @ SV54 ) )
| ~ ! [SY1898: $i] :
( ~ ( SV54 @ SY1898 )
| ( ( sK99_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1898 ) ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2722]) ).
thf(2763,plain,
! [SV216: $i > $o,SV497: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV497 )
| ~ ! [SY1886: $i] :
( ~ ( SV54 @ SY1886 )
| ( SV497 = SY1886 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2723]) ).
thf(2764,plain,
! [SV54: $i > $o,SV498: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV498 )
| ~ ! [SY1887: $i] :
( ~ ( SV216 @ SY1887 )
| ( SV498 = SY1887 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2724]) ).
thf(2765,plain,
! [SV216: $i > $o,SV491: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV491 ) )
= $true )
| ( ( ~ ! [SY1870: $i] :
( ~ ( SV54 @ SY1870 )
| ( SV491 = SY1870 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2766,plain,
! [SV54: $i > $o,SV492: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV492 ) )
= $true )
| ( ( ~ ! [SY1871: $i] :
( ~ ( SV216 @ SY1871 )
| ( SV492 = SY1871 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(2767,plain,
! [SV216: $i > $o,SV493: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV493 ) )
= $true )
| ( ( ~ ! [SY1872: $i] :
( ~ ( SV54 @ SY1872 )
| ( SV493 = SY1872 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2727]) ).
thf(2768,plain,
! [SV54: $i > $o,SV494: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV494 ) )
= $true )
| ( ( ~ ! [SY1873: $i] :
( ~ ( SV216 @ SY1873 )
| ( SV494 = SY1873 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2769,plain,
! [SV216: $i > $o,SV484: $i,SV54: $i > $o] :
( ( ( SV54 @ SV484 )
= $false )
| ( ( ~ ! [SY1862: $i] :
( ~ ( SV54 @ SY1862 )
| ( SV484 = SY1862 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(2770,plain,
! [SV54: $i > $o,SV485: $i,SV216: $i > $o] :
( ( ( SV216 @ SV485 )
= $false )
| ( ( ~ ! [SY1863: $i] :
( ~ ( SV216 @ SY1863 )
| ( SV485 = SY1863 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(2771,plain,
! [SV399: $i,SV499: $i,SV126: $i > $o] :
( ( ( SV126 @ SV499 )
= $false )
| ( ( ( sK78_SY1375 @ SV399 @ SV126 )
= SV499 )
= $true )
| ( ( SV126 @ ( sK29_SY1770 @ SV399 @ SV126 ) )
= $true )
| ( ( ( sK29_SY1770 @ SV399 @ SV126 )
= SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2772,plain,
! [SV127: $i,SV271: $i > $o,SV446: $i] :
( ( ( in @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
= $true )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( SV271 @ SV446 )
= $false )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2734]) ).
thf(2773,plain,
! [SV446: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
= ( setadjoin @ ( sK85_SY1633 @ SV446 @ SV271 @ SV127 ) @ emptyset ) )
= $true )
| ( ( in @ SV446 @ SV127 )
= $false )
| ( ( SV271 @ SV446 )
= $false )
| ( ( in @ ( sK30_SY1771 @ SV271 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2735]) ).
thf(2774,plain,
! [SV127: $i,SV271: $i > $o,SV454: $i] :
( ( ( ~ ( in @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) ) )
= $false )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( SV271 @ SV454 )
= $false )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2775,plain,
! [SV454: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 ) @ emptyset ) )
= $false )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( SV271 @ SV454 )
= $false )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2776,plain,
! [SV127: $i,SV271: $i > $o,SV465: $i] :
( ( ( ~ ( in @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
| ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( SV271 @ SV465 )
= $false )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2777,plain,
! [SV127: $i,SV271: $i > $o,SV455: $i] :
( ( ( ~ ( in @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) ) )
= $false )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( SV271 @ SV455 )
= $false )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2738]) ).
thf(2778,plain,
! [SV455: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 ) @ emptyset ) )
= $false )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( SV271 @ SV455 )
= $false )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2738]) ).
thf(2779,plain,
! [SV442: $i,SV139: $i > $o,SV502: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV502 )
| ~ ! [SY1899: $i] :
( ~ ( SV282 @ SY1899 )
| ( SV502 = SY1899 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(2780,plain,
! [SV442: $i,SV139: $i > $o,SV500: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV500 )
| ~ ! [SY1896: $i] :
( ~ ( SV282 @ SY1896 )
| ( SV500 = SY1896 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2781,plain,
! [SV282: $i > $o,SV479: $i,SV139: $i > $o] :
( ( ( ! [SY1859: $i] :
( ~ ( SV139 @ SY1859 )
| ( SV479 = SY1859 ) ) )
= $false )
| ( ( SV139 @ SV479 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2782,plain,
! [SV472: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
| ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV472 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2742]) ).
thf(2783,plain,
! [SV473: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
| ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV473 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2743]) ).
thf(2784,plain,
! [SV470: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV470 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2785,plain,
! [SV139: $i > $o,SV282: $i > $o,SV470: $i] :
( ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV139 @ SV470 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2786,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( ~ ( ~ ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
| ~ ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) ) )
= $false )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2745]) ).
thf(2787,plain,
! [SV141: $i,SV488: $i,SV435: $i,SV443: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV443 ) )
= $true )
| ( ( in @ SV501 @ SV435 )
= $true )
| ( ( in @ SV488 @ SV443 )
= $true )
| ( ( in @ SV488 @ SV435 )
= $false )
| ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2746]) ).
thf(2788,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ! [SY1890: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ SY1890 @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
| ~ ! [SY1892: $i] :
( ~ ( in @ SY1892 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SY1892 )
| ( in @ SY1893 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ SY1890 @ SY1892 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(2789,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
| ~ ! [SY1901: $i] :
( ~ ( in @ SY1901 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1881: $i] :
( ~ ( in @ SY1881 @ SY1901 )
| ( in @ SY1881 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SY1901 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2748]) ).
thf(2790,plain,
! [SV146: $i,SV287: $i > $o,SV447: $i] :
( ( ( in @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
= $true )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( SV287 @ SV447 )
= $false )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2749]) ).
thf(2791,plain,
! [SV447: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
= ( setadjoin @ ( sK86_SY1666 @ SV447 @ SV287 @ SV146 ) @ emptyset ) )
= $true )
| ( ( in @ SV447 @ SV146 )
= $false )
| ( ( SV287 @ SV447 )
= $false )
| ( ( in @ ( sK31_SY1780 @ SV287 @ SV146 ) @ SV146 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2750]) ).
thf(2792,plain,
! [SV146: $i,SV287: $i > $o,SV458: $i] :
( ( ( ~ ( in @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) ) )
= $false )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( SV287 @ SV458 )
= $false )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2793,plain,
! [SV458: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 ) @ emptyset ) )
= $false )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( SV287 @ SV458 )
= $false )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2794,plain,
! [SV146: $i,SV287: $i > $o,SV467: $i] :
( ( ( ~ ( in @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
| ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( SV287 @ SV467 )
= $false )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2795,plain,
! [SV146: $i,SV287: $i > $o,SV459: $i] :
( ( ( ~ ( in @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) ) )
= $false )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( SV287 @ SV459 )
= $false )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2753]) ).
thf(2796,plain,
! [SV459: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 ) @ emptyset ) )
= $false )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( SV287 @ SV459 )
= $false )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2753]) ).
thf(2797,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) ) )
= $true )
| ( ( ~ ! [SY1868: $i] :
~ ~ ( ~ ( in @ SY1868 @ SV304 )
| ~ ( SV161 @ SY1868 @ SV489 ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(2798,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ SV304 )
| ~ ( SV161 @ SY1869 @ SV489 ) ) )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2756]) ).
thf(2799,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV481: $i] :
( ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV304 )
| ~ ( SV161 @ SY1860 @ SV481 ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2800,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV304 )
| ~ ( SV161 @ SY1861 @ SV481 ) ) )
= $false )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2801,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK104_SY1562 @ SV461 @ SV54 @ SV216 ) )
| ~ ! [SY1903: $i] :
( ~ ( SV216 @ SY1903 )
| ( ( sK104_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1903 ) ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2759]) ).
thf(2802,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK98_SY1562 @ SV461 @ SV54 @ SV216 ) )
| ~ ! [SY1897: $i] :
( ~ ( SV216 @ SY1897 )
| ( ( sK98_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1897 ) ) ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2760]) ).
thf(2803,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK105_SY1228 @ SV462 @ SV216 @ SV54 ) )
| ~ ! [SY1904: $i] :
( ~ ( SV54 @ SY1904 )
| ( ( sK105_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1904 ) ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2761]) ).
thf(2804,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK99_SY1228 @ SV462 @ SV216 @ SV54 ) )
| ~ ! [SY1898: $i] :
( ~ ( SV54 @ SY1898 )
| ( ( sK99_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1898 ) ) ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2762]) ).
thf(2805,plain,
! [SV216: $i > $o,SV497: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV497 ) )
= $true )
| ( ( ~ ! [SY1886: $i] :
( ~ ( SV54 @ SY1886 )
| ( SV497 = SY1886 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2806,plain,
! [SV54: $i > $o,SV498: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV498 ) )
= $true )
| ( ( ~ ! [SY1887: $i] :
( ~ ( SV216 @ SY1887 )
| ( SV498 = SY1887 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(2807,plain,
! [SV216: $i > $o,SV491: $i,SV54: $i > $o] :
( ( ( SV54 @ SV491 )
= $false )
| ( ( ~ ! [SY1870: $i] :
( ~ ( SV54 @ SY1870 )
| ( SV491 = SY1870 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2808,plain,
! [SV54: $i > $o,SV492: $i,SV216: $i > $o] :
( ( ( SV216 @ SV492 )
= $false )
| ( ( ~ ! [SY1871: $i] :
( ~ ( SV216 @ SY1871 )
| ( SV492 = SY1871 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(2809,plain,
! [SV216: $i > $o,SV493: $i,SV54: $i > $o] :
( ( ( SV54 @ SV493 )
= $false )
| ( ( ~ ! [SY1872: $i] :
( ~ ( SV54 @ SY1872 )
| ( SV493 = SY1872 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2810,plain,
! [SV54: $i > $o,SV494: $i,SV216: $i > $o] :
( ( ( SV216 @ SV494 )
= $false )
| ( ( ~ ! [SY1873: $i] :
( ~ ( SV216 @ SY1873 )
| ( SV494 = SY1873 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(2811,plain,
! [SV216: $i > $o,SV484: $i,SV54: $i > $o] :
( ( ( ! [SY1862: $i] :
( ~ ( SV54 @ SY1862 )
| ( SV484 = SY1862 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2812,plain,
! [SV54: $i > $o,SV485: $i,SV216: $i > $o] :
( ( ( ! [SY1863: $i] :
( ~ ( SV216 @ SY1863 )
| ( SV485 = SY1863 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2813,plain,
! [SV127: $i,SV271: $i > $o,SV454: $i] :
( ( ( in @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
= $true )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( SV271 @ SV454 )
= $false )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2774]) ).
thf(2814,plain,
! [SV454: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
= ( setadjoin @ ( sK89_SY1633 @ SV454 @ SV271 @ SV127 ) @ emptyset ) )
= $true )
| ( ( in @ SV454 @ SV127 )
= $false )
| ( ( SV271 @ SV454 )
= $false )
| ( ( SV271 @ ( sK14_SY1630 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2775]) ).
thf(2815,plain,
! [SV127: $i,SV271: $i > $o,SV465: $i] :
( ( ( ~ ( in @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) ) )
= $false )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( SV271 @ SV465 )
= $false )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2776]) ).
thf(2816,plain,
! [SV465: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
!= ( setadjoin @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 ) @ emptyset ) )
= $false )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( SV271 @ SV465 )
= $false )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2776]) ).
thf(2817,plain,
! [SV127: $i,SV271: $i > $o,SV455: $i] :
( ( ( in @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
= $true )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( SV271 @ SV455 )
= $false )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2777]) ).
thf(2818,plain,
! [SV455: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
= ( setadjoin @ ( sK90_SY1633 @ SV455 @ SV271 @ SV127 ) @ emptyset ) )
= $true )
| ( ( in @ SV455 @ SV127 )
= $false )
| ( ( SV271 @ SV455 )
= $false )
| ( ( ( sK14_SY1630 @ SV271 @ SV127 )
= ( sK30_SY1771 @ SV271 @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2778]) ).
thf(2819,plain,
! [SV442: $i,SV139: $i > $o,SV502: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV502 )
| ~ ! [SY1899: $i] :
( ~ ( SV282 @ SY1899 )
| ( SV502 = SY1899 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(2820,plain,
! [SV442: $i,SV139: $i > $o,SV500: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV500 )
| ~ ! [SY1896: $i] :
( ~ ( SV282 @ SY1896 )
| ( SV500 = SY1896 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2780]) ).
thf(2821,plain,
! [SV479: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
| ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV479 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2781]) ).
thf(2822,plain,
! [SV472: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV472 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2823,plain,
! [SV139: $i > $o,SV282: $i > $o,SV472: $i] :
( ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ SV472 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2824,plain,
! [SV473: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV473 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(2825,plain,
! [SV139: $i > $o,SV282: $i > $o,SV473: $i] :
( ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV139 @ SV473 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(2826,plain,
! [SV470: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2784]) ).
thf(2827,plain,
! [SV470: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(2828,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) ) )
= $false )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2786]) ).
thf(2829,plain,
! [SV141: $i,SV466: $i,SV457: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
| ~ ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) ) )
= $false )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2786]) ).
