%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU620^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 10:45:38 AM UTC 2026
% Result : Theorem 187.14s 31.95s
% Output : CNFRefutation 187.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 141
% Syntax : Number of formulae : 2622 ( 885 unt; 0 typ; 140 def)
% Number of atoms : 20689 (8776 equ; 0 cnn)
% Maximal formula atoms : 137 ( 7 avg)
% Number of connectives : 45589 (10035 ~;8047 |; 167 &;26077 @)
% ( 56 <=>;1207 =>; 0 <=; 0 <~>)
% Maximal formula depth : 142 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1704 (1704 >; 0 *; 0 +; 0 <<)
% Number of symbols : 281 ( 278 usr; 142 con; 0-4 aty)
% Number of variables : 10020 ( 536 ^;9313 !; 171 ?;10020 :)
% Comments :
%------------------------------------------------------------------------------
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_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_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_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $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_SY1095,type,
sK100_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK101_SY1225,type,
sK101_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK102_SY1095,type,
sK102_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK103_SY1225,type,
sK103_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK104_SY1095,type,
sK104_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK105_SY1225,type,
sK105_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK106_SY1095,type,
sK106_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK107_SY1225,type,
sK107_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK108_SY1095,type,
sK108_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK109_SY1225,type,
sK109_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK10_SY1177,type,
sK10_SY1177: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK110_SY1095,type,
sK110_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK111_SY1225,type,
sK111_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK112_SY1095,type,
sK112_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK113_SY1382,type,
sK113_SY1382: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK114_SY1384,type,
sK114_SY1384: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK115_SY1385,type,
sK115_SY1385: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK116_SY1386,type,
sK116_SY1386: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK117_SY1390,type,
sK117_SY1390: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK118_SY1391,type,
sK118_SY1391: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK119_SY1392,type,
sK119_SY1392: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY1197,type,
sK11_SY1197: $i > $i > $i ).
thf(tp_sK120_SY1399,type,
sK120_SY1399: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK12_SY1207,type,
sK12_SY1207: $i > $i > $i ).
thf(tp_sK13_SY1209,type,
sK13_SY1209: ( $i > $o ) > $i > $i ).
thf(tp_sK14_SY1220,type,
sK14_SY1220: $i > $i > $i ).
thf(tp_sK15_SY1221,type,
sK15_SY1221: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK16_SY1282,type,
sK16_SY1282: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK17_SY1006,type,
sK17_SY1006: $i > $i ).
thf(tp_sK18_SY1289,type,
sK18_SY1289: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK19_SY1109,type,
sK19_SY1109: $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY1138,type,
sK20_SY1138: ( $i > $o ) > $i > $i ).
thf(tp_sK21_SY1140,type,
sK21_SY1140: $i > $i > $i ).
thf(tp_sK22_SY1286,type,
sK22_SY1286: $i > ( $i > $o ) > $i ).
thf(tp_sK23_SY1238,type,
sK23_SY1238: ( $i > $o ) > $i > $i ).
thf(tp_sK24_SY1269,type,
sK24_SY1269: $o > $i > $i > $i ).
thf(tp_sK25_SX0,type,
sK25_SX0: $i > $i > $i ).
thf(tp_sK26_SX0,type,
sK26_SX0: $i > $i > $i ).
thf(tp_sK27_SY908,type,
sK27_SY908: $i > $i > $i ).
thf(tp_sK28_SY1157,type,
sK28_SY1157: $i > $i > $i ).
thf(tp_sK29_SY1039,type,
sK29_SY1039: $i > $i ).
thf(tp_sK2_SY874,type,
sK2_SY874: $i > $i ).
thf(tp_sK30_SY1291,type,
sK30_SY1291: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK31_SY1165,type,
sK31_SY1165: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK32_SY990,type,
sK32_SY990: $i > ( $i > $o ) > $i ).
thf(tp_sK33_SY1198,type,
sK33_SY1198: $i > $i > $i ).
thf(tp_sK34_SY1203,type,
sK34_SY1203: $i > $i > $i ).
thf(tp_sK35_SY1173,type,
sK35_SY1173: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK36_SY1308,type,
sK36_SY1308: $i > ( $i > $o ) > $i ).
thf(tp_sK37_SY1194,type,
sK37_SY1194: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK38_SY1198,type,
sK38_SY1198: $i > $i > $i ).
thf(tp_sK39_SY1268,type,
sK39_SY1268: $i > $i > $i ).
thf(tp_sK3_SY1133,type,
sK3_SY1133: $i ).
thf(tp_sK40_SY1272,type,
sK40_SY1272: $i > ( $i > $o ) > $i ).
thf(tp_sK41_SY1304,type,
sK41_SY1304: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK42_SY1278,type,
sK42_SY1278: $i > ( $i > $o ) > $i ).
thf(tp_sK43_SY1283,type,
sK43_SY1283: $i > ( $i > $o ) > $i ).
thf(tp_sK44_SY1285,type,
sK44_SY1285: $i > ( $i > $o ) > $i ).
thf(tp_sK45_SY1287,type,
sK45_SY1287: $i > ( $i > $o ) > $i ).
thf(tp_sK46_SY1288,type,
sK46_SY1288: $i > ( $i > $o ) > $i ).
thf(tp_sK47_SY1290,type,
sK47_SY1290: $i > ( $i > $o ) > $i ).
thf(tp_sK48_SY1295,type,
sK48_SY1295: $i > $i > $i ).
thf(tp_sK49_SY921,type,
sK49_SY921: $i > ( $i > $o ) > $i ).
thf(tp_sK4_SY892,type,
sK4_SY892: $i > $i ).
thf(tp_sK50_SY1303,type,
sK50_SY1303: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK51_SY992,type,
sK51_SY992: $i > ( $i > $o ) > $i ).
thf(tp_sK52_SY992,type,
sK52_SY992: $i > ( $i > $o ) > $i ).
thf(tp_sK53_SY1027,type,
sK53_SY1027: $i > ( $i > $o ) > $i ).
thf(tp_sK54_SY1043,type,
sK54_SY1043: $i > ( $i > $o ) > $i ).
thf(tp_sK55_SY1213,type,
sK55_SY1213: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK56_SY1074,type,
sK56_SY1074: $i > ( $i > $o ) > $i ).
thf(tp_sK57_SY921,type,
sK57_SY921: $i > ( $i > $o ) > $i ).
thf(tp_sK58_SY992,type,
sK58_SY992: $i > ( $i > $o ) > $i ).
thf(tp_sK59_SY1027,type,
sK59_SY1027: $i > ( $i > $o ) > $i ).
thf(tp_sK5_SY940,type,
sK5_SY940: $i > $i ).
thf(tp_sK60_SY1043,type,
sK60_SY1043: $i > ( $i > $o ) > $i ).
thf(tp_sK61_SY1062,type,
sK61_SY1062: $i > ( $i > $o ) > $i ).
thf(tp_sK62_SY1074,type,
sK62_SY1074: $i > ( $i > $o ) > $i ).
thf(tp_sK63_SY1062,type,
sK63_SY1062: $i > ( $i > $o ) > $i ).
thf(tp_sK64_SY1062,type,
sK64_SY1062: $i > ( $i > $o ) > $i ).
thf(tp_sK65_SY1165,type,
sK65_SY1165: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK66_SY1062,type,
sK66_SY1062: $i > ( $i > $o ) > $i ).
thf(tp_sK67_SY1312,type,
sK67_SY1312: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK68_SY1165,type,
sK68_SY1165: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK69_SY1316,type,
sK69_SY1316: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK6_SY1216,type,
sK6_SY1216: $i > $i > $i ).
thf(tp_sK70_SY1297,type,
sK70_SY1297: $i > $i > $i > $i ).
thf(tp_sK71_SY1335,type,
sK71_SY1335: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK72_SY1336,type,
sK72_SY1336: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK73_SY1297,type,
sK73_SY1297: $i > $i > $i > $i ).
thf(tp_sK74_SY1342,type,
sK74_SY1342: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK75_SY1329,type,
sK75_SY1329: $i > $i > $i > $i ).
thf(tp_sK76_SY1356,type,
sK76_SY1356: $i > $i > $i > $i ).
thf(tp_sK77_SY1347,type,
sK77_SY1347: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK78_SY1348,type,
sK78_SY1348: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK79_SY1225,type,
sK79_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK7_SY1143,type,
sK7_SY1143: $i > $i > $i ).
thf(tp_sK80_SY1095,type,
sK80_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK81_SY1364,type,
sK81_SY1364: $i > $i > $i > $i ).
thf(tp_sK82_SY1351,type,
sK82_SY1351: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK83_SY1225,type,
sK83_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK84_SY1095,type,
sK84_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK85_SY1349,type,
sK85_SY1349: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK86_SY1354,type,
sK86_SY1354: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK87_SY1355,type,
sK87_SY1355: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY1352,type,
sK88_SY1352: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK89_SY1360,type,
sK89_SY1360: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY1159,type,
sK8_SY1159: $i > $i > $i ).
thf(tp_sK90_SY1361,type,
sK90_SY1361: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK91_SY1362,type,
sK91_SY1362: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK92_SY1363,type,
sK92_SY1363: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK93_SY1368,type,
sK93_SY1368: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK94_SY1369,type,
sK94_SY1369: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK95_SY1370,type,
sK95_SY1370: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK96_SY1225,type,
sK96_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK97_SY1095,type,
sK97_SY1095: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK98_SY1374,type,
sK98_SY1374: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK99_SY1225,type,
sK99_SY1225: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK9_SY1162,type,
sK9_SY1162: ( $i > $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_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_setunion__Cong,type,
setunion__Cong: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $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_uniqinunit,type,
uniqinunit: $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_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/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(iskpair,definition,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
& ? [Xy: $i] :
( ( in @ Xy @ ( setunion @ A ) )
& ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).
thf(kpair,definition,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
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
=> ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY22: $i > $i > $o,SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ? [SY26: $i] :
( ( SY22 @ SY24 @ SY26 )
& ! [SY27: $i] :
( ( SY22 @ SY24 @ SY27 )
=> ( SY26 = SY27 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY23 )
& ( SY22 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY54: $i > $o] :
( ? [SY56: $i] :
( ( SY54 @ SY56 )
& ! [SY57: $i] :
( ( SY54 @ SY57 )
=> ( SY56 = SY57 ) ) )
=> ( SY54
@ ( descr
@ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY71: $i > $o] :
( ? [SY73: $i] :
( ( SY71 @ SY73 )
& ! [SY74: $i] :
( ( SY71 @ SY74 )
=> ( SY73 = SY74 ) ) )
=> ? [Xx: $i] :
( ( SY71 @ Xx )
& ! [Xy: $i] :
( ( SY71 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) )
=> ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
( ( in @ SY104 @ SY102 )
=> ( ( SY103 @ SY104 )
=> ( ( dsetconstr @ SY102
@ ^ [Xy: $i] : ( SY103 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
=> ( ! [SY139: $i > $o] :
( ? [SY141: $i] :
( ( SY139 @ SY141 )
& ! [SY142: $i] :
( ( SY139 @ SY142 )
=> ( SY141 = SY142 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY139 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) )
=> ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [SY194: $i > $o] :
( ? [Xx: $i] :
( ( SY194 @ Xx )
& ! [Xy: $i] :
( ( SY194 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY198: $i] :
( ( SY194 @ SY198 )
& ! [SY199: $i] :
( ( SY194 @ SY199 )
=> ( SY198 = SY199 ) ) ) )
=> ( ! [SY200: $i > $o] :
( ? [Xx: $i] : ( SY200 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY200 @ Xx )
=> ( ( SY200 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY205: $i] :
( ( SY200 @ SY205 )
& ! [SY206: $i] :
( ( SY200 @ SY206 )
=> ( SY205 = SY206 ) ) ) ) )
=> ( ! [SY207: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY207 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY211: $i] :
( ( SY207 @ SY211 )
& ! [SY212: $i] :
( ( SY207 @ SY212 )
=> ( SY211 = SY212 ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [SY221: $i > $o] :
( ? [SY223: $i] :
( ( SY221 @ SY223 )
& ! [SY224: $i] :
( ( SY221 @ SY224 )
=> ( SY223 = SY224 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY221 @ Xx )
=> ( ( SY221 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY227: $i > $o,SY228: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY227 @ Xx )
<=> ( SY228 @ Xy ) ) )
=> ( ? [SY232: $i] :
( ( SY227 @ SY232 )
& ! [SY233: $i] :
( ( SY227 @ SY233 )
=> ( SY232 = SY233 ) ) )
<=> ? [SY235: $i] :
( ( SY228 @ SY235 )
& ! [SY236: $i] :
( ( SY228 @ SY236 )
=> ( SY235 = SY236 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ( omega = omega )
=> ( ! [SY245: $i > $o] :
( ? [SY247: $i] :
( ( SY245 @ SY247 )
& ! [SY248: $i] :
( ( SY245 @ SY248 )
=> ( SY247 = SY248 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY245 @ Xx )
=> ( ( SY245 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY251: $i > $o,SY252: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY251 @ Xx )
<=> ( SY252 @ Xy ) ) )
=> ( ? [SY256: $i] :
( ( SY251 @ SY256 )
& ! [SY257: $i] :
( ( SY251 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ? [SY259: $i] :
( ( SY252 @ SY259 )
& ! [SY260: $i] :
( ( SY252 @ SY260 )
=> ( SY259 = SY260 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] : ( subset @ emptyset @ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) )
=> ( ! [A: $i] : ( subset @ A @ A )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) )
=> ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i] : ( in @ A @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [SY421: $i,SY422: $i] :
? [SY423: $i] :
( ( in @ SY423 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY424: $i] :
( ( in @ SY424 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY423 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY423 @ ( setadjoin @ SY424 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ! [SY0: $i,SY1: $i] :
? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,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,
( ( ! [SY22: $i > $i > $o,SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ? [SY26: $i] :
( ( SY22 @ SY24 @ SY26 )
& ! [SY27: $i] :
( ( SY22 @ SY24 @ SY27 )
=> ( SY26 = SY27 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY23 )
& ( SY22 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY54: $i > $o] :
( ? [SY56: $i] :
( ( SY54 @ SY56 )
& ! [SY57: $i] :
( ( SY54 @ SY57 )
=> ( SY56 = SY57 ) ) )
=> ( SY54
@ ( descr
@ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY71: $i > $o] :
( ? [SY73: $i] :
( ( SY71 @ SY73 )
& ! [SY74: $i] :
( ( SY71 @ SY74 )
=> ( SY73 = SY74 ) ) )
=> ? [Xx: $i] :
( ( SY71 @ Xx )
& ! [Xy: $i] :
( ( SY71 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
( ( in @ SY104 @ SY102 )
=> ( ( SY103 @ SY104 )
=> ( ( dsetconstr @ SY102
@ ^ [Xy: $i] : ( SY103 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [SY139: $i > $o] :
( ? [SY141: $i] :
( ( SY139 @ SY141 )
& ! [SY142: $i] :
( ( SY139 @ SY142 )
=> ( SY141 = SY142 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY139 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(47,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(49,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(52,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(53,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(54,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(55,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(56,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(57,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(58,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(59,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(60,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [SY194: $i > $o] :
( ? [Xx: $i] :
( ( SY194 @ Xx )
& ! [Xy: $i] :
( ( SY194 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY198: $i] :
( ( SY194 @ SY198 )
& ! [SY199: $i] :
( ( SY194 @ SY199 )
=> ( SY198 = SY199 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY200: $i > $o] :
( ? [Xx: $i] : ( SY200 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY200 @ Xx )
=> ( ( SY200 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY205: $i] :
( ( SY200 @ SY205 )
& ! [SY206: $i] :
( ( SY200 @ SY206 )
=> ( SY205 = SY206 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY207: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY207 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY211: $i] :
( ( SY207 @ SY211 )
& ! [SY212: $i] :
( ( SY207 @ SY212 )
=> ( SY211 = SY212 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [SY221: $i > $o] :
( ? [SY223: $i] :
( ( SY221 @ SY223 )
& ! [SY224: $i] :
( ( SY221 @ SY224 )
=> ( SY223 = SY224 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY221 @ Xx )
=> ( ( SY221 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY227: $i > $o,SY228: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY227 @ Xx )
<=> ( SY228 @ Xy ) ) )
=> ( ? [SY232: $i] :
( ( SY227 @ SY232 )
& ! [SY233: $i] :
( ( SY227 @ SY233 )
=> ( SY232 = SY233 ) ) )
<=> ? [SY235: $i] :
( ( SY228 @ SY235 )
& ! [SY236: $i] :
( ( SY228 @ SY236 )
=> ( SY235 = SY236 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(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(76,plain,
( ( ! [SY245: $i > $o] :
( ? [SY247: $i] :
( ( SY245 @ SY247 )
& ! [SY248: $i] :
( ( SY245 @ SY248 )
=> ( SY247 = SY248 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY245 @ Xx )
=> ( ( SY245 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY251: $i > $o,SY252: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY251 @ Xx )
<=> ( SY252 @ Xy ) ) )
=> ( ? [SY256: $i] :
( ( SY251 @ SY256 )
& ! [SY257: $i] :
( ( SY251 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ? [SY259: $i] :
( ( SY252 @ SY259 )
& ! [SY260: $i] :
( ( SY252 @ SY260 )
=> ( SY259 = SY260 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(83,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(84,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(89,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(91,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(92,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(98,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(100,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(101,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(103,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(104,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(105,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(120,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(136,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(137,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(138,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(139,plain,
( ( ! [SY421: $i,SY422: $i] :
? [SY423: $i] :
( ( in @ SY423 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY424: $i] :
( ( in @ SY424 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY423 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY423 @ ( setadjoin @ SY424 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(140,plain,
( ( ! [SY0: $i,SY1: $i] :
? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(141,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[140]) ).
thf(142,plain,
( ( ! [SY421: $i,SY422: $i] :
? [SY423: $i] :
( ( in @ SY423 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY424: $i] :
( ( in @ SY424 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY421 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY421 @ ( setadjoin @ SY422 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY423 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY423 @ ( setadjoin @ SY424 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(143,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(144,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(145,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(146,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(147,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(148,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(149,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(150,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(151,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(153,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(154,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(155,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(156,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(157,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(158,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(159,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(160,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(161,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(162,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(163,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(164,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(166,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(167,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(168,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(169,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(170,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(171,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(172,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(173,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(175,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(176,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(177,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(178,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(179,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(180,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(181,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(183,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(186,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(187,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(189,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(190,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(191,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(192,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(193,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(195,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(196,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(197,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(198,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(202,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(203,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(204,plain,
( ( ! [SY251: $i > $o,SY252: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY251 @ Xx )
<=> ( SY252 @ Xy ) ) )
=> ( ? [SY256: $i] :
( ( SY251 @ SY256 )
& ! [SY257: $i] :
( ( SY251 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ? [SY259: $i] :
( ( SY252 @ SY259 )
& ! [SY260: $i] :
( ( SY252 @ SY260 )
=> ( SY259 = SY260 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(205,plain,
( ( ! [SY245: $i > $o] :
( ? [SY247: $i] :
( ( SY245 @ SY247 )
& ! [SY248: $i] :
( ( SY245 @ SY248 )
=> ( SY247 = SY248 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY245 @ Xx )
=> ( ( SY245 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(207,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(208,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(209,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(211,plain,
( ( ! [SY227: $i > $o,SY228: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY227 @ Xx )
<=> ( SY228 @ Xy ) ) )
=> ( ? [SY232: $i] :
( ( SY227 @ SY232 )
& ! [SY233: $i] :
( ( SY227 @ SY233 )
=> ( SY232 = SY233 ) ) )
<=> ? [SY235: $i] :
( ( SY228 @ SY235 )
& ! [SY236: $i] :
( ( SY228 @ SY236 )
=> ( SY235 = SY236 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(212,plain,
( ( ! [SY221: $i > $o] :
( ? [SY223: $i] :
( ( SY221 @ SY223 )
& ! [SY224: $i] :
( ( SY221 @ SY224 )
=> ( SY223 = SY224 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY221 @ Xx )
=> ( ( SY221 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(213,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(214,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(215,plain,
( ( ! [SY207: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY207 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY211: $i] :
( ( SY207 @ SY211 )
& ! [SY212: $i] :
( ( SY207 @ SY212 )
=> ( SY211 = SY212 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(216,plain,
( ( ! [SY200: $i > $o] :
( ? [Xx: $i] : ( SY200 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY200 @ Xx )
=> ( ( SY200 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY205: $i] :
( ( SY200 @ SY205 )
& ! [SY206: $i] :
( ( SY200 @ SY206 )
=> ( SY205 = SY206 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(217,plain,
( ( ! [SY194: $i > $o] :
( ? [Xx: $i] :
( ( SY194 @ Xx )
& ! [Xy: $i] :
( ( SY194 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY198: $i] :
( ( SY194 @ SY198 )
& ! [SY199: $i] :
( ( SY194 @ SY199 )
=> ( SY198 = SY199 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(218,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(219,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(220,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(221,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(222,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(223,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(224,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(225,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(226,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(227,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(228,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(229,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(230,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(231,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(232,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(233,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(234,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(235,plain,
( ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(236,plain,
( ( ! [SY139: $i > $o] :
( ? [SY141: $i] :
( ( SY139 @ SY141 )
& ! [SY142: $i] :
( ( SY139 @ SY142 )
=> ( SY141 = SY142 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY139 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(237,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(238,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(239,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(240,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(241,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(242,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(243,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(244,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(245,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(246,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(247,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(248,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(249,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(250,plain,
( ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(251,plain,
( ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
( ( in @ SY104 @ SY102 )
=> ( ( SY103 @ SY104 )
=> ( ( dsetconstr @ SY102
@ ^ [Xy: $i] : ( SY103 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(252,plain,
( ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(253,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(254,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(255,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(256,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(257,plain,
( ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(258,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(259,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(260,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(261,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(262,plain,
( ( ! [SY71: $i > $o] :
( ? [SY73: $i] :
( ( SY71 @ SY73 )
& ! [SY74: $i] :
( ( SY71 @ SY74 )
=> ( SY73 = SY74 ) ) )
=> ? [Xx: $i] :
( ( SY71 @ Xx )
& ! [Xy: $i] :
( ( SY71 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(263,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(264,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(265,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(266,plain,
( ( ! [SY54: $i > $o] :
( ? [SY56: $i] :
( ( SY54 @ SY56 )
& ! [SY57: $i] :
( ( SY54 @ SY57 )
=> ( SY56 = SY57 ) ) )
=> ( SY54
@ ( descr
@ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(267,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(268,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(269,plain,
( ( ! [SY22: $i > $i > $o,SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ? [SY26: $i] :
( ( SY22 @ SY24 @ SY26 )
& ! [SY27: $i] :
( ( SY22 @ SY24 @ SY27 )
=> ( SY26 = SY27 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY23 )
& ( SY22 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(270,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(271,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(272,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(273,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(274,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(275,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(276,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(278,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
? [SY3: $i] :
( ( in @ SY3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY4: $i] :
( ( in @ SY4 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3 @ ( setadjoin @ SY4 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(279,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)],[238,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(280,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(281,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(282,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(283,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)],[265,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(284,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(285,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : 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,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(286,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)],[267,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(287,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(288,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(289,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(290,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(291,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(292,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(293,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)],[223,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(294,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(295,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(296,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)],[268,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(297,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(298,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(299,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(300,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)],[214,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(301,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ 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,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(302,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)],[236,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(303,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)],[203,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(304,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(305,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)],[266,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(306,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(307,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(308,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(309,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(310,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(311,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(312,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[261,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(313,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(314,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(315,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)],[274,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(316,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(317,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(318,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ 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,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(319,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)],[150,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(320,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ 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,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(321,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)],[269,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(322,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(323,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)],[227,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(324,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(325,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[259,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(326,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)],[225,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(327,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)],[213,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(328,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(329,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)],[204,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(330,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(331,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)],[216,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(332,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)],[275,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(333,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(334,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(335,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)],[253,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(336,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(337,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(338,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(339,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(340,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)],[218,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(341,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(342,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( 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,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(343,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(344,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)],[256,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(345,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(346,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(347,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(348,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(349,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(350,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(351,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)],[273,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(352,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)],[209,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(353,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)],[270,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(354,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)],[217,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(355,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)],[277,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(356,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(357,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(358,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(359,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)],[224,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(360,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(361,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(362,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)],[222,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(363,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)],[215,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(364,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)],[251,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(365,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)],[212,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(366,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(367,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)],[262,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(368,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(369,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(370,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)],[264,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(371,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(372,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( 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,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(373,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)],[211,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(374,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(375,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)],[176,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(376,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(377,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(378,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(379,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(380,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)],[246,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(381,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(382,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(383,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)],[205,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(384,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(385,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)],[219,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(386,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(387,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kpair,kpairiskpair,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,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,uniqinunit,upairset2IR,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(388,plain,
! [SV1: $i] :
( ( ! [SY839: $i] : ( in @ SY839 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY839 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(389,plain,
! [SV2: $i] :
( ( ! [SY840: $i] : ( in @ SV2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY840 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(390,plain,
! [SV3: $i] :
( ( ! [SY841: $i] : ( in @ SY841 @ ( setadjoin @ SV3 @ ( setadjoin @ SY841 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(391,plain,
! [SV4: $i] :
( ( ! [SY842: $i] : ( subset @ ( setminus @ SV4 @ SY842 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(392,plain,
! [SV5: $i] :
( ( ! [SY843: $i,SY844: $i] :
( ( binintersect @ SV5 @ ( binunion @ SY843 @ SY844 ) )
= ( binunion @ ( binintersect @ SV5 @ SY843 ) @ ( binintersect @ SV5 @ SY844 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(393,plain,
! [SV6: $i] :
( ( ! [SY845: $i] : ( subset @ ( binintersect @ SV6 @ SY845 ) @ SY845 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(394,plain,
! [SV7: $i] :
( ( ! [SY846: $i] : ( subset @ ( binintersect @ SV7 @ SY846 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(395,plain,
! [SV8: $i] :
( ( ! [SY847: $i] : ( subset @ SY847 @ ( binunion @ SV8 @ SY847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(396,plain,
! [SV9: $i] :
( ( ! [SY848: $i] : ( subset @ SV9 @ ( binunion @ SV9 @ SY848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(397,plain,
! [SV10: $i] :
( ( ! [SY849: $i] : ( in @ SY849 @ ( setadjoin @ SV10 @ ( setadjoin @ SY849 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(398,plain,
! [SV11: $i] :
( ( ! [SY850: $i > $o] :
( subset
@ ( dsetconstr @ SV11
@ ^ [Xx: $i] : ( SY850 @ Xx ) )
@ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(399,plain,
! [SV12: $i] :
( ( ! [SY852: $i > $o] :
( in
@ ( dsetconstr @ SV12
@ ^ [Xx: $i] : ( SY852 @ Xx ) )
@ ( powerset @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(400,plain,
! [SV13: $i] :
( ( in @ SV13 @ ( powerset @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(401,plain,
! [SV14: $i] :
( ( ! [SY854: $i] : ( subset @ SY854 @ ( setadjoin @ SV14 @ SY854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(402,plain,
! [SV15: $i] :
( ( subset @ SV15 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(403,plain,
! [SV16: $i] :
( ( subset @ emptyset @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(404,plain,
! [SV17: $i] :
( ( ! [SY855: $i] : ( in @ SY855 @ ( setadjoin @ SV17 @ ( setadjoin @ SY855 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(405,plain,
! [SV18: $i] :
( ( ! [SY856: $i] : ( in @ SV18 @ ( setadjoin @ SV18 @ ( setadjoin @ SY856 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(406,plain,
! [SV19: $i] :
( ( in @ emptyset @ ( powerset @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(407,plain,
! [SV20: $i] :
( ( in @ emptyset @ ( powerset @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(408,plain,
! [SV21: $i] :
( ( ( dsetconstr @ SV21
@ ^ [Xx: $i] : $true )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(409,plain,
! [SV22: $i] :
( ( ! [SY858: $i] : ( in @ SV22 @ ( setadjoin @ SV22 @ SY858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(410,plain,
! [SV23: $i] :
( ( ~ ( in @ SV23 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(411,plain,
! [SV24: $i] :
( ( ~ ( in @ SV24 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(412,plain,
! [SV25: $i] :
( ( ! [SY859: $i] :
( ~ ( in @ SY859 @ ( setunion @ SV25 ) )
| ! [SY860: $o] :
( ~ ! [SY861: $i] :
( ~ ( in @ SY859 @ SY861 )
| ~ ( in @ SY861 @ SV25 )
| SY860 )
| SY860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(413,plain,
! [SV26: $i] :
( ( ! [SY862: $i > $o,SY863: $i] :
( ~ ( in @ SY863
@ ( dsetconstr @ SV26
@ ^ [SX3: $i] : ( SY862 @ SX3 ) ) )
| ( SY862 @ SY863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(414,plain,
! [SV27: $i] :
( ( ! [SY865: $i,SY866: $i] :
( ~ ( in @ SY866 @ SY865 )
| ( in @ SY866 @ ( binunion @ SV27 @ SY865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(415,plain,
! [SV28: $i] :
( ( ! [SY867: $i] :
( ( SV28 != SY867 )
| ( in @ SV28 @ ( setadjoin @ SY867 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(416,plain,
! [SV29: $i] :
( ( ! [SY868: $i > $o,SY869: $i] :
( ~ ( in @ SY869 @ SV29 )
| ~ ( SY868 @ SY869 )
| ( in @ SY869
@ ( dsetconstr @ SV29
@ ^ [SX3: $i] : ( SY868 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(417,plain,
! [SV30: $i] :
( ( ! [SY871: $i,SY872: $i] :
( ~ ( subset @ SV30 @ SY871 )
| ~ ( subset @ SY871 @ SY872 )
| ( subset @ SV30 @ SY872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(418,plain,
! [SV31: $i] :
( ( ~ ( in @ SV31 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(419,plain,
! [SV32: $i] :
( ( ~ ! [SY874: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY875: $i] :
( ~ ( in @ SY875 @ SY874 )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY875 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY877: $i,SY878: $i] :
( ~ ~ ( ~ ( in @ SY877 @ SV32 )
| ~ ( in @ SY878 @ SV32 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY874 )
| ~ ( ~ ( ~ ( in @ SY877 @ SX4 )
| ( in @ SY878 @ SX4 ) )
| ~ ( ~ ( in @ SY878 @ SX4 )
| ( in @ SY877 @ SX4 ) ) ) )
| ( SY877 = SY878 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY874 )
| ~ ( in @ SX3 @ SY874 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY884: $i] :
( ~ ~ ( ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SY884 )
| ( in @ SY885 @ SV32 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY884 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY874 )
| ~ ( in @ SX4 @ SY884 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY884 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY874 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(420,plain,
! [SV33: $i] :
( ( ~ ! [SY892: $i] :
~ ( in @ SY892 @ SV33 )
| ( SV33 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(421,plain,
! [SV34: $i] :
( ( ! [SY893: $i,SY894: $i] :
( ~ ( in @ SY894 @ ( binintersect @ SV34 @ SY893 ) )
| ( in @ SY894 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(422,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(423,plain,
! [SV35: $i] :
( ( ! [SY895: $i,SY896: $i] :
( ~ ( in @ SY896 @ ( setminus @ SV35 @ SY895 ) )
| ~ ( in @ SY896 @ SY895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(424,plain,
! [SV36: $i] :
( ( ! [SY897: $i] :
( ( ( setminus @ SV36 @ SY897 )
!= emptyset )
| ( subset @ SV36 @ SY897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(425,plain,
! [SV37: $i] :
( ( ! [SY898: $i,SY899: $i] :
( ~ ~ ( in @ SY899 @ SV37 )
| ~ ( in @ SY899 @ ( setminus @ SV37 @ SY898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(426,plain,
! [SV38: $i] :
( ( ! [SY900: $i > $o] :
( ~ ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV38 )
| ~ ( SY900 @ SY901 ) )
| ! [SY902: $i] :
( ~ ( in @ SY902 @ SV38 )
| ~ ( SY900 @ SY902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(427,plain,
! [SV39: $i] :
( ( ! [SY903: $i] :
( ~ ~ ~ ! [SY904: $i] :
~ ~ ( ~ ( in @ SY904 @ SV39 )
| ~ ( in @ SY904 @ SY903 ) )
| ( ( binintersect @ SV39 @ SY903 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(428,plain,
! [SV40: $i] :
( ( ! [SY905: $i,SY906: $i] :
( ~ ( in @ SY906 @ SV40 )
| ~ ~ ( in @ SY906 @ SY905 )
| ( SV40 != SY905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(429,plain,
! [SV41: $i] :
( ( ~ ~ ! [SY907: $i] :
~ ( in @ SY907 @ SV41 )
| ~ ! [SY908: $i] :
~ ~ ( ~ ( in @ SY908 @ SV41 )
| ~ ~ ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SY908 )
| ~ ( in @ SY909 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(430,plain,
! [SV42: $i] :
( ( ! [SY910: $i,SY911: $i] :
( ~ ~ ( in @ SY911 @ SV42 )
| ~ ~ ( in @ SY911 @ SY910 )
| ~ ( in @ SY911 @ ( symdiff @ SV42 @ SY910 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(431,plain,
! [SV43: $o] :
( ( ~ SV43
| ( set2prop @ ( prop2set @ SV43 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[298]) ).
thf(432,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[298]) ).
thf(434,plain,
! [SV44: $i] :
( ( ! [SY912: $i] :
( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ SV44 )
| ( in @ SY913 @ SY912 ) )
| ( subset @ SV44 @ SY912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(435,plain,
! [SV45: $i] :
( ( ! [SY914: $i] :
( ( SV45 != SY914 )
| ! [SY915: $i,SY916: $i] :
( ( SY915 != SY916 )
| ~ ( in @ SY915 @ SV45 )
| ( in @ SY916 @ SY914 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(436,plain,
! [SV46: $i] :
( ( ! [SY917: $i,SY918: $i] :
( ~ ( subset @ SV46 @ SY917 )
| ~ ( in @ SY918 @ SV46 )
| ( in @ SY918 @ SY917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(437,plain,
! [SV47: $i > $o] :
( ( ~ ~ ! [SY919: $i] :
~ ~ ( ~ ( SV47 @ SY919 )
| ~ ! [SY920: $i] :
( ~ ( SV47 @ SY920 )
| ( SY919 = SY920 ) ) )
| ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(438,plain,
! [SV48: $i] :
( ( ! [SY923: $i] :
( ( SV48 != SY923 )
| ! [SY924: $i > $o,SY925: $i > $o] :
( ~ ! [SY926: $i] :
( ~ ( in @ SY926 @ SV48 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY923 )
| ( SY926 != SX5 )
| ~ ( ~ ( ~ ( SY924 @ SY926 )
| ( SY925 @ SX5 ) )
| ~ ( ~ ( SY925 @ SX5 )
| ( SY924 @ SY926 ) ) ) ) )
| ( ( dsetconstr @ SV48
@ ^ [SX4: $i] : ( SY924 @ SX4 ) )
= ( dsetconstr @ SY923
@ ^ [SX4: $i] : ( SY925 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(439,plain,
! [SV49: $i] :
( ( ! [SY930: $i] :
( ( SV49 != SY930 )
| ( subset @ SY930 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(440,plain,
! [SV50: $i > $o] :
( ( ~ ~ ! [SY931: $i] :
~ ~ ( ~ ( SV50 @ SY931 )
| ~ ! [SY932: $i] :
( ~ ( SV50 @ SY932 )
| ( SY931 = SY932 ) ) )
| ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(441,plain,
! [SV51: $i] :
( ( ! [SY934: $i] :
( ( SV51 != SY934 )
| ( subset @ SV51 @ SY934 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(442,plain,
! [SV52: $i] :
( ( ! [SY935: $i,SY936: $i] :
( ~ ( in @ SY936 @ ( binintersect @ SV52 @ SY935 ) )
| ( in @ SY936 @ SY935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(443,plain,
! [SV53: $i] :
( ( ! [SY937: $i,SY938: $i] :
( ~ ( in @ SY938 @ SV53 )
| ( in @ SY938 @ ( binunion @ SV53 @ SY937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(444,plain,
! [SV54: $i] :
( ( ! [SY939: $i] :
( ( SV54 != SY939 )
| ( ( setunion @ SV54 )
= ( setunion @ SY939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(445,plain,
! [SV55: $i] :
( ( ~ ! [SY940: $i] :
~ ( in @ SY940 @ SV55 )
| ( SV55 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(446,plain,
! [SV56: $i] :
( ( ! [SY941: $i] :
( ~ ( ( SV56 != SY941 ) )
| ~ ( in @ SY941 @ ( setadjoin @ SV56 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(447,plain,
! [SV57: $o] :
( ( ! [SY942: $i] :
( ~ ( in @ SY942 @ ( prop2set @ SV57 ) )
| SV57 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[312]) ).
thf(449,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[312]) ).
thf(450,plain,
! [SV58: $i] :
( ( ! [SY943: $i] :
( ~ ( in @ SY943 @ ( powerset @ SV58 ) )
| ( subset @ SY943 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(451,plain,
! [SV59: $i] :
( ( ! [SY944: $i,SY945: $i] :
( ~ ~ ( in @ SY945 @ SV59 )
| ~ ( in @ SY945 @ SY944 )
| ( in @ SY945 @ ( symdiff @ SV59 @ SY944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(452,plain,
! [SV60: $i] :
( ( ! [SY946: $i] :
~ ( ~ ( ~ ( in @ SY946 @ ( powerset @ SV60 ) )
| ! [SY947: $i] :
( ~ ( in @ SY947 @ SY946 )
| ( in @ SY947 @ SV60 ) ) )
| ~ ( ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ SY946 )
| ( in @ SY948 @ SV60 ) )
| ( in @ SY946 @ ( powerset @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(453,plain,
! [SV61: $i] :
( ( ! [SY949: $i,SY950: $i] :
( ~ ( subset @ SY950 @ SV61 )
| ~ ( subset @ SY950 @ SY949 )
| ( subset @ SY950 @ ( binintersect @ SV61 @ SY949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(454,plain,
! [SV62: $i] :
( ( ! [SY951: $i] :
( ~ ~ ( subset @ SV62 @ SY951 )
| ( SV62 != SY951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(455,plain,
! [SV63: $i] :
( ( ! [SY952: $i] :
( ~ ! [SY953: $i] :
( ~ ( in @ SY953 @ SY952 )
| ( in @ SY953 @ SV63 ) )
| ( in @ SY952 @ ( powerset @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(456,plain,
! [SV64: $i] :
( ( ! [SY954: $i,SY955: $i] :
( ~ ( in @ SY955 @ ( symdiff @ SV64 @ SY954 ) )
| ! [SY956: $o] :
( ~ ( ~ ( in @ SY955 @ SV64 )
| ~ ~ ( in @ SY955 @ SY954 )
| SY956 )
| ~ ( ~ ~ ( in @ SY955 @ SV64 )
| ~ ( in @ SY955 @ SY954 )
| SY956 )
| SY956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(457,plain,
! [SV65: $i] :
( ( ! [SY957: $i] :
( ( SV65 != SY957 )
| ( ( powerset @ SV65 )
= ( powerset @ SY957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(458,plain,
! [SV66: $i > $i > $o] :
( ( ! [SY958: $i] :
( ~ ! [SY959: $i] :
( ~ ( in @ SY959 @ SY958 )
| ~ ! [SY960: $i] :
~ ~ ( ~ ( SV66 @ SY959 @ SY960 )
| ~ ! [SY961: $i] :
( ~ ( SV66 @ SY959 @ SY961 )
| ( SY960 = SY961 ) ) ) )
| ~ ! [SY962: $i] :
~ ! [SY963: $i] :
~ ( ~ ( ~ ( in @ SY963 @ SY962 )
| ~ ! [SY964: $i] :
~ ~ ( ~ ( in @ SY964 @ SY958 )
| ~ ( SV66 @ SY964 @ SY963 ) ) )
| ~ ( ~ ~ ! [SY965: $i] :
~ ~ ( ~ ( in @ SY965 @ SY958 )
| ~ ( SV66 @ SY965 @ SY963 ) )
| ( in @ SY963 @ SY962 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(459,plain,
! [SV67: $i] :
( ( ! [SY966: $i,SY967: $i] :
( ~ ( in @ SY967 @ SV67 )
| ~ ( in @ SY967 @ SY966 )
| ( in @ SY967 @ ( binintersect @ SV67 @ SY966 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(460,plain,
! [SV68: $i] :
( ( ! [SY968: $i > $o] :
( ~ ~ ! [SY969: $i] :
~ ~ ( ~ ( in @ SY969 @ SV68 )
| ~ ( SY968 @ SY969 ) )
| ( ( dsetconstr @ SV68
@ ^ [SX2: $i] : ( SY968 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(461,plain,
! [SV69: $i] :
( ( ~ ( in @ SV69 @ omega )
| ( in @ ( setadjoin @ SV69 @ SV69 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(462,plain,
! [SV70: $i] :
( ( ~ ( in @ SV70 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(463,plain,
! [SV71: $i] :
( ( ! [SY971: $i > $o] :
( ~ ~ ! [SY972: $i] :
( ~ ( in @ SY972 @ SV71 )
| ( SY971 @ SY972 ) )
| ~ ! [SY973: $i] :
~ ~ ( ~ ( in @ SY973 @ SV71 )
| ~ ~ ( SY971 @ SY973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(464,plain,
! [SV72: $i] :
( ( ! [SY974: $i] :
( ( SV72 != SY974 )
| ! [SY975: $i,SY976: $i] :
( ( SY975 != SY976 )
| ~ ( ~ ( ~ ( in @ SY975 @ SV72 )
| ( in @ SY976 @ SY974 ) )
| ~ ( ~ ( in @ SY976 @ SY974 )
| ( in @ SY975 @ SV72 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(465,plain,
! [SV73: $i] :
( ( ! [SY977: $i,SY978: $i] :
( ~ ( in @ SY978 @ SV73 )
| ~ ~ ( in @ SY978 @ SY977 )
| ~ ( subset @ SV73 @ SY977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(466,plain,
! [SV74: $i > $o] :
( ( ! [SY979: $i > $o] :
( ~ ! [SY980: $i,SY981: $i] :
( ( SY980 != SY981 )
| ~ ( ~ ( ~ ( SV74 @ SY980 )
| ( SY979 @ SY981 ) )
| ~ ( ~ ( SY979 @ SY981 )
| ( SV74 @ SY980 ) ) ) )
| ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY979 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY979 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SX2: $i] : ( SY979 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(467,plain,
! [SV75: $i] :
( ( ! [SY988: $i] :
( ~ ( subset @ SV75 @ SY988 )
| ( ( binintersect @ SV75 @ SY988 )
= SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(468,plain,
! [SV76: $i > $o] :
( ( ~ ~ ! [SY989: $i] :
~ ( SV76 @ SY989 )
| ~ ! [SY990: $i,SY991: $i] :
( ~ ( SV76 @ SY990 )
| ~ ( SV76 @ SY991 )
| ( SY990 = SY991 ) )
| ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(469,plain,
! [SV77: $i] :
( ( ! [SY994: $i,SY995: $i] :
~ ( ~ ( ~ ( in @ SY995 @ ( setadjoin @ SV77 @ SY994 ) )
| ( SY995 = SV77 )
| ( in @ SY995 @ SY994 ) )
| ~ ( ~ ( ( SY995 = SV77 )
| ( in @ SY995 @ SY994 ) )
| ( in @ SY995 @ ( setadjoin @ SV77 @ SY994 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(470,plain,
! [SV78: $i] :
( ( ! [SY996: $i,SY997: $i] :
( ~ ( subset @ SV78 @ SY997 )
| ( subset @ SV78 @ ( setadjoin @ SY996 @ SY997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(471,plain,
! [SV79: $i] :
( ( ! [SY998: $i,SY999: $i] :
( ~ ( in @ SY998 @ SY999 )
| ~ ( in @ SY999 @ SV79 )
| ( in @ SY998 @ ( setunion @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(472,plain,
! [SV80: $i] :
( ( ! [SY1000: $i > $o,SY1001: $i] :
( ~ ( in @ SY1001 @ SV80 )
| ~ ( ~ ( ~ ( in @ SY1001
@ ( dsetconstr @ SV80
@ ^ [SX3: $i] : ( SY1000 @ SX3 ) ) )
| ( SY1000 @ SY1001 ) )
| ~ ( ~ ( SY1000 @ SY1001 )
| ( in @ SY1001
@ ( dsetconstr @ SV80
@ ^ [SX3: $i] : ( SY1000 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(473,plain,
! [SV81: $i] :
( ( ! [SY1004: $i,SY1005: $i] :
( ~ ( in @ SY1005 @ SV81 )
| ~ ~ ( in @ SY1005 @ SY1004 )
| ( in @ SY1005 @ ( symdiff @ SV81 @ SY1004 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(474,plain,
! [SV82: $i] :
( ( ~ ( ( SV82 != emptyset ) )
| ~ ! [SY1006: $i] :
~ ( in @ SY1006 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(475,plain,
! [SV83: $i] :
( ( ! [SY1007: $i,SY1008: $i] :
( ~ ( in @ SY1008 @ ( setadjoin @ SV83 @ ( setadjoin @ SY1007 @ emptyset ) ) )
| ( SY1008 = SV83 )
| ( SY1008 = SY1007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(476,plain,
! [SV84: $i] :
( ( ! [SY1009: $i] :
( ~ ( subset @ SY1009 @ SV84 )
| ( ( binintersect @ SV84 @ SY1009 )
= SY1009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(477,plain,
! [SV85: $i] :
( ( ! [SY1010: $i > $o] :
( ~ ~ ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV85 )
| ( SY1010 @ SY1011 ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( in @ SY1012 @ SV85 )
| ~ ~ ( SY1010 @ SY1012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(478,plain,
! [SV86: $i] :
( ( ! [SY1013: $i,SY1014: $i] :
( ~ ( in @ SY1013 @ ( powerset @ SV86 ) )
| ~ ( in @ SY1014 @ SY1013 )
| ( in @ SY1014 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(479,plain,
! [SV87: $i] :
( ( ! [SY1015: $i] :
( ~ ( in @ SV87 @ ( setadjoin @ SY1015 @ emptyset ) )
| ( SV87 = SY1015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(480,plain,
! [SV88: $i] :
( ( ! [SY1016: $i,SY1017: $i] :
( ~ ( in @ SY1017 @ SV88 )
| ~ ( in @ SY1017 @ SY1016 )
| ~ ( in @ SY1017 @ ( symdiff @ SV88 @ SY1016 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(481,plain,
! [SV89: $i] :
( ( ! [SY1018: $i] :
( ~ ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV89 )
| ( in @ SY1019 @ SY1018 ) )
| ~ ! [SY1020: $i] :
( ~ ( in @ SY1020 @ SY1018 )
| ( in @ SY1020 @ SV89 ) )
| ( SV89 = SY1018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(482,plain,
! [SV90: $i] :
( ( ! [SY1021: $i,SY1022: $i] :
( ~ ~ ( in @ SY1022 @ ( setminus @ SV90 @ SY1021 ) )
| ~ ~ ( in @ SY1022 @ SY1021 )
| ~ ( in @ SY1022 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(483,plain,
! [SV91: $i] :
( ( ! [SY1023: $i,SY1024: $i] :
( ~ ( subset @ SV91 @ SY1023 )
| ~ ~ ( in @ SY1024 @ SY1023 )
| ~ ( in @ SY1024 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(484,plain,
! [SV92: $i > $o] :
( ( ~ ~ ! [SY1025: $i] :
~ ~ ( ~ ( SV92 @ SY1025 )
| ~ ! [SY1026: $i] :
( ~ ( SV92 @ SY1026 )
| ( SY1025 = SY1026 ) ) )
| ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(485,plain,
! [SV93: $i] :
( ( ! [SY1028: $i,SY1029: $i] :
( ~ ~ ( in @ SY1029 @ ( setminus @ SV93 @ SY1028 ) )
| ~ ( in @ SY1029 @ SV93 )
| ( in @ SY1029 @ SY1028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(486,plain,
! [SV94: $i] :
( ( ! [SY1030: $i,SY1031: $i] :
( ~ ( in @ SY1031 @ ( setadjoin @ SV94 @ SY1030 ) )
| ( SY1031 = SV94 )
| ( in @ SY1031 @ SY1030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(487,plain,
! [SV95: $i] :
( ( ! [SY1032: $i] :
( ( ( binintersect @ SV95 @ SY1032 )
!= SY1032 )
| ( subset @ SY1032 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(488,plain,
! [SV96: $i] :
( ( ! [SY1033: $i] :
~ ( ~ ( ~ ( in @ SY1033 @ ( setunion @ SV96 ) )
| ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1033 @ SY1034 )
| ~ ( in @ SY1034 @ SV96 ) ) )
| ~ ( ~ ~ ! [SY1035: $i] :
~ ~ ( ~ ( in @ SY1033 @ SY1035 )
| ~ ( in @ SY1035 @ SV96 ) )
| ( in @ SY1033 @ ( setunion @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(489,plain,
! [SV97: $i] :
( ( ! [SY1036: $i] :
( ( SV97 != SY1036 )
| ! [SY1037: $i,SY1038: $i] :
( ( SY1037 != SY1038 )
| ( ( setadjoin @ SV97 @ SY1037 )
= ( setadjoin @ SY1036 @ SY1038 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(490,plain,
! [SV98: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV98 )
| ~ ! [SY1039: $i] :
( ~ ~ ( ~ ( in @ SY1039 @ omega )
| ~ ( in @ SY1039 @ SV98 ) )
| ( in @ ( setadjoin @ SY1039 @ SY1039 ) @ SV98 ) ) )
| ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(491,plain,
! [SV99: $i > $o] :
( ( ~ ~ ! [SY1041: $i] :
~ ~ ( ~ ( SV99 @ SY1041 )
| ~ ! [SY1042: $i] :
( ~ ( SV99 @ SY1042 )
| ( SY1041 = SY1042 ) ) )
| ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(492,plain,
! [SV100: $i] :
( ( ! [SY1045: $i] :
( ~ ! [SY1046: $i] :
~ ( ~ ( ~ ( in @ SY1046 @ SV100 )
| ( in @ SY1046 @ SY1045 ) )
| ~ ( ~ ( in @ SY1046 @ SY1045 )
| ( in @ SY1046 @ SV100 ) ) )
| ( SV100 = SY1045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(493,plain,
! [SV101: $i] :
( ( ! [SY1047: $i] :
( ~ ( subset @ SY1047 @ SV101 )
| ( in @ SY1047 @ ( powerset @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(494,plain,
! [SV102: $i] :
( ( ~ ~ ! [SY1048: $i] :
~ ( in @ SY1048 @ SV102 )
| ( SV102 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(495,plain,
! [SV103: $i] :
( ( ! [SY1049: $i,SY1050: $i] :
( ~ ( in @ SY1050 @ SY1049 )
| ~ ( in @ SY1050 @ ( setminus @ SV103 @ SY1049 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(496,plain,
! [SV104: $i] :
( ( ! [SY1051: $i > $o] :
( ~ ! [SY1052: $i] :
( ~ ( in @ SY1052 @ SV104 )
| ~ ( SY1051 @ SY1052 ) )
| ~ ~ ! [SY1053: $i] :
~ ~ ( ~ ( in @ SY1053 @ SV104 )
| ~ ( SY1051 @ SY1053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(497,plain,
! [SV105: $i] :
( ( ! [SY1054: $i,SY1055: $i] :
( ~ ( in @ SY1055 @ ( binunion @ SV105 @ SY1054 ) )
| ( in @ SY1055 @ SV105 )
| ( in @ SY1055 @ SY1054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(498,plain,
! [SV106: $i] :
( ( ! [SY1056: $i] :
( ( ( binintersect @ SV106 @ SY1056 )
!= SV106 )
| ( subset @ SV106 @ SY1056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(499,plain,
! [SV107: $i] :
( ( ! [SY1057: $i > $o] :
( ~ ~ ! [SY1058: $i] :
~ ~ ( ~ ( in @ SY1058 @ SV107 )
| ~ ~ ( SY1057 @ SY1058 ) )
| ~ ! [SY1059: $i] :
( ~ ( in @ SY1059 @ SV107 )
| ( SY1057 @ SY1059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(500,plain,
! [SV108: $i > $o] :
( ( ~ ~ ! [SY1060: $i] :
~ ! [SY1061: $i] :
~ ( ~ ( ~ ( SV108 @ SY1061 )
| ( SY1061 = SY1060 ) )
| ~ ( ( SY1061 != SY1060 )
| ( SV108 @ SY1061 ) ) )
| ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(501,plain,
! [SV109: $i] :
( ( ! [SY1064: $i > $o,SY1065: $i] :
( ~ ( in @ SY1065 @ SV109 )
| ~ ( SY1064 @ SY1065 )
| ( ( dsetconstr @ SV109
@ ^ [SX3: $i] : ( SY1064 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(502,plain,
! [SV110: $i > $o] :
( ( ~ ~ ! [SY1067: $i] :
~ ~ ( ~ ( SV110 @ SY1067 )
| ~ ! [SY1068: $i] :
( ~ ( SV110 @ SY1068 )
| ( SY1067 = SY1068 ) ) )
| ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(503,plain,
! [SV111: $i] :
( ( ! [SY1071: $i] :
( ~ ( subset @ SV111 @ SY1071 )
| ( ( setminus @ SV111 @ SY1071 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(504,plain,
! [SV112: $i > $o] :
( ( ~ ~ ! [SY1072: $i] :
~ ~ ( ~ ( SV112 @ SY1072 )
| ~ ! [SY1073: $i] :
( ~ ( SV112 @ SY1073 )
| ( SY1072 = SY1073 ) ) )
| ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(505,plain,
! [SV113: $i] :
( ( ! [SY1076: $i] :
~ ! [SY1077: $i] :
~ ~ ( ~ ( in @ SY1077 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SY1076 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1078: $i] :
~ ~ ( ~ ( in @ SY1078 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SY1076 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SY1076 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1077 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1077 @ ( setadjoin @ SY1078 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(506,plain,
! [SV114: $i] :
( ( ! [SY1079: $i] :
( ~ ( subset @ SV114 @ SY1079 )
| ~ ( subset @ SY1079 @ SV114 )
| ( SV114 = SY1079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(507,plain,
! [SV115: $i] :
( ( ! [SY1080: $i > $o,SY1081: $i] :
( ~ ( in @ SY1081
@ ( dsetconstr @ SV115
@ ^ [SX3: $i] : ( SY1080 @ SX3 ) ) )
| ( in @ SY1081 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(508,plain,
! [SV116: $i] :
( ( ! [SY1083: $i] :
( ~ ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV116 )
| ( in @ SY1084 @ SY1083 ) )
| ( subset @ SV116 @ SY1083 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(509,plain,
! [SV117: $i > $o] :
( ( ! [SY1085: $i] :
( ~ ( in @ SY1085 @ emptyset )
| ( SV117 @ SY1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(510,plain,
! [SV118: $i > $o] :
( ( ! [SY1086: $i > $o] :
( ~ ! [SY1087: $i,SY1088: $i] :
( ( SY1087 != SY1088 )
| ~ ( ~ ( ~ ( SV118 @ SY1087 )
| ( SY1086 @ SY1088 ) )
| ~ ( ~ ( SY1086 @ SY1088 )
| ( SV118 @ SY1087 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1086 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1086 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1086 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1086 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(511,plain,
! [SV119: $i] :
( ( ~ ( subset @ SV119 @ emptyset )
| ( SV119 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(512,plain,
! [SV120: $i] :
( ( ! [SY1097: $i,SY1098: $i,SY1099: $o] :
( ~ ( in @ SY1098 @ ( binunion @ SV120 @ SY1097 ) )
| ~ ( ~ ( in @ SY1098 @ SV120 )
| SY1099 )
| ~ ( ~ ( in @ SY1098 @ SY1097 )
| SY1099 )
| SY1099 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(513,plain,
! [SV121: $i] :
( ( ! [SY1100: $i,SY1101: $i] :
( ~ ( in @ SY1101 @ SY1100 )
| ( in @ SY1101 @ ( setadjoin @ SV121 @ SY1100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(514,plain,
! [SV122: $i] :
( ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV122 )
| ( in @ SY1102 @ ( powerset @ ( setunion @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(515,plain,
! [SV123: $i] :
( ( ! [SY1103: $i] :
( ~ ( in @ SV123 @ ( setadjoin @ SY1103 @ emptyset ) )
| ( in @ SY1103 @ ( setadjoin @ SV123 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(516,plain,
! [SV124: $i] :
( ( ! [SY1104: $i,SY1105: $i] :
( ~ ( in @ SY1105 @ ( setminus @ SV124 @ SY1104 ) )
| ( in @ SY1105 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(517,plain,
! [SV125: $i] :
( ( ! [SY1106: $i,SY1107: $i] :
( ~ ( in @ SY1107 @ ( setadjoin @ SV125 @ SY1106 ) )
| ! [SY1108: $o] :
( ~ ( ( SY1107 != SV125 )
| SY1108 )
| ~ ( ~ ( in @ SY1107 @ SY1106 )
| SY1108 )
| SY1108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(518,plain,
! [SV126: $i] :
( ( ~ ( ( SV126 != emptyset ) )
| ~ ! [SY1109: $i] :
~ ~ ( ~ ( in @ SY1109 @ SV126 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(519,plain,
! [SV127: $i] :
( ( ! [SY1110: $i,SY1111: $i] :
( ~ ( in @ SY1111 @ SV127 )
| ~ ~ ( in @ SY1111 @ SY1110 )
| ( in @ SY1111 @ ( setminus @ SV127 @ SY1110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(520,plain,
! [SV128: $i > $o] :
( ( ~ ~ ! [SY1112: $i] :
~ ~ ( ~ ( SV128 @ SY1112 )
| ~ ! [SY1113: $i] :
( ~ ( SV128 @ SY1113 )
| ( SY1112 = SY1113 ) ) )
| ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(521,plain,
! [SV129: $o] :
( ( ~ SV129
| ( in @ emptyset @ ( prop2set @ SV129 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[384]) ).
thf(522,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[384]) ).
thf(524,plain,
! [SV130: $i] :
( ( ! [SY1116: $i > $o] :
( ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ SV130 )
| ~ ( SY1116 @ SY1117 ) )
| ! [SY1118: $i] :
( ~ ( in @ SY1118 @ SV130 )
| ~ ( SY1116 @ SY1118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(525,plain,
! [SV131: $i] :
( ( ! [SY1119: $i] :
( ~ ( subset @ SV131 @ SY1119 )
| ( in @ SV131 @ ( powerset @ SY1119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(526,plain,
! [SV132: $i] :
( ( ! [SY1120: $i] :
( ~ ( subset @ SV132 @ SY1120 )
| ( subset @ ( powerset @ SV132 ) @ ( powerset @ SY1120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(527,plain,
! [SV1: $i,SV133: $i] :
( ( in @ SV133 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV133 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(528,plain,
! [SV134: $i,SV2: $i] :
( ( in @ SV2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV134 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(529,plain,
! [SV3: $i,SV135: $i] :
( ( in @ SV135 @ ( setadjoin @ SV3 @ ( setadjoin @ SV135 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(530,plain,
! [SV136: $i,SV4: $i] :
( ( subset @ ( setminus @ SV4 @ SV136 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(531,plain,
! [SV137: $i,SV5: $i] :
( ( ! [SY1121: $i] :
( ( binintersect @ SV5 @ ( binunion @ SV137 @ SY1121 ) )
= ( binunion @ ( binintersect @ SV5 @ SV137 ) @ ( binintersect @ SV5 @ SY1121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(532,plain,
! [SV138: $i,SV6: $i] :
( ( subset @ ( binintersect @ SV6 @ SV138 ) @ SV138 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(533,plain,
! [SV139: $i,SV7: $i] :
( ( subset @ ( binintersect @ SV7 @ SV139 ) @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(534,plain,
! [SV8: $i,SV140: $i] :
( ( subset @ SV140 @ ( binunion @ SV8 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(535,plain,
! [SV141: $i,SV9: $i] :
( ( subset @ SV9 @ ( binunion @ SV9 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(536,plain,
! [SV10: $i,SV142: $i] :
( ( in @ SV142 @ ( setadjoin @ SV10 @ ( setadjoin @ SV142 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(537,plain,
! [SV143: $i > $o,SV11: $i] :
( ( subset
@ ( dsetconstr @ SV11
@ ^ [SY1122: $i] : ( SV143 @ SY1122 ) )
@ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(538,plain,
! [SV144: $i > $o,SV12: $i] :
( ( in
@ ( dsetconstr @ SV12
@ ^ [SY1123: $i] : ( SV144 @ SY1123 ) )
@ ( powerset @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(539,plain,
! [SV14: $i,SV145: $i] :
( ( subset @ SV145 @ ( setadjoin @ SV14 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(540,plain,
! [SV17: $i,SV146: $i] :
( ( in @ SV146 @ ( setadjoin @ SV17 @ ( setadjoin @ SV146 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(541,plain,
! [SV147: $i,SV18: $i] :
( ( in @ SV18 @ ( setadjoin @ SV18 @ ( setadjoin @ SV147 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(542,plain,
! [SV148: $i,SV22: $i] :
( ( in @ SV22 @ ( setadjoin @ SV22 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(543,plain,
! [SV23: $i] :
( ( in @ SV23 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(544,plain,
! [SV24: $i] :
( ( in @ SV24 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(545,plain,
! [SV25: $i,SV149: $i] :
( ( ~ ( in @ SV149 @ ( setunion @ SV25 ) )
| ! [SY1124: $o] :
( ~ ! [SY1125: $i] :
( ~ ( in @ SV149 @ SY1125 )
| ~ ( in @ SY1125 @ SV25 )
| SY1124 )
| SY1124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(546,plain,
! [SV150: $i > $o,SV26: $i] :
( ( ! [SY1126: $i] :
( ~ ( in @ SY1126
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) )
| ( SV150 @ SY1126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(547,plain,
! [SV27: $i,SV151: $i] :
( ( ! [SY1128: $i] :
( ~ ( in @ SY1128 @ SV151 )
| ( in @ SY1128 @ ( binunion @ SV27 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(548,plain,
! [SV152: $i,SV28: $i] :
( ( ( SV28 != SV152 )
| ( in @ SV28 @ ( setadjoin @ SV152 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(549,plain,
! [SV153: $i > $o,SV29: $i] :
( ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV29 )
| ~ ( SV153 @ SY1129 )
| ( in @ SY1129
@ ( dsetconstr @ SV29
@ ^ [SY1130: $i] : ( SV153 @ SY1130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(550,plain,
! [SV154: $i,SV30: $i] :
( ( ! [SY1131: $i] :
( ~ ( subset @ SV30 @ SV154 )
| ~ ( subset @ SV154 @ SY1131 )
| ( subset @ SV30 @ SY1131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(551,plain,
! [SV31: $i] :
( ( ( ~ ( in @ SV31 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(552,plain,
! [SV32: $i] :
( ( ! [SY874: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY875: $i] :
( ~ ( in @ SY875 @ SY874 )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY875 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY877: $i,SY878: $i] :
( ~ ~ ( ~ ( in @ SY877 @ SV32 )
| ~ ( in @ SY878 @ SV32 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY874 )
| ~ ( ~ ( ~ ( in @ SY877 @ SX4 )
| ( in @ SY878 @ SX4 ) )
| ~ ( ~ ( in @ SY878 @ SX4 )
| ( in @ SY877 @ SX4 ) ) ) )
| ( SY877 = SY878 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY874 )
| ~ ( in @ SX3 @ SY874 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY884: $i] :
( ~ ~ ( ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SY884 )
| ( in @ SY885 @ SV32 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY884 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY874 )
| ~ ( in @ SX4 @ SY884 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY884 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY874 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(553,plain,
! [SV33: $i] :
( ( ( ~ ! [SY892: $i] :
~ ( in @ SY892 @ SV33 ) )
= $true )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(554,plain,
! [SV155: $i,SV34: $i] :
( ( ! [SY1132: $i] :
( ~ ( in @ SY1132 @ ( binintersect @ SV34 @ SV155 ) )
| ( in @ SY1132 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(555,plain,
( ( ! [SY1133: $i] :
~ ! [SY1134: $i] :
~ ~ ( ~ ( in @ SY1134 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1135: $i] :
~ ~ ( ~ ( in @ SY1135 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1134 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1134 @ ( setadjoin @ SY1135 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[422]) ).