thf(2830,plain,
! [SV141: $i,SV488: $i,SV435: $i,SV443: $i,SV501: $i] :
( ( ( in @ SV501 @ SV443 )
= $false )
| ( ( in @ SV501 @ SV435 )
= $true )
| ( ( in @ SV488 @ SV443 )
= $true )
| ( ( in @ SV488 @ SV435 )
= $false )
| ( ( in @ SV435 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ SV443 @ ( sK3_SY1423 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2831,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
| ~ ! [SY1906: $i] :
( ~ ( in @ SY1906 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SY1906 )
| ( in @ SY1893 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SY1906 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2788]) ).
thf(2832,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
| ~ ! [SY1901: $i] :
( ~ ( in @ SY1901 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1881: $i] :
( ~ ( in @ SY1881 @ SY1901 )
| ( in @ SY1881 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SY1901 ) ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2789]) ).
thf(2833,plain,
! [SV146: $i,SV287: $i > $o,SV458: $i] :
( ( ( in @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
= $true )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( SV287 @ SV458 )
= $false )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2834,plain,
! [SV458: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
= ( setadjoin @ ( sK92_SY1666 @ SV458 @ SV287 @ SV146 ) @ emptyset ) )
= $true )
| ( ( in @ SV458 @ SV146 )
= $false )
| ( ( SV287 @ SV458 )
= $false )
| ( ( SV287 @ ( sK18_SY1663 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2793]) ).
thf(2835,plain,
! [SV146: $i,SV287: $i > $o,SV467: $i] :
( ( ( ~ ( in @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) ) )
= $false )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( SV287 @ SV467 )
= $false )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2794]) ).
thf(2836,plain,
! [SV467: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
!= ( setadjoin @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 ) @ emptyset ) )
= $false )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( SV287 @ SV467 )
= $false )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2794]) ).
thf(2837,plain,
! [SV146: $i,SV287: $i > $o,SV459: $i] :
( ( ( in @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
= $true )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( SV287 @ SV459 )
= $false )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2795]) ).
thf(2838,plain,
! [SV459: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
= ( setadjoin @ ( sK93_SY1666 @ SV459 @ SV287 @ SV146 ) @ emptyset ) )
= $true )
| ( ( in @ SV459 @ SV146 )
= $false )
| ( ( SV287 @ SV459 )
= $false )
| ( ( ( sK18_SY1663 @ SV287 @ SV146 )
= ( sK31_SY1780 @ SV287 @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2796]) ).
thf(2839,plain,
! [SV304: $i,SV161: $i > $i > $o,SV429: $i,SV489: $i] :
( ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( ~ ! [SY1868: $i] :
~ ~ ( ~ ( in @ SY1868 @ SV304 )
| ~ ( SV161 @ SY1868 @ SV489 ) ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(2840,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ SV304 )
| ~ ( SV161 @ SY1869 @ SV489 ) ) )
= $false )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2841,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV304 )
| ~ ( SV161 @ SY1860 @ SV481 ) ) )
= $false )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(2842,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV304 )
| ~ ( SV161 @ SY1861 @ SV481 ) ) )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2800]) ).
thf(2843,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK104_SY1562 @ SV461 @ SV54 @ SV216 ) )
| ~ ! [SY1903: $i] :
( ~ ( SV216 @ SY1903 )
| ( ( sK104_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1903 ) ) ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2801]) ).
thf(2844,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK98_SY1562 @ SV461 @ SV54 @ SV216 ) )
| ~ ! [SY1897: $i] :
( ~ ( SV216 @ SY1897 )
| ( ( sK98_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1897 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2845,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK105_SY1228 @ SV462 @ SV216 @ SV54 ) )
| ~ ! [SY1904: $i] :
( ~ ( SV54 @ SY1904 )
| ( ( sK105_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1904 ) ) ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2846,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK99_SY1228 @ SV462 @ SV216 @ SV54 ) )
| ~ ! [SY1898: $i] :
( ~ ( SV54 @ SY1898 )
| ( ( sK99_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1898 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(2847,plain,
! [SV216: $i > $o,SV497: $i,SV54: $i > $o] :
( ( ( SV54 @ SV497 )
= $false )
| ( ( ~ ! [SY1886: $i] :
( ~ ( SV54 @ SY1886 )
| ( SV497 = SY1886 ) ) )
= $true )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(2848,plain,
! [SV54: $i > $o,SV498: $i,SV216: $i > $o] :
( ( ( SV216 @ SV498 )
= $false )
| ( ( ~ ! [SY1887: $i] :
( ~ ( SV216 @ SY1887 )
| ( SV498 = SY1887 ) ) )
= $true )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2849,plain,
! [SV216: $i > $o,SV491: $i,SV54: $i > $o] :
( ( ( ! [SY1870: $i] :
( ~ ( SV54 @ SY1870 )
| ( SV491 = SY1870 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2850,plain,
! [SV54: $i > $o,SV492: $i,SV216: $i > $o] :
( ( ( ! [SY1871: $i] :
( ~ ( SV216 @ SY1871 )
| ( SV492 = SY1871 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(2851,plain,
! [SV216: $i > $o,SV493: $i,SV54: $i > $o] :
( ( ( ! [SY1872: $i] :
( ~ ( SV54 @ SY1872 )
| ( SV493 = SY1872 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2852,plain,
! [SV54: $i > $o,SV494: $i,SV216: $i > $o] :
( ( ( ! [SY1873: $i] :
( ~ ( SV216 @ SY1873 )
| ( SV494 = SY1873 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2853,plain,
! [SV484: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
| ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2811]) ).
thf(2854,plain,
! [SV485: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
| ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2812]) ).
thf(2855,plain,
! [SV127: $i,SV271: $i > $o,SV465: $i] :
( ( ( in @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 )
@ ( dsetconstr @ SV127
@ ^ [SY1634: $i] : ( SV271 @ SY1634 ) ) )
= $true )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( SV271 @ SV465 )
= $false )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2815]) ).
thf(2856,plain,
! [SV465: $i,SV271: $i > $o,SV127: $i] :
( ( ( ( dsetconstr @ SV127
@ ^ [SY1635: $i] : ( SV271 @ SY1635 ) )
= ( setadjoin @ ( sK94_SY1633 @ SV465 @ SV271 @ SV127 ) @ emptyset ) )
= $true )
| ( ( in @ SV465 @ SV127 )
= $false )
| ( ( SV271 @ SV465 )
= $false )
| ( ( SV271 @ ( sK30_SY1771 @ SV271 @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2857,plain,
! [SV442: $i,SV139: $i > $o,SV502: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV502 )
| ~ ! [SY1899: $i] :
( ~ ( SV282 @ SY1899 )
| ( SV502 = SY1899 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2819]) ).
thf(2858,plain,
! [SV442: $i,SV139: $i > $o,SV500: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV500 ) )
= $true )
| ( ( ~ ! [SY1896: $i] :
( ~ ( SV282 @ SY1896 )
| ( SV500 = SY1896 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(2859,plain,
! [SV479: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV479 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(2860,plain,
! [SV139: $i > $o,SV282: $i > $o,SV479: $i] :
( ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ SV479 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(2861,plain,
! [SV472: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2822]) ).
thf(2862,plain,
! [SV472: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(2863,plain,
! [SV473: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2824]) ).
thf(2864,plain,
! [SV473: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(2865,plain,
! [SV470: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(2866,plain,
! [SV470: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(2867,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( in @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2828]) ).
thf(2868,plain,
! [SV141: $i,SV466: $i,SV457: $i] :
( ( ( ~ ( ~ ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
| ~ ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2829]) ).
thf(2869,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
| ~ ! [SY1906: $i] :
( ~ ( in @ SY1906 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SY1906 )
| ( in @ SY1893 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SY1906 ) ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2831]) ).
thf(2870,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
| ~ ! [SY1901: $i] :
( ~ ( in @ SY1901 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1881: $i] :
( ~ ( in @ SY1881 @ SY1901 )
| ( in @ SY1881 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SY1901 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(2871,plain,
! [SV146: $i,SV287: $i > $o,SV467: $i] :
( ( ( in @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 )
@ ( dsetconstr @ SV146
@ ^ [SY1667: $i] : ( SV287 @ SY1667 ) ) )
= $true )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( SV287 @ SV467 )
= $false )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2872,plain,
! [SV467: $i,SV287: $i > $o,SV146: $i] :
( ( ( ( dsetconstr @ SV146
@ ^ [SY1668: $i] : ( SV287 @ SY1668 ) )
= ( setadjoin @ ( sK96_SY1666 @ SV467 @ SV287 @ SV146 ) @ emptyset ) )
= $true )
| ( ( in @ SV467 @ SV146 )
= $false )
| ( ( SV287 @ SV467 )
= $false )
| ( ( SV287 @ ( sK31_SY1780 @ SV287 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(2873,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1868: $i] :
~ ~ ( ~ ( in @ SY1868 @ SV304 )
| ~ ( SV161 @ SY1868 @ SV489 ) ) )
= $false )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2874,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i] :
( ( ( ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ SV304 )
| ~ ( SV161 @ SY1869 @ SV489 ) ) )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2840]) ).
thf(2875,plain,
! [SV304: $i,SV161: $i > $i > $o,SV481: $i,SV429: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV481 ) ) )
= $false )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2841]) ).
thf(2876,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i,SV503: $i] :
( ( ( ~ ~ ( ~ ( in @ SV503 @ SV304 )
| ~ ( SV161 @ SV503 @ SV481 ) ) )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(2877,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK104_SY1562 @ SV461 @ SV54 @ SV216 ) )
| ~ ! [SY1903: $i] :
( ~ ( SV216 @ SY1903 )
| ( ( sK104_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1903 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(2878,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK98_SY1562 @ SV461 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2879,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1897: $i] :
( ~ ( SV216 @ SY1897 )
| ( ( sK98_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1897 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2844]) ).
thf(2880,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK105_SY1228 @ SV462 @ SV216 @ SV54 ) )
| ~ ! [SY1904: $i] :
( ~ ( SV54 @ SY1904 )
| ( ( sK105_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1904 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(2881,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK99_SY1228 @ SV462 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2846]) ).
thf(2882,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1898: $i] :
( ~ ( SV54 @ SY1898 )
| ( ( sK99_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1898 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2846]) ).
thf(2883,plain,
! [SV216: $i > $o,SV497: $i,SV54: $i > $o] :
( ( ( ! [SY1886: $i] :
( ~ ( SV54 @ SY1886 )
| ( SV497 = SY1886 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(2884,plain,
! [SV54: $i > $o,SV498: $i,SV216: $i > $o] :
( ( ( ! [SY1887: $i] :
( ~ ( SV216 @ SY1887 )
| ( SV498 = SY1887 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2885,plain,
! [SV491: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
| ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2849]) ).
thf(2886,plain,
! [SV492: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
| ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2850]) ).
thf(2887,plain,
! [SV493: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
| ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2851]) ).
thf(2888,plain,
! [SV494: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
| ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2852]) ).
thf(2889,plain,
! [SV484: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2853]) ).
thf(2890,plain,
! [SV54: $i > $o,SV216: $i > $o,SV484: $i] :
( ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2853]) ).
thf(2891,plain,
! [SV485: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2892,plain,
! [SV216: $i > $o,SV54: $i > $o,SV485: $i] :
( ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2893,plain,
! [SV442: $i,SV139: $i > $o,SV502: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV502 ) )
= $true )
| ( ( ~ ! [SY1899: $i] :
( ~ ( SV282 @ SY1899 )
| ( SV502 = SY1899 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(2894,plain,
! [SV442: $i,SV139: $i > $o,SV500: $i,SV282: $i > $o] :
( ( ( SV282 @ SV500 )
= $false )
| ( ( ~ ! [SY1896: $i] :
( ~ ( SV282 @ SY1896 )
| ( SV500 = SY1896 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2895,plain,
! [SV479: $i,SV282: $i > $o,SV139: $i > $o] :
( ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) )
| ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2859]) ).
thf(2896,plain,
! [SV479: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(2897,plain,
! [SV472: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(2898,plain,
! [SV472: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(2899,plain,
! [SV473: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(2900,plain,
! [SV473: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(2901,plain,
! [SV470: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2902,plain,
! [SV470: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2866]) ).
thf(2903,plain,
! [SV141: $i,SV466: $i,SV457: $i] :
( ( ( ~ ( ~ ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(2904,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
| ~ ! [SY1906: $i] :
( ~ ( in @ SY1906 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SY1906 )
| ( in @ SY1893 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SY1906 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(2905,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2870]) ).
thf(2906,plain,
! [SV428: $i,SV474: $i,SV141: $i] :
( ( ( ~ ! [SY1901: $i] :
( ~ ( in @ SY1901 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1881: $i] :
( ~ ( in @ SY1881 @ SY1901 )
| ( in @ SY1881 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SY1901 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2870]) ).
thf(2907,plain,
! [SV304: $i,SV161: $i > $i > $o,SV489: $i,SV429: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV489 ) ) )
= $false )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2873]) ).
thf(2908,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i,SV504: $i] :
( ( ( ~ ~ ( ~ ( in @ SV504 @ SV304 )
| ~ ( SV161 @ SV504 @ SV489 ) ) )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(2909,plain,
! [SV304: $i,SV161: $i > $i > $o,SV481: $i,SV429: $i] :
( ( ( ~ ( ~ ( in @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV481 ) ) )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2875]) ).
thf(2910,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i,SV503: $i] :
( ( ( ~ ( ~ ( in @ SV503 @ SV304 )
| ~ ( SV161 @ SV503 @ SV481 ) ) )
= $false )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(2911,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK104_SY1562 @ SV461 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2877]) ).
thf(2912,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1903: $i] :
( ~ ( SV216 @ SY1903 )
| ( ( sK104_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1903 ) ) )
= $false )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2877]) ).
thf(2913,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK98_SY1562 @ SV461 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2878]) ).
thf(2914,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ! [SY1897: $i] :
( ~ ( SV216 @ SY1897 )
| ( ( sK98_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1897 ) ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(2915,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK105_SY1228 @ SV462 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2880]) ).
thf(2916,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1904: $i] :
( ~ ( SV54 @ SY1904 )
| ( ( sK105_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1904 ) ) )
= $false )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2880]) ).
thf(2917,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK99_SY1228 @ SV462 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2881]) ).
thf(2918,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ! [SY1898: $i] :
( ~ ( SV54 @ SY1898 )
| ( ( sK99_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1898 ) ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2882]) ).
thf(2919,plain,
! [SV497: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
| ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2883]) ).
thf(2920,plain,
! [SV498: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
| ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2884]) ).
thf(2921,plain,
! [SV491: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(2922,plain,
! [SV54: $i > $o,SV216: $i > $o,SV491: $i] :
( ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(2923,plain,
! [SV492: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2886]) ).
thf(2924,plain,
! [SV216: $i > $o,SV54: $i > $o,SV492: $i] :
( ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2886]) ).
thf(2925,plain,
! [SV493: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(2926,plain,
! [SV54: $i > $o,SV216: $i > $o,SV493: $i] :
( ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(2927,plain,
! [SV494: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(2928,plain,
! [SV216: $i > $o,SV54: $i > $o,SV494: $i] :
( ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(2929,plain,
! [SV484: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2889]) ).
thf(2930,plain,
! [SV484: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(2931,plain,
! [SV485: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2891]) ).
thf(2932,plain,
! [SV485: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(2933,plain,
! [SV442: $i,SV139: $i > $o,SV502: $i,SV282: $i > $o] :
( ( ( SV282 @ SV502 )
= $false )
| ( ( ~ ! [SY1899: $i] :
( ~ ( SV282 @ SY1899 )
| ( SV502 = SY1899 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(2934,plain,
! [SV442: $i,SV139: $i > $o,SV500: $i,SV282: $i > $o] :
( ( ( ! [SY1896: $i] :
( ~ ( SV282 @ SY1896 )
| ( SV500 = SY1896 ) ) )
= $false )
| ( ( SV282 @ SV500 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2894]) ).
thf(2935,plain,
! [SV479: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(2936,plain,
! [SV479: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(2937,plain,
! [SV472: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(2938,plain,
! [SV472: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(2939,plain,
! [SV473: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2899]) ).
thf(2940,plain,
! [SV473: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2900]) ).
thf(2941,plain,
! [SV470: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2901]) ).
thf(2942,plain,
! [SV470: $i,SV139: $i > $o,SV505: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV505 )
| ~ ! [SY1908: $i] :
( ~ ( SV282 @ SY1908 )
| ( SV505 = SY1908 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(2943,plain,
! [SV141: $i,SV466: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2944,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(2945,plain,
! [SV428: $i,SV480: $i,SV141: $i] :
( ( ( ~ ! [SY1906: $i] :
( ~ ( in @ SY1906 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SY1906 )
| ( in @ SY1893 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SY1906 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(2946,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2905]) ).
thf(2947,plain,
! [SV428: $i,SV474: $i,SV141: $i] :
( ( ( ! [SY1901: $i] :
( ~ ( in @ SY1901 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1881: $i] :
( ~ ( in @ SY1881 @ SY1901 )
| ( in @ SY1881 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SY1901 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2906]) ).
thf(2948,plain,
! [SV304: $i,SV161: $i > $i > $o,SV489: $i,SV429: $i] :
( ( ( ~ ( ~ ( in @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV489 ) ) )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2907]) ).
thf(2949,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i,SV504: $i] :
( ( ( ~ ( ~ ( in @ SV504 @ SV304 )
| ~ ( SV161 @ SV504 @ SV489 ) ) )
= $false )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(2950,plain,
! [SV304: $i,SV161: $i > $i > $o,SV481: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV481 ) )
= $false )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(2951,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV304 )
| ~ ( SV161 @ SV503 @ SV481 ) )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2910]) ).
thf(2952,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK104_SY1562 @ SV461 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2911]) ).
thf(2953,plain,
! [SV54: $i > $o,SV461: $i,SV216: $i > $o] :
( ( ( ! [SY1903: $i] :
( ~ ( SV216 @ SY1903 )
| ( ( sK104_SY1562 @ SV461 @ SV54 @ SV216 )
= SY1903 ) ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2912]) ).
thf(2954,plain,
! [SV54: $i > $o,SV461: $i,SV506: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV506 )
| ( ( sK98_SY1562 @ SV461 @ SV54 @ SV216 )
= SV506 ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(2955,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK105_SY1228 @ SV462 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2915]) ).
thf(2956,plain,
! [SV216: $i > $o,SV462: $i,SV54: $i > $o] :
( ( ( ! [SY1904: $i] :
( ~ ( SV54 @ SY1904 )
| ( ( sK105_SY1228 @ SV462 @ SV216 @ SV54 )
= SY1904 ) ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2916]) ).
thf(2957,plain,
! [SV216: $i > $o,SV462: $i,SV507: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV507 )
| ( ( sK99_SY1228 @ SV462 @ SV216 @ SV54 )
= SV507 ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(2958,plain,
! [SV497: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2919]) ).
thf(2959,plain,
! [SV54: $i > $o,SV216: $i > $o,SV497: $i] :
( ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2919]) ).
thf(2960,plain,
! [SV498: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2920]) ).
thf(2961,plain,
! [SV216: $i > $o,SV54: $i > $o,SV498: $i] :
( ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2920]) ).
thf(2962,plain,
! [SV491: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2921]) ).
thf(2963,plain,
! [SV491: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(2964,plain,
! [SV492: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2923]) ).
thf(2965,plain,
! [SV492: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(2966,plain,
! [SV493: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2925]) ).
thf(2967,plain,
! [SV493: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(2968,plain,
! [SV494: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(2969,plain,
! [SV494: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(2970,plain,
! [SV484: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(2971,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK118_SY1562 @ SV484 @ SV54 @ SV216 ) )
| ~ ! [SY1909: $i] :
( ~ ( SV216 @ SY1909 )
| ( ( sK118_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1909 ) ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2930]) ).
thf(2972,plain,
! [SV485: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2931]) ).
thf(2973,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK119_SY1228 @ SV485 @ SV216 @ SV54 ) )
| ~ ! [SY1910: $i] :
( ~ ( SV54 @ SY1910 )
| ( ( sK119_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1910 ) ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2932]) ).
thf(2974,plain,
! [SV442: $i,SV139: $i > $o,SV502: $i,SV282: $i > $o] :
( ( ( ! [SY1899: $i] :
( ~ ( SV282 @ SY1899 )
| ( SV502 = SY1899 ) ) )
= $false )
| ( ( SV282 @ SV502 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(2975,plain,
! [SV500: $i,SV139: $i > $o,SV442: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK120_SY1896 @ SV442 @ SV139 @ SV500 @ SV282 ) )
| ( SV500
= ( sK120_SY1896 @ SV442 @ SV139 @ SV500 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV500 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2934]) ).
thf(2976,plain,
! [SV479: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ~ ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(2977,plain,
! [SV479: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2936]) ).
thf(2978,plain,
! [SV472: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(2979,plain,
! [SV472: $i,SV139: $i > $o,SV508: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV508 )
| ~ ! [SY1911: $i] :
( ~ ( SV282 @ SY1911 )
| ( SV508 = SY1911 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(2980,plain,
! [SV473: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2939]) ).
thf(2981,plain,
! [SV473: $i,SV139: $i > $o,SV509: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV509 )
| ~ ! [SY1912: $i] :
( ~ ( SV282 @ SY1912 )
| ( SV509 = SY1912 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(2982,plain,
! [SV470: $i,SV139: $i > $o,SV510: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV510 )
| ~ ! [SY1913: $i] :
( ~ ( SV282 @ SY1913 )
| ( SV510 = SY1913 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(2983,plain,
! [SV470: $i,SV139: $i > $o,SV505: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV505 )
| ~ ! [SY1908: $i] :
( ~ ( SV282 @ SY1908 )
| ( SV505 = SY1908 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(2984,plain,
! [SV141: $i,SV466: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2943]) ).
thf(2985,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2943]) ).
thf(2986,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2944]) ).
thf(2987,plain,
! [SV428: $i,SV480: $i,SV141: $i] :
( ( ( ! [SY1906: $i] :
( ~ ( in @ SY1906 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SY1906 )
| ( in @ SY1893 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SY1906 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2945]) ).
thf(2988,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) )
| ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(2989,plain,
! [SV428: $i,SV474: $i,SV141: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1914: $i] :
( ~ ( in @ SY1914 @ SV511 )
| ( in @ SY1914 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV511 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(2990,plain,
! [SV304: $i,SV161: $i > $i > $o,SV489: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV304 )
| ~ ( SV161 @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV489 ) )
= $false )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(2991,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV304 )
| ~ ( SV161 @ SV504 @ SV489 ) )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2949]) ).
thf(2992,plain,
! [SV304: $i,SV161: $i > $i > $o,SV481: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV304 ) )
= $false )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2950]) ).
thf(2993,plain,
! [SV304: $i,SV481: $i,SV429: $i,SV161: $i > $i > $o] :
( ( ( ~ ( SV161 @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV481 ) )
= $false )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2950]) ).
thf(2994,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV304 ) )
= $true )
| ( ( ~ ( SV161 @ SV503 @ SV481 ) )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2951]) ).
thf(2995,plain,
! [SV54: $i > $o,SV461: $i,SV512: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV512 )
| ( ( sK104_SY1562 @ SV461 @ SV54 @ SV216 )
= SV512 ) )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(2996,plain,
! [SV54: $i > $o,SV461: $i,SV506: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV506 ) )
= $true )
| ( ( ( sK98_SY1562 @ SV461 @ SV54 @ SV216 )
= SV506 )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2954]) ).
thf(2997,plain,
! [SV216: $i > $o,SV462: $i,SV513: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV513 )
| ( ( sK105_SY1228 @ SV462 @ SV216 @ SV54 )
= SV513 ) )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(2998,plain,
! [SV216: $i > $o,SV462: $i,SV507: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV507 ) )
= $true )
| ( ( ( sK99_SY1228 @ SV462 @ SV216 @ SV54 )
= SV507 )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2957]) ).
thf(2999,plain,
! [SV497: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( ~ ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2958]) ).
thf(3000,plain,
! [SV497: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(3001,plain,
! [SV498: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( ~ ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2960]) ).
thf(3002,plain,
! [SV498: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3003,plain,
! [SV491: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3004,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK121_SY1562 @ SV491 @ SV54 @ SV216 ) )
| ~ ! [SY1915: $i] :
( ~ ( SV216 @ SY1915 )
| ( ( sK121_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1915 ) ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2963]) ).
thf(3005,plain,
! [SV492: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3006,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK122_SY1228 @ SV492 @ SV216 @ SV54 ) )
| ~ ! [SY1916: $i] :
( ~ ( SV54 @ SY1916 )
| ( ( sK122_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1916 ) ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2965]) ).
thf(3007,plain,
! [SV493: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3008,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK123_SY1562 @ SV493 @ SV54 @ SV216 ) )
| ~ ! [SY1917: $i] :
( ~ ( SV216 @ SY1917 )
| ( ( sK123_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1917 ) ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2967]) ).
thf(3009,plain,
! [SV494: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3010,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK124_SY1228 @ SV494 @ SV216 @ SV54 ) )
| ~ ! [SY1918: $i] :
( ~ ( SV54 @ SY1918 )
| ( ( sK124_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1918 ) ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2969]) ).
thf(3011,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK125_SY1562 @ SV484 @ SV54 @ SV216 ) )
| ~ ! [SY1919: $i] :
( ~ ( SV216 @ SY1919 )
| ( ( sK125_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1919 ) ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2970]) ).
thf(3012,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK118_SY1562 @ SV484 @ SV54 @ SV216 ) )
| ~ ! [SY1909: $i] :
( ~ ( SV216 @ SY1909 )
| ( ( sK118_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1909 ) ) ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2971]) ).
thf(3013,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK126_SY1228 @ SV485 @ SV216 @ SV54 ) )
| ~ ! [SY1920: $i] :
( ~ ( SV54 @ SY1920 )
| ( ( sK126_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1920 ) ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2972]) ).
thf(3014,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK119_SY1228 @ SV485 @ SV216 @ SV54 ) )
| ~ ! [SY1910: $i] :
( ~ ( SV54 @ SY1910 )
| ( ( sK119_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1910 ) ) ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2973]) ).
thf(3015,plain,
! [SV502: $i,SV139: $i > $o,SV442: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK127_SY1899 @ SV442 @ SV139 @ SV502 @ SV282 ) )
| ( SV502
= ( sK127_SY1899 @ SV442 @ SV139 @ SV502 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV502 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2974]) ).
thf(3016,plain,
! [SV500: $i,SV139: $i > $o,SV442: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK120_SY1896 @ SV442 @ SV139 @ SV500 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV500 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2975]) ).
thf(3017,plain,
! [SV282: $i > $o,SV139: $i > $o,SV442: $i,SV500: $i] :
( ( ( SV500
= ( sK120_SY1896 @ SV442 @ SV139 @ SV500 @ SV282 ) )
= $false )
| ( ( SV282 @ SV500 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2975]) ).
thf(3018,plain,
! [SV479: $i,SV139: $i > $o,SV282: $i > $o] :
( ( ( ! [SY1655: $i] :
~ ~ ( ~ ( SV282 @ SY1655 )
| ~ ! [SY1656: $i] :
( ~ ( SV282 @ SY1656 )
| ( SY1655 = SY1656 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2976]) ).