thf(556,plain,
! [SV156: $i,SV35: $i] :
( ( ! [SY1136: $i] :
( ~ ( in @ SY1136 @ ( setminus @ SV35 @ SV156 ) )
| ~ ( in @ SY1136 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(557,plain,
! [SV157: $i,SV36: $i] :
( ( ( ( setminus @ SV36 @ SV157 )
!= emptyset )
| ( subset @ SV36 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(558,plain,
! [SV158: $i,SV37: $i] :
( ( ! [SY1137: $i] :
( ~ ~ ( in @ SY1137 @ SV37 )
| ~ ( in @ SY1137 @ ( setminus @ SV37 @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(559,plain,
! [SV159: $i > $o,SV38: $i] :
( ( ~ ~ ~ ! [SY1138: $i] :
~ ~ ( ~ ( in @ SY1138 @ SV38 )
| ~ ( SV159 @ SY1138 ) )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(560,plain,
! [SV160: $i,SV39: $i] :
( ( ~ ~ ~ ! [SY1140: $i] :
~ ~ ( ~ ( in @ SY1140 @ SV39 )
| ~ ( in @ SY1140 @ SV160 ) )
| ( ( binintersect @ SV39 @ SV160 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(561,plain,
! [SV161: $i,SV40: $i] :
( ( ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV40 )
| ~ ~ ( in @ SY1141 @ SV161 )
| ( SV40 != SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(562,plain,
! [SV41: $i] :
( ( ( ~ ~ ! [SY907: $i] :
~ ( in @ SY907 @ SV41 ) )
= $true )
| ( ( ~ ! [SY908: $i] :
~ ~ ( ~ ( in @ SY908 @ SV41 )
| ~ ~ ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SY908 )
| ~ ( in @ SY909 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(563,plain,
! [SV162: $i,SV42: $i] :
( ( ! [SY1142: $i] :
( ~ ~ ( in @ SY1142 @ SV42 )
| ~ ~ ( in @ SY1142 @ SV162 )
| ~ ( in @ SY1142 @ ( symdiff @ SV42 @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(564,plain,
! [SV43: $o] :
( ( ( ~ SV43 ) = $true )
| ( ( set2prop @ ( prop2set @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(565,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(567,plain,
! [SV163: $i,SV44: $i] :
( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV44 )
| ( in @ SY1143 @ SV163 ) )
| ( subset @ SV44 @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(568,plain,
! [SV164: $i,SV45: $i] :
( ( ( SV45 != SV164 )
| ! [SY1144: $i,SY1145: $i] :
( ( SY1144 != SY1145 )
| ~ ( in @ SY1144 @ SV45 )
| ( in @ SY1145 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(569,plain,
! [SV165: $i,SV46: $i] :
( ( ! [SY1146: $i] :
( ~ ( subset @ SV46 @ SV165 )
| ~ ( in @ SY1146 @ SV46 )
| ( in @ SY1146 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(570,plain,
! [SV47: $i > $o] :
( ( ( ~ ~ ! [SY919: $i] :
~ ~ ( ~ ( SV47 @ SY919 )
| ~ ! [SY920: $i] :
( ~ ( SV47 @ SY920 )
| ( SY919 = SY920 ) ) ) )
= $true )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(571,plain,
! [SV166: $i,SV48: $i] :
( ( ( SV48 != SV166 )
| ! [SY1147: $i > $o,SY1148: $i > $o] :
( ~ ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV48 )
| ! [SY1150: $i] :
( ~ ( in @ SY1150 @ SV166 )
| ( SY1149 != SY1150 )
| ~ ( ~ ( ~ ( SY1147 @ SY1149 )
| ( SY1148 @ SY1150 ) )
| ~ ( ~ ( SY1148 @ SY1150 )
| ( SY1147 @ SY1149 ) ) ) ) )
| ( ( dsetconstr @ SV48
@ ^ [SX4: $i] : ( SY1147 @ SX4 ) )
= ( dsetconstr @ SV166
@ ^ [SX4: $i] : ( SY1148 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(572,plain,
! [SV167: $i,SV49: $i] :
( ( ( SV49 != SV167 )
| ( subset @ SV167 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(573,plain,
! [SV50: $i > $o] :
( ( ( ~ ~ ! [SY931: $i] :
~ ~ ( ~ ( SV50 @ SY931 )
| ~ ! [SY932: $i] :
( ~ ( SV50 @ SY932 )
| ( SY931 = SY932 ) ) ) )
= $true )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(574,plain,
! [SV168: $i,SV51: $i] :
( ( ( SV51 != SV168 )
| ( subset @ SV51 @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(575,plain,
! [SV169: $i,SV52: $i] :
( ( ! [SY1153: $i] :
( ~ ( in @ SY1153 @ ( binintersect @ SV52 @ SV169 ) )
| ( in @ SY1153 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(576,plain,
! [SV170: $i,SV53: $i] :
( ( ! [SY1154: $i] :
( ~ ( in @ SY1154 @ SV53 )
| ( in @ SY1154 @ ( binunion @ SV53 @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(577,plain,
! [SV171: $i,SV54: $i] :
( ( ( SV54 != SV171 )
| ( ( setunion @ SV54 )
= ( setunion @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(578,plain,
! [SV55: $i] :
( ( ( ~ ! [SY940: $i] :
~ ( in @ SY940 @ SV55 ) )
= $true )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(579,plain,
! [SV172: $i,SV56: $i] :
( ( ~ ( ( SV56 != SV172 ) )
| ~ ( in @ SV172 @ ( setadjoin @ SV56 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(580,plain,
! [SV57: $o,SV173: $i] :
( ( ~ ( in @ SV173 @ ( prop2set @ SV57 ) )
| SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(582,plain,
! [SV175: $i] :
( ( ~ ( in @ SV175 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(583,plain,
! [SV58: $i,SV176: $i] :
( ( ~ ( in @ SV176 @ ( powerset @ SV58 ) )
| ( subset @ SV176 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(584,plain,
! [SV177: $i,SV59: $i] :
( ( ! [SY1155: $i] :
( ~ ~ ( in @ SY1155 @ SV59 )
| ~ ( in @ SY1155 @ SV177 )
| ( in @ SY1155 @ ( symdiff @ SV59 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(585,plain,
! [SV60: $i,SV178: $i] :
( ( ~ ( ~ ( ~ ( in @ SV178 @ ( powerset @ SV60 ) )
| ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV178 )
| ( in @ SY1156 @ SV60 ) ) )
| ~ ( ~ ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV178 )
| ( in @ SY1157 @ SV60 ) )
| ( in @ SV178 @ ( powerset @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(586,plain,
! [SV179: $i,SV61: $i] :
( ( ! [SY1158: $i] :
( ~ ( subset @ SY1158 @ SV61 )
| ~ ( subset @ SY1158 @ SV179 )
| ( subset @ SY1158 @ ( binintersect @ SV61 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(587,plain,
! [SV180: $i,SV62: $i] :
( ( ~ ~ ( subset @ SV62 @ SV180 )
| ( SV62 != SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(588,plain,
! [SV63: $i,SV181: $i] :
( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV181 )
| ( in @ SY1159 @ SV63 ) )
| ( in @ SV181 @ ( powerset @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(589,plain,
! [SV182: $i,SV64: $i] :
( ( ! [SY1160: $i] :
( ~ ( in @ SY1160 @ ( symdiff @ SV64 @ SV182 ) )
| ! [SY1161: $o] :
( ~ ( ~ ( in @ SY1160 @ SV64 )
| ~ ~ ( in @ SY1160 @ SV182 )
| SY1161 )
| ~ ( ~ ~ ( in @ SY1160 @ SV64 )
| ~ ( in @ SY1160 @ SV182 )
| SY1161 )
| SY1161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(590,plain,
! [SV183: $i,SV65: $i] :
( ( ( SV65 != SV183 )
| ( ( powerset @ SV65 )
= ( powerset @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(591,plain,
! [SV66: $i > $i > $o,SV184: $i] :
( ( ~ ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV184 )
| ~ ! [SY960: $i] :
~ ~ ( ~ ( SV66 @ SY1162 @ SY960 )
| ~ ! [SY961: $i] :
( ~ ( SV66 @ SY1162 @ SY961 )
| ( SY960 = SY961 ) ) ) )
| ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(592,plain,
! [SV185: $i,SV67: $i] :
( ( ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV67 )
| ~ ( in @ SY1169 @ SV185 )
| ( in @ SY1169 @ ( binintersect @ SV67 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(593,plain,
! [SV186: $i > $o,SV68: $i] :
( ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV68 )
| ~ ( SV186 @ SY1170 ) )
| ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(594,plain,
! [SV69: $i] :
( ( ( ~ ( in @ SV69 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV69 @ SV69 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(595,plain,
! [SV70: $i] :
( ( ( ~ ( in @ SV70 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(596,plain,
! [SV187: $i > $o,SV71: $i] :
( ( ~ ~ ! [SY1172: $i] :
( ~ ( in @ SY1172 @ SV71 )
| ( SV187 @ SY1172 ) )
| ~ ! [SY1173: $i] :
~ ~ ( ~ ( in @ SY1173 @ SV71 )
| ~ ~ ( SV187 @ SY1173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(597,plain,
! [SV188: $i,SV72: $i] :
( ( ( SV72 != SV188 )
| ! [SY1174: $i,SY1175: $i] :
( ( SY1174 != SY1175 )
| ~ ( ~ ( ~ ( in @ SY1174 @ SV72 )
| ( in @ SY1175 @ SV188 ) )
| ~ ( ~ ( in @ SY1175 @ SV188 )
| ( in @ SY1174 @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(598,plain,
! [SV189: $i,SV73: $i] :
( ( ! [SY1176: $i] :
( ~ ( in @ SY1176 @ SV73 )
| ~ ~ ( in @ SY1176 @ SV189 )
| ~ ( subset @ SV73 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(599,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ~ ! [SY1177: $i,SY1178: $i] :
( ( SY1177 != SY1178 )
| ~ ( ~ ( ~ ( SV74 @ SY1177 )
| ( SV190 @ SY1178 ) )
| ~ ( ~ ( SV190 @ SY1178 )
| ( SV74 @ SY1177 ) ) ) )
| ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(600,plain,
! [SV191: $i,SV75: $i] :
( ( ~ ( subset @ SV75 @ SV191 )
| ( ( binintersect @ SV75 @ SV191 )
= SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(601,plain,
! [SV76: $i > $o] :
( ( ( ~ ~ ! [SY989: $i] :
~ ( SV76 @ SY989 ) )
= $true )
| ( ( ~ ! [SY990: $i,SY991: $i] :
( ~ ( SV76 @ SY990 )
| ~ ( SV76 @ SY991 )
| ( SY990 = SY991 ) )
| ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(602,plain,
! [SV192: $i,SV77: $i] :
( ( ! [SY1185: $i] :
~ ( ~ ( ~ ( in @ SY1185 @ ( setadjoin @ SV77 @ SV192 ) )
| ( SY1185 = SV77 )
| ( in @ SY1185 @ SV192 ) )
| ~ ( ~ ( ( SY1185 = SV77 )
| ( in @ SY1185 @ SV192 ) )
| ( in @ SY1185 @ ( setadjoin @ SV77 @ SV192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(603,plain,
! [SV193: $i,SV78: $i] :
( ( ! [SY1186: $i] :
( ~ ( subset @ SV78 @ SY1186 )
| ( subset @ SV78 @ ( setadjoin @ SV193 @ SY1186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(604,plain,
! [SV79: $i,SV194: $i] :
( ( ! [SY1187: $i] :
( ~ ( in @ SV194 @ SY1187 )
| ~ ( in @ SY1187 @ SV79 )
| ( in @ SV194 @ ( setunion @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(605,plain,
! [SV195: $i > $o,SV80: $i] :
( ( ! [SY1188: $i] :
( ~ ( in @ SY1188 @ SV80 )
| ~ ( ~ ( ~ ( in @ SY1188
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) )
| ( SV195 @ SY1188 ) )
| ~ ( ~ ( SV195 @ SY1188 )
| ( in @ SY1188
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(606,plain,
! [SV196: $i,SV81: $i] :
( ( ! [SY1191: $i] :
( ~ ( in @ SY1191 @ SV81 )
| ~ ~ ( in @ SY1191 @ SV196 )
| ( in @ SY1191 @ ( symdiff @ SV81 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(607,plain,
! [SV82: $i] :
( ( ( ~ ( ( SV82 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY1006: $i] :
~ ( in @ SY1006 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(608,plain,
! [SV197: $i,SV83: $i] :
( ( ! [SY1192: $i] :
( ~ ( in @ SY1192 @ ( setadjoin @ SV83 @ ( setadjoin @ SV197 @ emptyset ) ) )
| ( SY1192 = SV83 )
| ( SY1192 = SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(609,plain,
! [SV84: $i,SV198: $i] :
( ( ~ ( subset @ SV198 @ SV84 )
| ( ( binintersect @ SV84 @ SV198 )
= SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(610,plain,
! [SV199: $i > $o,SV85: $i] :
( ( ~ ~ ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV85 )
| ( SV199 @ SY1193 ) )
| ~ ! [SY1194: $i] :
~ ~ ( ~ ( in @ SY1194 @ SV85 )
| ~ ~ ( SV199 @ SY1194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(611,plain,
! [SV86: $i,SV200: $i] :
( ( ! [SY1195: $i] :
( ~ ( in @ SV200 @ ( powerset @ SV86 ) )
| ~ ( in @ SY1195 @ SV200 )
| ( in @ SY1195 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(612,plain,
! [SV201: $i,SV87: $i] :
( ( ~ ( in @ SV87 @ ( setadjoin @ SV201 @ emptyset ) )
| ( SV87 = SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(613,plain,
! [SV202: $i,SV88: $i] :
( ( ! [SY1196: $i] :
( ~ ( in @ SY1196 @ SV88 )
| ~ ( in @ SY1196 @ SV202 )
| ~ ( in @ SY1196 @ ( symdiff @ SV88 @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(614,plain,
! [SV203: $i,SV89: $i] :
( ( ~ ! [SY1197: $i] :
( ~ ( in @ SY1197 @ SV89 )
| ( in @ SY1197 @ SV203 ) )
| ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) )
| ( SV89 = SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(615,plain,
! [SV204: $i,SV90: $i] :
( ( ! [SY1199: $i] :
( ~ ~ ( in @ SY1199 @ ( setminus @ SV90 @ SV204 ) )
| ~ ~ ( in @ SY1199 @ SV204 )
| ~ ( in @ SY1199 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(616,plain,
! [SV205: $i,SV91: $i] :
( ( ! [SY1200: $i] :
( ~ ( subset @ SV91 @ SV205 )
| ~ ~ ( in @ SY1200 @ SV205 )
| ~ ( in @ SY1200 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(617,plain,
! [SV92: $i > $o] :
( ( ( ~ ~ ! [SY1025: $i] :
~ ~ ( ~ ( SV92 @ SY1025 )
| ~ ! [SY1026: $i] :
( ~ ( SV92 @ SY1026 )
| ( SY1025 = SY1026 ) ) ) )
= $true )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(618,plain,
! [SV206: $i,SV93: $i] :
( ( ! [SY1201: $i] :
( ~ ~ ( in @ SY1201 @ ( setminus @ SV93 @ SV206 ) )
| ~ ( in @ SY1201 @ SV93 )
| ( in @ SY1201 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(619,plain,
! [SV207: $i,SV94: $i] :
( ( ! [SY1202: $i] :
( ~ ( in @ SY1202 @ ( setadjoin @ SV94 @ SV207 ) )
| ( SY1202 = SV94 )
| ( in @ SY1202 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(620,plain,
! [SV208: $i,SV95: $i] :
( ( ( ( binintersect @ SV95 @ SV208 )
!= SV208 )
| ( subset @ SV208 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(621,plain,
! [SV96: $i,SV209: $i] :
( ( ~ ( ~ ( ~ ( in @ SV209 @ ( setunion @ SV96 ) )
| ~ ! [SY1203: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1203 )
| ~ ( in @ SY1203 @ SV96 ) ) )
| ~ ( ~ ~ ! [SY1204: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1204 )
| ~ ( in @ SY1204 @ SV96 ) )
| ( in @ SV209 @ ( setunion @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(622,plain,
! [SV210: $i,SV97: $i] :
( ( ( SV97 != SV210 )
| ! [SY1205: $i,SY1206: $i] :
( ( SY1205 != SY1206 )
| ( ( setadjoin @ SV97 @ SY1205 )
= ( setadjoin @ SV210 @ SY1206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(623,plain,
! [SV98: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV98 )
| ~ ! [SY1039: $i] :
( ~ ~ ( ~ ( in @ SY1039 @ omega )
| ~ ( in @ SY1039 @ SV98 ) )
| ( in @ ( setadjoin @ SY1039 @ SY1039 ) @ SV98 ) ) ) )
= $true )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(624,plain,
! [SV99: $i > $o] :
( ( ( ~ ~ ! [SY1041: $i] :
~ ~ ( ~ ( SV99 @ SY1041 )
| ~ ! [SY1042: $i] :
( ~ ( SV99 @ SY1042 )
| ( SY1041 = SY1042 ) ) ) )
= $true )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(625,plain,
! [SV211: $i,SV100: $i] :
( ( ~ ! [SY1207: $i] :
~ ( ~ ( ~ ( in @ SY1207 @ SV100 )
| ( in @ SY1207 @ SV211 ) )
| ~ ( ~ ( in @ SY1207 @ SV211 )
| ( in @ SY1207 @ SV100 ) ) )
| ( SV100 = SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(626,plain,
! [SV101: $i,SV212: $i] :
( ( ~ ( subset @ SV212 @ SV101 )
| ( in @ SV212 @ ( powerset @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(627,plain,
! [SV102: $i] :
( ( ( ~ ~ ! [SY1048: $i] :
~ ( in @ SY1048 @ SV102 ) )
= $true )
| ( ( SV102 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(628,plain,
! [SV103: $i,SV213: $i] :
( ( ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SV213 )
| ~ ( in @ SY1208 @ ( setminus @ SV103 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(629,plain,
! [SV214: $i > $o,SV104: $i] :
( ( ~ ! [SY1209: $i] :
( ~ ( in @ SY1209 @ SV104 )
| ~ ( SV214 @ SY1209 ) )
| ~ ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(630,plain,
! [SV215: $i,SV105: $i] :
( ( ! [SY1211: $i] :
( ~ ( in @ SY1211 @ ( binunion @ SV105 @ SV215 ) )
| ( in @ SY1211 @ SV105 )
| ( in @ SY1211 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(631,plain,
! [SV216: $i,SV106: $i] :
( ( ( ( binintersect @ SV106 @ SV216 )
!= SV106 )
| ( subset @ SV106 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(632,plain,
! [SV217: $i > $o,SV107: $i] :
( ( ~ ~ ! [SY1212: $i] :
~ ~ ( ~ ( in @ SY1212 @ SV107 )
| ~ ~ ( SV217 @ SY1212 ) )
| ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(633,plain,
! [SV108: $i > $o] :
( ( ( ~ ~ ! [SY1060: $i] :
~ ! [SY1061: $i] :
~ ( ~ ( ~ ( SV108 @ SY1061 )
| ( SY1061 = SY1060 ) )
| ~ ( ( SY1061 != SY1060 )
| ( SV108 @ SY1061 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(634,plain,
! [SV218: $i > $o,SV109: $i] :
( ( ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SV109 )
| ~ ( SV218 @ SY1214 )
| ( ( dsetconstr @ SV109
@ ^ [SY1215: $i] : ( SV218 @ SY1215 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(635,plain,
! [SV110: $i > $o] :
( ( ( ~ ~ ! [SY1067: $i] :
~ ~ ( ~ ( SV110 @ SY1067 )
| ~ ! [SY1068: $i] :
( ~ ( SV110 @ SY1068 )
| ( SY1067 = SY1068 ) ) ) )
= $true )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(636,plain,
! [SV219: $i,SV111: $i] :
( ( ~ ( subset @ SV111 @ SV219 )
| ( ( setminus @ SV111 @ SV219 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(637,plain,
! [SV112: $i > $o] :
( ( ( ~ ~ ! [SY1072: $i] :
~ ~ ( ~ ( SV112 @ SY1072 )
| ~ ! [SY1073: $i] :
( ~ ( SV112 @ SY1073 )
| ( SY1072 = SY1073 ) ) ) )
= $true )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(638,plain,
! [SV220: $i,SV113: $i] :
( ( ~ ! [SY1216: $i] :
~ ~ ( ~ ( in @ SY1216 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1217: $i] :
~ ~ ( ~ ( in @ SY1217 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1216 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1216 @ ( setadjoin @ SY1217 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(639,plain,
! [SV221: $i,SV114: $i] :
( ( ~ ( subset @ SV114 @ SV221 )
| ~ ( subset @ SV221 @ SV114 )
| ( SV114 = SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(640,plain,
! [SV222: $i > $o,SV115: $i] :
( ( ! [SY1218: $i] :
( ~ ( in @ SY1218
@ ( dsetconstr @ SV115
@ ^ [SY1219: $i] : ( SV222 @ SY1219 ) ) )
| ( in @ SY1218 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(641,plain,
! [SV223: $i,SV116: $i] :
( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ SV116 )
| ( in @ SY1220 @ SV223 ) )
| ( subset @ SV116 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(642,plain,
! [SV117: $i > $o,SV224: $i] :
( ( ~ ( in @ SV224 @ emptyset )
| ( SV117 @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(643,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ~ ! [SY1221: $i,SY1222: $i] :
( ( SY1221 != SY1222 )
| ~ ( ~ ( ~ ( SV118 @ SY1221 )
| ( SV225 @ SY1222 ) )
| ~ ( ~ ( SV225 @ SY1222 )
| ( SV118 @ SY1221 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(644,plain,
! [SV119: $i] :
( ( ( ~ ( subset @ SV119 @ emptyset ) )
= $true )
| ( ( SV119 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(645,plain,
! [SV226: $i,SV120: $i] :
( ( ! [SY1231: $i,SY1232: $o] :
( ~ ( in @ SY1231 @ ( binunion @ SV120 @ SV226 ) )
| ~ ( ~ ( in @ SY1231 @ SV120 )
| SY1232 )
| ~ ( ~ ( in @ SY1231 @ SV226 )
| SY1232 )
| SY1232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(646,plain,
! [SV121: $i,SV227: $i] :
( ( ! [SY1233: $i] :
( ~ ( in @ SY1233 @ SV227 )
| ( in @ SY1233 @ ( setadjoin @ SV121 @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(647,plain,
! [SV122: $i,SV228: $i] :
( ( ~ ( in @ SV228 @ SV122 )
| ( in @ SV228 @ ( powerset @ ( setunion @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(648,plain,
! [SV229: $i,SV123: $i] :
( ( ~ ( in @ SV123 @ ( setadjoin @ SV229 @ emptyset ) )
| ( in @ SV229 @ ( setadjoin @ SV123 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(649,plain,
! [SV230: $i,SV124: $i] :
( ( ! [SY1234: $i] :
( ~ ( in @ SY1234 @ ( setminus @ SV124 @ SV230 ) )
| ( in @ SY1234 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(650,plain,
! [SV231: $i,SV125: $i] :
( ( ! [SY1235: $i] :
( ~ ( in @ SY1235 @ ( setadjoin @ SV125 @ SV231 ) )
| ! [SY1236: $o] :
( ~ ( ( SY1235 != SV125 )
| SY1236 )
| ~ ( ~ ( in @ SY1235 @ SV231 )
| SY1236 )
| SY1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(651,plain,
! [SV126: $i] :
( ( ( ~ ( ( SV126 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY1109: $i] :
~ ~ ( ~ ( in @ SY1109 @ SV126 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(652,plain,
! [SV232: $i,SV127: $i] :
( ( ! [SY1237: $i] :
( ~ ( in @ SY1237 @ SV127 )
| ~ ~ ( in @ SY1237 @ SV232 )
| ( in @ SY1237 @ ( setminus @ SV127 @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(653,plain,
! [SV128: $i > $o] :
( ( ( ~ ~ ! [SY1112: $i] :
~ ~ ( ~ ( SV128 @ SY1112 )
| ~ ! [SY1113: $i] :
( ~ ( SV128 @ SY1113 )
| ( SY1112 = SY1113 ) ) ) )
= $true )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(654,plain,
! [SV129: $o] :
( ( ( ~ SV129 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(655,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(657,plain,
! [SV233: $i > $o,SV130: $i] :
( ( ~ ~ ~ ! [SY1238: $i] :
~ ~ ( ~ ( in @ SY1238 @ SV130 )
| ~ ( SV233 @ SY1238 ) )
| ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(658,plain,
! [SV234: $i,SV131: $i] :
( ( ~ ( subset @ SV131 @ SV234 )
| ( in @ SV131 @ ( powerset @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(659,plain,
! [SV235: $i,SV132: $i] :
( ( ~ ( subset @ SV132 @ SV235 )
| ( subset @ ( powerset @ SV132 ) @ ( powerset @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(660,plain,
! [SV236: $i,SV137: $i,SV5: $i] :
( ( ( binintersect @ SV5 @ ( binunion @ SV137 @ SV236 ) )
= ( binunion @ ( binintersect @ SV5 @ SV137 ) @ ( binintersect @ SV5 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(661,plain,
! [SV25: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ ( setunion @ SV25 ) ) )
= $true )
| ( ( ! [SY1124: $o] :
( ~ ! [SY1125: $i] :
( ~ ( in @ SV149 @ SY1125 )
| ~ ( in @ SY1125 @ SV25 )
| SY1124 )
| SY1124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(662,plain,
! [SV150: $i > $o,SV26: $i,SV237: $i] :
( ( ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) )
| ( SV150 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(663,plain,
! [SV27: $i,SV151: $i,SV238: $i] :
( ( ~ ( in @ SV238 @ SV151 )
| ( in @ SV238 @ ( binunion @ SV27 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(664,plain,
! [SV152: $i,SV28: $i] :
( ( ( SV28 != SV152 )
= $true )
| ( ( in @ SV28 @ ( setadjoin @ SV152 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(665,plain,
! [SV153: $i > $o,SV29: $i,SV239: $i] :
( ( ~ ( in @ SV239 @ SV29 )
| ~ ( SV153 @ SV239 )
| ( in @ SV239
@ ( dsetconstr @ SV29
@ ^ [SY1130: $i] : ( SV153 @ SY1130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(666,plain,
! [SV240: $i,SV154: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV154 )
| ~ ( subset @ SV154 @ SV240 )
| ( subset @ SV30 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(667,plain,
! [SV31: $i] :
( ( ( in @ SV31 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(668,plain,
! [SV32: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ~ ( ~ ( in @ SY1247 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1248 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1247 )
| ( in @ SX4 @ SY1248 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1248 )
| ( in @ SX4 @ SY1247 ) ) ) )
| ~ ! [SY1251: $i] :
( ~ ~ ( ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SY1251 )
| ( in @ SY885 @ SV32 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1251 ) )
| ~ ! [SY1254: $i] :
~ ~ ! [SY1255: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1254 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1255 @ SY1251 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1254 )
| ~ ( in @ SX5 @ SY1251 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1254 ) )
| ( in @ SY1255 @ SY1257 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[552]) ).
thf(669,plain,
! [SV33: $i] :
( ( ( ! [SY892: $i] :
~ ( in @ SY892 @ SV33 ) )
= $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(670,plain,
! [SV155: $i,SV34: $i,SV241: $i] :
( ( ~ ( in @ SV241 @ ( binintersect @ SV34 @ SV155 ) )
| ( in @ SV241 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(671,plain,
( ( ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1260: $i] :
~ ~ ( ~ ( in @ SY1260 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1259 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1259 @ ( setadjoin @ SY1260 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[555]) ).