thf(3019,plain,
! [SV479: $i,SV139: $i > $o,SV514: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV514 )
| ~ ! [SY1921: $i] :
( ~ ( SV282 @ SY1921 )
| ( SV514 = SY1921 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3020,plain,
! [SV472: $i,SV139: $i > $o,SV515: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV515 )
| ~ ! [SY1922: $i] :
( ~ ( SV282 @ SY1922 )
| ( SV515 = SY1922 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3021,plain,
! [SV472: $i,SV139: $i > $o,SV508: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV508 )
| ~ ! [SY1911: $i] :
( ~ ( SV282 @ SY1911 )
| ( SV508 = SY1911 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3022,plain,
! [SV473: $i,SV139: $i > $o,SV516: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV516 )
| ~ ! [SY1923: $i] :
( ~ ( SV282 @ SY1923 )
| ( SV516 = SY1923 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3023,plain,
! [SV473: $i,SV139: $i > $o,SV509: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV509 )
| ~ ! [SY1912: $i] :
( ~ ( SV282 @ SY1912 )
| ( SV509 = SY1912 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3024,plain,
! [SV470: $i,SV139: $i > $o,SV510: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV510 )
| ~ ! [SY1913: $i] :
( ~ ( SV282 @ SY1913 )
| ( SV510 = SY1913 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3025,plain,
! [SV470: $i,SV139: $i > $o,SV505: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV505 )
| ~ ! [SY1908: $i] :
( ~ ( SV282 @ SY1908 )
| ( SV505 = SY1908 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2983]) ).
thf(3026,plain,
! [SV141: $i,SV466: $i,SV457: $i] :
( ( ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2984]) ).
thf(3027,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
= $false )
| ( ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $false )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3028,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) )
| ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3029,plain,
! [SV428: $i,SV480: $i,SV141: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ ( sK3_SY1423 @ SV141 ) )
| ! [SY1924: $i] :
( ~ ( in @ SY1924 @ SV517 )
| ( in @ SY1924 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV517 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3030,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2988]) ).
thf(3031,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2988]) ).
thf(3032,plain,
! [SV428: $i,SV474: $i,SV141: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ ( sK3_SY1423 @ SV141 ) ) )
= $true )
| ( ( ! [SY1914: $i] :
( ~ ( in @ SY1914 @ SV511 )
| ( in @ SY1914 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV511 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2989]) ).
thf(3033,plain,
! [SV304: $i,SV161: $i > $i > $o,SV489: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV304 ) )
= $false )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2990]) ).
thf(3034,plain,
! [SV304: $i,SV489: $i,SV429: $i,SV161: $i > $i > $o] :
( ( ( ~ ( SV161 @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV489 ) )
= $false )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2990]) ).
thf(3035,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV304 ) )
= $true )
| ( ( ~ ( SV161 @ SV504 @ SV489 ) )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2991]) ).
thf(3036,plain,
! [SV304: $i,SV161: $i > $i > $o,SV481: $i,SV429: $i] :
( ( ( in @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2992]) ).
thf(3037,plain,
! [SV304: $i,SV481: $i,SV429: $i,SV161: $i > $i > $o] :
( ( ( SV161 @ ( sK110_SY1860 @ SV429 @ SV481 @ SV161 @ SV304 ) @ SV481 )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2993]) ).
thf(3038,plain,
! [SV429: $i,SV481: $i,SV161: $i > $i > $o,SV304: $i,SV503: $i] :
( ( ( in @ SV503 @ SV304 )
= $false )
| ( ( ~ ( SV161 @ SV503 @ SV481 ) )
= $true )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3039,plain,
! [SV54: $i > $o,SV461: $i,SV512: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV512 ) )
= $true )
| ( ( ( sK104_SY1562 @ SV461 @ SV54 @ SV216 )
= SV512 )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3040,plain,
! [SV54: $i > $o,SV461: $i,SV506: $i,SV216: $i > $o] :
( ( ( SV216 @ SV506 )
= $false )
| ( ( ( sK98_SY1562 @ SV461 @ SV54 @ SV216 )
= SV506 )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV461
= ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3041,plain,
! [SV216: $i > $o,SV462: $i,SV513: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV513 ) )
= $true )
| ( ( ( sK105_SY1228 @ SV462 @ SV216 @ SV54 )
= SV513 )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3042,plain,
! [SV216: $i > $o,SV462: $i,SV507: $i,SV54: $i > $o] :
( ( ( SV54 @ SV507 )
= $false )
| ( ( ( sK99_SY1228 @ SV462 @ SV216 @ SV54 )
= SV507 )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV462
= ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $false )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3043,plain,
! [SV497: $i,SV54: $i > $o,SV216: $i > $o] :
( ( ( ! [SY1562: $i] :
~ ~ ( ~ ( SV216 @ SY1562 )
| ~ ! [SY1563: $i] :
( ~ ( SV216 @ SY1563 )
| ( SY1562 = SY1563 ) ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3044,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK128_SY1562 @ SV497 @ SV54 @ SV216 ) )
| ~ ! [SY1925: $i] :
( ~ ( SV216 @ SY1925 )
| ( ( sK128_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1925 ) ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3000]) ).
thf(3045,plain,
! [SV498: $i,SV216: $i > $o,SV54: $i > $o] :
( ( ( ! [SY1228: $i] :
~ ~ ( ~ ( SV54 @ SY1228 )
| ~ ! [SY1229: $i] :
( ~ ( SV54 @ SY1229 )
| ( SY1228 = SY1229 ) ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3046,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK129_SY1228 @ SV498 @ SV216 @ SV54 ) )
| ~ ! [SY1926: $i] :
( ~ ( SV54 @ SY1926 )
| ( ( sK129_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1926 ) ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3002]) ).
thf(3047,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK130_SY1562 @ SV491 @ SV54 @ SV216 ) )
| ~ ! [SY1927: $i] :
( ~ ( SV216 @ SY1927 )
| ( ( sK130_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1927 ) ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3003]) ).
thf(3048,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK121_SY1562 @ SV491 @ SV54 @ SV216 ) )
| ~ ! [SY1915: $i] :
( ~ ( SV216 @ SY1915 )
| ( ( sK121_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1915 ) ) ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3004]) ).
thf(3049,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK131_SY1228 @ SV492 @ SV216 @ SV54 ) )
| ~ ! [SY1928: $i] :
( ~ ( SV54 @ SY1928 )
| ( ( sK131_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1928 ) ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3005]) ).
thf(3050,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK122_SY1228 @ SV492 @ SV216 @ SV54 ) )
| ~ ! [SY1916: $i] :
( ~ ( SV54 @ SY1916 )
| ( ( sK122_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1916 ) ) ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3006]) ).
thf(3051,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK132_SY1562 @ SV493 @ SV54 @ SV216 ) )
| ~ ! [SY1929: $i] :
( ~ ( SV216 @ SY1929 )
| ( ( sK132_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1929 ) ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3007]) ).
thf(3052,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK123_SY1562 @ SV493 @ SV54 @ SV216 ) )
| ~ ! [SY1917: $i] :
( ~ ( SV216 @ SY1917 )
| ( ( sK123_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1917 ) ) ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3008]) ).
thf(3053,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK133_SY1228 @ SV494 @ SV216 @ SV54 ) )
| ~ ! [SY1930: $i] :
( ~ ( SV54 @ SY1930 )
| ( ( sK133_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1930 ) ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3009]) ).
thf(3054,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK124_SY1228 @ SV494 @ SV216 @ SV54 ) )
| ~ ! [SY1918: $i] :
( ~ ( SV54 @ SY1918 )
| ( ( sK124_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1918 ) ) ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3010]) ).
thf(3055,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK125_SY1562 @ SV484 @ SV54 @ SV216 ) )
| ~ ! [SY1919: $i] :
( ~ ( SV216 @ SY1919 )
| ( ( sK125_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1919 ) ) ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3011]) ).
thf(3056,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK118_SY1562 @ SV484 @ SV54 @ SV216 ) )
| ~ ! [SY1909: $i] :
( ~ ( SV216 @ SY1909 )
| ( ( sK118_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1909 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3057,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK126_SY1228 @ SV485 @ SV216 @ SV54 ) )
| ~ ! [SY1920: $i] :
( ~ ( SV54 @ SY1920 )
| ( ( sK126_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1920 ) ) ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3013]) ).
thf(3058,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK119_SY1228 @ SV485 @ SV216 @ SV54 ) )
| ~ ! [SY1910: $i] :
( ~ ( SV54 @ SY1910 )
| ( ( sK119_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1910 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3059,plain,
! [SV502: $i,SV139: $i > $o,SV442: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK127_SY1899 @ SV442 @ SV139 @ SV502 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV502 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3015]) ).
thf(3060,plain,
! [SV282: $i > $o,SV139: $i > $o,SV442: $i,SV502: $i] :
( ( ( SV502
= ( sK127_SY1899 @ SV442 @ SV139 @ SV502 @ SV282 ) )
= $false )
| ( ( SV282 @ SV502 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3015]) ).
thf(3061,plain,
! [SV500: $i,SV139: $i > $o,SV442: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK120_SY1896 @ SV442 @ SV139 @ SV500 @ SV282 ) )
= $true )
| ( ( SV282 @ SV500 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV442
= ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $false )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3016]) ).
thf(3062,plain,
! [SV479: $i,SV139: $i > $o,SV518: $i,SV282: $i > $o] :
( ( ( ~ ~ ( ~ ( SV282 @ SV518 )
| ~ ! [SY1931: $i] :
( ~ ( SV282 @ SY1931 )
| ( SV518 = SY1931 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3063,plain,
! [SV479: $i,SV139: $i > $o,SV514: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV514 )
| ~ ! [SY1921: $i] :
( ~ ( SV282 @ SY1921 )
| ( SV514 = SY1921 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3064,plain,
! [SV472: $i,SV139: $i > $o,SV515: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV515 )
| ~ ! [SY1922: $i] :
( ~ ( SV282 @ SY1922 )
| ( SV515 = SY1922 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3065,plain,
! [SV472: $i,SV139: $i > $o,SV508: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV508 )
| ~ ! [SY1911: $i] :
( ~ ( SV282 @ SY1911 )
| ( SV508 = SY1911 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3021]) ).
thf(3066,plain,
! [SV473: $i,SV139: $i > $o,SV516: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV516 )
| ~ ! [SY1923: $i] :
( ~ ( SV282 @ SY1923 )
| ( SV516 = SY1923 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3067,plain,
! [SV473: $i,SV139: $i > $o,SV509: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV509 )
| ~ ! [SY1912: $i] :
( ~ ( SV282 @ SY1912 )
| ( SV509 = SY1912 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3023]) ).
thf(3068,plain,
! [SV470: $i,SV139: $i > $o,SV510: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV510 )
| ~ ! [SY1913: $i] :
( ~ ( SV282 @ SY1913 )
| ( SV510 = SY1913 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3024]) ).
thf(3069,plain,
! [SV470: $i,SV139: $i > $o,SV505: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV505 ) )
= $true )
| ( ( ~ ! [SY1908: $i] :
( ~ ( SV282 @ SY1908 )
| ( SV505 = SY1908 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3025]) ).
thf(3070,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
| ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
= $false )
| ( ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3071,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
= $false )
| ( ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $false )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3072,plain,
! [SV141: $i,SV466: $i,SV457: $i] :
( ( ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $false )
| ( ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $false )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3027]) ).
thf(3073,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3074,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3075,plain,
! [SV428: $i,SV480: $i,SV141: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ ( sK3_SY1423 @ SV141 ) ) )
= $true )
| ( ( ! [SY1924: $i] :
( ~ ( in @ SY1924 @ SV517 )
| ( in @ SY1924 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV517 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3076,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3030]) ).
thf(3077,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3031]) ).
thf(3078,plain,
! [SV428: $i,SV474: $i,SV141: $i,SV511: $i] :
( ( ( in @ SV511 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( ! [SY1914: $i] :
( ~ ( in @ SY1914 @ SV511 )
| ( in @ SY1914 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
| ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV511 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3079,plain,
! [SV304: $i,SV161: $i > $i > $o,SV489: $i,SV429: $i] :
( ( ( in @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3033]) ).
thf(3080,plain,
! [SV304: $i,SV489: $i,SV429: $i,SV161: $i > $i > $o] :
( ( ( SV161 @ ( sK115_SY1868 @ SV429 @ SV489 @ SV161 @ SV304 ) @ SV489 )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3034]) ).
thf(3081,plain,
! [SV429: $i,SV489: $i,SV161: $i > $i > $o,SV304: $i,SV504: $i] :
( ( ( in @ SV504 @ SV304 )
= $false )
| ( ( ~ ( SV161 @ SV504 @ SV489 ) )
= $true )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3082,plain,
! [SV429: $i,SV304: $i,SV481: $i,SV503: $i,SV161: $i > $i > $o] :
( ( ( SV161 @ SV503 @ SV481 )
= $false )
| ( ( in @ SV503 @ SV304 )
= $false )
| ( ( in @ SV481 @ ( sK79_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV429
= ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3083,plain,
! [SV54: $i > $o,SV461: $i,SV512: $i,SV216: $i > $o] :
( ( ( SV216 @ SV512 )
= $false )
| ( ( ( sK104_SY1562 @ SV461 @ SV54 @ SV216 )
= SV512 )
= $true )
| ( ( SV54 @ SV461 )
= $false )
| ( ( SV54 @ ( sK87_SY1834 @ SV216 @ SV461 @ SV54 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3084,plain,
! [SV216: $i > $o,SV462: $i,SV513: $i,SV54: $i > $o] :
( ( ( SV54 @ SV513 )
= $false )
| ( ( ( sK105_SY1228 @ SV462 @ SV216 @ SV54 )
= SV513 )
= $true )
| ( ( SV216 @ SV462 )
= $false )
| ( ( SV216 @ ( sK88_SY1835 @ SV54 @ SV462 @ SV216 ) )
= $true )
| ( ( ( sK10_SY1558 @ SV216 @ SV54 )
= ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3085,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ~ ( ~ ( SV216 @ ( sK134_SY1562 @ SV497 @ SV54 @ SV216 ) )
| ~ ! [SY1932: $i] :
( ~ ( SV216 @ SY1932 )
| ( ( sK134_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1932 ) ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3043]) ).
thf(3086,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK128_SY1562 @ SV497 @ SV54 @ SV216 ) )
| ~ ! [SY1925: $i] :
( ~ ( SV216 @ SY1925 )
| ( ( sK128_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1925 ) ) ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3044]) ).
thf(3087,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ~ ( ~ ( SV54 @ ( sK135_SY1228 @ SV498 @ SV216 @ SV54 ) )
| ~ ! [SY1933: $i] :
( ~ ( SV54 @ SY1933 )
| ( ( sK135_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1933 ) ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3045]) ).
thf(3088,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK129_SY1228 @ SV498 @ SV216 @ SV54 ) )
| ~ ! [SY1926: $i] :
( ~ ( SV54 @ SY1926 )
| ( ( sK129_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1926 ) ) ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3046]) ).
thf(3089,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK130_SY1562 @ SV491 @ SV54 @ SV216 ) )
| ~ ! [SY1927: $i] :
( ~ ( SV216 @ SY1927 )
| ( ( sK130_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1927 ) ) ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3047]) ).
thf(3090,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK121_SY1562 @ SV491 @ SV54 @ SV216 ) )
| ~ ! [SY1915: $i] :
( ~ ( SV216 @ SY1915 )
| ( ( sK121_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1915 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3091,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK131_SY1228 @ SV492 @ SV216 @ SV54 ) )
| ~ ! [SY1928: $i] :
( ~ ( SV54 @ SY1928 )
| ( ( sK131_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1928 ) ) ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3049]) ).
thf(3092,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK122_SY1228 @ SV492 @ SV216 @ SV54 ) )
| ~ ! [SY1916: $i] :
( ~ ( SV54 @ SY1916 )
| ( ( sK122_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1916 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3093,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK132_SY1562 @ SV493 @ SV54 @ SV216 ) )
| ~ ! [SY1929: $i] :
( ~ ( SV216 @ SY1929 )
| ( ( sK132_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1929 ) ) ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3051]) ).
thf(3094,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK123_SY1562 @ SV493 @ SV54 @ SV216 ) )
| ~ ! [SY1917: $i] :
( ~ ( SV216 @ SY1917 )
| ( ( sK123_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1917 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3095,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK133_SY1228 @ SV494 @ SV216 @ SV54 ) )
| ~ ! [SY1930: $i] :
( ~ ( SV54 @ SY1930 )
| ( ( sK133_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1930 ) ) ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3053]) ).
thf(3096,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK124_SY1228 @ SV494 @ SV216 @ SV54 ) )
| ~ ! [SY1918: $i] :
( ~ ( SV54 @ SY1918 )
| ( ( sK124_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1918 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3097,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK125_SY1562 @ SV484 @ SV54 @ SV216 ) )
| ~ ! [SY1919: $i] :
( ~ ( SV216 @ SY1919 )
| ( ( sK125_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1919 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3098,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK118_SY1562 @ SV484 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3056]) ).
thf(3099,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1909: $i] :
( ~ ( SV216 @ SY1909 )
| ( ( sK118_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1909 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3056]) ).
thf(3100,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK126_SY1228 @ SV485 @ SV216 @ SV54 ) )
| ~ ! [SY1920: $i] :
( ~ ( SV54 @ SY1920 )
| ( ( sK126_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1920 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3101,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK119_SY1228 @ SV485 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3058]) ).
thf(3102,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1910: $i] :
( ~ ( SV54 @ SY1910 )
| ( ( sK119_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1910 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3058]) ).
thf(3103,plain,
! [SV502: $i,SV139: $i > $o,SV442: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK127_SY1899 @ SV442 @ SV139 @ SV502 @ SV282 ) )
= $true )
| ( ( SV282 @ SV502 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV442 )
= $false )
| ( ( SV139 @ ( sK81_SY1814 @ SV282 @ SV442 @ SV139 ) )
= $true )
| ( ( ( sK16_SY1651 @ SV282 @ SV139 )
= ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3059]) ).
thf(3104,plain,
! [SV479: $i,SV139: $i > $o,SV518: $i,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ SV518 )
| ~ ! [SY1931: $i] :
( ~ ( SV282 @ SY1931 )
| ( SV518 = SY1931 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3105,plain,
! [SV479: $i,SV139: $i > $o,SV514: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV514 )
| ~ ! [SY1921: $i] :
( ~ ( SV282 @ SY1921 )
| ( SV514 = SY1921 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3063]) ).
thf(3106,plain,
! [SV472: $i,SV139: $i > $o,SV515: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV515 )
| ~ ! [SY1922: $i] :
( ~ ( SV282 @ SY1922 )
| ( SV515 = SY1922 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3064]) ).
thf(3107,plain,
! [SV472: $i,SV139: $i > $o,SV508: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV508 ) )
= $true )
| ( ( ~ ! [SY1911: $i] :
( ~ ( SV282 @ SY1911 )
| ( SV508 = SY1911 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3065]) ).
thf(3108,plain,
! [SV473: $i,SV139: $i > $o,SV516: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV516 )
| ~ ! [SY1923: $i] :
( ~ ( SV282 @ SY1923 )
| ( SV516 = SY1923 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3066]) ).
thf(3109,plain,
! [SV473: $i,SV139: $i > $o,SV509: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV509 ) )
= $true )
| ( ( ~ ! [SY1912: $i] :
( ~ ( SV282 @ SY1912 )
| ( SV509 = SY1912 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3067]) ).
thf(3110,plain,
! [SV470: $i,SV139: $i > $o,SV510: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV510 ) )
= $true )
| ( ( ~ ! [SY1913: $i] :
( ~ ( SV282 @ SY1913 )
| ( SV510 = SY1913 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3111,plain,
! [SV470: $i,SV139: $i > $o,SV505: $i,SV282: $i > $o] :
( ( ( SV282 @ SV505 )
= $false )
| ( ( ~ ! [SY1908: $i] :
( ~ ( SV282 @ SY1908 )
| ( SV505 = SY1908 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3112,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) ) )
= $false )
| ( ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3113,plain,
! [SV141: $i,SV466: $i,SV457: $i] :
( ( ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $false )
| ( ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3114,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $true )
| ( ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $false )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3071]) ).
thf(3115,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3073]) ).
thf(3116,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3117,plain,
! [SV428: $i,SV480: $i,SV141: $i,SV517: $i] :
( ( ( in @ SV517 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( ! [SY1924: $i] :
( ~ ( in @ SY1924 @ SV517 )
| ( in @ SY1924 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
| ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV517 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3118,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3119,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3120,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV511: $i] :
( ( ( ! [SY1914: $i] :
( ~ ( in @ SY1914 @ SV511 )
| ( in @ SY1914 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) ) )
= $true )
| ( ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV511 )
= $true )
| ( ( in @ SV511 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3121,plain,
! [SV429: $i,SV304: $i,SV489: $i,SV504: $i,SV161: $i > $i > $o] :
( ( ( SV161 @ SV504 @ SV489 )
= $false )
| ( ( in @ SV504 @ SV304 )
= $false )
| ( ( in @ SV489 @ ( sK84_SY1692 @ SV429 @ SV161 @ SV304 ) )
= $true )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ SV429 )
= $false )
| ( ( SV161 @ ( sK19_SY1689 @ SV161 @ SV304 ) @ ( sK67_SY1803 @ SV429 @ SV304 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3122,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ( ~ ( SV216 @ ( sK134_SY1562 @ SV497 @ SV54 @ SV216 ) )
| ~ ! [SY1932: $i] :
( ~ ( SV216 @ SY1932 )
| ( ( sK134_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1932 ) ) ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3085]) ).
thf(3123,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK128_SY1562 @ SV497 @ SV54 @ SV216 ) )
| ~ ! [SY1925: $i] :
( ~ ( SV216 @ SY1925 )
| ( ( sK128_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1925 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3124,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ( ~ ( SV54 @ ( sK135_SY1228 @ SV498 @ SV216 @ SV54 ) )
| ~ ! [SY1933: $i] :
( ~ ( SV54 @ SY1933 )
| ( ( sK135_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1933 ) ) ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3087]) ).
thf(3125,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK129_SY1228 @ SV498 @ SV216 @ SV54 ) )
| ~ ! [SY1926: $i] :
( ~ ( SV54 @ SY1926 )
| ( ( sK129_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1926 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3088]) ).
thf(3126,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK130_SY1562 @ SV491 @ SV54 @ SV216 ) )
| ~ ! [SY1927: $i] :
( ~ ( SV216 @ SY1927 )
| ( ( sK130_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1927 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3127,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK121_SY1562 @ SV491 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3128,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1915: $i] :
( ~ ( SV216 @ SY1915 )
| ( ( sK121_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1915 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3090]) ).
thf(3129,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK131_SY1228 @ SV492 @ SV216 @ SV54 ) )
| ~ ! [SY1928: $i] :
( ~ ( SV54 @ SY1928 )
| ( ( sK131_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1928 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3130,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK122_SY1228 @ SV492 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3092]) ).
thf(3131,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1916: $i] :
( ~ ( SV54 @ SY1916 )
| ( ( sK122_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1916 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3092]) ).
thf(3132,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK132_SY1562 @ SV493 @ SV54 @ SV216 ) )
| ~ ! [SY1929: $i] :
( ~ ( SV216 @ SY1929 )
| ( ( sK132_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1929 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3133,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK123_SY1562 @ SV493 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3134,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1917: $i] :
( ~ ( SV216 @ SY1917 )
| ( ( sK123_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1917 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3094]) ).
thf(3135,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK133_SY1228 @ SV494 @ SV216 @ SV54 ) )
| ~ ! [SY1930: $i] :
( ~ ( SV54 @ SY1930 )
| ( ( sK133_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1930 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3136,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK124_SY1228 @ SV494 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3137,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1918: $i] :
( ~ ( SV54 @ SY1918 )
| ( ( sK124_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1918 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3138,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK125_SY1562 @ SV484 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3139,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1919: $i] :
( ~ ( SV216 @ SY1919 )
| ( ( sK125_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1919 ) ) )
= $false )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3140,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK118_SY1562 @ SV484 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3098]) ).
thf(3141,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ! [SY1909: $i] :
( ~ ( SV216 @ SY1909 )
| ( ( sK118_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1909 ) ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3099]) ).
thf(3142,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK126_SY1228 @ SV485 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3143,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1920: $i] :
( ~ ( SV54 @ SY1920 )
| ( ( sK126_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1920 ) ) )
= $false )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3144,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK119_SY1228 @ SV485 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3101]) ).
thf(3145,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ! [SY1910: $i] :
( ~ ( SV54 @ SY1910 )
| ( ( sK119_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1910 ) ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3102]) ).
thf(3146,plain,
! [SV479: $i,SV139: $i > $o,SV518: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV518 )
| ~ ! [SY1931: $i] :
( ~ ( SV282 @ SY1931 )
| ( SV518 = SY1931 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3104]) ).
thf(3147,plain,
! [SV479: $i,SV139: $i > $o,SV514: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV514 ) )
= $true )
| ( ( ~ ! [SY1921: $i] :
( ~ ( SV282 @ SY1921 )
| ( SV514 = SY1921 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3148,plain,
! [SV472: $i,SV139: $i > $o,SV515: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV515 ) )
= $true )
| ( ( ~ ! [SY1922: $i] :
( ~ ( SV282 @ SY1922 )
| ( SV515 = SY1922 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3106]) ).
thf(3149,plain,
! [SV472: $i,SV139: $i > $o,SV508: $i,SV282: $i > $o] :
( ( ( SV282 @ SV508 )
= $false )
| ( ( ~ ! [SY1911: $i] :
( ~ ( SV282 @ SY1911 )
| ( SV508 = SY1911 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3150,plain,
! [SV473: $i,SV139: $i > $o,SV516: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV516 ) )
= $true )
| ( ( ~ ! [SY1923: $i] :
( ~ ( SV282 @ SY1923 )
| ( SV516 = SY1923 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3151,plain,
! [SV473: $i,SV139: $i > $o,SV509: $i,SV282: $i > $o] :
( ( ( SV282 @ SV509 )
= $false )
| ( ( ~ ! [SY1912: $i] :
( ~ ( SV282 @ SY1912 )
| ( SV509 = SY1912 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3152,plain,
! [SV470: $i,SV139: $i > $o,SV510: $i,SV282: $i > $o] :
( ( ( SV282 @ SV510 )
= $false )
| ( ( ~ ! [SY1913: $i] :
( ~ ( SV282 @ SY1913 )
| ( SV510 = SY1913 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3153,plain,
! [SV470: $i,SV139: $i > $o,SV505: $i,SV282: $i > $o] :
( ( ( ! [SY1908: $i] :
( ~ ( SV282 @ SY1908 )
| ( SV505 = SY1908 ) ) )
= $false )
| ( ( SV282 @ SV505 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3154,plain,
! [SV141: $i,SV457: $i,SV466: $i] :
( ( ( in @ SV466 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $true )
| ( ( in @ SV457 @ ( sK102_SY1841 @ SV466 @ SV457 @ SV141 ) )
= $true )
| ( ( SV457 = SV466 )
= $true )
| ( ( in @ SV457 @ SV141 )
= $false )
| ( ( in @ SV466 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3155,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
| ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3156,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3157,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV517: $i] :
( ( ( ! [SY1924: $i] :
( ~ ( in @ SY1924 @ SV517 )
| ( in @ SY1924 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) ) )
= $true )
| ( ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV517 )
= $true )
| ( ( in @ SV517 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3117]) ).