thf(672,plain,
! [SV156: $i,SV35: $i,SV242: $i] :
( ( ~ ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
| ~ ( in @ SV242 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(673,plain,
! [SV157: $i,SV36: $i] :
( ( ( ( setminus @ SV36 @ SV157 )
!= emptyset )
= $true )
| ( ( subset @ SV36 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(674,plain,
! [SV158: $i,SV37: $i,SV243: $i] :
( ( ~ ~ ( in @ SV243 @ SV37 )
| ~ ( in @ SV243 @ ( setminus @ SV37 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(675,plain,
! [SV159: $i > $o,SV38: $i] :
( ( ( ~ ~ ~ ! [SY1138: $i] :
~ ~ ( ~ ( in @ SY1138 @ SV38 )
| ~ ( SV159 @ SY1138 ) ) )
= $true )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(676,plain,
! [SV160: $i,SV39: $i] :
( ( ( ~ ~ ~ ! [SY1140: $i] :
~ ~ ( ~ ( in @ SY1140 @ SV39 )
| ~ ( in @ SY1140 @ SV160 ) ) )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(677,plain,
! [SV161: $i,SV40: $i,SV244: $i] :
( ( ~ ( in @ SV244 @ SV40 )
| ~ ~ ( in @ SV244 @ SV161 )
| ( SV40 != SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(678,plain,
! [SV41: $i] :
( ( ( ~ ! [SY907: $i] :
~ ( in @ SY907 @ SV41 ) )
= $false )
| ( ( ~ ! [SY908: $i] :
~ ~ ( ~ ( in @ SY908 @ SV41 )
| ~ ~ ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SY908 )
| ~ ( in @ SY909 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(679,plain,
! [SV162: $i,SV42: $i,SV245: $i] :
( ( ~ ~ ( in @ SV245 @ SV42 )
| ~ ~ ( in @ SV245 @ SV162 )
| ~ ( in @ SV245 @ ( symdiff @ SV42 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(680,plain,
! [SV43: $o] :
( ( SV43 = $false )
| ( ( set2prop @ ( prop2set @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(681,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(683,plain,
! [SV163: $i,SV44: $i] :
( ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV44 )
| ( in @ SY1143 @ SV163 ) ) )
= $true )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(684,plain,
! [SV164: $i,SV45: $i] :
( ( ( SV45 != SV164 )
= $true )
| ( ( ! [SY1144: $i,SY1145: $i] :
( ( SY1144 != SY1145 )
| ~ ( in @ SY1144 @ SV45 )
| ( in @ SY1145 @ SV164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(685,plain,
! [SV246: $i,SV165: $i,SV46: $i] :
( ( ~ ( subset @ SV46 @ SV165 )
| ~ ( in @ SV246 @ SV46 )
| ( in @ SV246 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(686,plain,
! [SV47: $i > $o] :
( ( ( ~ ! [SY919: $i] :
~ ~ ( ~ ( SV47 @ SY919 )
| ~ ! [SY920: $i] :
( ~ ( SV47 @ SY920 )
| ( SY919 = SY920 ) ) ) )
= $false )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(687,plain,
! [SV166: $i,SV48: $i] :
( ( ( SV48 != SV166 )
= $true )
| ( ( ! [SY1147: $i > $o,SY1148: $i > $o] :
( ~ ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV48 )
| ! [SY1150: $i] :
( ~ ( in @ SY1150 @ SV166 )
| ( SY1149 != SY1150 )
| ~ ( ~ ( ~ ( SY1147 @ SY1149 )
| ( SY1148 @ SY1150 ) )
| ~ ( ~ ( SY1148 @ SY1150 )
| ( SY1147 @ SY1149 ) ) ) ) )
| ( ( dsetconstr @ SV48
@ ^ [SX4: $i] : ( SY1147 @ SX4 ) )
= ( dsetconstr @ SV166
@ ^ [SX4: $i] : ( SY1148 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(688,plain,
! [SV167: $i,SV49: $i] :
( ( ( SV49 != SV167 )
= $true )
| ( ( subset @ SV167 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(689,plain,
! [SV50: $i > $o] :
( ( ( ~ ! [SY931: $i] :
~ ~ ( ~ ( SV50 @ SY931 )
| ~ ! [SY932: $i] :
( ~ ( SV50 @ SY932 )
| ( SY931 = SY932 ) ) ) )
= $false )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(690,plain,
! [SV168: $i,SV51: $i] :
( ( ( SV51 != SV168 )
= $true )
| ( ( subset @ SV51 @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(691,plain,
! [SV169: $i,SV52: $i,SV247: $i] :
( ( ~ ( in @ SV247 @ ( binintersect @ SV52 @ SV169 ) )
| ( in @ SV247 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(692,plain,
! [SV170: $i,SV53: $i,SV248: $i] :
( ( ~ ( in @ SV248 @ SV53 )
| ( in @ SV248 @ ( binunion @ SV53 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(693,plain,
! [SV171: $i,SV54: $i] :
( ( ( SV54 != SV171 )
= $true )
| ( ( ( setunion @ SV54 )
= ( setunion @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(694,plain,
! [SV55: $i] :
( ( ( ! [SY940: $i] :
~ ( in @ SY940 @ SV55 ) )
= $false )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(695,plain,
! [SV172: $i,SV56: $i] :
( ( ( ~ ( ( SV56 != SV172 ) ) )
= $true )
| ( ( ~ ( in @ SV172 @ ( setadjoin @ SV56 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(696,plain,
! [SV57: $o,SV173: $i] :
( ( ( ~ ( in @ SV173 @ ( prop2set @ SV57 ) ) )
= $true )
| ( SV57 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(698,plain,
! [SV175: $i] :
( ( ( ~ ( in @ SV175 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(699,plain,
! [SV58: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ ( powerset @ SV58 ) ) )
= $true )
| ( ( subset @ SV176 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(700,plain,
! [SV177: $i,SV59: $i,SV249: $i] :
( ( ~ ~ ( in @ SV249 @ SV59 )
| ~ ( in @ SV249 @ SV177 )
| ( in @ SV249 @ ( symdiff @ SV59 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(701,plain,
! [SV60: $i,SV178: $i] :
( ( ~ ( ~ ( in @ SV178 @ ( powerset @ SV60 ) )
| ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV178 )
| ( in @ SY1156 @ SV60 ) ) )
| ~ ( ~ ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV178 )
| ( in @ SY1157 @ SV60 ) )
| ( in @ SV178 @ ( powerset @ SV60 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(702,plain,
! [SV179: $i,SV61: $i,SV250: $i] :
( ( ~ ( subset @ SV250 @ SV61 )
| ~ ( subset @ SV250 @ SV179 )
| ( subset @ SV250 @ ( binintersect @ SV61 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(703,plain,
! [SV180: $i,SV62: $i] :
( ( ( ~ ~ ( subset @ SV62 @ SV180 ) )
= $true )
| ( ( SV62 != SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(704,plain,
! [SV63: $i,SV181: $i] :
( ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV181 )
| ( in @ SY1159 @ SV63 ) ) )
= $true )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(705,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ~ ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
| ! [SY1261: $o] :
( ~ ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| SY1261 )
| ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SY1261 )
| SY1261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(706,plain,
! [SV183: $i,SV65: $i] :
( ( ( SV65 != SV183 )
= $true )
| ( ( ( powerset @ SV65 )
= ( powerset @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(707,plain,
! [SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV184 )
| ~ ! [SY960: $i] :
~ ~ ( ~ ( SV66 @ SY1162 @ SY960 )
| ~ ! [SY961: $i] :
( ~ ( SV66 @ SY1162 @ SY961 )
| ( SY960 = SY961 ) ) ) ) )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(708,plain,
! [SV185: $i,SV67: $i,SV252: $i] :
( ( ~ ( in @ SV252 @ SV67 )
| ~ ( in @ SV252 @ SV185 )
| ( in @ SV252 @ ( binintersect @ SV67 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(709,plain,
! [SV186: $i > $o,SV68: $i] :
( ( ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV68 )
| ~ ( SV186 @ SY1170 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(710,plain,
! [SV69: $i] :
( ( ( in @ SV69 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV69 @ SV69 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(711,plain,
! [SV70: $i] :
( ( ( in @ SV70 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(712,plain,
! [SV187: $i > $o,SV71: $i] :
( ( ( ~ ~ ! [SY1172: $i] :
( ~ ( in @ SY1172 @ SV71 )
| ( SV187 @ SY1172 ) ) )
= $true )
| ( ( ~ ! [SY1173: $i] :
~ ~ ( ~ ( in @ SY1173 @ SV71 )
| ~ ~ ( SV187 @ SY1173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(713,plain,
! [SV188: $i,SV72: $i] :
( ( ( SV72 != SV188 )
= $true )
| ( ( ! [SY1174: $i,SY1175: $i] :
( ( SY1174 != SY1175 )
| ~ ( ~ ( ~ ( in @ SY1174 @ SV72 )
| ( in @ SY1175 @ SV188 ) )
| ~ ( ~ ( in @ SY1175 @ SV188 )
| ( in @ SY1174 @ SV72 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(714,plain,
! [SV189: $i,SV73: $i,SV253: $i] :
( ( ~ ( in @ SV253 @ SV73 )
| ~ ~ ( in @ SV253 @ SV189 )
| ~ ( subset @ SV73 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(715,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ! [SY1177: $i,SY1178: $i] :
( ( SY1177 != SY1178 )
| ~ ( ~ ( ~ ( SV74 @ SY1177 )
| ( SV190 @ SY1178 ) )
| ~ ( ~ ( SV190 @ SY1178 )
| ( SV74 @ SY1177 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(716,plain,
! [SV191: $i,SV75: $i] :
( ( ( ~ ( subset @ SV75 @ SV191 ) )
= $true )
| ( ( ( binintersect @ SV75 @ SV191 )
= SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(717,plain,
! [SV76: $i > $o] :
( ( ( ~ ! [SY989: $i] :
~ ( SV76 @ SY989 ) )
= $false )
| ( ( ~ ! [SY990: $i,SY991: $i] :
( ~ ( SV76 @ SY990 )
| ~ ( SV76 @ SY991 )
| ( SY990 = SY991 ) )
| ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(718,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ~ ( ~ ( ~ ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
| ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
| ~ ( ~ ( ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
| ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(719,plain,
! [SV193: $i,SV255: $i,SV78: $i] :
( ( ~ ( subset @ SV78 @ SV255 )
| ( subset @ SV78 @ ( setadjoin @ SV193 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(720,plain,
! [SV79: $i,SV256: $i,SV194: $i] :
( ( ~ ( in @ SV194 @ SV256 )
| ~ ( in @ SV256 @ SV79 )
| ( in @ SV194 @ ( setunion @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(721,plain,
! [SV195: $i > $o,SV80: $i,SV257: $i] :
( ( ~ ( in @ SV257 @ SV80 )
| ~ ( ~ ( ~ ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) )
| ( SV195 @ SV257 ) )
| ~ ( ~ ( SV195 @ SV257 )
| ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(722,plain,
! [SV196: $i,SV81: $i,SV258: $i] :
( ( ~ ( in @ SV258 @ SV81 )
| ~ ~ ( in @ SV258 @ SV196 )
| ( in @ SV258 @ ( symdiff @ SV81 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(723,plain,
! [SV82: $i] :
( ( ( SV82 != emptyset )
= $false )
| ( ( ~ ! [SY1006: $i] :
~ ( in @ SY1006 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(724,plain,
! [SV197: $i,SV83: $i,SV259: $i] :
( ( ~ ( in @ SV259 @ ( setadjoin @ SV83 @ ( setadjoin @ SV197 @ emptyset ) ) )
| ( SV259 = SV83 )
| ( SV259 = SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(725,plain,
! [SV84: $i,SV198: $i] :
( ( ( ~ ( subset @ SV198 @ SV84 ) )
= $true )
| ( ( ( binintersect @ SV84 @ SV198 )
= SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(726,plain,
! [SV199: $i > $o,SV85: $i] :
( ( ( ~ ~ ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV85 )
| ( SV199 @ SY1193 ) ) )
= $true )
| ( ( ~ ! [SY1194: $i] :
~ ~ ( ~ ( in @ SY1194 @ SV85 )
| ~ ~ ( SV199 @ SY1194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(727,plain,
! [SV260: $i,SV86: $i,SV200: $i] :
( ( ~ ( in @ SV200 @ ( powerset @ SV86 ) )
| ~ ( in @ SV260 @ SV200 )
| ( in @ SV260 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(728,plain,
! [SV201: $i,SV87: $i] :
( ( ( ~ ( in @ SV87 @ ( setadjoin @ SV201 @ emptyset ) ) )
= $true )
| ( ( SV87 = SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(729,plain,
! [SV202: $i,SV88: $i,SV261: $i] :
( ( ~ ( in @ SV261 @ SV88 )
| ~ ( in @ SV261 @ SV202 )
| ~ ( in @ SV261 @ ( symdiff @ SV88 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(730,plain,
! [SV203: $i,SV89: $i] :
( ( ( ~ ! [SY1197: $i] :
( ~ ( in @ SY1197 @ SV89 )
| ( in @ SY1197 @ SV203 ) ) )
= $true )
| ( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) )
| ( SV89 = SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(731,plain,
! [SV204: $i,SV90: $i,SV262: $i] :
( ( ~ ~ ( in @ SV262 @ ( setminus @ SV90 @ SV204 ) )
| ~ ~ ( in @ SV262 @ SV204 )
| ~ ( in @ SV262 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(732,plain,
! [SV263: $i,SV205: $i,SV91: $i] :
( ( ~ ( subset @ SV91 @ SV205 )
| ~ ~ ( in @ SV263 @ SV205 )
| ~ ( in @ SV263 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(733,plain,
! [SV92: $i > $o] :
( ( ( ~ ! [SY1025: $i] :
~ ~ ( ~ ( SV92 @ SY1025 )
| ~ ! [SY1026: $i] :
( ~ ( SV92 @ SY1026 )
| ( SY1025 = SY1026 ) ) ) )
= $false )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(734,plain,
! [SV206: $i,SV93: $i,SV264: $i] :
( ( ~ ~ ( in @ SV264 @ ( setminus @ SV93 @ SV206 ) )
| ~ ( in @ SV264 @ SV93 )
| ( in @ SV264 @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(735,plain,
! [SV207: $i,SV94: $i,SV265: $i] :
( ( ~ ( in @ SV265 @ ( setadjoin @ SV94 @ SV207 ) )
| ( SV265 = SV94 )
| ( in @ SV265 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(736,plain,
! [SV208: $i,SV95: $i] :
( ( ( ( binintersect @ SV95 @ SV208 )
!= SV208 )
= $true )
| ( ( subset @ SV208 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(737,plain,
! [SV96: $i,SV209: $i] :
( ( ~ ( ~ ( in @ SV209 @ ( setunion @ SV96 ) )
| ~ ! [SY1203: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1203 )
| ~ ( in @ SY1203 @ SV96 ) ) )
| ~ ( ~ ~ ! [SY1204: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1204 )
| ~ ( in @ SY1204 @ SV96 ) )
| ( in @ SV209 @ ( setunion @ SV96 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(738,plain,
! [SV210: $i,SV97: $i] :
( ( ( SV97 != SV210 )
= $true )
| ( ( ! [SY1205: $i,SY1206: $i] :
( ( SY1205 != SY1206 )
| ( ( setadjoin @ SV97 @ SY1205 )
= ( setadjoin @ SV210 @ SY1206 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(739,plain,
! [SV98: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV98 )
| ~ ! [SY1039: $i] :
( ~ ~ ( ~ ( in @ SY1039 @ omega )
| ~ ( in @ SY1039 @ SV98 ) )
| ( in @ ( setadjoin @ SY1039 @ SY1039 ) @ SV98 ) ) ) )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(740,plain,
! [SV99: $i > $o] :
( ( ( ~ ! [SY1041: $i] :
~ ~ ( ~ ( SV99 @ SY1041 )
| ~ ! [SY1042: $i] :
( ~ ( SV99 @ SY1042 )
| ( SY1041 = SY1042 ) ) ) )
= $false )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(741,plain,
! [SV211: $i,SV100: $i] :
( ( ( ~ ! [SY1207: $i] :
~ ( ~ ( ~ ( in @ SY1207 @ SV100 )
| ( in @ SY1207 @ SV211 ) )
| ~ ( ~ ( in @ SY1207 @ SV211 )
| ( in @ SY1207 @ SV100 ) ) ) )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(742,plain,
! [SV101: $i,SV212: $i] :
( ( ( ~ ( subset @ SV212 @ SV101 ) )
= $true )
| ( ( in @ SV212 @ ( powerset @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(743,plain,
! [SV102: $i] :
( ( ( ~ ! [SY1048: $i] :
~ ( in @ SY1048 @ SV102 ) )
= $false )
| ( ( SV102 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(744,plain,
! [SV103: $i,SV213: $i,SV266: $i] :
( ( ~ ( in @ SV266 @ SV213 )
| ~ ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(745,plain,
! [SV214: $i > $o,SV104: $i] :
( ( ( ~ ! [SY1209: $i] :
( ~ ( in @ SY1209 @ SV104 )
| ~ ( SV214 @ SY1209 ) ) )
= $true )
| ( ( ~ ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(746,plain,
! [SV215: $i,SV105: $i,SV267: $i] :
( ( ~ ( in @ SV267 @ ( binunion @ SV105 @ SV215 ) )
| ( in @ SV267 @ SV105 )
| ( in @ SV267 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(747,plain,
! [SV216: $i,SV106: $i] :
( ( ( ( binintersect @ SV106 @ SV216 )
!= SV106 )
= $true )
| ( ( subset @ SV106 @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(748,plain,
! [SV217: $i > $o,SV107: $i] :
( ( ( ~ ~ ! [SY1212: $i] :
~ ~ ( ~ ( in @ SY1212 @ SV107 )
| ~ ~ ( SV217 @ SY1212 ) ) )
= $true )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(749,plain,
! [SV108: $i > $o] :
( ( ( ~ ! [SY1060: $i] :
~ ! [SY1061: $i] :
~ ( ~ ( ~ ( SV108 @ SY1061 )
| ( SY1061 = SY1060 ) )
| ~ ( ( SY1061 != SY1060 )
| ( SV108 @ SY1061 ) ) ) )
= $false )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(750,plain,
! [SV218: $i > $o,SV109: $i,SV268: $i] :
( ( ~ ( in @ SV268 @ SV109 )
| ~ ( SV218 @ SV268 )
| ( ( dsetconstr @ SV109
@ ^ [SY1215: $i] : ( SV218 @ SY1215 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(751,plain,
! [SV110: $i > $o] :
( ( ( ~ ! [SY1067: $i] :
~ ~ ( ~ ( SV110 @ SY1067 )
| ~ ! [SY1068: $i] :
( ~ ( SV110 @ SY1068 )
| ( SY1067 = SY1068 ) ) ) )
= $false )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(752,plain,
! [SV219: $i,SV111: $i] :
( ( ( ~ ( subset @ SV111 @ SV219 ) )
= $true )
| ( ( ( setminus @ SV111 @ SV219 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(753,plain,
! [SV112: $i > $o] :
( ( ( ~ ! [SY1072: $i] :
~ ~ ( ~ ( SV112 @ SY1072 )
| ~ ! [SY1073: $i] :
( ~ ( SV112 @ SY1073 )
| ( SY1072 = SY1073 ) ) ) )
= $false )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(754,plain,
! [SV220: $i,SV113: $i] :
( ( ! [SY1216: $i] :
~ ~ ( ~ ( in @ SY1216 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1217: $i] :
~ ~ ( ~ ( in @ SY1217 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1216 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1216 @ ( setadjoin @ SY1217 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(755,plain,
! [SV221: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ SV221 ) )
= $true )
| ( ( ~ ( subset @ SV221 @ SV114 )
| ( SV114 = SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(756,plain,
! [SV222: $i > $o,SV115: $i,SV269: $i] :
( ( ~ ( in @ SV269
@ ( dsetconstr @ SV115
@ ^ [SY1219: $i] : ( SV222 @ SY1219 ) ) )
| ( in @ SV269 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(757,plain,
! [SV223: $i,SV116: $i] :
( ( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ SV116 )
| ( in @ SY1220 @ SV223 ) ) )
= $true )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(758,plain,
! [SV117: $i > $o,SV224: $i] :
( ( ( ~ ( in @ SV224 @ emptyset ) )
= $true )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(759,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ! [SY1221: $i,SY1222: $i] :
( ( SY1221 != SY1222 )
| ~ ( ~ ( ~ ( SV118 @ SY1221 )
| ( SV225 @ SY1222 ) )
| ~ ( ~ ( SV225 @ SY1222 )
| ( SV118 @ SY1221 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(760,plain,
! [SV119: $i] :
( ( ( subset @ SV119 @ emptyset )
= $false )
| ( ( SV119 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(761,plain,
! [SV226: $i,SV120: $i,SV270: $i] :
( ( ! [SY1266: $o] :
( ~ ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
| ~ ( ~ ( in @ SV270 @ SV120 )
| SY1266 )
| ~ ( ~ ( in @ SV270 @ SV226 )
| SY1266 )
| SY1266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(762,plain,
! [SV121: $i,SV227: $i,SV271: $i] :
( ( ~ ( in @ SV271 @ SV227 )
| ( in @ SV271 @ ( setadjoin @ SV121 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(763,plain,
! [SV122: $i,SV228: $i] :
( ( ( ~ ( in @ SV228 @ SV122 ) )
= $true )
| ( ( in @ SV228 @ ( powerset @ ( setunion @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(764,plain,
! [SV229: $i,SV123: $i] :
( ( ( ~ ( in @ SV123 @ ( setadjoin @ SV229 @ emptyset ) ) )
= $true )
| ( ( in @ SV229 @ ( setadjoin @ SV123 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(765,plain,
! [SV230: $i,SV124: $i,SV272: $i] :
( ( ~ ( in @ SV272 @ ( setminus @ SV124 @ SV230 ) )
| ( in @ SV272 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(766,plain,
! [SV231: $i,SV125: $i,SV273: $i] :
( ( ~ ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
| ! [SY1267: $o] :
( ~ ( ( SV273 != SV125 )
| SY1267 )
| ~ ( ~ ( in @ SV273 @ SV231 )
| SY1267 )
| SY1267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(767,plain,
! [SV126: $i] :
( ( ( SV126 != emptyset )
= $false )
| ( ( ~ ! [SY1109: $i] :
~ ~ ( ~ ( in @ SY1109 @ SV126 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(768,plain,
! [SV232: $i,SV127: $i,SV274: $i] :
( ( ~ ( in @ SV274 @ SV127 )
| ~ ~ ( in @ SV274 @ SV232 )
| ( in @ SV274 @ ( setminus @ SV127 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(769,plain,
! [SV128: $i > $o] :
( ( ( ~ ! [SY1112: $i] :
~ ~ ( ~ ( SV128 @ SY1112 )
| ~ ! [SY1113: $i] :
( ~ ( SV128 @ SY1113 )
| ( SY1112 = SY1113 ) ) ) )
= $false )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(770,plain,
! [SV129: $o] :
( ( SV129 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(771,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(773,plain,
! [SV233: $i > $o,SV130: $i] :
( ( ( ~ ~ ~ ! [SY1238: $i] :
~ ~ ( ~ ( in @ SY1238 @ SV130 )
| ~ ( SV233 @ SY1238 ) ) )
= $true )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(774,plain,
! [SV234: $i,SV131: $i] :
( ( ( ~ ( subset @ SV131 @ SV234 ) )
= $true )
| ( ( in @ SV131 @ ( powerset @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(775,plain,
! [SV235: $i,SV132: $i] :
( ( ( ~ ( subset @ SV132 @ SV235 ) )
= $true )
| ( ( subset @ ( powerset @ SV132 ) @ ( powerset @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(776,plain,
! [SV25: $i,SV149: $i] :
( ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false )
| ( ( ! [SY1124: $o] :
( ~ ! [SY1125: $i] :
( ~ ( in @ SV149 @ SY1125 )
| ~ ( in @ SY1125 @ SV25 )
| SY1124 )
| SY1124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(777,plain,
! [SV150: $i > $o,SV26: $i,SV237: $i] :
( ( ( ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) ) )
= $true )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(778,plain,
! [SV27: $i,SV151: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV151 ) )
= $true )
| ( ( in @ SV238 @ ( binunion @ SV27 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(779,plain,
! [SV152: $i,SV28: $i] :
( ( ( SV28 = SV152 )
= $false )
| ( ( in @ SV28 @ ( setadjoin @ SV152 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(780,plain,
! [SV153: $i > $o,SV29: $i,SV239: $i] :
( ( ( ~ ( in @ SV239 @ SV29 ) )
= $true )
| ( ( ~ ( SV153 @ SV239 )
| ( in @ SV239
@ ( dsetconstr @ SV29
@ ^ [SY1130: $i] : ( SV153 @ SY1130 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(781,plain,
! [SV240: $i,SV154: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV154 ) )
= $true )
| ( ( ~ ( subset @ SV154 @ SV240 )
| ( subset @ SV30 @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(782,plain,
! [SV31: $i,SV275: $o] :
( ( SV275 = $true )
| ( ( in @ SV31 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[667]) ).
thf(784,plain,
! [SV31: $i] :
( ( $false = $true )
| ( ( in @ SV31 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[667]) ).
thf(785,plain,
! [SV32: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ~ ( ~ ( in @ SY1247 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1248 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1247 )
| ( in @ SX4 @ SY1248 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1248 )
| ( in @ SX4 @ SY1247 ) ) ) )
| ~ ! [SY1251: $i] :
( ~ ~ ( ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SY1251 )
| ( in @ SY885 @ SV32 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1251 ) )
| ~ ! [SY1254: $i] :
~ ~ ! [SY1255: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1254 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1255 @ SY1251 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1254 )
| ~ ( in @ SX5 @ SY1251 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1254 ) )
| ( in @ SY1255 @ SY1257 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(786,plain,
! [SV33: $i] :
( ( ( ~ ( in @ ( sK4_SY892 @ SV33 ) @ SV33 ) )
= $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[669]) ).
thf(787,plain,
! [SV155: $i,SV34: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ ( binintersect @ SV34 @ SV155 ) ) )
= $true )
| ( ( in @ SV241 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(788,plain,
( ( ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1260: $i] :
~ ~ ( ~ ( in @ SY1260 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1259 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1259 @ ( setadjoin @ SY1260 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(789,plain,
! [SV156: $i,SV35: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) ) )
= $true )
| ( ( ~ ( in @ SV242 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(790,plain,
! [SV157: $i,SV36: $i] :
( ( ( ( setminus @ SV36 @ SV157 )
= emptyset )
= $false )
| ( ( subset @ SV36 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(791,plain,
! [SV158: $i,SV37: $i,SV243: $i] :
( ( ( ~ ~ ( in @ SV243 @ SV37 ) )
= $true )
| ( ( ~ ( in @ SV243 @ ( setminus @ SV37 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(792,plain,
! [SV159: $i > $o,SV38: $i] :
( ( ( ~ ~ ! [SY1138: $i] :
~ ~ ( ~ ( in @ SY1138 @ SV38 )
| ~ ( SV159 @ SY1138 ) ) )
= $false )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(793,plain,
! [SV160: $i,SV39: $i] :
( ( ( ~ ~ ! [SY1140: $i] :
~ ~ ( ~ ( in @ SY1140 @ SV39 )
| ~ ( in @ SY1140 @ SV160 ) ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(794,plain,
! [SV161: $i,SV40: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV40 ) )
= $true )
| ( ( ~ ~ ( in @ SV244 @ SV161 )
| ( SV40 != SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(795,plain,
! [SV41: $i] :
( ( ( ! [SY907: $i] :
~ ( in @ SY907 @ SV41 ) )
= $true )
| ( ( ~ ! [SY908: $i] :
~ ~ ( ~ ( in @ SY908 @ SV41 )
| ~ ~ ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SY908 )
| ~ ( in @ SY909 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(796,plain,
! [SV162: $i,SV42: $i,SV245: $i] :
( ( ( ~ ~ ( in @ SV245 @ SV42 ) )
= $true )
| ( ( ~ ~ ( in @ SV245 @ SV162 )
| ~ ( in @ SV245 @ ( symdiff @ SV42 @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(797,plain,
! [SV163: $i,SV44: $i] :
( ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV44 )
| ( in @ SY1143 @ SV163 ) ) )
= $false )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(798,plain,
! [SV164: $i,SV45: $i] :
( ( ( SV45 = SV164 )
= $false )
| ( ( ! [SY1144: $i,SY1145: $i] :
( ( SY1144 != SY1145 )
| ~ ( in @ SY1144 @ SV45 )
| ( in @ SY1145 @ SV164 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(799,plain,
! [SV246: $i,SV165: $i,SV46: $i] :
( ( ( ~ ( subset @ SV46 @ SV165 ) )
= $true )
| ( ( ~ ( in @ SV246 @ SV46 )
| ( in @ SV246 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(800,plain,
! [SV47: $i > $o] :
( ( ( ! [SY919: $i] :
~ ~ ( ~ ( SV47 @ SY919 )
| ~ ! [SY920: $i] :
( ~ ( SV47 @ SY920 )
| ( SY919 = SY920 ) ) ) )
= $true )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(801,plain,
! [SV166: $i,SV48: $i] :
( ( ( SV48 = SV166 )
= $false )
| ( ( ! [SY1147: $i > $o,SY1148: $i > $o] :
( ~ ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV48 )
| ! [SY1150: $i] :
( ~ ( in @ SY1150 @ SV166 )
| ( SY1149 != SY1150 )
| ~ ( ~ ( ~ ( SY1147 @ SY1149 )
| ( SY1148 @ SY1150 ) )
| ~ ( ~ ( SY1148 @ SY1150 )
| ( SY1147 @ SY1149 ) ) ) ) )
| ( ( dsetconstr @ SV48
@ ^ [SX4: $i] : ( SY1147 @ SX4 ) )
= ( dsetconstr @ SV166
@ ^ [SX4: $i] : ( SY1148 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(802,plain,
! [SV167: $i,SV49: $i] :
( ( ( SV49 = SV167 )
= $false )
| ( ( subset @ SV167 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(803,plain,
! [SV50: $i > $o] :
( ( ( ! [SY931: $i] :
~ ~ ( ~ ( SV50 @ SY931 )
| ~ ! [SY932: $i] :
( ~ ( SV50 @ SY932 )
| ( SY931 = SY932 ) ) ) )
= $true )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(804,plain,
! [SV168: $i,SV51: $i] :
( ( ( SV51 = SV168 )
= $false )
| ( ( subset @ SV51 @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(805,plain,
! [SV169: $i,SV52: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ ( binintersect @ SV52 @ SV169 ) ) )
= $true )
| ( ( in @ SV247 @ SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(806,plain,
! [SV170: $i,SV53: $i,SV248: $i] :
( ( ( ~ ( in @ SV248 @ SV53 ) )
= $true )
| ( ( in @ SV248 @ ( binunion @ SV53 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(807,plain,
! [SV171: $i,SV54: $i] :
( ( ( SV54 = SV171 )
= $false )
| ( ( ( setunion @ SV54 )
= ( setunion @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(808,plain,
! [SV55: $i] :
( ( ( ~ ( in @ ( sK5_SY940 @ SV55 ) @ SV55 ) )
= $false )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[694]) ).
thf(809,plain,
! [SV172: $i,SV56: $i] :
( ( ( SV56 != SV172 )
= $false )
| ( ( ~ ( in @ SV172 @ ( setadjoin @ SV56 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(810,plain,
! [SV57: $o,SV173: $i] :
( ( ( in @ SV173 @ ( prop2set @ SV57 ) )
= $false )
| ( SV57 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(812,plain,
! [SV175: $i] :
( ( ( in @ SV175 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(813,plain,
! [SV58: $i,SV176: $i] :
( ( ( in @ SV176 @ ( powerset @ SV58 ) )
= $false )
| ( ( subset @ SV176 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(814,plain,
! [SV177: $i,SV59: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV59 ) )
= $true )
| ( ( ~ ( in @ SV249 @ SV177 )
| ( in @ SV249 @ ( symdiff @ SV59 @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(815,plain,
! [SV60: $i,SV178: $i] :
( ( ~ ( ~ ( in @ SV178 @ ( powerset @ SV60 ) )
| ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV178 )
| ( in @ SY1156 @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(816,plain,
! [SV60: $i,SV178: $i] :
( ( ~ ( ~ ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV178 )
| ( in @ SY1157 @ SV60 ) )
| ( in @ SV178 @ ( powerset @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(817,plain,
! [SV179: $i,SV61: $i,SV250: $i] :
( ( ( ~ ( subset @ SV250 @ SV61 ) )
= $true )
| ( ( ~ ( subset @ SV250 @ SV179 )
| ( subset @ SV250 @ ( binintersect @ SV61 @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(818,plain,
! [SV180: $i,SV62: $i] :
( ( ( ~ ( subset @ SV62 @ SV180 ) )
= $false )
| ( ( SV62 != SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(819,plain,
! [SV63: $i,SV181: $i] :
( ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV181 )
| ( in @ SY1159 @ SV63 ) ) )
= $false )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(820,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) ) )
= $true )
| ( ( ! [SY1261: $o] :
( ~ ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| SY1261 )
| ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SY1261 )
| SY1261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(821,plain,
! [SV183: $i,SV65: $i] :
( ( ( SV65 = SV183 )
= $false )
| ( ( ( powerset @ SV65 )
= ( powerset @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(822,plain,
! [SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV184 )
| ~ ! [SY960: $i] :
~ ~ ( ~ ( SV66 @ SY1162 @ SY960 )
| ~ ! [SY961: $i] :
( ~ ( SV66 @ SY1162 @ SY961 )
| ( SY960 = SY961 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(823,plain,
! [SV185: $i,SV67: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV67 ) )
= $true )
| ( ( ~ ( in @ SV252 @ SV185 )
| ( in @ SV252 @ ( binintersect @ SV67 @ SV185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(824,plain,
! [SV186: $i > $o,SV68: $i] :
( ( ( ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV68 )
| ~ ( SV186 @ SY1170 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(825,plain,
! [SV187: $i > $o,SV71: $i] :
( ( ( ~ ! [SY1172: $i] :
( ~ ( in @ SY1172 @ SV71 )
| ( SV187 @ SY1172 ) ) )
= $false )
| ( ( ~ ! [SY1173: $i] :
~ ~ ( ~ ( in @ SY1173 @ SV71 )
| ~ ~ ( SV187 @ SY1173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(826,plain,
! [SV188: $i,SV72: $i] :
( ( ( SV72 = SV188 )
= $false )
| ( ( ! [SY1174: $i,SY1175: $i] :
( ( SY1174 != SY1175 )
| ~ ( ~ ( ~ ( in @ SY1174 @ SV72 )
| ( in @ SY1175 @ SV188 ) )
| ~ ( ~ ( in @ SY1175 @ SV188 )
| ( in @ SY1174 @ SV72 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(827,plain,
! [SV189: $i,SV73: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV73 ) )
= $true )
| ( ( ~ ~ ( in @ SV253 @ SV189 )
| ~ ( subset @ SV73 @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(828,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ! [SY1177: $i,SY1178: $i] :
( ( SY1177 != SY1178 )
| ~ ( ~ ( ~ ( SV74 @ SY1177 )
| ( SV190 @ SY1178 ) )
| ~ ( ~ ( SV190 @ SY1178 )
| ( SV74 @ SY1177 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(829,plain,
! [SV191: $i,SV75: $i] :
( ( ( subset @ SV75 @ SV191 )
= $false )
| ( ( ( binintersect @ SV75 @ SV191 )
= SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(830,plain,
! [SV76: $i > $o] :
( ( ( ! [SY989: $i] :
~ ( SV76 @ SY989 ) )
= $true )
| ( ( ~ ! [SY990: $i,SY991: $i] :
( ~ ( SV76 @ SY990 )
| ~ ( SV76 @ SY991 )
| ( SY990 = SY991 ) )
| ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(831,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ~ ( ~ ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
| ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
| ~ ( ~ ( ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
| ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(832,plain,
! [SV193: $i,SV255: $i,SV78: $i] :
( ( ( ~ ( subset @ SV78 @ SV255 ) )
= $true )
| ( ( subset @ SV78 @ ( setadjoin @ SV193 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(833,plain,
! [SV79: $i,SV256: $i,SV194: $i] :
( ( ( ~ ( in @ SV194 @ SV256 ) )
= $true )
| ( ( ~ ( in @ SV256 @ SV79 )
| ( in @ SV194 @ ( setunion @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(834,plain,
! [SV195: $i > $o,SV80: $i,SV257: $i] :
( ( ( ~ ( in @ SV257 @ SV80 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) )
| ( SV195 @ SV257 ) )
| ~ ( ~ ( SV195 @ SV257 )
| ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(835,plain,
! [SV196: $i,SV81: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ SV81 ) )
= $true )
| ( ( ~ ~ ( in @ SV258 @ SV196 )
| ( in @ SV258 @ ( symdiff @ SV81 @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(836,plain,
! [SV82: $i] :
( ( ( SV82 = emptyset )
= $true )
| ( ( ~ ! [SY1006: $i] :
~ ( in @ SY1006 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(837,plain,
! [SV197: $i,SV83: $i,SV259: $i] :
( ( ( ~ ( in @ SV259 @ ( setadjoin @ SV83 @ ( setadjoin @ SV197 @ emptyset ) ) ) )
= $true )
| ( ( ( SV259 = SV83 )
| ( SV259 = SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(838,plain,
! [SV84: $i,SV198: $i] :
( ( ( subset @ SV198 @ SV84 )
= $false )
| ( ( ( binintersect @ SV84 @ SV198 )
= SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(839,plain,
! [SV199: $i > $o,SV85: $i] :
( ( ( ~ ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV85 )
| ( SV199 @ SY1193 ) ) )
= $false )
| ( ( ~ ! [SY1194: $i] :
~ ~ ( ~ ( in @ SY1194 @ SV85 )
| ~ ~ ( SV199 @ SY1194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(840,plain,
! [SV260: $i,SV86: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ ( powerset @ SV86 ) ) )
= $true )
| ( ( ~ ( in @ SV260 @ SV200 )
| ( in @ SV260 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(841,plain,
! [SV201: $i,SV87: $i] :
( ( ( in @ SV87 @ ( setadjoin @ SV201 @ emptyset ) )
= $false )
| ( ( SV87 = SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(842,plain,
! [SV202: $i,SV88: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ SV88 ) )
= $true )
| ( ( ~ ( in @ SV261 @ SV202 )
| ~ ( in @ SV261 @ ( symdiff @ SV88 @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(843,plain,
! [SV203: $i,SV89: $i] :
( ( ( ! [SY1197: $i] :
( ~ ( in @ SY1197 @ SV89 )
| ( in @ SY1197 @ SV203 ) ) )
= $false )
| ( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) )
| ( SV89 = SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(844,plain,
! [SV204: $i,SV90: $i,SV262: $i] :
( ( ( ~ ~ ( in @ SV262 @ ( setminus @ SV90 @ SV204 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV262 @ SV204 )
| ~ ( in @ SV262 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(845,plain,
! [SV263: $i,SV205: $i,SV91: $i] :
( ( ( ~ ( subset @ SV91 @ SV205 ) )
= $true )
| ( ( ~ ~ ( in @ SV263 @ SV205 )
| ~ ( in @ SV263 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(846,plain,
! [SV92: $i > $o] :
( ( ( ! [SY1025: $i] :
~ ~ ( ~ ( SV92 @ SY1025 )
| ~ ! [SY1026: $i] :
( ~ ( SV92 @ SY1026 )
| ( SY1025 = SY1026 ) ) ) )
= $true )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(847,plain,
! [SV206: $i,SV93: $i,SV264: $i] :
( ( ( ~ ~ ( in @ SV264 @ ( setminus @ SV93 @ SV206 ) ) )
= $true )
| ( ( ~ ( in @ SV264 @ SV93 )
| ( in @ SV264 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(848,plain,
! [SV207: $i,SV94: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ ( setadjoin @ SV94 @ SV207 ) ) )
= $true )
| ( ( ( SV265 = SV94 )
| ( in @ SV265 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(849,plain,
! [SV208: $i,SV95: $i] :
( ( ( ( binintersect @ SV95 @ SV208 )
= SV208 )
= $false )
| ( ( subset @ SV208 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(850,plain,
! [SV96: $i,SV209: $i] :
( ( ~ ( ~ ( in @ SV209 @ ( setunion @ SV96 ) )
| ~ ! [SY1203: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1203 )
| ~ ( in @ SY1203 @ SV96 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(851,plain,
! [SV96: $i,SV209: $i] :
( ( ~ ( ~ ~ ! [SY1204: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1204 )
| ~ ( in @ SY1204 @ SV96 ) )
| ( in @ SV209 @ ( setunion @ SV96 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(852,plain,
! [SV210: $i,SV97: $i] :
( ( ( SV97 = SV210 )
= $false )
| ( ( ! [SY1205: $i,SY1206: $i] :
( ( SY1205 != SY1206 )
| ( ( setadjoin @ SV97 @ SY1205 )
= ( setadjoin @ SV210 @ SY1206 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(853,plain,
! [SV98: $i] :
( ( ( ~ ( in @ emptyset @ SV98 )
| ~ ! [SY1039: $i] :
( ~ ~ ( ~ ( in @ SY1039 @ omega )
| ~ ( in @ SY1039 @ SV98 ) )
| ( in @ ( setadjoin @ SY1039 @ SY1039 ) @ SV98 ) ) )
= $true )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(854,plain,
! [SV99: $i > $o] :
( ( ( ! [SY1041: $i] :
~ ~ ( ~ ( SV99 @ SY1041 )
| ~ ! [SY1042: $i] :
( ~ ( SV99 @ SY1042 )
| ( SY1041 = SY1042 ) ) ) )
= $true )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(855,plain,
! [SV211: $i,SV100: $i] :
( ( ( ! [SY1207: $i] :
~ ( ~ ( ~ ( in @ SY1207 @ SV100 )
| ( in @ SY1207 @ SV211 ) )
| ~ ( ~ ( in @ SY1207 @ SV211 )
| ( in @ SY1207 @ SV100 ) ) ) )
= $false )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(856,plain,
! [SV101: $i,SV212: $i] :
( ( ( subset @ SV212 @ SV101 )
= $false )
| ( ( in @ SV212 @ ( powerset @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(857,plain,
! [SV102: $i] :
( ( ( ! [SY1048: $i] :
~ ( in @ SY1048 @ SV102 ) )
= $true )
| ( ( SV102 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(858,plain,
! [SV103: $i,SV213: $i,SV266: $i] :
( ( ( ~ ( in @ SV266 @ SV213 ) )
= $true )
| ( ( ~ ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(859,plain,
! [SV214: $i > $o,SV104: $i] :
( ( ( ! [SY1209: $i] :
( ~ ( in @ SY1209 @ SV104 )
| ~ ( SV214 @ SY1209 ) ) )
= $false )
| ( ( ~ ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(860,plain,
! [SV215: $i,SV105: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( binunion @ SV105 @ SV215 ) ) )
= $true )
| ( ( ( in @ SV267 @ SV105 )
| ( in @ SV267 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(861,plain,
! [SV216: $i,SV106: $i] :
( ( ( ( binintersect @ SV106 @ SV216 )
= SV106 )
= $false )
| ( ( subset @ SV106 @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(862,plain,
! [SV217: $i > $o,SV107: $i] :
( ( ( ~ ! [SY1212: $i] :
~ ~ ( ~ ( in @ SY1212 @ SV107 )
| ~ ~ ( SV217 @ SY1212 ) ) )
= $false )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(863,plain,
! [SV108: $i > $o] :
( ( ( ! [SY1060: $i] :
~ ! [SY1061: $i] :
~ ( ~ ( ~ ( SV108 @ SY1061 )
| ( SY1061 = SY1060 ) )
| ~ ( ( SY1061 != SY1060 )
| ( SV108 @ SY1061 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(864,plain,
! [SV218: $i > $o,SV109: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ SV109 ) )
= $true )
| ( ( ~ ( SV218 @ SV268 )
| ( ( dsetconstr @ SV109
@ ^ [SY1215: $i] : ( SV218 @ SY1215 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(865,plain,
! [SV110: $i > $o] :
( ( ( ! [SY1067: $i] :
~ ~ ( ~ ( SV110 @ SY1067 )
| ~ ! [SY1068: $i] :
( ~ ( SV110 @ SY1068 )
| ( SY1067 = SY1068 ) ) ) )
= $true )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(866,plain,
! [SV219: $i,SV111: $i] :
( ( ( subset @ SV111 @ SV219 )
= $false )
| ( ( ( setminus @ SV111 @ SV219 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(867,plain,
! [SV112: $i > $o] :
( ( ( ! [SY1072: $i] :
~ ~ ( ~ ( SV112 @ SY1072 )
| ~ ! [SY1073: $i] :
( ~ ( SV112 @ SY1073 )
| ( SY1072 = SY1073 ) ) ) )
= $true )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(868,plain,
! [SV113: $i,SV220: $i] :
( ( ~ ~ ( ~ ( in @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1268: $i] :
~ ~ ( ~ ( in @ SY1268 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ SY1268 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[754]) ).
thf(869,plain,
! [SV221: $i,SV114: $i] :
( ( ( subset @ SV114 @ SV221 )
= $false )
| ( ( ~ ( subset @ SV221 @ SV114 )
| ( SV114 = SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(870,plain,
! [SV222: $i > $o,SV115: $i,SV269: $i] :
( ( ( ~ ( in @ SV269
@ ( dsetconstr @ SV115
@ ^ [SY1219: $i] : ( SV222 @ SY1219 ) ) ) )
= $true )
| ( ( in @ SV269 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(871,plain,
! [SV223: $i,SV116: $i] :
( ( ( ! [SY1220: $i] :
( ~ ( in @ SY1220 @ SV116 )
| ( in @ SY1220 @ SV223 ) ) )
= $false )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(872,plain,
! [SV117: $i > $o,SV224: $i] :
( ( ( in @ SV224 @ emptyset )
= $false )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(873,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1221: $i,SY1222: $i] :
( ( SY1221 != SY1222 )
| ~ ( ~ ( ~ ( SV118 @ SY1221 )
| ( SV225 @ SY1222 ) )
| ~ ( ~ ( SV225 @ SY1222 )
| ( SV118 @ SY1221 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(874,plain,
! [SV276: $o,SV226: $i,SV120: $i,SV270: $i] :
( ( ~ ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
| ~ ( ~ ( in @ SV270 @ SV120 )
| SV276 )
| ~ ( ~ ( in @ SV270 @ SV226 )
| SV276 )
| SV276 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[761]) ).
thf(876,plain,
! [SV226: $i,SV120: $i,SV270: $i] :
( ( ~ ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
| ~ ( ~ ( in @ SV270 @ SV120 )
| $false )
| ~ ( ~ ( in @ SV270 @ SV226 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[761]) ).
thf(877,plain,
! [SV121: $i,SV227: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV227 ) )
= $true )
| ( ( in @ SV271 @ ( setadjoin @ SV121 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(878,plain,
! [SV122: $i,SV228: $i] :
( ( ( in @ SV228 @ SV122 )
= $false )
| ( ( in @ SV228 @ ( powerset @ ( setunion @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(879,plain,
! [SV229: $i,SV123: $i] :
( ( ( in @ SV123 @ ( setadjoin @ SV229 @ emptyset ) )
= $false )
| ( ( in @ SV229 @ ( setadjoin @ SV123 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(880,plain,
! [SV230: $i,SV124: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ ( setminus @ SV124 @ SV230 ) ) )
= $true )
| ( ( in @ SV272 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(881,plain,
! [SV231: $i,SV125: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) ) )
= $true )
| ( ( ! [SY1267: $o] :
( ~ ( ( SV273 != SV125 )
| SY1267 )
| ~ ( ~ ( in @ SV273 @ SV231 )
| SY1267 )
| SY1267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(882,plain,
! [SV126: $i] :
( ( ( SV126 = emptyset )
= $true )
| ( ( ~ ! [SY1109: $i] :
~ ~ ( ~ ( in @ SY1109 @ SV126 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(883,plain,
! [SV232: $i,SV127: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV127 ) )
= $true )
| ( ( ~ ~ ( in @ SV274 @ SV232 )
| ( in @ SV274 @ ( setminus @ SV127 @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(884,plain,
! [SV128: $i > $o] :
( ( ( ! [SY1112: $i] :
~ ~ ( ~ ( SV128 @ SY1112 )
| ~ ! [SY1113: $i] :
( ~ ( SV128 @ SY1113 )
| ( SY1112 = SY1113 ) ) ) )
= $true )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[769]) ).
thf(885,plain,
! [SV233: $i > $o,SV130: $i] :
( ( ( ~ ~ ! [SY1238: $i] :
~ ~ ( ~ ( in @ SY1238 @ SV130 )
| ~ ( SV233 @ SY1238 ) ) )
= $false )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(886,plain,
! [SV234: $i,SV131: $i] :
( ( ( subset @ SV131 @ SV234 )
= $false )
| ( ( in @ SV131 @ ( powerset @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(887,plain,
! [SV235: $i,SV132: $i] :
( ( ( subset @ SV132 @ SV235 )
= $false )
| ( ( subset @ ( powerset @ SV132 ) @ ( powerset @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(888,plain,
! [SV277: $o,SV25: $i,SV149: $i] :
( ( ( ~ ! [SY1269: $i] :
( ~ ( in @ SV149 @ SY1269 )
| ~ ( in @ SY1269 @ SV25 )
| SV277 )
| SV277 )
= $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[776]) ).
thf(890,plain,
! [SV25: $i,SV149: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV149 @ SX0 )
| ~ ( in @ SX0 @ SV25 )
| $false )
| $false )
= $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[776]) ).
thf(891,plain,
! [SV150: $i > $o,SV26: $i,SV237: $i] :
( ( ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) )
= $false )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(892,plain,
! [SV27: $i,SV151: $i,SV238: $i] :
( ( ( in @ SV238 @ SV151 )
= $false )
| ( ( in @ SV238 @ ( binunion @ SV27 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(893,plain,
! [SV153: $i > $o,SV29: $i,SV239: $i] :
( ( ( in @ SV239 @ SV29 )
= $false )
| ( ( ~ ( SV153 @ SV239 )
| ( in @ SV239
@ ( dsetconstr @ SV29
@ ^ [SY1130: $i] : ( SV153 @ SY1130 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(894,plain,
! [SV240: $i,SV154: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV154 )
= $false )
| ( ( ~ ( subset @ SV154 @ SV240 )
| ( subset @ SV30 @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(895,plain,
! [SV32: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ~ ( ~ ( in @ SY1247 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1248 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1247 )
| ( in @ SX4 @ SY1248 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1248 )
| ( in @ SX4 @ SY1247 ) ) ) )
| ~ ! [SY1251: $i] :
( ~ ~ ( ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SY1251 )
| ( in @ SY885 @ SV32 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1251 ) )
| ~ ! [SY1254: $i] :
~ ~ ! [SY1255: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1254 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1255 @ SY1251 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1254 )
| ~ ( in @ SX5 @ SY1251 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1254 ) )
| ( in @ SY1255 @ SY1257 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(896,plain,
! [SV33: $i] :
( ( ( in @ ( sK4_SY892 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(897,plain,
! [SV155: $i,SV34: $i,SV241: $i] :
( ( ( in @ SV241 @ ( binintersect @ SV34 @ SV155 ) )
= $false )
| ( ( in @ SV241 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(898,plain,
! [SV278: $i] :
( ( ~ ~ ( ~ ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( in @ SY1270 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1270 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(899,plain,
! [SV156: $i,SV35: $i,SV242: $i] :
( ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false )
| ( ( ~ ( in @ SV242 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(900,plain,
! [SV158: $i,SV37: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV37 ) )
= $false )
| ( ( ~ ( in @ SV243 @ ( setminus @ SV37 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(901,plain,
! [SV159: $i > $o,SV38: $i] :
( ( ( ~ ! [SY1138: $i] :
~ ~ ( ~ ( in @ SY1138 @ SV38 )
| ~ ( SV159 @ SY1138 ) ) )
= $true )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(902,plain,
! [SV160: $i,SV39: $i] :
( ( ( ~ ! [SY1140: $i] :
~ ~ ( ~ ( in @ SY1140 @ SV39 )
| ~ ( in @ SY1140 @ SV160 ) ) )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(903,plain,
! [SV161: $i,SV40: $i,SV244: $i] :
( ( ( in @ SV244 @ SV40 )
= $false )
| ( ( ~ ~ ( in @ SV244 @ SV161 )
| ( SV40 != SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(904,plain,
! [SV41: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ SV41 ) )
= $true )
| ( ( ~ ! [SY908: $i] :
~ ~ ( ~ ( in @ SY908 @ SV41 )
| ~ ~ ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SY908 )
| ~ ( in @ SY909 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(905,plain,
! [SV162: $i,SV42: $i,SV245: $i] :
( ( ( ~ ( in @ SV245 @ SV42 ) )
= $false )
| ( ( ~ ~ ( in @ SV245 @ SV162 )
| ~ ( in @ SV245 @ ( symdiff @ SV42 @ SV162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(906,plain,
! [SV44: $i,SV163: $i] :
( ( ( ~ ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
| ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV163 ) )
= $false )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[797]) ).
thf(907,plain,
! [SV164: $i,SV45: $i,SV280: $i] :
( ( ( ! [SY1271: $i] :
( ( SV280 != SY1271 )
| ~ ( in @ SV280 @ SV45 )
| ( in @ SY1271 @ SV164 ) ) )
= $true )
| ( ( SV45 = SV164 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(908,plain,
! [SV246: $i,SV165: $i,SV46: $i] :
( ( ( subset @ SV46 @ SV165 )
= $false )
| ( ( ~ ( in @ SV246 @ SV46 )
| ( in @ SV246 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(909,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ~ ~ ( ~ ( SV47 @ SV281 )
| ~ ! [SY1272: $i] :
( ~ ( SV47 @ SY1272 )
| ( SV281 = SY1272 ) ) ) )
= $true )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(910,plain,
! [SV282: $i > $o,SV166: $i,SV48: $i] :
( ( ( ! [SY1273: $i > $o] :
( ~ ! [SY1274: $i] :
( ~ ( in @ SY1274 @ SV48 )
| ! [SY1275: $i] :
( ~ ( in @ SY1275 @ SV166 )
| ( SY1274 != SY1275 )
| ~ ( ~ ( ~ ( SV282 @ SY1274 )
| ( SY1273 @ SY1275 ) )
| ~ ( ~ ( SY1273 @ SY1275 )
| ( SV282 @ SY1274 ) ) ) ) )
| ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SX4: $i] : ( SY1273 @ SX4 ) ) ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(911,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( ~ ~ ( ~ ( SV50 @ SV283 )
| ~ ! [SY1278: $i] :
( ~ ( SV50 @ SY1278 )
| ( SV283 = SY1278 ) ) ) )
= $true )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(912,plain,
! [SV169: $i,SV52: $i,SV247: $i] :
( ( ( in @ SV247 @ ( binintersect @ SV52 @ SV169 ) )
= $false )
| ( ( in @ SV247 @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(913,plain,
! [SV170: $i,SV53: $i,SV248: $i] :
( ( ( in @ SV248 @ SV53 )
= $false )
| ( ( in @ SV248 @ ( binunion @ SV53 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(914,plain,
! [SV55: $i] :
( ( ( in @ ( sK5_SY940 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(915,plain,
! [SV172: $i,SV56: $i] :
( ( ( SV56 = SV172 )
= $true )
| ( ( ~ ( in @ SV172 @ ( setadjoin @ SV56 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(916,plain,
! [SV177: $i,SV59: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV59 ) )
= $false )
| ( ( ~ ( in @ SV249 @ SV177 )
| ( in @ SV249 @ ( symdiff @ SV59 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(917,plain,
! [SV60: $i,SV178: $i] :
( ( ~ ( in @ SV178 @ ( powerset @ SV60 ) )
| ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV178 )
| ( in @ SY1156 @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(918,plain,
! [SV60: $i,SV178: $i] :
( ( ~ ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV178 )
| ( in @ SY1157 @ SV60 ) )
| ( in @ SV178 @ ( powerset @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(919,plain,
! [SV179: $i,SV61: $i,SV250: $i] :
( ( ( subset @ SV250 @ SV61 )
= $false )
| ( ( ~ ( subset @ SV250 @ SV179 )
| ( subset @ SV250 @ ( binintersect @ SV61 @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(920,plain,
! [SV180: $i,SV62: $i] :
( ( ( subset @ SV62 @ SV180 )
= $true )
| ( ( SV62 != SV180 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(921,plain,
! [SV181: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
| ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV63 ) )
= $false )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[819]) ).
thf(922,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false )
| ( ( ! [SY1261: $o] :
( ~ ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| SY1261 )
| ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SY1261 )
| SY1261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(923,plain,
! [SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
| ~ ! [SY1279: $i] :
~ ~ ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1279 )
| ~ ! [SY1280: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1280 )
| ( SY1279 = SY1280 ) ) ) )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[822]) ).
thf(924,plain,
! [SV185: $i,SV67: $i,SV252: $i] :
( ( ( in @ SV252 @ SV67 )
= $false )
| ( ( ~ ( in @ SV252 @ SV185 )
| ( in @ SV252 @ ( binintersect @ SV67 @ SV185 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(925,plain,
! [SV186: $i > $o,SV68: $i] :
( ( ( ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV68 )
| ~ ( SV186 @ SY1170 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(926,plain,
! [SV187: $i > $o,SV71: $i] :
( ( ( ! [SY1172: $i] :
( ~ ( in @ SY1172 @ SV71 )
| ( SV187 @ SY1172 ) ) )
= $true )
| ( ( ~ ! [SY1173: $i] :
~ ~ ( ~ ( in @ SY1173 @ SV71 )
| ~ ~ ( SV187 @ SY1173 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(927,plain,
! [SV188: $i,SV72: $i,SV284: $i] :
( ( ( ! [SY1281: $i] :
( ( SV284 != SY1281 )
| ~ ( ~ ( ~ ( in @ SV284 @ SV72 )
| ( in @ SY1281 @ SV188 ) )
| ~ ( ~ ( in @ SY1281 @ SV188 )
| ( in @ SV284 @ SV72 ) ) ) ) )
= $true )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(928,plain,
! [SV189: $i,SV73: $i,SV253: $i] :
( ( ( in @ SV253 @ SV73 )
= $false )
| ( ( ~ ~ ( in @ SV253 @ SV189 )
| ~ ( subset @ SV73 @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(929,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( ! [SY1282: $i] :
( ( ( sK10_SY1177 @ SV190 @ SV74 )
!= SY1282 )
| ~ ( ~ ( ~ ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
| ( SV190 @ SY1282 ) )
| ~ ( ~ ( SV190 @ SY1282 )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[828]) ).
thf(930,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV285 ) )
= $true )
| ( ( ~ ! [SY990: $i,SY991: $i] :
( ~ ( SV76 @ SY990 )
| ~ ( SV76 @ SY991 )
| ( SY990 = SY991 ) )
| ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(931,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ~ ( ~ ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
| ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(932,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ~ ( ~ ( ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
| ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(933,plain,
! [SV193: $i,SV255: $i,SV78: $i] :
( ( ( subset @ SV78 @ SV255 )
= $false )
| ( ( subset @ SV78 @ ( setadjoin @ SV193 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(934,plain,
! [SV79: $i,SV256: $i,SV194: $i] :
( ( ( in @ SV194 @ SV256 )
= $false )
| ( ( ~ ( in @ SV256 @ SV79 )
| ( in @ SV194 @ ( setunion @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(935,plain,
! [SV195: $i > $o,SV80: $i,SV257: $i] :
( ( ( in @ SV257 @ SV80 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) )
| ( SV195 @ SV257 ) )
| ~ ( ~ ( SV195 @ SV257 )
| ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(936,plain,
! [SV196: $i,SV81: $i,SV258: $i] :
( ( ( in @ SV258 @ SV81 )
= $false )
| ( ( ~ ~ ( in @ SV258 @ SV196 )
| ( in @ SV258 @ ( symdiff @ SV81 @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(937,plain,
! [SV82: $i] :
( ( ( ! [SY1006: $i] :
~ ( in @ SY1006 @ SV82 ) )
= $false )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(938,plain,
! [SV197: $i,SV83: $i,SV259: $i] :
( ( ( in @ SV259 @ ( setadjoin @ SV83 @ ( setadjoin @ SV197 @ emptyset ) ) )
= $false )
| ( ( ( SV259 = SV83 )
| ( SV259 = SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(939,plain,
! [SV199: $i > $o,SV85: $i] :
( ( ( ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV85 )
| ( SV199 @ SY1193 ) ) )
= $true )
| ( ( ~ ! [SY1194: $i] :
~ ~ ( ~ ( in @ SY1194 @ SV85 )
| ~ ~ ( SV199 @ SY1194 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(940,plain,
! [SV260: $i,SV86: $i,SV200: $i] :
( ( ( in @ SV200 @ ( powerset @ SV86 ) )
= $false )
| ( ( ~ ( in @ SV260 @ SV200 )
| ( in @ SV260 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(941,plain,
! [SV202: $i,SV88: $i,SV261: $i] :
( ( ( in @ SV261 @ SV88 )
= $false )
| ( ( ~ ( in @ SV261 @ SV202 )
| ~ ( in @ SV261 @ ( symdiff @ SV88 @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(942,plain,
! [SV89: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 )
| ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV203 ) )
= $false )
| ( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) )
| ( SV89 = SV203 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[843]) ).
thf(943,plain,
! [SV204: $i,SV90: $i,SV262: $i] :
( ( ( ~ ( in @ SV262 @ ( setminus @ SV90 @ SV204 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV262 @ SV204 )
| ~ ( in @ SV262 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(944,plain,
! [SV263: $i,SV205: $i,SV91: $i] :
( ( ( subset @ SV91 @ SV205 )
= $false )
| ( ( ~ ~ ( in @ SV263 @ SV205 )
| ~ ( in @ SV263 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(945,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ~ ~ ( ~ ( SV92 @ SV286 )
| ~ ! [SY1283: $i] :
( ~ ( SV92 @ SY1283 )
| ( SV286 = SY1283 ) ) ) )
= $true )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(946,plain,
! [SV206: $i,SV93: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ ( setminus @ SV93 @ SV206 ) ) )
= $false )
| ( ( ~ ( in @ SV264 @ SV93 )
| ( in @ SV264 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(947,plain,
! [SV207: $i,SV94: $i,SV265: $i] :
( ( ( in @ SV265 @ ( setadjoin @ SV94 @ SV207 ) )
= $false )
| ( ( ( SV265 = SV94 )
| ( in @ SV265 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(948,plain,
! [SV96: $i,SV209: $i] :
( ( ~ ( in @ SV209 @ ( setunion @ SV96 ) )
| ~ ! [SY1203: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1203 )
| ~ ( in @ SY1203 @ SV96 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(949,plain,
! [SV96: $i,SV209: $i] :
( ( ~ ~ ! [SY1204: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1204 )
| ~ ( in @ SY1204 @ SV96 ) )
| ( in @ SV209 @ ( setunion @ SV96 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(950,plain,
! [SV210: $i,SV97: $i,SV287: $i] :
( ( ( ! [SY1284: $i] :
( ( SV287 != SY1284 )
| ( ( setadjoin @ SV97 @ SV287 )
= ( setadjoin @ SV210 @ SY1284 ) ) ) )
= $true )
| ( ( SV97 = SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(951,plain,
! [SV98: $i] :
( ( ( ~ ( in @ emptyset @ SV98 ) )
= $true )
| ( ( ~ ! [SY1039: $i] :
( ~ ~ ( ~ ( in @ SY1039 @ omega )
| ~ ( in @ SY1039 @ SV98 ) )
| ( in @ ( setadjoin @ SY1039 @ SY1039 ) @ SV98 ) ) )
= $true )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(952,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ~ ( ~ ( SV99 @ SV288 )
| ~ ! [SY1285: $i] :
( ~ ( SV99 @ SY1285 )
| ( SV288 = SY1285 ) ) ) )
= $true )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(953,plain,
! [SV100: $i,SV211: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 ) )
| ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) ) ) )
= $false )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[855]) ).
thf(954,plain,
! [SV102: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ SV102 ) )
= $true )
| ( ( SV102 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(955,plain,
! [SV103: $i,SV213: $i,SV266: $i] :
( ( ( in @ SV266 @ SV213 )
= $false )
| ( ( ~ ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(956,plain,
! [SV104: $i,SV214: $i > $o] :
( ( ( ~ ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
| ~ ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) ) )
= $false )
| ( ( ~ ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[859]) ).
thf(957,plain,
! [SV215: $i,SV105: $i,SV267: $i] :
( ( ( in @ SV267 @ ( binunion @ SV105 @ SV215 ) )
= $false )
| ( ( ( in @ SV267 @ SV105 )
| ( in @ SV267 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(958,plain,
! [SV217: $i > $o,SV107: $i] :
( ( ( ! [SY1212: $i] :
~ ~ ( ~ ( in @ SY1212 @ SV107 )
| ~ ~ ( SV217 @ SY1212 ) ) )
= $true )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(959,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ! [SY1286: $i] :
~ ( ~ ( ~ ( SV108 @ SY1286 )
| ( SY1286 = SV290 ) )
| ~ ( ( SY1286 != SV290 )
| ( SV108 @ SY1286 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(960,plain,
! [SV218: $i > $o,SV109: $i,SV268: $i] :
( ( ( in @ SV268 @ SV109 )
= $false )
| ( ( ~ ( SV218 @ SV268 )
| ( ( dsetconstr @ SV109
@ ^ [SY1215: $i] : ( SV218 @ SY1215 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(961,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( ~ ~ ( ~ ( SV110 @ SV291 )
| ~ ! [SY1287: $i] :
( ~ ( SV110 @ SY1287 )
| ( SV291 = SY1287 ) ) ) )
= $true )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(962,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ~ ( ~ ( SV112 @ SV292 )
| ~ ! [SY1288: $i] :
( ~ ( SV112 @ SY1288 )
| ( SV292 = SY1288 ) ) ) )
= $true )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(963,plain,
! [SV113: $i,SV220: $i] :
( ( ~ ( ~ ( in @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1268: $i] :
~ ~ ( ~ ( in @ SY1268 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ SY1268 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(964,plain,
! [SV114: $i,SV221: $i] :
( ( ( ~ ( subset @ SV221 @ SV114 ) )
= $true )
| ( ( SV114 = SV221 )
= $true )
| ( ( subset @ SV114 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(965,plain,
! [SV222: $i > $o,SV115: $i,SV269: $i] :
( ( ( in @ SV269
@ ( dsetconstr @ SV115
@ ^ [SY1219: $i] : ( SV222 @ SY1219 ) ) )
= $false )
| ( ( in @ SV269 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(966,plain,
! [SV116: $i,SV223: $i] :
( ( ( ~ ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
| ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV223 ) )
= $false )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[871]) ).
thf(967,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1289: $i] :
( ( ( sK15_SY1221 @ SV225 @ SV118 )
!= SY1289 )
| ~ ( ~ ( ~ ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
| ( SV225 @ SY1289 ) )
| ~ ( ~ ( SV225 @ SY1289 )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[873]) ).
thf(968,plain,
! [SV276: $o,SV226: $i,SV120: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV270 @ SV120 )
| SV276 )
| ~ ( ~ ( in @ SV270 @ SV226 )
| SV276 )
| SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(970,plain,
! [SV226: $i,SV120: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV270 @ SV120 )
| $false )
| ~ ( ~ ( in @ SV270 @ SV226 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(971,plain,
! [SV121: $i,SV227: $i,SV271: $i] :
( ( ( in @ SV271 @ SV227 )
= $false )
| ( ( in @ SV271 @ ( setadjoin @ SV121 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(972,plain,
! [SV230: $i,SV124: $i,SV272: $i] :
( ( ( in @ SV272 @ ( setminus @ SV124 @ SV230 ) )
= $false )
| ( ( in @ SV272 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(973,plain,
! [SV231: $i,SV125: $i,SV273: $i] :
( ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false )
| ( ( ! [SY1267: $o] :
( ~ ( ( SV273 != SV125 )
| SY1267 )
| ~ ( ~ ( in @ SV273 @ SV231 )
| SY1267 )
| SY1267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(974,plain,
! [SV126: $i] :
( ( ( ! [SY1109: $i] :
~ ~ ( ~ ( in @ SY1109 @ SV126 )
| ~ $true ) )
= $false )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(975,plain,
! [SV232: $i,SV127: $i,SV274: $i] :
( ( ( in @ SV274 @ SV127 )
= $false )
| ( ( ~ ~ ( in @ SV274 @ SV232 )
| ( in @ SV274 @ ( setminus @ SV127 @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(976,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( ~ ~ ( ~ ( SV128 @ SV293 )
| ~ ! [SY1290: $i] :
( ~ ( SV128 @ SY1290 )
| ( SV293 = SY1290 ) ) ) )
= $true )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(977,plain,
! [SV233: $i > $o,SV130: $i] :
( ( ( ~ ! [SY1238: $i] :
~ ~ ( ~ ( in @ SY1238 @ SV130 )
| ~ ( SV233 @ SY1238 ) ) )
= $true )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(978,plain,
! [SV277: $o,SV25: $i,SV149: $i] :
( ( ( ~ ! [SY1269: $i] :
( ~ ( in @ SV149 @ SY1269 )
| ~ ( in @ SY1269 @ SV25 )
| SV277 ) )
= $true )
| ( SV277 = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(980,plain,
! [SV25: $i,SV149: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV149 @ SX0 )
| ~ ( in @ SX0 @ SV25 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(981,plain,
! [SV29: $i,SV239: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV239 ) )
= $true )
| ( ( in @ SV239
@ ( dsetconstr @ SV29
@ ^ [SY1130: $i] : ( SV153 @ SY1130 ) ) )
= $true )
| ( ( in @ SV239 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(982,plain,
! [SV30: $i,SV240: $i,SV154: $i] :
( ( ( ~ ( subset @ SV154 @ SV240 ) )
= $true )
| ( ( subset @ SV30 @ SV240 )
= $true )
| ( ( subset @ SV30 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(983,plain,
! [SV32: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ~ ( ~ ( in @ SY1247 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1248 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1247 )
| ( in @ SX4 @ SY1248 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1248 )
| ( in @ SX4 @ SY1247 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(984,plain,
! [SV32: $i] :
( ( ~ ! [SY1251: $i] :
( ~ ~ ( ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SY1251 )
| ( in @ SY885 @ SV32 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1251 ) )
| ~ ! [SY1254: $i] :
~ ~ ! [SY1255: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1254 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1255 @ SY1251 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1254 )
| ~ ( in @ SX5 @ SY1251 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1254 ) )
| ( in @ SY1255 @ SY1257 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(985,plain,
! [SV278: $i] :
( ( ~ ( ~ ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( in @ SY1270 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1270 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(986,plain,
! [SV35: $i,SV156: $i,SV242: $i] :
( ( ( in @ SV242 @ SV156 )
= $false )
| ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(987,plain,
! [SV158: $i,SV37: $i,SV243: $i] :
( ( ( in @ SV243 @ SV37 )
= $true )
| ( ( ~ ( in @ SV243 @ ( setminus @ SV37 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(988,plain,
! [SV159: $i > $o,SV38: $i] :
( ( ( ! [SY1138: $i] :
~ ~ ( ~ ( in @ SY1138 @ SV38 )
| ~ ( SV159 @ SY1138 ) ) )
= $false )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(989,plain,
! [SV160: $i,SV39: $i] :
( ( ( ! [SY1140: $i] :
~ ~ ( ~ ( in @ SY1140 @ SV39 )
| ~ ( in @ SY1140 @ SV160 ) ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(990,plain,
! [SV40: $i,SV161: $i,SV244: $i] :
( ( ( ~ ~ ( in @ SV244 @ SV161 ) )
= $true )
| ( ( SV40 != SV161 )
= $true )
| ( ( in @ SV244 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(991,plain,
! [SV41: $i,SV279: $i] :
( ( ( in @ SV279 @ SV41 )
= $false )
| ( ( ~ ! [SY908: $i] :
~ ~ ( ~ ( in @ SY908 @ SV41 )
| ~ ~ ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SY908 )
| ~ ( in @ SY909 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(992,plain,
! [SV162: $i,SV42: $i,SV245: $i] :
( ( ( in @ SV245 @ SV42 )
= $true )
| ( ( ~ ~ ( in @ SV245 @ SV162 )
| ~ ( in @ SV245 @ ( symdiff @ SV42 @ SV162 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(993,plain,
! [SV44: $i,SV163: $i] :
( ( ( ~ ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 ) )
= $false )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(994,plain,
! [SV44: $i,SV163: $i] :
( ( ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV163 )
= $false )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(995,plain,
! [SV164: $i,SV45: $i,SV294: $i,SV280: $i] :
( ( ( ( SV280 != SV294 )
| ~ ( in @ SV280 @ SV45 )
| ( in @ SV294 @ SV164 ) )
= $true )
| ( ( SV45 = SV164 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(996,plain,
! [SV165: $i,SV46: $i,SV246: $i] :
( ( ( ~ ( in @ SV246 @ SV46 ) )
= $true )
| ( ( in @ SV246 @ SV165 )
= $true )
| ( ( subset @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(997,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ SV281 )
| ~ ! [SY1272: $i] :
( ~ ( SV47 @ SY1272 )
| ( SV281 = SY1272 ) ) ) )
= $false )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(998,plain,
! [SV295: $i > $o,SV282: $i > $o,SV166: $i,SV48: $i] :
( ( ( ~ ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV48 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV166 )
| ( SY1291 != SY1292 )
| ~ ( ~ ( ~ ( SV282 @ SY1291 )
| ( SV295 @ SY1292 ) )
| ~ ( ~ ( SV295 @ SY1292 )
| ( SV282 @ SY1291 ) ) ) ) )
| ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(999,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ SV283 )
| ~ ! [SY1278: $i] :
( ~ ( SV50 @ SY1278 )
| ( SV283 = SY1278 ) ) ) )
= $false )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1000,plain,
! [SV56: $i,SV172: $i] :
( ( ( in @ SV172 @ ( setadjoin @ SV56 @ emptyset ) )
= $false )
| ( ( SV56 = SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(1001,plain,
! [SV177: $i,SV59: $i,SV249: $i] :
( ( ( in @ SV249 @ SV59 )
= $true )
| ( ( ~ ( in @ SV249 @ SV177 )
| ( in @ SV249 @ ( symdiff @ SV59 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(1002,plain,
! [SV60: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ ( powerset @ SV60 ) ) )
= $true )
| ( ( ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV178 )
| ( in @ SY1156 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1003,plain,
! [SV60: $i,SV178: $i] :
( ( ( ~ ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV178 )
| ( in @ SY1157 @ SV60 ) ) )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1004,plain,
! [SV61: $i,SV179: $i,SV250: $i] :
( ( ( ~ ( subset @ SV250 @ SV179 ) )
= $true )
| ( ( subset @ SV250 @ ( binintersect @ SV61 @ SV179 ) )
= $true )
| ( ( subset @ SV250 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1005,plain,
! [SV180: $i,SV62: $i] :
( ( ( SV62 = SV180 )
= $false )
| ( ( subset @ SV62 @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1006,plain,
! [SV181: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 ) )
= $false )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[921]) ).