thf(3158,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3118]) ).
thf(3159,plain,
! [SV474: $i,SV428: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3118]) ).
thf(3160,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( ! [SY1879: $i] :
~ ~ ( ~ ( in @ SY1879 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SY1879 @ SV428 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3161,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV511: $i,SV519: $i] :
( ( ( ~ ( in @ SV519 @ SV511 )
| ( in @ SV519 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
= $true )
| ( ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV511 )
= $true )
| ( ( in @ SV511 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3162,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK134_SY1562 @ SV497 @ SV54 @ SV216 ) )
| ~ ! [SY1932: $i] :
( ~ ( SV216 @ SY1932 )
| ( ( sK134_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1932 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3163,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK128_SY1562 @ SV497 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3123]) ).
thf(3164,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1925: $i] :
( ~ ( SV216 @ SY1925 )
| ( ( sK128_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1925 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3123]) ).
thf(3165,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK135_SY1228 @ SV498 @ SV216 @ SV54 ) )
| ~ ! [SY1933: $i] :
( ~ ( SV54 @ SY1933 )
| ( ( sK135_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1933 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3124]) ).
thf(3166,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK129_SY1228 @ SV498 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3125]) ).
thf(3167,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1926: $i] :
( ~ ( SV54 @ SY1926 )
| ( ( sK129_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1926 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3125]) ).
thf(3168,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK130_SY1562 @ SV491 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3169,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1927: $i] :
( ~ ( SV216 @ SY1927 )
| ( ( sK130_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1927 ) ) )
= $false )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3170,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK121_SY1562 @ SV491 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3127]) ).
thf(3171,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ! [SY1915: $i] :
( ~ ( SV216 @ SY1915 )
| ( ( sK121_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1915 ) ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3172,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK131_SY1228 @ SV492 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3129]) ).
thf(3173,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1928: $i] :
( ~ ( SV54 @ SY1928 )
| ( ( sK131_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1928 ) ) )
= $false )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3129]) ).
thf(3174,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK122_SY1228 @ SV492 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3130]) ).
thf(3175,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ! [SY1916: $i] :
( ~ ( SV54 @ SY1916 )
| ( ( sK122_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1916 ) ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3131]) ).
thf(3176,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK132_SY1562 @ SV493 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3132]) ).
thf(3177,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1929: $i] :
( ~ ( SV216 @ SY1929 )
| ( ( sK132_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1929 ) ) )
= $false )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3132]) ).
thf(3178,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK123_SY1562 @ SV493 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3133]) ).
thf(3179,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ! [SY1917: $i] :
( ~ ( SV216 @ SY1917 )
| ( ( sK123_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1917 ) ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3134]) ).
thf(3180,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK133_SY1228 @ SV494 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3135]) ).
thf(3181,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1930: $i] :
( ~ ( SV54 @ SY1930 )
| ( ( sK133_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1930 ) ) )
= $false )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3135]) ).
thf(3182,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK124_SY1228 @ SV494 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3136]) ).
thf(3183,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ! [SY1918: $i] :
( ~ ( SV54 @ SY1918 )
| ( ( sK124_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1918 ) ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3137]) ).
thf(3184,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK125_SY1562 @ SV484 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3138]) ).
thf(3185,plain,
! [SV54: $i > $o,SV484: $i,SV216: $i > $o] :
( ( ( ! [SY1919: $i] :
( ~ ( SV216 @ SY1919 )
| ( ( sK125_SY1562 @ SV484 @ SV54 @ SV216 )
= SY1919 ) ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3139]) ).
thf(3186,plain,
! [SV54: $i > $o,SV484: $i,SV520: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV520 )
| ( ( sK118_SY1562 @ SV484 @ SV54 @ SV216 )
= SV520 ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3187,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK126_SY1228 @ SV485 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3142]) ).
thf(3188,plain,
! [SV216: $i > $o,SV485: $i,SV54: $i > $o] :
( ( ( ! [SY1920: $i] :
( ~ ( SV54 @ SY1920 )
| ( ( sK126_SY1228 @ SV485 @ SV216 @ SV54 )
= SY1920 ) ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3143]) ).
thf(3189,plain,
! [SV216: $i > $o,SV485: $i,SV521: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV521 )
| ( ( sK119_SY1228 @ SV485 @ SV216 @ SV54 )
= SV521 ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3190,plain,
! [SV479: $i,SV139: $i > $o,SV518: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ SV518 ) )
= $true )
| ( ( ~ ! [SY1931: $i] :
( ~ ( SV282 @ SY1931 )
| ( SV518 = SY1931 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3191,plain,
! [SV479: $i,SV139: $i > $o,SV514: $i,SV282: $i > $o] :
( ( ( SV282 @ SV514 )
= $false )
| ( ( ~ ! [SY1921: $i] :
( ~ ( SV282 @ SY1921 )
| ( SV514 = SY1921 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3147]) ).
thf(3192,plain,
! [SV472: $i,SV139: $i > $o,SV515: $i,SV282: $i > $o] :
( ( ( SV282 @ SV515 )
= $false )
| ( ( ~ ! [SY1922: $i] :
( ~ ( SV282 @ SY1922 )
| ( SV515 = SY1922 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3193,plain,
! [SV472: $i,SV139: $i > $o,SV508: $i,SV282: $i > $o] :
( ( ( ! [SY1911: $i] :
( ~ ( SV282 @ SY1911 )
| ( SV508 = SY1911 ) ) )
= $false )
| ( ( SV282 @ SV508 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3194,plain,
! [SV473: $i,SV139: $i > $o,SV516: $i,SV282: $i > $o] :
( ( ( SV282 @ SV516 )
= $false )
| ( ( ~ ! [SY1923: $i] :
( ~ ( SV282 @ SY1923 )
| ( SV516 = SY1923 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3195,plain,
! [SV473: $i,SV139: $i > $o,SV509: $i,SV282: $i > $o] :
( ( ( ! [SY1912: $i] :
( ~ ( SV282 @ SY1912 )
| ( SV509 = SY1912 ) ) )
= $false )
| ( ( SV282 @ SV509 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3151]) ).
thf(3196,plain,
! [SV470: $i,SV139: $i > $o,SV510: $i,SV282: $i > $o] :
( ( ( ! [SY1913: $i] :
( ~ ( SV282 @ SY1913 )
| ( SV510 = SY1913 ) ) )
= $false )
| ( ( SV282 @ SV510 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3197,plain,
! [SV505: $i,SV139: $i > $o,SV470: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK136_SY1908 @ SV470 @ SV139 @ SV505 @ SV282 ) )
| ( SV505
= ( sK136_SY1908 @ SV470 @ SV139 @ SV505 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV505 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3153]) ).
thf(3198,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ~ ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3155]) ).
thf(3199,plain,
! [SV480: $i,SV428: $i,SV141: $i] :
( ( ( ~ ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3155]) ).
thf(3200,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( ! [SY1891: $i] :
~ ~ ( ~ ( in @ SY1891 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SY1891 @ SV428 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3156]) ).
thf(3201,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV517: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV517 )
| ( in @ SV522 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
= $true )
| ( ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV517 )
= $true )
| ( ( in @ SV517 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3202,plain,
! [SV141: $i,SV428: $i,SV474: $i] :
( ( ( in @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3158]) ).
thf(3203,plain,
! [SV474: $i,SV428: $i,SV141: $i] :
( ( ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV428 )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3159]) ).
thf(3204,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV523: $i] :
( ( ( ~ ~ ( ~ ( in @ SV523 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SV523 @ SV428 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3205,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV511: $i,SV519: $i] :
( ( ( ~ ( in @ SV519 @ SV511 ) )
= $true )
| ( ( in @ SV519 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
= $true )
| ( ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV511 )
= $true )
| ( ( in @ SV511 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3161]) ).
thf(3206,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK134_SY1562 @ SV497 @ SV54 @ SV216 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3162]) ).
thf(3207,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ~ ! [SY1932: $i] :
( ~ ( SV216 @ SY1932 )
| ( ( sK134_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1932 ) ) )
= $false )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3162]) ).
thf(3208,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK128_SY1562 @ SV497 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3163]) ).
thf(3209,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ! [SY1925: $i] :
( ~ ( SV216 @ SY1925 )
| ( ( sK128_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1925 ) ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3164]) ).
thf(3210,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ ( sK135_SY1228 @ SV498 @ SV216 @ SV54 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3165]) ).
thf(3211,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ~ ! [SY1933: $i] :
( ~ ( SV54 @ SY1933 )
| ( ( sK135_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1933 ) ) )
= $false )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3165]) ).
thf(3212,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK129_SY1228 @ SV498 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3166]) ).
thf(3213,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ! [SY1926: $i] :
( ~ ( SV54 @ SY1926 )
| ( ( sK129_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1926 ) ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3167]) ).
thf(3214,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK130_SY1562 @ SV491 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3168]) ).
thf(3215,plain,
! [SV54: $i > $o,SV491: $i,SV216: $i > $o] :
( ( ( ! [SY1927: $i] :
( ~ ( SV216 @ SY1927 )
| ( ( sK130_SY1562 @ SV491 @ SV54 @ SV216 )
= SY1927 ) ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3169]) ).
thf(3216,plain,
! [SV54: $i > $o,SV491: $i,SV524: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV524 )
| ( ( sK121_SY1562 @ SV491 @ SV54 @ SV216 )
= SV524 ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3217,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK131_SY1228 @ SV492 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3172]) ).
thf(3218,plain,
! [SV216: $i > $o,SV492: $i,SV54: $i > $o] :
( ( ( ! [SY1928: $i] :
( ~ ( SV54 @ SY1928 )
| ( ( sK131_SY1228 @ SV492 @ SV216 @ SV54 )
= SY1928 ) ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3173]) ).
thf(3219,plain,
! [SV216: $i > $o,SV492: $i,SV525: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV525 )
| ( ( sK122_SY1228 @ SV492 @ SV216 @ SV54 )
= SV525 ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3220,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK132_SY1562 @ SV493 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3176]) ).
thf(3221,plain,
! [SV54: $i > $o,SV493: $i,SV216: $i > $o] :
( ( ( ! [SY1929: $i] :
( ~ ( SV216 @ SY1929 )
| ( ( sK132_SY1562 @ SV493 @ SV54 @ SV216 )
= SY1929 ) ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3177]) ).
thf(3222,plain,
! [SV54: $i > $o,SV493: $i,SV526: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV526 )
| ( ( sK123_SY1562 @ SV493 @ SV54 @ SV216 )
= SV526 ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3223,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK133_SY1228 @ SV494 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3180]) ).
thf(3224,plain,
! [SV216: $i > $o,SV494: $i,SV54: $i > $o] :
( ( ( ! [SY1930: $i] :
( ~ ( SV54 @ SY1930 )
| ( ( sK133_SY1228 @ SV494 @ SV216 @ SV54 )
= SY1930 ) ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3181]) ).
thf(3225,plain,
! [SV216: $i > $o,SV494: $i,SV527: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV527 )
| ( ( sK124_SY1228 @ SV494 @ SV216 @ SV54 )
= SV527 ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3226,plain,
! [SV54: $i > $o,SV484: $i,SV528: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV528 )
| ( ( sK125_SY1562 @ SV484 @ SV54 @ SV216 )
= SV528 ) )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3227,plain,
! [SV54: $i > $o,SV484: $i,SV520: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV520 ) )
= $true )
| ( ( ( sK118_SY1562 @ SV484 @ SV54 @ SV216 )
= SV520 )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3186]) ).
thf(3228,plain,
! [SV216: $i > $o,SV485: $i,SV529: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV529 )
| ( ( sK126_SY1228 @ SV485 @ SV216 @ SV54 )
= SV529 ) )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3229,plain,
! [SV216: $i > $o,SV485: $i,SV521: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV521 ) )
= $true )
| ( ( ( sK119_SY1228 @ SV485 @ SV216 @ SV54 )
= SV521 )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3230,plain,
! [SV479: $i,SV139: $i > $o,SV518: $i,SV282: $i > $o] :
( ( ( SV282 @ SV518 )
= $false )
| ( ( ~ ! [SY1931: $i] :
( ~ ( SV282 @ SY1931 )
| ( SV518 = SY1931 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3190]) ).
thf(3231,plain,
! [SV479: $i,SV139: $i > $o,SV514: $i,SV282: $i > $o] :
( ( ( ! [SY1921: $i] :
( ~ ( SV282 @ SY1921 )
| ( SV514 = SY1921 ) ) )
= $false )
| ( ( SV282 @ SV514 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3232,plain,
! [SV472: $i,SV139: $i > $o,SV515: $i,SV282: $i > $o] :
( ( ( ! [SY1922: $i] :
( ~ ( SV282 @ SY1922 )
| ( SV515 = SY1922 ) ) )
= $false )
| ( ( SV282 @ SV515 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3233,plain,
! [SV508: $i,SV139: $i > $o,SV472: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK137_SY1911 @ SV472 @ SV139 @ SV508 @ SV282 ) )
| ( SV508
= ( sK137_SY1911 @ SV472 @ SV139 @ SV508 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV508 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3193]) ).
thf(3234,plain,
! [SV473: $i,SV139: $i > $o,SV516: $i,SV282: $i > $o] :
( ( ( ! [SY1923: $i] :
( ~ ( SV282 @ SY1923 )
| ( SV516 = SY1923 ) ) )
= $false )
| ( ( SV282 @ SV516 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3194]) ).
thf(3235,plain,
! [SV509: $i,SV139: $i > $o,SV473: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK138_SY1912 @ SV473 @ SV139 @ SV509 @ SV282 ) )
| ( SV509
= ( sK138_SY1912 @ SV473 @ SV139 @ SV509 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV509 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3195]) ).