thf(1007,plain,
! [SV181: $i,SV63: $i] :
( ( ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV63 )
= $false )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[921]) ).
thf(1008,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| SV296 )
| ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[922]) ).
thf(1010,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| $false )
| ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[922]) ).
thf(1011,plain,
! [SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 ) )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(1012,plain,
! [SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ! [SY1279: $i] :
~ ~ ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1279 )
| ~ ! [SY1280: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1280 )
| ( SY1279 = SY1280 ) ) ) )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(1013,plain,
! [SV67: $i,SV185: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV185 ) )
= $true )
| ( ( in @ SV252 @ ( binintersect @ SV67 @ SV185 ) )
= $true )
| ( ( in @ SV252 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1014,plain,
! [SV186: $i > $o,SV68: $i,SV297: $i] :
( ( ( ~ ~ ( ~ ( in @ SV297 @ SV68 )
| ~ ( SV186 @ SV297 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1015,plain,
! [SV187: $i > $o,SV71: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV71 )
| ( SV187 @ SV298 ) )
= $true )
| ( ( ~ ! [SY1173: $i] :
~ ~ ( ~ ( in @ SY1173 @ SV71 )
| ~ ~ ( SV187 @ SY1173 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1016,plain,
! [SV188: $i,SV72: $i,SV299: $i,SV284: $i] :
( ( ( ( SV284 != SV299 )
| ~ ( ~ ( ~ ( in @ SV284 @ SV72 )
| ( in @ SV299 @ SV188 ) )
| ~ ( ~ ( in @ SV299 @ SV188 )
| ( in @ SV284 @ SV72 ) ) ) )
= $true )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1017,plain,
! [SV73: $i,SV189: $i,SV253: $i] :
( ( ( ~ ~ ( in @ SV253 @ SV189 ) )
= $true )
| ( ( ~ ( subset @ SV73 @ SV189 ) )
= $true )
| ( ( in @ SV253 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1018,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( ( ( sK10_SY1177 @ SV190 @ SV74 )
!= ( sK16_SY1282 @ SV74 @ SV190 ) )
| ~ ( ~ ( ~ ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
| ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) ) )
| ~ ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[929]) ).
thf(1019,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( SV76 @ SV285 )
= $false )
| ( ( ~ ! [SY990: $i,SY991: $i] :
( ~ ( SV76 @ SY990 )
| ~ ( SV76 @ SY991 )
| ( SY990 = SY991 ) )
| ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1020,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ~ ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
| ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(1021,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ~ ( ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
| ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(1022,plain,
! [SV194: $i,SV79: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ SV79 ) )
= $true )
| ( ( in @ SV194 @ ( setunion @ SV79 ) )
= $true )
| ( ( in @ SV194 @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1023,plain,
! [SV195: $i > $o,SV80: $i,SV257: $i] :
( ( ( ~ ( ~ ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) )
| ( SV195 @ SV257 ) )
| ~ ( ~ ( SV195 @ SV257 )
| ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) ) ) )
= $false )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1024,plain,
! [SV81: $i,SV196: $i,SV258: $i] :
( ( ( ~ ~ ( in @ SV258 @ SV196 ) )
= $true )
| ( ( in @ SV258 @ ( symdiff @ SV81 @ SV196 ) )
= $true )
| ( ( in @ SV258 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1025,plain,
! [SV82: $i] :
( ( ( ~ ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 ) )
= $false )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[937]) ).
thf(1026,plain,
! [SV197: $i,SV83: $i,SV259: $i] :
( ( ( SV259 = SV83 )
= $true )
| ( ( SV259 = SV197 )
= $true )
| ( ( in @ SV259 @ ( setadjoin @ SV83 @ ( setadjoin @ SV197 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1027,plain,
! [SV199: $i > $o,SV85: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV85 )
| ( SV199 @ SV300 ) )
= $true )
| ( ( ~ ! [SY1194: $i] :
~ ~ ( ~ ( in @ SY1194 @ SV85 )
| ~ ~ ( SV199 @ SY1194 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1028,plain,
! [SV86: $i,SV200: $i,SV260: $i] :
( ( ( ~ ( in @ SV260 @ SV200 ) )
= $true )
| ( ( in @ SV260 @ SV86 )
= $true )
| ( ( in @ SV200 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1029,plain,
! [SV88: $i,SV202: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ SV202 ) )
= $true )
| ( ( ~ ( in @ SV261 @ ( symdiff @ SV88 @ SV202 ) ) )
= $true )
| ( ( in @ SV261 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1030,plain,
! [SV89: $i,SV203: $i] :
( ( ( ~ ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) )
| ( SV89 = SV203 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1031,plain,
! [SV89: $i,SV203: $i] :
( ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV203 )
= $false )
| ( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) )
| ( SV89 = SV203 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1032,plain,
! [SV204: $i,SV90: $i,SV262: $i] :
( ( ( in @ SV262 @ ( setminus @ SV90 @ SV204 ) )
= $true )
| ( ( ~ ~ ( in @ SV262 @ SV204 )
| ~ ( in @ SV262 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1033,plain,
! [SV91: $i,SV205: $i,SV263: $i] :
( ( ( ~ ~ ( in @ SV263 @ SV205 ) )
= $true )
| ( ( ~ ( in @ SV263 @ SV91 ) )
= $true )
| ( ( subset @ SV91 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1034,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ~ ( ~ ( SV92 @ SV286 )
| ~ ! [SY1283: $i] :
( ~ ( SV92 @ SY1283 )
| ( SV286 = SY1283 ) ) ) )
= $false )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1035,plain,
! [SV206: $i,SV93: $i,SV264: $i] :
( ( ( in @ SV264 @ ( setminus @ SV93 @ SV206 ) )
= $true )
| ( ( ~ ( in @ SV264 @ SV93 )
| ( in @ SV264 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(1036,plain,
! [SV207: $i,SV94: $i,SV265: $i] :
( ( ( SV265 = SV94 )
= $true )
| ( ( in @ SV265 @ SV207 )
= $true )
| ( ( in @ SV265 @ ( setadjoin @ SV94 @ SV207 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1037,plain,
! [SV96: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ ( setunion @ SV96 ) ) )
= $true )
| ( ( ~ ! [SY1203: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1203 )
| ~ ( in @ SY1203 @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1038,plain,
! [SV96: $i,SV209: $i] :
( ( ( ~ ~ ! [SY1204: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1204 )
| ~ ( in @ SY1204 @ SV96 ) ) )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1039,plain,
! [SV210: $i,SV97: $i,SV301: $i,SV287: $i] :
( ( ( ( SV287 != SV301 )
| ( ( setadjoin @ SV97 @ SV287 )
= ( setadjoin @ SV210 @ SV301 ) ) )
= $true )
| ( ( SV97 = SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1040,plain,
! [SV98: $i] :
( ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ~ ! [SY1039: $i] :
( ~ ~ ( ~ ( in @ SY1039 @ omega )
| ~ ( in @ SY1039 @ SV98 ) )
| ( in @ ( setadjoin @ SY1039 @ SY1039 ) @ SV98 ) ) )
= $true )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1041,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( ~ ( SV99 @ SV288 )
| ~ ! [SY1285: $i] :
( ~ ( SV99 @ SY1285 )
| ( SV288 = SY1285 ) ) ) )
= $false )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1042,plain,
! [SV100: $i,SV211: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 ) )
| ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(1043,plain,
! [SV102: $i,SV289: $i] :
( ( ( in @ SV289 @ SV102 )
= $false )
| ( ( SV102 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1044,plain,
! [SV213: $i,SV103: $i,SV266: $i] :
( ( ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
= $false )
| ( ( in @ SV266 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1045,plain,
! [SV104: $i,SV214: $i > $o] :
( ( ( ~ ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 ) )
= $false )
| ( ( ~ ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(1046,plain,
! [SV104: $i,SV214: $i > $o] :
( ( ( ~ ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) ) )
= $false )
| ( ( ~ ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(1047,plain,
! [SV215: $i,SV105: $i,SV267: $i] :
( ( ( in @ SV267 @ SV105 )
= $true )
| ( ( in @ SV267 @ SV215 )
= $true )
| ( ( in @ SV267 @ ( binunion @ SV105 @ SV215 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1048,plain,
! [SV217: $i > $o,SV107: $i,SV302: $i] :
( ( ( ~ ~ ( ~ ( in @ SV302 @ SV107 )
| ~ ~ ( SV217 @ SV302 ) ) )
= $true )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1049,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ! [SY1286: $i] :
~ ( ~ ( ~ ( SV108 @ SY1286 )
| ( SY1286 = SV290 ) )
| ~ ( ( SY1286 != SV290 )
| ( SV108 @ SY1286 ) ) ) )
= $false )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1050,plain,
! [SV109: $i,SV268: $i,SV218: $i > $o] :
( ( ( ~ ( SV218 @ SV268 ) )
= $true )
| ( ( ( dsetconstr @ SV109
@ ^ [SY1215: $i] : ( SV218 @ SY1215 ) )
!= emptyset )
= $true )
| ( ( in @ SV268 @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1051,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( ~ ( ~ ( SV110 @ SV291 )
| ~ ! [SY1287: $i] :
( ~ ( SV110 @ SY1287 )
| ( SV291 = SY1287 ) ) ) )
= $false )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1052,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( ~ ( SV112 @ SV292 )
| ~ ! [SY1288: $i] :
( ~ ( SV112 @ SY1288 )
| ( SV292 = SY1288 ) ) ) )
= $false )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1053,plain,
! [SV113: $i,SV220: $i] :
( ( ~ ( in @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1268: $i] :
~ ~ ( ~ ( in @ SY1268 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ SY1268 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1054,plain,
! [SV114: $i,SV221: $i] :
( ( ( subset @ SV221 @ SV114 )
= $false )
| ( ( SV114 = SV221 )
= $true )
| ( ( subset @ SV114 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1055,plain,
! [SV116: $i,SV223: $i] :
( ( ( ~ ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 ) )
= $false )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(1056,plain,
! [SV116: $i,SV223: $i] :
( ( ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV223 )
= $false )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(1057,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ( ( sK15_SY1221 @ SV225 @ SV118 )
!= ( sK18_SY1289 @ SV118 @ SV225 ) )
| ~ ( ~ ( ~ ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
| ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) ) )
| ~ ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[967]) ).
thf(1058,plain,
! [SV276: $o,SV226: $i,SV120: $i,SV270: $i] :
( ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV270 @ SV120 )
| SV276 )
| ~ ( ~ ( in @ SV270 @ SV226 )
| SV276 )
| SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1060,plain,
! [SV226: $i,SV120: $i,SV270: $i] :
( ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV270 @ SV120 )
| $false )
| ~ ( ~ ( in @ SV270 @ SV226 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1061,plain,
! [SV231: $i,SV303: $o,SV125: $i,SV273: $i] :
( ( ( ~ ( ( SV273 != SV125 )
| SV303 )
| ~ ( ~ ( in @ SV273 @ SV231 )
| SV303 )
| SV303 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[973]) ).
thf(1063,plain,
! [SV231: $i,SV125: $i,SV273: $i] :
( ( ( ~ ( ( SV273 != SV125 )
| $false )
| ~ ( ~ ( in @ SV273 @ SV231 )
| $false )
| $false )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[973]) ).
thf(1064,plain,
! [SV126: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
| ~ $true ) )
= $false )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[974]) ).
thf(1065,plain,
! [SV127: $i,SV232: $i,SV274: $i] :
( ( ( ~ ~ ( in @ SV274 @ SV232 ) )
= $true )
| ( ( in @ SV274 @ ( setminus @ SV127 @ SV232 ) )
= $true )
| ( ( in @ SV274 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1066,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( ~ ( ~ ( SV128 @ SV293 )
| ~ ! [SY1290: $i] :
( ~ ( SV128 @ SY1290 )
| ( SV293 = SY1290 ) ) ) )
= $false )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1067,plain,
! [SV233: $i > $o,SV130: $i] :
( ( ( ! [SY1238: $i] :
~ ~ ( ~ ( in @ SY1238 @ SV130 )
| ~ ( SV233 @ SY1238 ) ) )
= $false )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1068,plain,
! [SV277: $o,SV25: $i,SV149: $i] :
( ( ( ! [SY1269: $i] :
( ~ ( in @ SV149 @ SY1269 )
| ~ ( in @ SY1269 @ SV25 )
| SV277 ) )
= $false )
| ( SV277 = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1070,plain,
! [SV25: $i,SV149: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV149 @ SX0 )
| ~ ( in @ SX0 @ SV25 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1071,plain,
! [SV29: $i,SV239: $i,SV153: $i > $o] :
( ( ( SV153 @ SV239 )
= $false )
| ( ( in @ SV239
@ ( dsetconstr @ SV29
@ ^ [SY1130: $i] : ( SV153 @ SY1130 ) ) )
= $true )
| ( ( in @ SV239 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1072,plain,
! [SV30: $i,SV240: $i,SV154: $i] :
( ( ( subset @ SV154 @ SV240 )
= $false )
| ( ( subset @ SV30 @ SV240 )
= $true )
| ( ( subset @ SV30 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1073,plain,
! [SV32: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ~ ( ~ ( in @ SY1247 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1248 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1247 )
| ( in @ SX4 @ SY1248 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1248 )
| ( in @ SX4 @ SY1247 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1074,plain,
! [SV32: $i] :
( ( ! [SY1251: $i] :
( ~ ~ ( ~ ! [SY885: $i] :
( ~ ( in @ SY885 @ SY1251 )
| ( in @ SY885 @ SV32 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1251 ) )
| ~ ! [SY1254: $i] :
~ ~ ! [SY1255: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1254 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1255 @ SY1251 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1254 )
| ~ ( in @ SX5 @ SY1251 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1254 ) )
| ( in @ SY1255 @ SY1257 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1075,plain,
! [SV278: $i] :
( ( ~ ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( in @ SY1270 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1270 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1076,plain,
! [SV158: $i,SV37: $i,SV243: $i] :
( ( ( in @ SV243 @ ( setminus @ SV37 @ SV158 ) )
= $false )
| ( ( in @ SV243 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1077,plain,
! [SV38: $i,SV159: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 )
| ~ ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) ) ) )
= $false )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[988]) ).
thf(1078,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 ) ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[989]) ).
thf(1079,plain,
! [SV40: $i,SV161: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV161 ) )
= $false )
| ( ( SV40 != SV161 )
= $true )
| ( ( in @ SV244 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1080,plain,
! [SV279: $i,SV41: $i] :
( ( ( ! [SY908: $i] :
~ ~ ( ~ ( in @ SY908 @ SV41 )
| ~ ~ ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SY908 )
| ~ ( in @ SY909 @ SV41 ) ) ) )
= $false )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1081,plain,
! [SV42: $i,SV162: $i,SV245: $i] :
( ( ( ~ ~ ( in @ SV245 @ SV162 ) )
= $true )
| ( ( ~ ( in @ SV245 @ ( symdiff @ SV42 @ SV162 ) ) )
= $true )
| ( ( in @ SV245 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1082,plain,
! [SV44: $i,SV163: $i] :
( ( ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
= $true )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1083,plain,
! [SV164: $i,SV45: $i,SV294: $i,SV280: $i] :
( ( ( SV280 != SV294 )
= $true )
| ( ( ~ ( in @ SV280 @ SV45 )
| ( in @ SV294 @ SV164 ) )
= $true )
| ( ( SV45 = SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1084,plain,
! [SV165: $i,SV46: $i,SV246: $i] :
( ( ( in @ SV246 @ SV46 )
= $false )
| ( ( in @ SV246 @ SV165 )
= $true )
| ( ( subset @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1085,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV281 )
| ~ ! [SY1272: $i] :
( ~ ( SV47 @ SY1272 )
| ( SV281 = SY1272 ) ) )
= $true )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1086,plain,
! [SV295: $i > $o,SV282: $i > $o,SV166: $i,SV48: $i] :
( ( ( ~ ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV48 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV166 )
| ( SY1291 != SY1292 )
| ~ ( ~ ( ~ ( SV282 @ SY1291 )
| ( SV295 @ SY1292 ) )
| ~ ( ~ ( SV295 @ SY1292 )
| ( SV282 @ SY1291 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1087,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV283 )
| ~ ! [SY1278: $i] :
( ~ ( SV50 @ SY1278 )
| ( SV283 = SY1278 ) ) )
= $true )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1088,plain,
! [SV59: $i,SV177: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV177 ) )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV59 @ SV177 ) )
= $true )
| ( ( in @ SV249 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1089,plain,
! [SV60: $i,SV178: $i] :
( ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $false )
| ( ( ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV178 )
| ( in @ SY1156 @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1090,plain,
! [SV60: $i,SV178: $i] :
( ( ( ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV178 )
| ( in @ SY1157 @ SV60 ) ) )
= $false )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1091,plain,
! [SV61: $i,SV179: $i,SV250: $i] :
( ( ( subset @ SV250 @ SV179 )
= $false )
| ( ( subset @ SV250 @ ( binintersect @ SV61 @ SV179 ) )
= $true )
| ( ( subset @ SV250 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1092,plain,
! [SV181: $i,SV63: $i] :
( ( ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
= $true )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1093,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| SV296 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1095,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1096,plain,
! [SV184: $i,SV66: $i > $i > $o] :
( ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1097,plain,
! [SV184: $i,SV66: $i > $i > $o] :
( ( ( ! [SY1279: $i] :
~ ~ ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1279 )
| ~ ! [SY1280: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1280 )
| ( SY1279 = SY1280 ) ) ) )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1098,plain,
! [SV67: $i,SV185: $i,SV252: $i] :
( ( ( in @ SV252 @ SV185 )
= $false )
| ( ( in @ SV252 @ ( binintersect @ SV67 @ SV185 ) )
= $true )
| ( ( in @ SV252 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1099,plain,
! [SV186: $i > $o,SV68: $i,SV297: $i] :
( ( ( ~ ( ~ ( in @ SV297 @ SV68 )
| ~ ( SV186 @ SV297 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1100,plain,
! [SV187: $i > $o,SV71: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV71 ) )
= $true )
| ( ( SV187 @ SV298 )
= $true )
| ( ( ~ ! [SY1173: $i] :
~ ~ ( ~ ( in @ SY1173 @ SV71 )
| ~ ~ ( SV187 @ SY1173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1101,plain,
! [SV188: $i,SV72: $i,SV299: $i,SV284: $i] :
( ( ( SV284 != SV299 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV284 @ SV72 )
| ( in @ SV299 @ SV188 ) )
| ~ ( ~ ( in @ SV299 @ SV188 )
| ( in @ SV284 @ SV72 ) ) ) )
= $true )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1102,plain,
! [SV73: $i,SV189: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV189 ) )
= $false )
| ( ( ~ ( subset @ SV73 @ SV189 ) )
= $true )
| ( ( in @ SV253 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1103,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( ( sK10_SY1177 @ SV190 @ SV74 )
!= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1104,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
| ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) ) )
| ~ ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1105,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ! [SY990: $i,SY991: $i] :
( ~ ( SV76 @ SY990 )
| ~ ( SV76 @ SY991 )
| ( SY990 = SY991 ) ) )
= $true )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1106,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) ) )
= $true )
| ( ( ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1107,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ( ~ ( ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) ) )
= $true )
| ( ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1108,plain,
! [SV194: $i,SV79: $i,SV256: $i] :
( ( ( in @ SV256 @ SV79 )
= $false )
| ( ( in @ SV194 @ ( setunion @ SV79 ) )
= $true )
| ( ( in @ SV194 @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1109,plain,
! [SV195: $i > $o,SV80: $i,SV257: $i] :
( ( ( ~ ( ~ ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) )
| ( SV195 @ SV257 ) ) )
= $false )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1110,plain,
! [SV80: $i,SV257: $i,SV195: $i > $o] :
( ( ( ~ ( ~ ( SV195 @ SV257 )
| ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) ) ) )
= $false )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1111,plain,
! [SV81: $i,SV196: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ SV196 ) )
= $false )
| ( ( in @ SV258 @ ( symdiff @ SV81 @ SV196 ) )
= $true )
| ( ( in @ SV258 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1112,plain,
! [SV82: $i] :
( ( ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1113,plain,
! [SV199: $i > $o,SV85: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV85 ) )
= $true )
| ( ( SV199 @ SV300 )
= $true )
| ( ( ~ ! [SY1194: $i] :
~ ~ ( ~ ( in @ SY1194 @ SV85 )
| ~ ~ ( SV199 @ SY1194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1114,plain,
! [SV86: $i,SV200: $i,SV260: $i] :
( ( ( in @ SV260 @ SV200 )
= $false )
| ( ( in @ SV260 @ SV86 )
= $true )
| ( ( in @ SV200 @ ( powerset @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1115,plain,
! [SV88: $i,SV202: $i,SV261: $i] :
( ( ( in @ SV261 @ SV202 )
= $false )
| ( ( ~ ( in @ SV261 @ ( symdiff @ SV88 @ SV202 ) ) )
= $true )
| ( ( in @ SV261 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1116,plain,
! [SV89: $i,SV203: $i] :
( ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 )
= $true )
| ( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) )
| ( SV89 = SV203 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1117,plain,
! [SV89: $i,SV203: $i] :
( ( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) ) )
= $true )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1118,plain,
! [SV90: $i,SV204: $i,SV262: $i] :
( ( ( ~ ~ ( in @ SV262 @ SV204 ) )
= $true )
| ( ( ~ ( in @ SV262 @ SV90 ) )
= $true )
| ( ( in @ SV262 @ ( setminus @ SV90 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1119,plain,
! [SV91: $i,SV205: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV205 ) )
= $false )
| ( ( ~ ( in @ SV263 @ SV91 ) )
= $true )
| ( ( subset @ SV91 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1120,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ~ ( SV92 @ SV286 )
| ~ ! [SY1283: $i] :
( ~ ( SV92 @ SY1283 )
| ( SV286 = SY1283 ) ) )
= $true )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1121,plain,
! [SV206: $i,SV93: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ SV93 ) )
= $true )
| ( ( in @ SV264 @ SV206 )
= $true )
| ( ( in @ SV264 @ ( setminus @ SV93 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1122,plain,
! [SV96: $i,SV209: $i] :
( ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false )
| ( ( ~ ! [SY1203: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1203 )
| ~ ( in @ SY1203 @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1123,plain,
! [SV96: $i,SV209: $i] :
( ( ( ~ ! [SY1204: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1204 )
| ~ ( in @ SY1204 @ SV96 ) ) )
= $false )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1124,plain,
! [SV210: $i,SV97: $i,SV301: $i,SV287: $i] :
( ( ( SV287 != SV301 )
= $true )
| ( ( ( setadjoin @ SV97 @ SV287 )
= ( setadjoin @ SV210 @ SV301 ) )
= $true )
| ( ( SV97 = SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1125,plain,
! [SV98: $i] :
( ( ( ! [SY1039: $i] :
( ~ ~ ( ~ ( in @ SY1039 @ omega )
| ~ ( in @ SY1039 @ SV98 ) )
| ( in @ ( setadjoin @ SY1039 @ SY1039 ) @ SV98 ) ) )
= $false )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1126,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ SV288 )
| ~ ! [SY1285: $i] :
( ~ ( SV99 @ SY1285 )
| ( SV288 = SY1285 ) ) )
= $true )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1127,plain,
! [SV100: $i,SV211: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1128,plain,
! [SV289: $i,SV102: $i] :
( ( ( SV102 = emptyset )
= $false )
| ( ( in @ SV289 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1129,plain,
! [SV104: $i,SV214: $i > $o] :
( ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true )
| ( ( ~ ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1130,plain,
! [SV104: $i,SV214: $i > $o] :
( ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true )
| ( ( ~ ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1131,plain,
! [SV217: $i > $o,SV107: $i,SV302: $i] :
( ( ( ~ ( ~ ( in @ SV302 @ SV107 )
| ~ ~ ( SV217 @ SV302 ) ) )
= $false )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1132,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
| ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 ) )
| ~ ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1049]) ).
thf(1133,plain,
! [SV109: $i,SV268: $i,SV218: $i > $o] :
( ( ( SV218 @ SV268 )
= $false )
| ( ( ( dsetconstr @ SV109
@ ^ [SY1215: $i] : ( SV218 @ SY1215 ) )
!= emptyset )
= $true )
| ( ( in @ SV268 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1134,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ SV291 )
| ~ ! [SY1287: $i] :
( ~ ( SV110 @ SY1287 )
| ( SV291 = SY1287 ) ) )
= $true )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1051]) ).
thf(1135,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ SV292 )
| ~ ! [SY1288: $i] :
( ~ ( SV112 @ SY1288 )
| ( SV292 = SY1288 ) ) )
= $true )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1136,plain,
! [SV113: $i,SV220: $i] :
( ( ~ ( in @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1137,plain,
! [SV220: $i,SV113: $i] :
( ( ~ ~ ! [SY1268: $i] :
~ ~ ( ~ ( in @ SY1268 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ SY1268 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1138,plain,
! [SV116: $i,SV223: $i] :
( ( ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
= $true )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1139,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ( sK15_SY1221 @ SV225 @ SV118 )
!= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1140,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
| ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) ) )
| ~ ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1141,plain,
! [SV226: $i,SV276: $o,SV120: $i,SV270: $i] :
( ( ( ~ ( ~ ( in @ SV270 @ SV120 )
| SV276 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| SV276 )
| SV276 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1143,plain,
! [SV226: $i,SV120: $i,SV270: $i] :
( ( ( ~ ( ~ ( in @ SV270 @ SV120 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| $false )
| $false )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1144,plain,
! [SV231: $i,SV303: $o,SV125: $i,SV273: $i] :
( ( ( ~ ( ( SV273 != SV125 )
| SV303 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| SV303 )
| SV303 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1146,plain,
! [SV231: $i,SV125: $i,SV273: $i] :
( ( ( ~ ( ( SV273 != SV125 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| $false )
| $false )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1147,plain,
! [SV126: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
| ~ $true ) )
= $true )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1148,plain,
! [SV127: $i,SV232: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV232 ) )
= $false )
| ( ( in @ SV274 @ ( setminus @ SV127 @ SV232 ) )
= $true )
| ( ( in @ SV274 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1149,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ SV293 )
| ~ ! [SY1290: $i] :
( ~ ( SV128 @ SY1290 )
| ( SV293 = SY1290 ) ) )
= $true )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1150,plain,
! [SV130: $i,SV233: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 )
| ~ ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) ) ) )
= $false )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1067]) ).
thf(1151,plain,
! [SV25: $i,SV277: $o,SV149: $i] :
( ( ( ~ ( in @ SV149 @ ( sK24_SY1269 @ SV277 @ SV25 @ SV149 ) )
| ~ ( in @ ( sK24_SY1269 @ SV277 @ SV25 @ SV149 ) @ SV25 )
| SV277 )
= $false )
| ( SV277 = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1068]) ).
thf(1153,plain,
! [SV25: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ ( sK26_SX0 @ SV25 @ SV149 ) )
| ~ ( in @ ( sK26_SX0 @ SV25 @ SV149 ) @ SV25 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1070]) ).
thf(1154,plain,
! [SV32: $i] :
( ( ~ ~ ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
| ~ ! [SY1247: $i,SY1248: $i] :
( ~ ~ ( ~ ( in @ SY1247 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1248 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1247 )
| ( in @ SX4 @ SY1248 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1248 )
| ( in @ SX4 @ SY1247 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1155,plain,
! [SV32: $i,SV304: $i] :
( ( ~ ~ ( ~ ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV304 )
| ( in @ SY1295 @ SV32 ) )
| ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
| ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1156,plain,
! [SV278: $i] :
( ( ( ~ ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( in @ SY1270 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1270 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1157,plain,
! [SV38: $i,SV159: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 )
| ~ ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) ) ) )
= $true )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1158,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 ) ) )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1159,plain,
! [SV40: $i,SV161: $i,SV244: $i] :
( ( ( in @ SV244 @ SV161 )
= $true )
| ( ( SV40 != SV161 )
= $true )
| ( ( in @ SV244 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1160,plain,
! [SV41: $i,SV279: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY908 @ SV279 @ SV41 ) @ SV41 )
| ~ ~ ~ ! [SY1302: $i] :
~ ~ ( ~ ( in @ SY1302 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SY1302 @ SV41 ) ) ) )
= $false )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1080]) ).
thf(1161,plain,
! [SV42: $i,SV162: $i,SV245: $i] :
( ( ( ~ ( in @ SV245 @ SV162 ) )
= $false )
| ( ( ~ ( in @ SV245 @ ( symdiff @ SV42 @ SV162 ) ) )
= $true )
| ( ( in @ SV245 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1162,plain,
! [SV164: $i,SV45: $i,SV294: $i,SV280: $i] :
( ( ( SV280 = SV294 )
= $false )
| ( ( ~ ( in @ SV280 @ SV45 )
| ( in @ SV294 @ SV164 ) )
= $true )
| ( ( SV45 = SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1163,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV281 ) )
= $true )
| ( ( ~ ! [SY1272: $i] :
( ~ ( SV47 @ SY1272 )
| ( SV281 = SY1272 ) ) )
= $true )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1164,plain,
! [SV295: $i > $o,SV282: $i > $o,SV166: $i,SV48: $i] :
( ( ( ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV48 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV166 )
| ( SY1291 != SY1292 )
| ~ ( ~ ( ~ ( SV282 @ SY1291 )
| ( SV295 @ SY1292 ) )
| ~ ( ~ ( SV295 @ SY1292 )
| ( SV282 @ SY1291 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1165,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV283 ) )
= $true )
| ( ( ~ ! [SY1278: $i] :
( ~ ( SV50 @ SY1278 )
| ( SV283 = SY1278 ) ) )
= $true )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1166,plain,
! [SV59: $i,SV177: $i,SV249: $i] :
( ( ( in @ SV249 @ SV177 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV59 @ SV177 ) )
= $true )
| ( ( in @ SV249 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1167,plain,
! [SV60: $i,SV178: $i,SV305: $i] :
( ( ( ~ ( in @ SV305 @ SV178 )
| ( in @ SV305 @ SV60 ) )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1168,plain,
! [SV178: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
| ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV60 ) )
= $false )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1090]) ).