thf(3236,plain,
! [SV510: $i,SV139: $i > $o,SV470: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK139_SY1913 @ SV470 @ SV139 @ SV510 @ SV282 ) )
| ( SV510
= ( sK139_SY1913 @ SV470 @ SV139 @ SV510 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV510 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3196]) ).
thf(3237,plain,
! [SV505: $i,SV139: $i > $o,SV470: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK136_SY1908 @ SV470 @ SV139 @ SV505 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV505 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3197]) ).
thf(3238,plain,
! [SV282: $i > $o,SV139: $i > $o,SV470: $i,SV505: $i] :
( ( ( SV505
= ( sK136_SY1908 @ SV470 @ SV139 @ SV505 @ SV282 ) )
= $false )
| ( ( SV282 @ SV505 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3197]) ).
thf(3239,plain,
! [SV141: $i,SV428: $i,SV480: $i] :
( ( ( in @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) @ ( sK3_SY1423 @ SV141 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3198]) ).
thf(3240,plain,
! [SV480: $i,SV428: $i,SV141: $i] :
( ( ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV428 )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3199]) ).
thf(3241,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV530: $i] :
( ( ( ~ ~ ( ~ ( in @ SV530 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SV530 @ SV428 ) ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3242,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV517: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV517 ) )
= $true )
| ( ( in @ SV522 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
= $true )
| ( ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV517 )
= $true )
| ( ( in @ SV517 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3243,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV523: $i] :
( ( ( ~ ( ~ ( in @ SV523 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SV523 @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3244,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV511: $i,SV519: $i] :
( ( ( in @ SV519 @ SV511 )
= $false )
| ( ( in @ SV519 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
= $true )
| ( ( in @ ( sK103_SY1878 @ SV141 @ SV428 @ SV474 ) @ SV511 )
= $true )
| ( ( in @ SV511 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3245,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK134_SY1562 @ SV497 @ SV54 @ SV216 ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3206]) ).
thf(3246,plain,
! [SV54: $i > $o,SV497: $i,SV216: $i > $o] :
( ( ( ! [SY1932: $i] :
( ~ ( SV216 @ SY1932 )
| ( ( sK134_SY1562 @ SV497 @ SV54 @ SV216 )
= SY1932 ) ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3207]) ).
thf(3247,plain,
! [SV54: $i > $o,SV497: $i,SV531: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV531 )
| ( ( sK128_SY1562 @ SV497 @ SV54 @ SV216 )
= SV531 ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3248,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( SV54 @ ( sK135_SY1228 @ SV498 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3249,plain,
! [SV216: $i > $o,SV498: $i,SV54: $i > $o] :
( ( ( ! [SY1933: $i] :
( ~ ( SV54 @ SY1933 )
| ( ( sK135_SY1228 @ SV498 @ SV216 @ SV54 )
= SY1933 ) ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3211]) ).
thf(3250,plain,
! [SV216: $i > $o,SV498: $i,SV532: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV532 )
| ( ( sK129_SY1228 @ SV498 @ SV216 @ SV54 )
= SV532 ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3251,plain,
! [SV54: $i > $o,SV491: $i,SV533: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV533 )
| ( ( sK130_SY1562 @ SV491 @ SV54 @ SV216 )
= SV533 ) )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3252,plain,
! [SV54: $i > $o,SV491: $i,SV524: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV524 ) )
= $true )
| ( ( ( sK121_SY1562 @ SV491 @ SV54 @ SV216 )
= SV524 )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3253,plain,
! [SV216: $i > $o,SV492: $i,SV534: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV534 )
| ( ( sK131_SY1228 @ SV492 @ SV216 @ SV54 )
= SV534 ) )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3254,plain,
! [SV216: $i > $o,SV492: $i,SV525: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV525 ) )
= $true )
| ( ( ( sK122_SY1228 @ SV492 @ SV216 @ SV54 )
= SV525 )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3219]) ).
thf(3255,plain,
! [SV54: $i > $o,SV493: $i,SV535: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV535 )
| ( ( sK132_SY1562 @ SV493 @ SV54 @ SV216 )
= SV535 ) )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3256,plain,
! [SV54: $i > $o,SV493: $i,SV526: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV526 ) )
= $true )
| ( ( ( sK123_SY1562 @ SV493 @ SV54 @ SV216 )
= SV526 )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3257,plain,
! [SV216: $i > $o,SV494: $i,SV536: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV536 )
| ( ( sK133_SY1228 @ SV494 @ SV216 @ SV54 )
= SV536 ) )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3258,plain,
! [SV216: $i > $o,SV494: $i,SV527: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV527 ) )
= $true )
| ( ( ( sK124_SY1228 @ SV494 @ SV216 @ SV54 )
= SV527 )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3259,plain,
! [SV54: $i > $o,SV484: $i,SV528: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV528 ) )
= $true )
| ( ( ( sK125_SY1562 @ SV484 @ SV54 @ SV216 )
= SV528 )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3260,plain,
! [SV54: $i > $o,SV484: $i,SV520: $i,SV216: $i > $o] :
( ( ( SV216 @ SV520 )
= $false )
| ( ( ( sK118_SY1562 @ SV484 @ SV54 @ SV216 )
= SV520 )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV484
= ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3261,plain,
! [SV216: $i > $o,SV485: $i,SV529: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV529 ) )
= $true )
| ( ( ( sK126_SY1228 @ SV485 @ SV216 @ SV54 )
= SV529 )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3262,plain,
! [SV216: $i > $o,SV485: $i,SV521: $i,SV54: $i > $o] :
( ( ( SV54 @ SV521 )
= $false )
| ( ( ( sK119_SY1228 @ SV485 @ SV216 @ SV54 )
= SV521 )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV485
= ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3229]) ).
thf(3263,plain,
! [SV479: $i,SV139: $i > $o,SV518: $i,SV282: $i > $o] :
( ( ( ! [SY1931: $i] :
( ~ ( SV282 @ SY1931 )
| ( SV518 = SY1931 ) ) )
= $false )
| ( ( SV282 @ SV518 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3264,plain,
! [SV514: $i,SV139: $i > $o,SV479: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK140_SY1921 @ SV479 @ SV139 @ SV514 @ SV282 ) )
| ( SV514
= ( sK140_SY1921 @ SV479 @ SV139 @ SV514 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV514 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3231]) ).
thf(3265,plain,
! [SV515: $i,SV139: $i > $o,SV472: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK141_SY1922 @ SV472 @ SV139 @ SV515 @ SV282 ) )
| ( SV515
= ( sK141_SY1922 @ SV472 @ SV139 @ SV515 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV515 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3232]) ).
thf(3266,plain,
! [SV508: $i,SV139: $i > $o,SV472: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK137_SY1911 @ SV472 @ SV139 @ SV508 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV508 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3233]) ).
thf(3267,plain,
! [SV282: $i > $o,SV139: $i > $o,SV472: $i,SV508: $i] :
( ( ( SV508
= ( sK137_SY1911 @ SV472 @ SV139 @ SV508 @ SV282 ) )
= $false )
| ( ( SV282 @ SV508 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3233]) ).
thf(3268,plain,
! [SV516: $i,SV139: $i > $o,SV473: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK142_SY1923 @ SV473 @ SV139 @ SV516 @ SV282 ) )
| ( SV516
= ( sK142_SY1923 @ SV473 @ SV139 @ SV516 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV516 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3234]) ).
thf(3269,plain,
! [SV509: $i,SV139: $i > $o,SV473: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK138_SY1912 @ SV473 @ SV139 @ SV509 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV509 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3235]) ).
thf(3270,plain,
! [SV282: $i > $o,SV139: $i > $o,SV473: $i,SV509: $i] :
( ( ( SV509
= ( sK138_SY1912 @ SV473 @ SV139 @ SV509 @ SV282 ) )
= $false )
| ( ( SV282 @ SV509 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3235]) ).
thf(3271,plain,
! [SV510: $i,SV139: $i > $o,SV470: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK139_SY1913 @ SV470 @ SV139 @ SV510 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV510 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3236]) ).
thf(3272,plain,
! [SV282: $i > $o,SV139: $i > $o,SV470: $i,SV510: $i] :
( ( ( SV510
= ( sK139_SY1913 @ SV470 @ SV139 @ SV510 @ SV282 ) )
= $false )
| ( ( SV282 @ SV510 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3236]) ).
thf(3273,plain,
! [SV505: $i,SV139: $i > $o,SV470: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK136_SY1908 @ SV470 @ SV139 @ SV505 @ SV282 ) )
= $true )
| ( ( SV282 @ SV505 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV470
= ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3237]) ).
thf(3274,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV530: $i] :
( ( ( ~ ( ~ ( in @ SV530 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SV530 @ SV428 ) ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3275,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV517: $i,SV522: $i] :
( ( ( in @ SV522 @ SV517 )
= $false )
| ( ( in @ SV522 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
= $true )
| ( ( in @ ( sK107_SY1890 @ SV141 @ SV428 @ SV480 ) @ SV517 )
= $true )
| ( ( in @ SV517 @ ( sK3_SY1423 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3276,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
| ~ ( in @ SV523 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3243]) ).
thf(3277,plain,
! [SV54: $i > $o,SV497: $i,SV537: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV537 )
| ( ( sK134_SY1562 @ SV497 @ SV54 @ SV216 )
= SV537 ) )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3278,plain,
! [SV54: $i > $o,SV497: $i,SV531: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV531 ) )
= $true )
| ( ( ( sK128_SY1562 @ SV497 @ SV54 @ SV216 )
= SV531 )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3247]) ).
thf(3279,plain,
! [SV216: $i > $o,SV498: $i,SV538: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV538 )
| ( ( sK135_SY1228 @ SV498 @ SV216 @ SV54 )
= SV538 ) )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3280,plain,
! [SV216: $i > $o,SV498: $i,SV532: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV532 ) )
= $true )
| ( ( ( sK129_SY1228 @ SV498 @ SV216 @ SV54 )
= SV532 )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3250]) ).
thf(3281,plain,
! [SV54: $i > $o,SV491: $i,SV533: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV533 ) )
= $true )
| ( ( ( sK130_SY1562 @ SV491 @ SV54 @ SV216 )
= SV533 )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3282,plain,
! [SV54: $i > $o,SV491: $i,SV524: $i,SV216: $i > $o] :
( ( ( SV216 @ SV524 )
= $false )
| ( ( ( sK121_SY1562 @ SV491 @ SV54 @ SV216 )
= SV524 )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV491
= ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3283,plain,
! [SV216: $i > $o,SV492: $i,SV534: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV534 ) )
= $true )
| ( ( ( sK131_SY1228 @ SV492 @ SV216 @ SV54 )
= SV534 )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3253]) ).
thf(3284,plain,
! [SV216: $i > $o,SV492: $i,SV525: $i,SV54: $i > $o] :
( ( ( SV54 @ SV525 )
= $false )
| ( ( ( sK122_SY1228 @ SV492 @ SV216 @ SV54 )
= SV525 )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV492
= ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3285,plain,
! [SV54: $i > $o,SV493: $i,SV535: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV535 ) )
= $true )
| ( ( ( sK132_SY1562 @ SV493 @ SV54 @ SV216 )
= SV535 )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3255]) ).
thf(3286,plain,
! [SV54: $i > $o,SV493: $i,SV526: $i,SV216: $i > $o] :
( ( ( SV216 @ SV526 )
= $false )
| ( ( ( sK123_SY1562 @ SV493 @ SV54 @ SV216 )
= SV526 )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV493
= ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3256]) ).
thf(3287,plain,
! [SV216: $i > $o,SV494: $i,SV536: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV536 ) )
= $true )
| ( ( ( sK133_SY1228 @ SV494 @ SV216 @ SV54 )
= SV536 )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3288,plain,
! [SV216: $i > $o,SV494: $i,SV527: $i,SV54: $i > $o] :
( ( ( SV54 @ SV527 )
= $false )
| ( ( ( sK124_SY1228 @ SV494 @ SV216 @ SV54 )
= SV527 )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV494
= ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3289,plain,
! [SV54: $i > $o,SV484: $i,SV528: $i,SV216: $i > $o] :
( ( ( SV216 @ SV528 )
= $false )
| ( ( ( sK125_SY1562 @ SV484 @ SV54 @ SV216 )
= SV528 )
= $true )
| ( ( SV54 @ SV484 )
= $false )
| ( ( SV54 @ ( sK108_SY1862 @ SV216 @ SV484 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3290,plain,
! [SV216: $i > $o,SV485: $i,SV529: $i,SV54: $i > $o] :
( ( ( SV54 @ SV529 )
= $false )
| ( ( ( sK126_SY1228 @ SV485 @ SV216 @ SV54 )
= SV529 )
= $true )
| ( ( SV216 @ SV485 )
= $false )
| ( ( SV216 @ ( sK109_SY1863 @ SV54 @ SV485 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3291,plain,
! [SV518: $i,SV139: $i > $o,SV479: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK143_SY1931 @ SV479 @ SV139 @ SV518 @ SV282 ) )
| ( SV518
= ( sK143_SY1931 @ SV479 @ SV139 @ SV518 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV518 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3263]) ).
thf(3292,plain,
! [SV514: $i,SV139: $i > $o,SV479: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK140_SY1921 @ SV479 @ SV139 @ SV514 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV514 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3264]) ).
thf(3293,plain,
! [SV282: $i > $o,SV139: $i > $o,SV479: $i,SV514: $i] :
( ( ( SV514
= ( sK140_SY1921 @ SV479 @ SV139 @ SV514 @ SV282 ) )
= $false )
| ( ( SV282 @ SV514 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3264]) ).