thf(1169,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| SV296 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1171,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV64 )
| ~ ~ ( in @ SV251 @ SV182 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1172,plain,
! [SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1173,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
| ~ ! [SY1303: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1303 )
| ( SV306 = SY1303 ) ) ) )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1174,plain,
! [SV186: $i > $o,SV68: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ SV68 )
| ~ ( SV186 @ SV297 ) )
= $true )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1175,plain,
! [SV187: $i > $o,SV71: $i,SV298: $i] :
( ( ( in @ SV298 @ SV71 )
= $false )
| ( ( SV187 @ SV298 )
= $true )
| ( ( ~ ! [SY1173: $i] :
~ ~ ( ~ ( in @ SY1173 @ SV71 )
| ~ ~ ( SV187 @ SY1173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1176,plain,
! [SV188: $i,SV72: $i,SV299: $i,SV284: $i] :
( ( ( SV284 = SV299 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV284 @ SV72 )
| ( in @ SV299 @ SV188 ) )
| ~ ( ~ ( in @ SV299 @ SV188 )
| ( in @ SV284 @ SV72 ) ) ) )
= $true )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1177,plain,
! [SV73: $i,SV189: $i,SV253: $i] :
( ( ( in @ SV253 @ SV189 )
= $true )
| ( ( ~ ( subset @ SV73 @ SV189 ) )
= $true )
| ( ( in @ SV253 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1178,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1179,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( ~ ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
| ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) ) )
| ~ ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1180,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ! [SY990: $i,SY991: $i] :
( ~ ( SV76 @ SY990 )
| ~ ( SV76 @ SY991 )
| ( SY990 = SY991 ) ) )
= $false )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1181,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
= $false )
| ( ( ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1182,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ( ( SV254 = SV77 )
| ( in @ SV254 @ SV192 ) )
= $false )
| ( ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1183,plain,
! [SV195: $i > $o,SV80: $i,SV257: $i] :
( ( ( ~ ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) )
| ( SV195 @ SV257 ) )
= $true )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1184,plain,
! [SV80: $i,SV257: $i,SV195: $i > $o] :
( ( ( ~ ( SV195 @ SV257 )
| ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) ) )
= $true )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1185,plain,
! [SV81: $i,SV196: $i,SV258: $i] :
( ( ( in @ SV258 @ SV196 )
= $true )
| ( ( in @ SV258 @ ( symdiff @ SV81 @ SV196 ) )
= $true )
| ( ( in @ SV258 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1186,plain,
! [SV199: $i > $o,SV85: $i,SV300: $i] :
( ( ( in @ SV300 @ SV85 )
= $false )
| ( ( SV199 @ SV300 )
= $true )
| ( ( ~ ! [SY1194: $i] :
~ ~ ( ~ ( in @ SY1194 @ SV85 )
| ~ ~ ( SV199 @ SY1194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1187,plain,
! [SV202: $i,SV88: $i,SV261: $i] :
( ( ( in @ SV261 @ ( symdiff @ SV88 @ SV202 ) )
= $false )
| ( ( in @ SV261 @ SV202 )
= $false )
| ( ( in @ SV261 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1188,plain,
! [SV89: $i,SV203: $i] :
( ( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) ) )
= $true )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1189,plain,
! [SV89: $i,SV203: $i] :
( ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) ) )
= $false )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1190,plain,
! [SV90: $i,SV204: $i,SV262: $i] :
( ( ( ~ ( in @ SV262 @ SV204 ) )
= $false )
| ( ( ~ ( in @ SV262 @ SV90 ) )
= $true )
| ( ( in @ SV262 @ ( setminus @ SV90 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1191,plain,
! [SV91: $i,SV205: $i,SV263: $i] :
( ( ( in @ SV263 @ SV205 )
= $true )
| ( ( ~ ( in @ SV263 @ SV91 ) )
= $true )
| ( ( subset @ SV91 @ SV205 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1192,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ~ ( SV92 @ SV286 ) )
= $true )
| ( ( ~ ! [SY1283: $i] :
( ~ ( SV92 @ SY1283 )
| ( SV286 = SY1283 ) ) )
= $true )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1193,plain,
! [SV206: $i,SV93: $i,SV264: $i] :
( ( ( in @ SV264 @ SV93 )
= $false )
| ( ( in @ SV264 @ SV206 )
= $true )
| ( ( in @ SV264 @ ( setminus @ SV93 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1194,plain,
! [SV96: $i,SV209: $i] :
( ( ( ! [SY1203: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1203 )
| ~ ( in @ SY1203 @ SV96 ) ) )
= $false )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1195,plain,
! [SV96: $i,SV209: $i] :
( ( ( ! [SY1204: $i] :
~ ~ ( ~ ( in @ SV209 @ SY1204 )
| ~ ( in @ SY1204 @ SV96 ) ) )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1196,plain,
! [SV210: $i,SV97: $i,SV301: $i,SV287: $i] :
( ( ( SV287 = SV301 )
= $false )
| ( ( ( setadjoin @ SV97 @ SV287 )
= ( setadjoin @ SV210 @ SV301 ) )
= $true )
| ( ( SV97 = SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1197,plain,
! [SV98: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY1039 @ SV98 ) @ omega )
| ~ ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 ) )
| ( in @ ( setadjoin @ ( sK29_SY1039 @ SV98 ) @ ( sK29_SY1039 @ SV98 ) ) @ SV98 ) )
= $false )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1125]) ).
thf(1198,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ SV288 ) )
= $true )
| ( ( ~ ! [SY1285: $i] :
( ~ ( SV99 @ SY1285 )
| ( SV288 = SY1285 ) ) )
= $true )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1199,plain,
! [SV100: $i,SV211: $i] :
( ( ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1200,plain,
! [SV214: $i > $o,SV104: $i] :
( ( ( ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $false )
| ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1201,plain,
! [SV214: $i > $o,SV104: $i] :
( ( ( ~ ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $false )
| ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1202,plain,
! [SV217: $i > $o,SV107: $i,SV302: $i] :
( ( ( ~ ( in @ SV302 @ SV107 )
| ~ ~ ( SV217 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1203,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( ~ ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
| ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 ) )
| ~ ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1132]) ).
thf(1204,plain,
! [SV268: $i,SV218: $i > $o,SV109: $i] :
( ( ( ( dsetconstr @ SV109
@ ^ [SY1215: $i] : ( SV218 @ SY1215 ) )
= emptyset )
= $false )
| ( ( SV218 @ SV268 )
= $false )
| ( ( in @ SV268 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1205,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ SV291 ) )
= $true )
| ( ( ~ ! [SY1287: $i] :
( ~ ( SV110 @ SY1287 )
| ( SV291 = SY1287 ) ) )
= $true )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1206,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ SV292 ) )
= $true )
| ( ( ~ ! [SY1288: $i] :
( ~ ( SV112 @ SY1288 )
| ( SV292 = SY1288 ) ) )
= $true )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1207,plain,
! [SV113: $i,SV220: $i] :
( ( in @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1208,plain,
! [SV220: $i,SV113: $i] :
( ( ~ ! [SY1268: $i] :
~ ~ ( ~ ( in @ SY1268 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ SY1268 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1209,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1210,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
| ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) ) )
| ~ ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1211,plain,
! [SV226: $i,SV276: $o,SV120: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV120 )
| SV276 )
= $false )
| ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| SV276 )
| SV276 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1213,plain,
! [SV226: $i,SV120: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV120 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| $false )
| $false )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1214,plain,
! [SV231: $i,SV303: $o,SV125: $i,SV273: $i] :
( ( ( ( SV273 != SV125 )
| SV303 )
= $false )
| ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| SV303 )
| SV303 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1216,plain,
! [SV231: $i,SV125: $i,SV273: $i] :
( ( ( ( SV273 != SV125 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| $false )
| $false )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1217,plain,
! [SV126: $i] :
( ( ( ~ ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
| ~ $true )
= $false )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1218,plain,
! [SV127: $i,SV232: $i,SV274: $i] :
( ( ( in @ SV274 @ SV232 )
= $true )
| ( ( in @ SV274 @ ( setminus @ SV127 @ SV232 ) )
= $true )
| ( ( in @ SV274 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1219,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ SV293 ) )
= $true )
| ( ( ~ ! [SY1290: $i] :
( ~ ( SV128 @ SY1290 )
| ( SV293 = SY1290 ) ) )
= $true )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1220,plain,
! [SV130: $i,SV233: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 )
| ~ ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) ) ) )
= $true )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1221,plain,
! [SV25: $i,SV277: $o,SV149: $i] :
( ( ( ~ ( in @ SV149 @ ( sK24_SY1269 @ SV277 @ SV25 @ SV149 ) ) )
= $false )
| ( SV277 = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1151]) ).
thf(1222,plain,
! [SV149: $i,SV25: $i,SV277: $o] :
( ( ( ~ ( in @ ( sK24_SY1269 @ SV277 @ SV25 @ SV149 ) @ SV25 )
| SV277 )
= $false )
| ( SV277 = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1151]) ).
thf(1225,plain,
! [SV25: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ ( sK26_SX0 @ SV25 @ SV149 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1153]) ).
thf(1226,plain,
! [SV149: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK26_SX0 @ SV25 @ SV149 ) @ SV25 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1153]) ).
thf(1227,plain,
! [SV32: $i] :
( ( ~ ~ ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1228,plain,
! [SV32: $i] :
( ( ~ ! [SY1247: $i,SY1248: $i] :
( ~ ~ ( ~ ( in @ SY1247 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1248 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1247 )
| ( in @ SX4 @ SY1248 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1248 )
| ( in @ SX4 @ SY1247 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1229,plain,
! [SV32: $i,SV304: $i] :
( ( ( ~ ~ ( ~ ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV304 )
| ( in @ SY1295 @ SV32 ) )
| ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1230,plain,
! [SV278: $i] :
( ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( in @ SY1270 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1270 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1231,plain,
! [SV38: $i,SV159: $i > $o] :
( ( ( ~ ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 )
| ~ ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) ) )
= $false )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1232,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
| ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1233,plain,
! [SV244: $i,SV161: $i,SV40: $i] :
( ( ( SV40 = SV161 )
= $false )
| ( ( in @ SV244 @ SV161 )
= $true )
| ( ( in @ SV244 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1234,plain,
! [SV41: $i,SV279: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_SY908 @ SV279 @ SV41 ) @ SV41 )
| ~ ~ ~ ! [SY1302: $i] :
~ ~ ( ~ ( in @ SY1302 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SY1302 @ SV41 ) ) ) )
= $true )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1235,plain,
! [SV42: $i,SV162: $i,SV245: $i] :
( ( ( in @ SV245 @ SV162 )
= $true )
| ( ( ~ ( in @ SV245 @ ( symdiff @ SV42 @ SV162 ) ) )
= $true )
| ( ( in @ SV245 @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1236,plain,
! [SV164: $i,SV294: $i,SV45: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ SV45 ) )
= $true )
| ( ( in @ SV294 @ SV164 )
= $true )
| ( ( SV280 = SV294 )
= $false )
| ( ( SV45 = SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1237,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( SV47 @ SV281 )
= $false )
| ( ( ~ ! [SY1272: $i] :
( ~ ( SV47 @ SY1272 )
| ( SV281 = SY1272 ) ) )
= $true )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1238,plain,
! [SV48: $i,SV166: $i,SV282: $i > $o,SV295: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) @ SV48 )
| ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV166 )
| ( ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 )
!= SY1304 )
| ~ ( ~ ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
| ( SV295 @ SY1304 ) )
| ~ ( ~ ( SV295 @ SY1304 )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1164]) ).
thf(1239,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( SV50 @ SV283 )
= $false )
| ( ( ~ ! [SY1278: $i] :
( ~ ( SV50 @ SY1278 )
| ( SV283 = SY1278 ) ) )
= $true )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1240,plain,
! [SV60: $i,SV178: $i,SV305: $i] :
( ( ( ~ ( in @ SV305 @ SV178 ) )
= $true )
| ( ( in @ SV305 @ SV60 )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1241,plain,
! [SV178: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 ) )
= $false )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1242,plain,
! [SV178: $i,SV60: $i] :
( ( ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV60 )
= $false )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1243,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV64 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1244,plain,
! [SV64: $i,SV296: $o,SV182: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV182 )
| SV296 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1247,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV64 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1248,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV182 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1249,plain,
! [SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ! [SY1305: $i] :
~ ( ~ ( ~ ( in @ SY1305 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1305 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1305 ) )
| ( in @ SY1305 @ ( sK31_SY1165 @ SV66 @ SV184 ) ) ) ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1172]) ).
thf(1250,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
| ~ ! [SY1303: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1303 )
| ( SV306 = SY1303 ) ) ) )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1251,plain,
! [SV186: $i > $o,SV68: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ SV68 ) )
= $true )
| ( ( ~ ( SV186 @ SV297 ) )
= $true )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1252,plain,
! [SV298: $i,SV187: $i > $o,SV71: $i] :
( ( ( ! [SY1173: $i] :
~ ~ ( ~ ( in @ SY1173 @ SV71 )
| ~ ~ ( SV187 @ SY1173 ) ) )
= $false )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1253,plain,
! [SV188: $i,SV299: $i,SV72: $i,SV284: $i] :
( ( ( ~ ( ~ ( in @ SV284 @ SV72 )
| ( in @ SV299 @ SV188 ) )
| ~ ( ~ ( in @ SV299 @ SV188 )
| ( in @ SV284 @ SV72 ) ) )
= $false )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1254,plain,
! [SV253: $i,SV189: $i,SV73: $i] :
( ( ( subset @ SV73 @ SV189 )
= $false )
| ( ( in @ SV253 @ SV189 )
= $true )
| ( ( in @ SV253 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1255,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1256,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( ~ ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
| ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1257,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ! [SY1308: $i] :
( ~ ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
| ~ ( SV76 @ SY1308 )
| ( ( sK32_SY990 @ SV285 @ SV76 )
= SY1308 ) ) )
= $false )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1180]) ).
thf(1258,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ( SV254 = SV77 )
= $true )
| ( ( in @ SV254 @ SV192 )
= $true )
| ( ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1259,plain,
! [SV192: $i,SV77: $i,SV254: $i] :
( ( ( SV254 = SV77 )
= $false )
| ( ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1260,plain,
! [SV77: $i,SV192: $i,SV254: $i] :
( ( ( in @ SV254 @ SV192 )
= $false )
| ( ( in @ SV254 @ ( setadjoin @ SV77 @ SV192 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1261,plain,
! [SV195: $i > $o,SV80: $i,SV257: $i] :
( ( ( ~ ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) ) )
= $true )
| ( ( SV195 @ SV257 )
= $true )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1262,plain,
! [SV80: $i,SV257: $i,SV195: $i > $o] :
( ( ( ~ ( SV195 @ SV257 ) )
= $true )
| ( ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) )
= $true )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1263,plain,
! [SV300: $i,SV199: $i > $o,SV85: $i] :
( ( ( ! [SY1194: $i] :
~ ~ ( ~ ( in @ SY1194 @ SV85 )
| ~ ~ ( SV199 @ SY1194 ) ) )
= $false )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1264,plain,
! [SV89: $i,SV203: $i] :
( ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV203 )
| ( in @ SY1198 @ SV89 ) ) )
= $false )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1265,plain,
! [SV203: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK33_SY1198 @ SV89 @ SV203 ) @ SV203 )
| ( in @ ( sK33_SY1198 @ SV89 @ SV203 ) @ SV89 ) )
= $false )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV203 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1189]) ).
thf(1266,plain,
! [SV90: $i,SV204: $i,SV262: $i] :
( ( ( in @ SV262 @ SV204 )
= $true )
| ( ( ~ ( in @ SV262 @ SV90 ) )
= $true )
| ( ( in @ SV262 @ ( setminus @ SV90 @ SV204 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1267,plain,
! [SV205: $i,SV91: $i,SV263: $i] :
( ( ( in @ SV263 @ SV91 )
= $false )
| ( ( in @ SV263 @ SV205 )
= $true )
| ( ( subset @ SV91 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1268,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( SV92 @ SV286 )
= $false )
| ( ( ~ ! [SY1283: $i] :
( ~ ( SV92 @ SY1283 )
| ( SV286 = SY1283 ) ) )
= $true )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1269,plain,
! [SV96: $i,SV209: $i] :
( ( ( ~ ~ ( ~ ( in @ SV209 @ ( sK34_SY1203 @ SV96 @ SV209 ) )
| ~ ( in @ ( sK34_SY1203 @ SV96 @ SV209 ) @ SV96 ) ) )
= $false )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1194]) ).
thf(1270,plain,
! [SV96: $i,SV307: $i,SV209: $i] :
( ( ( ~ ~ ( ~ ( in @ SV209 @ SV307 )
| ~ ( in @ SV307 @ SV96 ) ) )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1271,plain,
! [SV98: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY1039 @ SV98 ) @ omega )
| ~ ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 ) ) )
= $false )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1272,plain,
! [SV98: $i] :
( ( ( in @ ( setadjoin @ ( sK29_SY1039 @ SV98 ) @ ( sK29_SY1039 @ SV98 ) ) @ SV98 )
= $false )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1273,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( SV99 @ SV288 )
= $false )
| ( ( ~ ! [SY1285: $i] :
( ~ ( SV99 @ SY1285 )
| ( SV288 = SY1285 ) ) )
= $true )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1274,plain,
! [SV100: $i,SV211: $i] :
( ( ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1275,plain,
! [SV100: $i,SV211: $i] :
( ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1276,plain,
! [SV214: $i > $o,SV104: $i] :
( ( ( ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true )
| ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1277,plain,
! [SV214: $i > $o,SV104: $i] :
( ( ( ! [SY1210: $i] :
~ ~ ( ~ ( in @ SY1210 @ SV104 )
| ~ ( SV214 @ SY1210 ) ) )
= $true )
| ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1278,plain,
! [SV217: $i > $o,SV107: $i,SV302: $i] :
( ( ( ~ ( in @ SV302 @ SV107 ) )
= $true )
| ( ( ~ ~ ( SV217 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1279,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( ~ ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
| ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 ) ) )
= $true )
| ( ( ~ ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1280,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( SV110 @ SV291 )
= $false )
| ( ( ~ ! [SY1287: $i] :
( ~ ( SV110 @ SY1287 )
| ( SV291 = SY1287 ) ) )
= $true )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1281,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( SV112 @ SV292 )
= $false )
| ( ( ~ ! [SY1288: $i] :
( ~ ( SV112 @ SY1288 )
| ( SV292 = SY1288 ) ) )
= $true )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1282,plain,
! [SV220: $i,SV113: $i] :
( ( ! [SY1268: $i] :
~ ~ ( ~ ( in @ SY1268 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ SY1268 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1283,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1284,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
| ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1285,plain,
! [SV276: $o,SV226: $i,SV120: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV120 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| SV276 )
| SV276 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1211]) ).
thf(1289,plain,
! [SV226: $i,SV120: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV120 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| $false )
| $false )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1213]) ).
thf(1291,plain,
! [SV303: $o,SV231: $i,SV125: $i,SV273: $i] :
( ( ( SV273 != SV125 )
= $false )
| ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| SV303 )
| SV303 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1214]) ).
thf(1295,plain,
! [SV231: $i,SV125: $i,SV273: $i] :
( ( ( SV273 != SV125 )
= $false )
| ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| $false )
| $false )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1297,plain,
! [SV126: $i] :
( ( ( ~ ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 ) )
= $false )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1299,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( SV128 @ SV293 )
= $false )
| ( ( ~ ! [SY1290: $i] :
( ~ ( SV128 @ SY1290 )
| ( SV293 = SY1290 ) ) )
= $true )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1300,plain,
! [SV130: $i,SV233: $i > $o] :
( ( ( ~ ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 )
| ~ ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) ) )
= $false )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1301,plain,
! [SV25: $i,SV277: $o,SV149: $i] :
( ( ( in @ SV149 @ ( sK24_SY1269 @ SV277 @ SV25 @ SV149 ) )
= $true )
| ( SV277 = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1302,plain,
! [SV149: $i,SV25: $i,SV277: $o] :
( ( ( ~ ( in @ ( sK24_SY1269 @ SV277 @ SV25 @ SV149 ) @ SV25 ) )
= $false )
| ( SV277 = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1222]) ).
thf(1307,plain,
! [SV25: $i,SV149: $i] :
( ( ( in @ SV149 @ ( sK26_SX0 @ SV25 @ SV149 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1308,plain,
! [SV149: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK26_SX0 @ SV25 @ SV149 ) @ SV25 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1310,plain,
! [SV32: $i] :
( ( ~ ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1311,plain,
! [SV32: $i] :
( ( ! [SY1247: $i,SY1248: $i] :
( ~ ~ ( ~ ( in @ SY1247 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1248 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1247 )
| ( in @ SX4 @ SY1248 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1248 )
| ( in @ SX4 @ SY1247 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1312,plain,
! [SV32: $i,SV304: $i] :
( ( ( ~ ( ~ ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV304 )
| ( in @ SY1295 @ SV32 ) )
| ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) ) )
= $false )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1313,plain,
! [SV278: $i] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( in @ SY1270 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1270 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1314,plain,
! [SV38: $i,SV159: $i > $o] :
( ( ( ~ ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 ) )
= $false )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1315,plain,
! [SV38: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) ) )
= $false )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1316,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1232]) ).
thf(1317,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1232]) ).
thf(1318,plain,
! [SV41: $i,SV279: $i] :
( ( ( ~ ( in @ ( sK27_SY908 @ SV279 @ SV41 ) @ SV41 )
| ~ ~ ~ ! [SY1302: $i] :
~ ~ ( ~ ( in @ SY1302 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SY1302 @ SV41 ) ) )
= $false )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1319,plain,
! [SV162: $i,SV42: $i,SV245: $i] :
( ( ( in @ SV245 @ ( symdiff @ SV42 @ SV162 ) )
= $false )
| ( ( in @ SV245 @ SV162 )
= $true )
| ( ( in @ SV245 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1320,plain,
! [SV164: $i,SV294: $i,SV45: $i,SV280: $i] :
( ( ( in @ SV280 @ SV45 )
= $false )
| ( ( in @ SV294 @ SV164 )
= $true )
| ( ( SV280 = SV294 )
= $false )
| ( ( SV45 = SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1321,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ! [SY1272: $i] :
( ~ ( SV47 @ SY1272 )
| ( SV281 = SY1272 ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1322,plain,
! [SV48: $i,SV166: $i,SV282: $i > $o,SV295: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) @ SV48 ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1323,plain,
! [SV48: $i,SV282: $i > $o,SV295: $i > $o,SV166: $i] :
( ( ( ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV166 )
| ( ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 )
!= SY1304 )
| ~ ( ~ ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
| ( SV295 @ SY1304 ) )
| ~ ( ~ ( SV295 @ SY1304 )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1324,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( ! [SY1278: $i] :
( ~ ( SV50 @ SY1278 )
| ( SV283 = SY1278 ) ) )
= $false )
| ( ( SV50 @ SV283 )
= $false )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1325,plain,
! [SV60: $i,SV178: $i,SV305: $i] :
( ( ( in @ SV305 @ SV178 )
= $false )
| ( ( in @ SV305 @ SV60 )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1326,plain,
! [SV178: $i,SV60: $i] :
( ( ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1327,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( in @ SV251 @ SV64 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1328,plain,
! [SV296: $o,SV64: $i,SV182: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV182 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1244]) ).
thf(1333,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( in @ SV251 @ SV64 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1334,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV182 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1336,plain,
! [SV184: $i,SV66: $i > $i > $o] :
( ( ( ! [SY1305: $i] :
~ ( ~ ( ~ ( in @ SY1305 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1305 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1305 ) )
| ( in @ SY1305 @ ( sK31_SY1165 @ SV66 @ SV184 ) ) ) ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1337,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
| ~ ! [SY1303: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1303 )
| ( SV306 = SY1303 ) ) )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1338,plain,
! [SV186: $i > $o,SV68: $i,SV297: $i] :
( ( ( in @ SV297 @ SV68 )
= $false )
| ( ( ~ ( SV186 @ SV297 ) )
= $true )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1339,plain,
! [SV71: $i,SV187: $i > $o,SV298: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) @ SV71 )
| ~ ~ ( SV187 @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) ) ) )
= $false )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1252]) ).
thf(1340,plain,
! [SV188: $i,SV299: $i,SV72: $i,SV284: $i] :
( ( ( ~ ( ~ ( in @ SV284 @ SV72 )
| ( in @ SV299 @ SV188 ) ) )
= $false )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1253]) ).
thf(1341,plain,
! [SV72: $i,SV284: $i,SV188: $i,SV299: $i] :
( ( ( ~ ( ~ ( in @ SV299 @ SV188 )
| ( in @ SV284 @ SV72 ) ) )
= $false )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1253]) ).
thf(1342,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1343,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
| ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) ) )
= $false )
| ( ( ~ ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1344,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
| ~ ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
| ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) ) )
= $false )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1257]) ).
thf(1345,plain,
! [SV195: $i > $o,SV80: $i,SV257: $i] :
( ( ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1189: $i] : ( SV195 @ SY1189 ) ) )
= $false )
| ( ( SV195 @ SV257 )
= $true )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1346,plain,
! [SV80: $i,SV257: $i,SV195: $i > $o] :
( ( ( SV195 @ SV257 )
= $false )
| ( ( in @ SV257
@ ( dsetconstr @ SV80
@ ^ [SY1190: $i] : ( SV195 @ SY1190 ) ) )
= $true )
| ( ( in @ SV257 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1347,plain,
! [SV85: $i,SV199: $i > $o,SV300: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) @ SV85 )
| ~ ~ ( SV199 @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) ) ) )
= $false )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1263]) ).
thf(1348,plain,
! [SV203: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK38_SY1198 @ SV89 @ SV203 ) @ SV203 )
| ( in @ ( sK38_SY1198 @ SV89 @ SV203 ) @ SV89 ) )
= $false )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1264]) ).
thf(1349,plain,
! [SV203: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK33_SY1198 @ SV89 @ SV203 ) @ SV203 ) )
= $false )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1265]) ).
thf(1350,plain,
! [SV203: $i,SV89: $i] :
( ( ( in @ ( sK33_SY1198 @ SV89 @ SV203 ) @ SV89 )
= $false )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1265]) ).
thf(1351,plain,
! [SV204: $i,SV90: $i,SV262: $i] :
( ( ( in @ SV262 @ SV90 )
= $false )
| ( ( in @ SV262 @ SV204 )
= $true )
| ( ( in @ SV262 @ ( setminus @ SV90 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1352,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ! [SY1283: $i] :
( ~ ( SV92 @ SY1283 )
| ( SV286 = SY1283 ) ) )
= $false )
| ( ( SV92 @ SV286 )
= $false )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1353,plain,
! [SV96: $i,SV209: $i] :
( ( ( ~ ( ~ ( in @ SV209 @ ( sK34_SY1203 @ SV96 @ SV209 ) )
| ~ ( in @ ( sK34_SY1203 @ SV96 @ SV209 ) @ SV96 ) ) )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1354,plain,
! [SV96: $i,SV307: $i,SV209: $i] :
( ( ( ~ ( ~ ( in @ SV209 @ SV307 )
| ~ ( in @ SV307 @ SV96 ) ) )
= $false )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1355,plain,
! [SV98: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY1039 @ SV98 ) @ omega )
| ~ ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 ) ) )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1271]) ).
thf(1356,plain,
! [SV98: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ omega )
| ( in @ SV308 @ SV98 ) )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( setadjoin @ ( sK29_SY1039 @ SV98 ) @ ( sK29_SY1039 @ SV98 ) ) @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1357,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ! [SY1285: $i] :
( ~ ( SV99 @ SY1285 )
| ( SV288 = SY1285 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1358,plain,
! [SV100: $i,SV211: $i] :
( ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1274]) ).
thf(1359,plain,
! [SV100: $i,SV211: $i] :
( ( ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) )
= $false )
| ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
= $false )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1360,plain,
! [SV214: $i > $o,SV104: $i,SV309: $i] :
( ( ( ~ ~ ( ~ ( in @ SV309 @ SV104 )
| ~ ( SV214 @ SV309 ) ) )
= $true )
| ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1361,plain,
! [SV214: $i > $o,SV104: $i,SV310: $i] :
( ( ( ~ ~ ( ~ ( in @ SV310 @ SV104 )
| ~ ( SV214 @ SV310 ) ) )
= $true )
| ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1362,plain,
! [SV217: $i > $o,SV107: $i,SV302: $i] :
( ( ( in @ SV302 @ SV107 )
= $false )
| ( ( ~ ~ ( SV217 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1363,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
| ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 ) )
= $false )
| ( ( ~ ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1364,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( ! [SY1287: $i] :
( ~ ( SV110 @ SY1287 )
| ( SV291 = SY1287 ) ) )
= $false )
| ( ( SV110 @ SV291 )
= $false )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1365,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ! [SY1288: $i] :
( ~ ( SV112 @ SY1288 )
| ( SV292 = SY1288 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1366,plain,
! [SV113: $i,SV220: $i] :
( ( ~ ~ ( ~ ( in @ ( sK39_SY1268 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ ( sK39_SY1268 @ SV220 @ SV113 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1282]) ).
thf(1367,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1368,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1369,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
| ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) ) )
= $false )
| ( ( ~ ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1370,plain,
! [SV276: $o,SV226: $i,SV120: $i,SV270: $i] :
( ( ( in @ SV270 @ SV120 )
= $true )
| ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| SV276 )
| SV276 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1374,plain,
! [SV226: $i,SV120: $i,SV270: $i] :
( ( ( in @ SV270 @ SV120 )
= $true )
| ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| $false )
| $false )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1289]) ).
thf(1376,plain,
! [SV303: $o,SV231: $i,SV125: $i,SV273: $i] :
( ( ( SV273 = SV125 )
= $true )
| ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| SV303 )
| SV303 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1291]) ).
thf(1380,plain,
! [SV231: $i,SV125: $i,SV273: $i] :
( ( ( SV273 = SV125 )
= $true )
| ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| $false )
| $false )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1382,plain,
! [SV126: $i] :
( ( ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1297]) ).
thf(1384,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( ! [SY1290: $i] :
( ~ ( SV128 @ SY1290 )
| ( SV293 = SY1290 ) ) )
= $false )
| ( ( SV128 @ SV293 )
= $false )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1385,plain,
! [SV130: $i,SV233: $i > $o] :
( ( ( ~ ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 ) )
= $false )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1386,plain,
! [SV130: $i,SV233: $i > $o] :
( ( ( ~ ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) ) )
= $false )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1387,plain,
! [SV149: $i,SV25: $i,SV277: $o] :
( ( ( in @ ( sK24_SY1269 @ SV277 @ SV25 @ SV149 ) @ SV25 )
= $true )
| ( SV277 = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1389,plain,
! [SV149: $i,SV25: $i] :
( ( ( in @ ( sK26_SX0 @ SV25 @ SV149 ) @ SV25 )
= $true )
| ( $false = $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1390,plain,
! [SV32: $i] :
( ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) )
| ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1391,plain,
! [SV32: $i,SV311: $i] :
( ( ! [SY1309: $i] :
( ~ ~ ( ~ ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1309 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SY1310: $i] :
( ~ ( in @ SY1310 @ SV311 )
| ( in @ SY1310 @ SY1309 ) )
| ! [SY1311: $i] :
( ~ ( in @ SY1311 @ SY1309 )
| ( in @ SY1311 @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1392,plain,
! [SV32: $i,SV304: $i] :
( ( ( ~ ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV304 )
| ( in @ SY1295 @ SV32 ) )
| ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1393,plain,
! [SV278: $i] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( in @ SY1270 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1270 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1394,plain,
! [SV38: $i,SV159: $i > $o] :
( ( ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 )
= $true )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1395,plain,
! [SV38: $i,SV159: $i > $o] :
( ( ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) )
= $true )
| ( ( ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV38 )
| ~ ( SV159 @ SY1139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1315]) ).
thf(1396,plain,
! [SV39: $i,SV160: $i] :
( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1316]) ).
thf(1397,plain,
! [SV39: $i,SV160: $i] :
( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1317]) ).
thf(1398,plain,
! [SV41: $i,SV279: $i] :
( ( ( ~ ( in @ ( sK27_SY908 @ SV279 @ SV41 ) @ SV41 ) )
= $false )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1399,plain,
! [SV41: $i,SV279: $i] :
( ( ( ~ ~ ~ ! [SY1302: $i] :
~ ~ ( ~ ( in @ SY1302 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SY1302 @ SV41 ) ) )
= $false )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1400,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
| ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1321]) ).
thf(1401,plain,
! [SV48: $i,SV166: $i,SV282: $i > $o,SV295: $i > $o] :
( ( ( in @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) @ SV48 )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1322]) ).
thf(1402,plain,
! [SV166: $i,SV295: $i > $o,SV282: $i > $o,SV48: $i] :
( ( ( ~ ( in @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) @ SV166 )
| ( ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 )
!= ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ~ ( ~ ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
| ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) ) )
| ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1323]) ).
thf(1403,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK42_SY1278 @ SV283 @ SV50 ) )
| ( SV283
= ( sK42_SY1278 @ SV283 @ SV50 ) ) )
= $false )
| ( ( SV50 @ SV283 )
= $false )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1324]) ).
thf(1404,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 ) )
= $true )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1405,plain,
! [SV296: $o,SV64: $i,SV182: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV182 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1410,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1411,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV182 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1413,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
| ~ ! [SY1312: $i] :
~ ~ ( ~ ( in @ SY1312 @ SV184 )
| ~ ( SV66 @ SY1312 @ SV312 ) ) )
| ~ ( ~ ~ ! [SY1313: $i] :
~ ~ ( ~ ( in @ SY1313 @ SV184 )
| ~ ( SV66 @ SY1313 @ SV312 ) )
| ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) ) ) ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1414,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 ) )
= $true )
| ( ( ~ ! [SY1303: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1303 )
| ( SV306 = SY1303 ) ) )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1415,plain,
! [SV68: $i,SV297: $i,SV186: $i > $o] :
( ( ( SV186 @ SV297 )
= $false )
| ( ( in @ SV297 @ SV68 )
= $false )
| ( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1416,plain,
! [SV71: $i,SV187: $i > $o,SV298: $i] :
( ( ( ~ ( ~ ( in @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) @ SV71 )
| ~ ~ ( SV187 @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) ) ) )
= $true )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1339]) ).
thf(1417,plain,
! [SV188: $i,SV299: $i,SV72: $i,SV284: $i] :
( ( ( ~ ( in @ SV284 @ SV72 )
| ( in @ SV299 @ SV188 ) )
= $true )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1418,plain,
! [SV72: $i,SV284: $i,SV188: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV188 )
| ( in @ SV284 @ SV72 ) )
= $true )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1341]) ).
thf(1419,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1420,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) )
= $false )
| ( ( ~ ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1421,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( ~ ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1422,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) ) )
= $false )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1423,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
| ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) ) )
= $false )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1424,plain,
! [SV85: $i,SV199: $i > $o,SV300: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) @ SV85 )
| ~ ~ ( SV199 @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) ) ) )
= $true )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1425,plain,
! [SV203: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK38_SY1198 @ SV89 @ SV203 ) @ SV203 ) )
= $false )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1426,plain,
! [SV203: $i,SV89: $i] :
( ( ( in @ ( sK38_SY1198 @ SV89 @ SV203 ) @ SV89 )
= $false )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1427,plain,
! [SV203: $i,SV89: $i] :
( ( ( in @ ( sK33_SY1198 @ SV89 @ SV203 ) @ SV203 )
= $true )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1428,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ~ ( SV92 @ ( sK43_SY1283 @ SV286 @ SV92 ) )
| ( SV286
= ( sK43_SY1283 @ SV286 @ SV92 ) ) )
= $false )
| ( ( SV92 @ SV286 )
= $false )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1352]) ).