thf(3294,plain,
! [SV515: $i,SV139: $i > $o,SV472: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK141_SY1922 @ SV472 @ SV139 @ SV515 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV515 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3265]) ).
thf(3295,plain,
! [SV282: $i > $o,SV139: $i > $o,SV472: $i,SV515: $i] :
( ( ( SV515
= ( sK141_SY1922 @ SV472 @ SV139 @ SV515 @ SV282 ) )
= $false )
| ( ( SV282 @ SV515 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3265]) ).
thf(3296,plain,
! [SV508: $i,SV139: $i > $o,SV472: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK137_SY1911 @ SV472 @ SV139 @ SV508 @ SV282 ) )
= $true )
| ( ( SV282 @ SV508 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV472
= ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3266]) ).
thf(3297,plain,
! [SV516: $i,SV139: $i > $o,SV473: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK142_SY1923 @ SV473 @ SV139 @ SV516 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV516 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3268]) ).
thf(3298,plain,
! [SV282: $i > $o,SV139: $i > $o,SV473: $i,SV516: $i] :
( ( ( SV516
= ( sK142_SY1923 @ SV473 @ SV139 @ SV516 @ SV282 ) )
= $false )
| ( ( SV282 @ SV516 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3268]) ).
thf(3299,plain,
! [SV509: $i,SV139: $i > $o,SV473: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK138_SY1912 @ SV473 @ SV139 @ SV509 @ SV282 ) )
= $true )
| ( ( SV282 @ SV509 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV473
= ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3269]) ).
thf(3300,plain,
! [SV510: $i,SV139: $i > $o,SV470: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK139_SY1913 @ SV470 @ SV139 @ SV510 @ SV282 ) )
= $true )
| ( ( SV282 @ SV510 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV470 )
= $false )
| ( ( SV139 @ ( sK97_SY1846 @ SV282 @ SV470 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3271]) ).
thf(3301,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV530: $i] :
( ( ( ~ ( in @ SV530 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
| ~ ( in @ SV530 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3274]) ).
thf(3302,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) ) )
= $true )
| ( ( ~ ( in @ SV523 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3303,plain,
! [SV54: $i > $o,SV497: $i,SV537: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ SV537 ) )
= $true )
| ( ( ( sK134_SY1562 @ SV497 @ SV54 @ SV216 )
= SV537 )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3277]) ).
thf(3304,plain,
! [SV54: $i > $o,SV497: $i,SV531: $i,SV216: $i > $o] :
( ( ( SV216 @ SV531 )
= $false )
| ( ( ( sK128_SY1562 @ SV497 @ SV54 @ SV216 )
= SV531 )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV497
= ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3305,plain,
! [SV216: $i > $o,SV498: $i,SV538: $i,SV54: $i > $o] :
( ( ( ~ ( SV54 @ SV538 ) )
= $true )
| ( ( ( sK135_SY1228 @ SV498 @ SV216 @ SV54 )
= SV538 )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3279]) ).
thf(3306,plain,
! [SV216: $i > $o,SV498: $i,SV532: $i,SV54: $i > $o] :
( ( ( SV54 @ SV532 )
= $false )
| ( ( ( sK129_SY1228 @ SV498 @ SV216 @ SV54 )
= SV532 )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV498
= ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $false )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3307,plain,
! [SV54: $i > $o,SV491: $i,SV533: $i,SV216: $i > $o] :
( ( ( SV216 @ SV533 )
= $false )
| ( ( ( sK130_SY1562 @ SV491 @ SV54 @ SV216 )
= SV533 )
= $true )
| ( ( SV54 @ SV491 )
= $false )
| ( ( SV54 @ ( sK111_SY1870 @ SV216 @ SV491 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3281]) ).
thf(3308,plain,
! [SV216: $i > $o,SV492: $i,SV534: $i,SV54: $i > $o] :
( ( ( SV54 @ SV534 )
= $false )
| ( ( ( sK131_SY1228 @ SV492 @ SV216 @ SV54 )
= SV534 )
= $true )
| ( ( SV216 @ SV492 )
= $false )
| ( ( SV216 @ ( sK112_SY1871 @ SV54 @ SV492 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3309,plain,
! [SV54: $i > $o,SV493: $i,SV535: $i,SV216: $i > $o] :
( ( ( SV216 @ SV535 )
= $false )
| ( ( ( sK132_SY1562 @ SV493 @ SV54 @ SV216 )
= SV535 )
= $true )
| ( ( SV54 @ SV493 )
= $false )
| ( ( SV54 @ ( sK113_SY1872 @ SV216 @ SV493 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3285]) ).
thf(3310,plain,
! [SV216: $i > $o,SV494: $i,SV536: $i,SV54: $i > $o] :
( ( ( SV54 @ SV536 )
= $false )
| ( ( ( sK133_SY1228 @ SV494 @ SV216 @ SV54 )
= SV536 )
= $true )
| ( ( SV216 @ SV494 )
= $false )
| ( ( SV216 @ ( sK114_SY1873 @ SV54 @ SV494 @ SV216 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $false )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3287]) ).
thf(3311,plain,
! [SV518: $i,SV139: $i > $o,SV479: $i,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK143_SY1931 @ SV479 @ SV139 @ SV518 @ SV282 ) ) )
= $false )
| ( ( SV282 @ SV518 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3291]) ).
thf(3312,plain,
! [SV282: $i > $o,SV139: $i > $o,SV479: $i,SV518: $i] :
( ( ( SV518
= ( sK143_SY1931 @ SV479 @ SV139 @ SV518 @ SV282 ) )
= $false )
| ( ( SV282 @ SV518 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3291]) ).
thf(3313,plain,
! [SV514: $i,SV139: $i > $o,SV479: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK140_SY1921 @ SV479 @ SV139 @ SV514 @ SV282 ) )
= $true )
| ( ( SV282 @ SV514 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV479
= ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3292]) ).
thf(3314,plain,
! [SV515: $i,SV139: $i > $o,SV472: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK141_SY1922 @ SV472 @ SV139 @ SV515 @ SV282 ) )
= $true )
| ( ( SV282 @ SV515 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV472 )
= $false )
| ( ( SV139 @ ( sK100_SY1852 @ SV282 @ SV472 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3294]) ).
thf(3315,plain,
! [SV516: $i,SV139: $i > $o,SV473: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK142_SY1923 @ SV473 @ SV139 @ SV516 @ SV282 ) )
= $true )
| ( ( SV282 @ SV516 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV473 )
= $false )
| ( ( SV139 @ ( sK101_SY1853 @ SV282 @ SV473 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $false )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3297]) ).
thf(3316,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV530: $i] :
( ( ( ~ ( in @ SV530 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) ) )
= $true )
| ( ( ~ ( in @ SV530 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3317,plain,
! [SV141: $i,SV428: $i,SV474: $i,SV523: $i] :
( ( ( in @ SV523 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
= $false )
| ( ( ~ ( in @ SV523 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3302]) ).
thf(3318,plain,
! [SV54: $i > $o,SV497: $i,SV537: $i,SV216: $i > $o] :
( ( ( SV216 @ SV537 )
= $false )
| ( ( ( sK134_SY1562 @ SV497 @ SV54 @ SV216 )
= SV537 )
= $true )
| ( ( SV54 @ SV497 )
= $false )
| ( ( SV54 @ ( sK116_SY1886 @ SV216 @ SV497 @ SV54 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3319,plain,
! [SV216: $i > $o,SV498: $i,SV538: $i,SV54: $i > $o] :
( ( ( SV54 @ SV538 )
= $false )
| ( ( ( sK135_SY1228 @ SV498 @ SV216 @ SV54 )
= SV538 )
= $true )
| ( ( SV216 @ SV498 )
= $false )
| ( ( SV216 @ ( sK117_SY1887 @ SV54 @ SV498 @ SV216 ) )
= $true )
| ( ( SV54 @ ( sK10_SY1558 @ SV216 @ SV54 ) )
= $true )
| ( ( SV216 @ ( sK20_SY1762 @ SV54 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3320,plain,
! [SV518: $i,SV139: $i > $o,SV479: $i,SV282: $i > $o] :
( ( ( SV282 @ ( sK143_SY1931 @ SV479 @ SV139 @ SV518 @ SV282 ) )
= $true )
| ( ( SV282 @ SV518 )
= $false )
| ( ( ( descr
@ ^ [SY1419: $i] : ( SV139 @ SY1419 ) )
= ( descr
@ ^ [SY1658: $i] : ( SV282 @ SY1658 ) ) )
= $true )
| ( ( SV139 @ SV479 )
= $false )
| ( ( SV139 @ ( sK106_SY1859 @ SV282 @ SV479 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK16_SY1651 @ SV282 @ SV139 ) )
= $true )
| ( ( SV282 @ ( sK24_SY1779 @ SV139 @ SV282 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3311]) ).
thf(3321,plain,
! [SV141: $i,SV428: $i,SV480: $i,SV530: $i] :
( ( ( in @ SV530 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
= $false )
| ( ( ~ ( in @ SV530 @ SV428 ) )
= $true )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3322,plain,
! [SV141: $i,SV474: $i,SV428: $i,SV523: $i] :
( ( ( in @ SV523 @ SV428 )
= $false )
| ( ( in @ SV523 @ ( sK91_SY1798 @ SV474 @ SV428 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV141 )
= $false )
| ( ( in @ SV474 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3323,plain,
! [SV141: $i,SV480: $i,SV428: $i,SV530: $i] :
( ( ( in @ SV530 @ SV428 )
= $false )
| ( ( in @ SV530 @ ( sK95_SY1798 @ SV480 @ SV428 @ SV141 ) )
= $false )
| ( ( in @ ( sK66_SY1796 @ SV141 @ SV428 ) @ SV428 )
= $true )
| ( ( in @ SV480 @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3324,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[294,3323,3322,3320,3319,3318,3315,3314,3313,3312,3310,3309,3308,3307,3306,3304,3300,3299,3298,3296,3295,3293,3290,3289,3288,3286,3284,3282,3275,3273,3272,3270,3267,3262,3260,3248,3245,3244,3240,3239,3238,3223,3220,3217,3214,3212,3208,3203,3202,3187,3184,3182,3178,3174,3170,3154,3144,3140,3121,3114,3113,3103,3084,3083,3082,3080,3079,3072,3061,3060,3042,3040,3037,3036,3017,2955,2952,2917,2913,2872,2871,2867,2856,2855,2838,2837,2834,2833,2830,2818,2817,2814,2813,2791,2790,2773,2772,2771,2754,2733,2732,2718,2712,2711,2706,2705,2690,2689,2688,2684,2683,2682,2669,2668,2644,2633,2632,2631,2628,2616,2614,2592,2591,2582,2580,2577,2555,2541,2534,2525,2518,2517,2516,2509,2496,2494,2492,2457,2456,2453,2452,2451,2445,2431,2427,2426,2417,2416,2381,2380,2357,2356,2355,2354,2353,2352,2328,2313,2304,2303,2288,2285,2282,2272,2256,2240,2233,2232,2231,2219,2218,2212,2211,2210,2209,2206,2205,2204,2203,2200,2199,2198,2197,2194,2193,2185,2184,2183,2182,2181,2180,2179,2162,2140,2137,2117,2113,2110,2106,2103,2099,2096,2087,2086,2084,2083,2081,2080,2078,2077,2075,2074,2072,2071,2060,2055,2051,2031,2030,2024,2023,1989,1981,1978,1975,1972,1969,1966,1954,1953,1936,1935,1914,1884,1883,1882,1860,1851,1841,1840,1833,1832,1831,1799,1797,1792,1790,1789,1787,1786,1784,1747,1742,1741,1740,1731,1730,1729,1728,1724,1718,1717,1659,1658,1646,1640,1637,1636,1635,1626,1625,1624,1618,1600,1599,1598,1596,1594,1593,1590,1581,1574,1568,1554,1537,1525,1522,1518,1515,1514,1502,1500,1487,1486,1464,1461,1447,1441,1436,1419,1416,1414,1413,1402,1377,1368,1363,1357,1352,1351,1339,1337,1336,1334,1331,1317,1315,1313,1304,1300,1298,1296,1281,1272,1252,1250,1248,1236,1222,1218,1216,1203,1202,1200,1195,1193,1191,1183,1181,1178,1166,1151,1150,1149,1146,1142,1138,1134,1129,1124,1119,1113,1112,1104,1102,1101,1100,1099,1088,1076,1072,1071,1070,1069,1065,1063,1054,1049,1039,1036,987,956,955,954,926,916,912,911,910,889,870,717,716,715,714,713,712,711,710,709,708,707,706,705,703,702,701,700,699,698,697,696,540,539,538,535,534,532,517,516,515,360,336,298]) ).
thf(3325,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU664^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:28:30 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.62/7.19
% 41.62/7.19 No.of.Axioms: 0
% 41.62/7.19
% 41.62/7.19 Length.of.Defs: 38970
% 41.62/7.19
% 41.62/7.19 Contains.Choice.Funs: true
% 41.62/7.19 ........................................................................................................................
% 41.62/7.19
% 41.62/7.19 ********************************
% 41.62/7.19 * All subproblems solved! *
% 41.62/7.19 ********************************
% 41.62/7.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:180,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3324,loop_count:0,foatp_calls:1,translation:fof_full)
% 41.62/7.19
% 41.62/7.19 %**** Beginning of derivation protocol ****
% 41.62/7.19 % SZS output start CNFRefutation
% See solution above
% 7.17/7.21
% 7.17/7.21 %**** End of derivation protocol ****
% 7.17/7.21 %**** no. of clauses in derivation: 3325 ****
% 7.17/7.21 %**** clause counter: 3324 ****
% 7.17/7.21
% 7.17/7.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:180,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3324,loop_count:0,foatp_calls:1,translation:fof_full)
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