thf(1429,plain,
! [SV96: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ ( sK34_SY1203 @ SV96 @ SV209 ) )
| ~ ( in @ ( sK34_SY1203 @ SV96 @ SV209 ) @ SV96 ) )
= $false )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1430,plain,
! [SV96: $i,SV307: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV307 )
| ~ ( in @ SV307 @ SV96 ) )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1431,plain,
! [SV98: $i] :
( ( ( ~ ( in @ ( sK29_SY1039 @ SV98 ) @ omega )
| ~ ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 ) )
= $false )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1432,plain,
! [SV98: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ omega ) )
= $true )
| ( ( in @ SV308 @ SV98 )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( setadjoin @ ( sK29_SY1039 @ SV98 ) @ ( sK29_SY1039 @ SV98 ) ) @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1433,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
| ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1357]) ).
thf(1434,plain,
! [SV100: $i,SV211: $i] :
( ( ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
| ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 ) )
= $false )
| ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1436,plain,
! [SV100: $i,SV211: $i] :
( ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
= $false )
| ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
= $false )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1437,plain,
! [SV214: $i > $o,SV104: $i,SV309: $i] :
( ( ( ~ ( ~ ( in @ SV309 @ SV104 )
| ~ ( SV214 @ SV309 ) ) )
= $false )
| ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1438,plain,
! [SV214: $i > $o,SV104: $i,SV310: $i] :
( ( ( ~ ( ~ ( in @ SV310 @ SV104 )
| ~ ( SV214 @ SV310 ) ) )
= $false )
| ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1439,plain,
! [SV107: $i,SV302: $i,SV217: $i > $o] :
( ( ( ~ ( SV217 @ SV302 ) )
= $false )
| ( ( in @ SV302 @ SV107 )
= $false )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1440,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) )
= $false )
| ( ( ~ ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1441,plain,
! [SV108: $i > $o,SV290: $i] :
( ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( ~ ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1442,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) )
| ( SV291
= ( sK45_SY1287 @ SV291 @ SV110 ) ) )
= $false )
| ( ( SV110 @ SV291 )
= $false )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1364]) ).
thf(1443,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
| ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1365]) ).
thf(1444,plain,
! [SV113: $i,SV220: $i] :
( ( ~ ( ~ ( in @ ( sK39_SY1268 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ ( sK39_SY1268 @ SV220 @ SV113 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1445,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1446,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1368]) ).
thf(1447,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) )
= $false )
| ( ( ~ ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1448,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1449,plain,
! [SV120: $i,SV276: $o,SV226: $i,SV270: $i] :
( ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| SV276 ) )
= $true )
| ( SV276 = $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1453,plain,
! [SV120: $i,SV226: $i,SV270: $i] :
( ( ( ~ ( ~ ( in @ SV270 @ SV226 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1455,plain,
! [SV125: $i,SV303: $o,SV231: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| SV303 ) )
= $true )
| ( SV303 = $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1459,plain,
! [SV125: $i,SV231: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ SV273 @ SV231 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1461,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) )
| ( SV293
= ( sK47_SY1290 @ SV293 @ SV128 ) ) )
= $false )
| ( ( SV128 @ SV293 )
= $false )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1384]) ).
thf(1462,plain,
! [SV130: $i,SV233: $i > $o] :
( ( ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 )
= $true )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1463,plain,
! [SV130: $i,SV233: $i > $o] :
( ( ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) )
= $true )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV130 )
| ~ ( SV233 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1386]) ).
thf(1464,plain,
! [SV32: $i] :
( ( ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1465,plain,
! [SV32: $i] :
( ( ~ ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1466,plain,
! [SV313: $i,SV32: $i,SV311: $i] :
( ( ~ ~ ( ~ ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SV313 @ ( sK2_SY874 @ SV32 ) ) )
| ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV311 )
| ( in @ SY1314 @ SV313 ) )
| ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1467,plain,
! [SV32: $i,SV304: $i] :
( ( ( ~ ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV304 )
| ( in @ SY1295 @ SV32 ) ) )
= $true )
| ( ( ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1468,plain,
! [SV278: $i,SV314: $i] :
( ( ( ~ ~ ( ~ ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV314 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1469,plain,
! [SV159: $i > $o,SV38: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ SV38 )
| ~ ( SV159 @ SV315 ) )
= $true )
| ( ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1470,plain,
! [SV159: $i > $o,SV38: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ SV38 )
| ~ ( SV159 @ SV316 ) )
= $true )
| ( ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1471,plain,
! [SV41: $i,SV279: $i] :
( ( ( in @ ( sK27_SY908 @ SV279 @ SV41 ) @ SV41 )
= $true )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1472,plain,
! [SV41: $i,SV279: $i] :
( ( ( ~ ~ ! [SY1302: $i] :
~ ~ ( ~ ( in @ SY1302 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SY1302 @ SV41 ) ) )
= $true )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1473,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1474,plain,
! [SV47: $i > $o,SV281: $i] :
( ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1475,plain,
! [SV166: $i,SV295: $i > $o,SV282: $i > $o,SV48: $i] :
( ( ( ~ ( in @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) @ SV166 ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1476,plain,
! [SV48: $i,SV166: $i,SV282: $i > $o,SV295: $i > $o] :
( ( ( ( ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 )
!= ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ~ ( ~ ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
| ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) ) )
| ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1477,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK42_SY1278 @ SV283 @ SV50 ) ) )
= $false )
| ( ( SV50 @ SV283 )
= $false )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1478,plain,
! [SV50: $i > $o,SV283: $i] :
( ( ( SV283
= ( sK42_SY1278 @ SV283 @ SV50 ) )
= $false )
| ( ( SV50 @ SV283 )
= $false )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1479,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
= $false )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1480,plain,
! [SV296: $o,SV64: $i,SV182: $i,SV251: $i] :
( ( ( in @ SV251 @ SV182 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1485,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1486,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( in @ SV251 @ SV182 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1488,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ( ~ ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
| ~ ! [SY1312: $i] :
~ ~ ( ~ ( in @ SY1312 @ SV184 )
| ~ ( SV66 @ SY1312 @ SV312 ) ) )
| ~ ( ~ ~ ! [SY1313: $i] :
~ ~ ( ~ ( in @ SY1313 @ SV184 )
| ~ ( SV66 @ SY1313 @ SV312 ) )
| ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1489,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( ~ ! [SY1303: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1303 )
| ( SV306 = SY1303 ) ) )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1490,plain,
! [SV297: $i,SV186: $i > $o,SV68: $i] :
( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV297 @ SV68 )
= $false )
| ( ( SV186 @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1491,plain,
! [SV71: $i,SV187: $i > $o,SV298: $i] :
( ( ( ~ ( in @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) @ SV71 )
| ~ ~ ( SV187 @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) ) )
= $false )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1492,plain,
! [SV188: $i,SV299: $i,SV72: $i,SV284: $i] :
( ( ( ~ ( in @ SV284 @ SV72 ) )
= $true )
| ( ( in @ SV299 @ SV188 )
= $true )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1493,plain,
! [SV72: $i,SV284: $i,SV188: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV188 ) )
= $true )
| ( ( in @ SV284 @ SV72 )
= $true )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1494,plain,
! [SV190: $i > $o,SV317: $i,SV74: $i > $o] :
( ( ( ~ ~ ( ~ ( SV74 @ SV317 )
| ~ ! [SY1316: $i] :
( ~ ( SV74 @ SY1316 )
| ( SV317 = SY1316 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1495,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( ~ ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1496,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1497,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1422]) ).
thf(1498,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) ) )
= $false )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1499,plain,
! [SV76: $i > $o,SV285: $i] :
( ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1500,plain,
! [SV85: $i,SV199: $i > $o,SV300: $i] :
( ( ( ~ ( in @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) @ SV85 )
| ~ ~ ( SV199 @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) ) )
= $false )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1501,plain,
! [SV203: $i,SV89: $i] :
( ( ( in @ ( sK38_SY1198 @ SV89 @ SV203 ) @ SV203 )
= $true )
| ( ( SV89 = SV203 )
= $true )
| ( ( in @ ( sK11_SY1197 @ SV203 @ SV89 ) @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1502,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ~ ( SV92 @ ( sK43_SY1283 @ SV286 @ SV92 ) ) )
= $false )
| ( ( SV92 @ SV286 )
= $false )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1503,plain,
! [SV92: $i > $o,SV286: $i] :
( ( ( SV286
= ( sK43_SY1283 @ SV286 @ SV92 ) )
= $false )
| ( ( SV92 @ SV286 )
= $false )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1504,plain,
! [SV96: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ ( sK34_SY1203 @ SV96 @ SV209 ) ) )
= $false )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1505,plain,
! [SV209: $i,SV96: $i] :
( ( ( ~ ( in @ ( sK34_SY1203 @ SV96 @ SV209 ) @ SV96 ) )
= $false )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1506,plain,
! [SV96: $i,SV307: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV307 ) )
= $true )
| ( ( ~ ( in @ SV307 @ SV96 ) )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1507,plain,
! [SV98: $i] :
( ( ( ~ ( in @ ( sK29_SY1039 @ SV98 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1508,plain,
! [SV98: $i] :
( ( ( ~ ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 ) )
= $false )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1509,plain,
! [SV98: $i,SV308: $i] :
( ( ( in @ SV308 @ omega )
= $false )
| ( ( in @ SV308 @ SV98 )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( setadjoin @ ( sK29_SY1039 @ SV98 ) @ ( sK29_SY1039 @ SV98 ) ) @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1510,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1511,plain,
! [SV99: $i > $o,SV288: $i] :
( ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1512,plain,
! [SV100: $i,SV211: $i] :
( ( ( ~ ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 ) )
= $false )
| ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1515,plain,
! [SV214: $i > $o,SV104: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV104 )
| ~ ( SV214 @ SV309 ) )
= $true )
| ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1516,plain,
! [SV214: $i > $o,SV104: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV104 )
| ~ ( SV214 @ SV310 ) )
= $true )
| ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1517,plain,
! [SV107: $i,SV302: $i,SV217: $i > $o] :
( ( ( SV217 @ SV302 )
= $true )
| ( ( in @ SV302 @ SV107 )
= $false )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1518,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ~ ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1519,plain,
! [SV108: $i > $o,SV290: $i] :
( ( ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) )
= $false )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1520,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) ) )
= $false )
| ( ( SV110 @ SV291 )
= $false )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1521,plain,
! [SV110: $i > $o,SV291: $i] :
( ( ( SV291
= ( sK45_SY1287 @ SV291 @ SV110 ) )
= $false )
| ( ( SV110 @ SV291 )
= $false )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1522,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1523,plain,
! [SV112: $i > $o,SV292: $i] :
( ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1524,plain,
! [SV113: $i,SV220: $i] :
( ( ~ ( in @ ( sK39_SY1268 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ ( sK39_SY1268 @ SV220 @ SV113 ) @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1525,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1526,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1527,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( ~ ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1528,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1529,plain,
! [SV120: $i,SV276: $o,SV226: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV226 )
| SV276 )
= $false )
| ( SV276 = $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1535,plain,
! [SV120: $i,SV226: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV226 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1538,plain,
! [SV125: $i,SV303: $o,SV231: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV231 )
| SV303 )
= $false )
| ( SV303 = $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1544,plain,
! [SV125: $i,SV231: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV231 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1547,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) ) )
= $false )
| ( ( SV128 @ SV293 )
= $false )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1548,plain,
! [SV128: $i > $o,SV293: $i] :
( ( ( SV293
= ( sK47_SY1290 @ SV293 @ SV128 ) )
= $false )
| ( ( SV128 @ SV293 )
= $false )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1549,plain,
! [SV233: $i > $o,SV130: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV130 )
| ~ ( SV233 @ SV318 ) )
= $true )
| ( ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1550,plain,
! [SV233: $i > $o,SV130: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ SV130 )
| ~ ( SV233 @ SV319 ) )
= $true )
| ( ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1551,plain,
! [SV32: $i] :
( ( ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY874 @ SV32 ) )
| ! [SY876: $i] :
( ~ ( in @ SY876 @ SY1242 )
| ( in @ SY876 @ SV32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1552,plain,
! [SV32: $i] :
( ( ! [SY1244: $i,SY1245: $i] :
( ~ ~ ( ~ ( in @ SY1244 @ SV32 )
| ~ ( in @ SY1245 @ SV32 ) )
| ~ ! [SY1246: $i] :
( ~ ( in @ SY1246 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SY1244 @ SY1246 )
| ( in @ SY1245 @ SY1246 ) )
| ~ ( ~ ( in @ SY1245 @ SY1246 )
| ( in @ SY1244 @ SY1246 ) ) ) )
| ( SY1244 = SY1245 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1465]) ).
thf(1553,plain,
! [SV313: $i,SV32: $i,SV311: $i] :
( ( ( ~ ~ ( ~ ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SV313 @ ( sK2_SY874 @ SV32 ) ) ) )
= $true )
| ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV311 )
| ( in @ SY1314 @ SV313 ) )
| ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1554,plain,
! [SV32: $i,SV304: $i] :
( ( ( ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV304 )
| ( in @ SY1295 @ SV32 ) ) )
= $false )
| ( ( ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1555,plain,
! [SV278: $i,SV314: $i] :
( ( ( ~ ( ~ ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV314 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1556,plain,
! [SV159: $i > $o,SV38: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ SV38 ) )
= $true )
| ( ( ~ ( SV159 @ SV315 ) )
= $true )
| ( ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1557,plain,
! [SV159: $i > $o,SV38: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ SV38 ) )
= $true )
| ( ( ~ ( SV159 @ SV316 ) )
= $true )
| ( ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1558,plain,
! [SV41: $i,SV279: $i] :
( ( ( ~ ! [SY1302: $i] :
~ ~ ( ~ ( in @ SY1302 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SY1302 @ SV41 ) ) )
= $false )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1559,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( ~ ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1473]) ).
thf(1560,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1561,plain,
! [SV166: $i,SV295: $i > $o,SV282: $i > $o,SV48: $i] :
( ( ( in @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) @ SV166 )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1562,plain,
! [SV48: $i,SV166: $i,SV282: $i > $o,SV295: $i > $o] :
( ( ( ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 )
!= ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1476]) ).
thf(1563,plain,
! [SV48: $i,SV166: $i,SV295: $i > $o,SV282: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
| ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) ) )
| ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1476]) ).
thf(1564,plain,
! [SV283: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK42_SY1278 @ SV283 @ SV50 ) )
= $true )
| ( ( SV50 @ SV283 )
= $false )
| ( ( SV50
@ ( descr
@ ^ [SY933: $i] : ( SV50 @ SY933 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1566,plain,
! [SV64: $i,SV296: $o,SV182: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV182 )
| SV296 )
= $false )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1567,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 ) )
= $true )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1576,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV182 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1577,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1580,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ( ~ ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
| ~ ! [SY1312: $i] :
~ ~ ( ~ ( in @ SY1312 @ SV184 )
| ~ ( SV66 @ SY1312 @ SV312 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1581,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ( ~ ~ ! [SY1313: $i] :
~ ~ ( ~ ( in @ SY1313 @ SV184 )
| ~ ( SV66 @ SY1313 @ SV312 ) )
| ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) ) ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1582,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( ! [SY1303: $i] :
( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SY1303 )
| ( SV306 = SY1303 ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1583,plain,
! [SV297: $i,SV186: $i > $o,SV68: $i] :
( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV297 @ SV68 )
= $false )
| ( ( SV186 @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1584,plain,
! [SV71: $i,SV187: $i > $o,SV298: $i] :
( ( ( ~ ( in @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) @ SV71 ) )
= $false )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1585,plain,
! [SV71: $i,SV298: $i,SV187: $i > $o] :
( ( ( ~ ~ ( SV187 @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) ) )
= $false )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1586,plain,
! [SV188: $i,SV299: $i,SV72: $i,SV284: $i] :
( ( ( in @ SV284 @ SV72 )
= $false )
| ( ( in @ SV299 @ SV188 )
= $true )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1587,plain,
! [SV72: $i,SV284: $i,SV188: $i,SV299: $i] :
( ( ( in @ SV299 @ SV188 )
= $false )
| ( ( in @ SV284 @ SV72 )
= $true )
| ( ( SV284 = SV299 )
= $false )
| ( ( SV72 = SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1588,plain,
! [SV190: $i > $o,SV317: $i,SV74: $i > $o] :
( ( ( ~ ( ~ ( SV74 @ SV317 )
| ~ ! [SY1316: $i] :
( ~ ( SV74 @ SY1316 )
| ( SV317 = SY1316 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1589,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
| ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1591,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1592,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $false )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1593,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( ~ ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1594,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $false )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1595,plain,
! [SV85: $i,SV199: $i > $o,SV300: $i] :
( ( ( ~ ( in @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) @ SV85 ) )
= $false )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1596,plain,
! [SV85: $i,SV300: $i,SV199: $i > $o] :
( ( ( ~ ~ ( SV199 @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) ) )
= $false )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1597,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( SV92 @ ( sK43_SY1283 @ SV286 @ SV92 ) )
= $true )
| ( ( SV92 @ SV286 )
= $false )
| ( ( ~ ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1502]) ).
thf(1598,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $false )
| ( ( SV92 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1283 @ SV286 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1599,plain,
! [SV96: $i,SV209: $i] :
( ( ( in @ SV209 @ ( sK34_SY1203 @ SV96 @ SV209 ) )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1600,plain,
! [SV209: $i,SV96: $i] :
( ( ( in @ ( sK34_SY1203 @ SV96 @ SV209 ) @ SV96 )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1601,plain,
! [SV96: $i,SV307: $i,SV209: $i] :
( ( ( in @ SV209 @ SV307 )
= $false )
| ( ( ~ ( in @ SV307 @ SV96 ) )
= $true )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1602,plain,
! [SV98: $i] :
( ( ( in @ ( sK29_SY1039 @ SV98 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1603,plain,
! [SV98: $i] :
( ( ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( ! [SY1040: $i] :
( ~ ( in @ SY1040 @ omega )
| ( in @ SY1040 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1604,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( ~ ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1605,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1606,plain,
! [SV100: $i,SV211: $i] :
( ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV211 )
= $true )
| ( ( in @ ( sK12_SY1207 @ SV211 @ SV100 ) @ SV100 )
= $true )
| ( ( SV100 = SV211 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1607,plain,
! [SV214: $i > $o,SV104: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV104 ) )
= $true )
| ( ( ~ ( SV214 @ SV309 ) )
= $true )
| ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1608,plain,
! [SV214: $i > $o,SV104: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV104 ) )
= $true )
| ( ( ~ ( SV214 @ SV310 ) )
= $true )
| ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1609,plain,
! [SV302: $i,SV217: $i > $o,SV107: $i] :
( ( ( ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV107 )
| ( SV217 @ SY1213 ) ) )
= $false )
| ( ( in @ SV302 @ SV107 )
= $false )
| ( ( SV217 @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1610,plain,
! [SV108: $i > $o,SV290: $i] :
( ( ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
| ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) ) )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1612,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1519]) ).
thf(1613,plain,
! [SV291: $i,SV110: $i > $o] :
( ( ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( SV110 @ SY1069 )
| ~ ( SV110 @ SY1070 )
| ( SY1069 = SY1070 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1614,plain,
! [SV291: $i,SV320: $i,SV110: $i > $o] :
( ( ( ! [SY1317: $i] :
( ~ ( SV110 @ SV320 )
| ~ ( SV110 @ SY1317 )
| ( SV320 = SY1317 ) ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV291
= ( sK45_SY1287 @ SV291 @ SV110 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1615,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( ~ ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1522]) ).
thf(1616,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1617,plain,
! [SV113: $i,SV220: $i] :
( ( ~ ( in @ ( sK39_SY1268 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1618,plain,
! [SV220: $i,SV113: $i] :
( ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ ( sK39_SY1268 @ SV220 @ SV113 ) @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1619,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1620,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1621,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
| ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1623,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1624,plain,
! [SV120: $i,SV276: $o,SV226: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV226 ) )
= $false )
| ( SV276 = $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1630,plain,
! [SV120: $i,SV226: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV226 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1535]) ).
thf(1633,plain,
! [SV125: $i,SV303: $o,SV231: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV231 ) )
= $false )
| ( SV303 = $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1639,plain,
! [SV125: $i,SV231: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV231 ) )
= $false )
| ( $false = $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1642,plain,
! [SV293: $i,SV128: $i > $o] :
( ( ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( ! [SY1114: $i,SY1115: $i] :
( ~ ( SV128 @ SY1114 )
| ~ ( SV128 @ SY1115 )
| ( SY1114 = SY1115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1643,plain,
! [SV293: $i,SV321: $i,SV128: $i > $o] :
( ( ( ! [SY1318: $i] :
( ~ ( SV128 @ SV321 )
| ~ ( SV128 @ SY1318 )
| ( SV321 = SY1318 ) ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV293
= ( sK47_SY1290 @ SV293 @ SV128 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1644,plain,
! [SV233: $i > $o,SV130: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV130 ) )
= $true )
| ( ( ~ ( SV233 @ SV318 ) )
= $true )
| ( ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1645,plain,
! [SV233: $i > $o,SV130: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ SV130 ) )
= $true )
| ( ( ~ ( SV233 @ SV319 ) )
= $true )
| ( ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1646,plain,
! [SV32: $i,SV322: $i] :
( ( ~ ( in @ SV322 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1319: $i] :
( ~ ( in @ SY1319 @ SV322 )
| ( in @ SY1319 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1647,plain,
! [SV32: $i,SV323: $i] :
( ( ! [SY1320: $i] :
( ~ ~ ( ~ ( in @ SV323 @ SV32 )
| ~ ( in @ SY1320 @ SV32 ) )
| ~ ! [SY1321: $i] :
( ~ ( in @ SY1321 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1321 )
| ( in @ SY1320 @ SY1321 ) )
| ~ ( ~ ( in @ SY1320 @ SY1321 )
| ( in @ SV323 @ SY1321 ) ) ) )
| ( SV323 = SY1320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1648,plain,
! [SV313: $i,SV32: $i,SV311: $i] :
( ( ( ~ ( ~ ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SV313 @ ( sK2_SY874 @ SV32 ) ) ) )
= $false )
| ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV311 )
| ( in @ SY1314 @ SV313 ) )
| ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1649,plain,
! [SV304: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
| ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 ) )
= $false )
| ( ( ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1554]) ).
thf(1650,plain,
! [SV278: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV314 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1555]) ).
thf(1651,plain,
! [SV159: $i > $o,SV38: $i,SV315: $i] :
( ( ( in @ SV315 @ SV38 )
= $false )
| ( ( ~ ( SV159 @ SV315 ) )
= $true )
| ( ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1652,plain,
! [SV159: $i > $o,SV38: $i,SV316: $i] :
( ( ( in @ SV316 @ SV38 )
= $false )
| ( ( ~ ( SV159 @ SV316 ) )
= $true )
| ( ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1653,plain,
! [SV41: $i,SV279: $i] :
( ( ( ! [SY1302: $i] :
~ ~ ( ~ ( in @ SY1302 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SY1302 @ SV41 ) ) )
= $true )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1654,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ! [SY921: $i] :
~ ! [SY922: $i] :
~ ( ~ ( ~ ( SV47 @ SY922 )
| ( SY922 = SY921 ) )
| ~ ( ( SY922 != SY921 )
| ( SV47 @ SY922 ) ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1655,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ~ ! [SY1322: $i] :
~ ( ~ ( ~ ( SV47 @ SY1322 )
| ( SY1322
= ( sK49_SY921 @ SV281 @ SV47 ) ) )
| ~ ( ( SY1322
!= ( sK49_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SY1322 ) ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1560]) ).
thf(1656,plain,
! [SV48: $i,SV166: $i,SV282: $i > $o,SV295: $i > $o] :
( ( ( ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 )
= ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1657,plain,
! [SV48: $i,SV166: $i,SV295: $i > $o,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
| ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) ) )
| ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1659,plain,
! [SV64: $i,SV296: $o,SV182: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV182 ) )
= $false )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1661,plain,
! [SV296: $o,SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| SV296 )
= $false )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1673,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV182 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1576]) ).
thf(1675,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV64 )
| ~ ( in @ SV251 @ SV182 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1679,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
| ~ ! [SY1312: $i] :
~ ~ ( ~ ( in @ SY1312 @ SV184 )
| ~ ( SV66 @ SY1312 @ SV312 ) ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1680,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ~ ! [SY1313: $i] :
~ ~ ( ~ ( in @ SY1313 @ SV184 )
| ~ ( SV66 @ SY1313 @ SV312 ) )
| ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1681,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
| ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1582]) ).
thf(1682,plain,
! [SV71: $i,SV187: $i > $o,SV298: $i] :
( ( ( in @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) @ SV71 )
= $true )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1683,plain,
! [SV71: $i,SV298: $i,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) ) )
= $true )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1684,plain,
! [SV190: $i > $o,SV317: $i,SV74: $i > $o] :
( ( ( ~ ( SV74 @ SV317 )
| ~ ! [SY1316: $i] :
( ~ ( SV74 @ SY1316 )
| ( SV317 = SY1316 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1685,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1688,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1689,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ~ ( ~ ( SV76 @ ( sK51_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1323: $i] :
( ~ ( SV76 @ SY1323 )
| ( ( sK51_SY992 @ SV285 @ SV76 )
= SY1323 ) ) ) )
= $false )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1592]) ).
thf(1690,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ! [SY992: $i] :
~ ~ ( ~ ( SV76 @ SY992 )
| ~ ! [SY993: $i] :
( ~ ( SV76 @ SY993 )
| ( SY992 = SY993 ) ) ) )
= $false )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1691,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ~ ( ~ ( SV76 @ ( sK52_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1324: $i] :
( ~ ( SV76 @ SY1324 )
| ( ( sK52_SY992 @ SV285 @ SV76 )
= SY1324 ) ) ) )
= $false )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1594]) ).
thf(1692,plain,
! [SV85: $i,SV199: $i > $o,SV300: $i] :
( ( ( in @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) @ SV85 )
= $true )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1693,plain,
! [SV85: $i,SV300: $i,SV199: $i > $o] :
( ( ( ~ ( SV199 @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) ) )
= $true )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1694,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ! [SY1027: $i] :
~ ( SV92 @ SY1027 ) )
= $false )
| ( ( SV92 @ SV286 )
= $false )
| ( ( SV92 @ ( sK43_SY1283 @ SV286 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1695,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ~ ( SV92 @ ( sK53_SY1027 @ SV286 @ SV92 ) ) )
= $false )
| ( ( SV92 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1283 @ SV286 @ SV92 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1598]) ).
thf(1696,plain,
! [SV209: $i,SV96: $i,SV307: $i] :
( ( ( in @ SV307 @ SV96 )
= $false )
| ( ( in @ SV209 @ SV307 )
= $false )
| ( ( in @ SV209 @ ( setunion @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1697,plain,
! [SV98: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ omega )
| ( in @ SV324 @ SV98 ) )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( sK29_SY1039 @ SV98 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1698,plain,
! [SV98: $i,SV325: $i] :
( ( ( ~ ( in @ SV325 @ omega )
| ( in @ SV325 @ SV98 ) )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1699,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ! [SY1043: $i] :
~ ~ ( ~ ( SV99 @ SY1043 )
| ~ ! [SY1044: $i] :
( ~ ( SV99 @ SY1044 )
| ( SY1043 = SY1044 ) ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1700,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ~ ( ~ ( SV99 @ ( sK54_SY1043 @ SV288 @ SV99 ) )
| ~ ! [SY1325: $i] :
( ~ ( SV99 @ SY1325 )
| ( ( sK54_SY1043 @ SV288 @ SV99 )
= SY1325 ) ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1605]) ).
thf(1701,plain,
! [SV214: $i > $o,SV104: $i,SV309: $i] :
( ( ( in @ SV309 @ SV104 )
= $false )
| ( ( ~ ( SV214 @ SV309 ) )
= $true )
| ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1702,plain,
! [SV214: $i > $o,SV104: $i,SV310: $i] :
( ( ( in @ SV310 @ SV104 )
= $false )
| ( ( ~ ( SV214 @ SV310 ) )
= $true )
| ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1703,plain,
! [SV107: $i,SV217: $i > $o,SV302: $i] :
( ( ( ~ ( in @ ( sK55_SY1213 @ SV302 @ SV217 @ SV107 ) @ SV107 )
| ( SV217 @ ( sK55_SY1213 @ SV302 @ SV217 @ SV107 ) ) )
= $false )
| ( ( in @ SV302 @ SV107 )
= $false )
| ( ( SV217 @ SV302 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1609]) ).
thf(1704,plain,
! [SV108: $i > $o,SV290: $i] :
( ( ( ( sK22_SY1286 @ SV290 @ SV108 )
!= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1707,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $false )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1708,plain,
! [SV291: $i,SV326: $i,SV110: $i > $o] :
( ( ( ! [SY1326: $i] :
( ~ ( SV110 @ SV326 )
| ~ ( SV110 @ SY1326 )
| ( SV326 = SY1326 ) ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1709,plain,
! [SV291: $i,SV327: $i,SV320: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ SV320 )
| ~ ( SV110 @ SV327 )
| ( SV320 = SV327 ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV291
= ( sK45_SY1287 @ SV291 @ SV110 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1710,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ! [SY1074: $i] :
~ ~ ( ~ ( SV112 @ SY1074 )
| ~ ! [SY1075: $i] :
( ~ ( SV112 @ SY1075 )
| ( SY1074 = SY1075 ) ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1711,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ~ ( ~ ( SV112 @ ( sK56_SY1074 @ SV292 @ SV112 ) )
| ~ ! [SY1327: $i] :
( ~ ( SV112 @ SY1327 )
| ( ( sK56_SY1074 @ SV292 @ SV112 )
= SY1327 ) ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1616]) ).
thf(1712,plain,
! [SV113: $i,SV220: $i] :
( ( in @ ( sK39_SY1268 @ SV220 @ SV113 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1713,plain,
! [SV220: $i,SV113: $i] :
( ( ( setadjoin @ ( setadjoin @ SV113 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV113 @ ( setadjoin @ SV220 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK6_SY1216 @ SV220 @ SV113 ) @ ( setadjoin @ ( sK39_SY1268 @ SV220 @ SV113 ) @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1714,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1715,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1716,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1621]) ).
thf(1719,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1720,plain,
! [SV120: $i,SV276: $o,SV226: $i,SV270: $i] :
( ( ( in @ SV270 @ SV226 )
= $true )
| ( SV276 = $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1722,plain,
! [SV120: $i,SV226: $i,SV270: $i] :
( ( ( in @ SV270 @ SV226 )
= $true )
| ( $false = $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1723,plain,
! [SV125: $i,SV303: $o,SV231: $i,SV273: $i] :
( ( ( in @ SV273 @ SV231 )
= $true )
| ( SV303 = $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1725,plain,
! [SV125: $i,SV231: $i,SV273: $i] :
( ( ( in @ SV273 @ SV231 )
= $true )
| ( $false = $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1726,plain,
! [SV293: $i,SV328: $i,SV128: $i > $o] :
( ( ( ! [SY1328: $i] :
( ~ ( SV128 @ SV328 )
| ~ ( SV128 @ SY1328 )
| ( SV328 = SY1328 ) ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1727,plain,
! [SV293: $i,SV329: $i,SV321: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ SV321 )
| ~ ( SV128 @ SV329 )
| ( SV321 = SV329 ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV293
= ( sK47_SY1290 @ SV293 @ SV128 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1728,plain,
! [SV233: $i > $o,SV130: $i,SV318: $i] :
( ( ( in @ SV318 @ SV130 )
= $false )
| ( ( ~ ( SV233 @ SV318 ) )
= $true )
| ( ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1729,plain,
! [SV233: $i > $o,SV130: $i,SV319: $i] :
( ( ( in @ SV319 @ SV130 )
= $false )
| ( ( ~ ( SV233 @ SV319 ) )
= $true )
| ( ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1730,plain,
! [SV32: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ ( sK2_SY874 @ SV32 ) ) )
= $true )
| ( ( ! [SY1319: $i] :
( ~ ( in @ SY1319 @ SV322 )
| ( in @ SY1319 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1731,plain,
! [SV330: $i,SV32: $i,SV323: $i] :
( ( ~ ~ ( ~ ( in @ SV323 @ SV32 )
| ~ ( in @ SV330 @ SV32 ) )
| ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) )
| ( SV323 = SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1732,plain,
! [SV313: $i,SV32: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SV313 @ ( sK2_SY874 @ SV32 ) ) )
= $true )
| ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV311 )
| ( in @ SY1314 @ SV313 ) )
| ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1733,plain,
! [SV304: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 ) )
= $false )
| ( ( ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1734,plain,
! [SV304: $i,SV32: $i] :
( ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1735,plain,
! [SV278: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV314 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1736,plain,
! [SV38: $i,SV315: $i,SV159: $i > $o] :
( ( ( SV159 @ SV315 )
= $false )
| ( ( in @ SV315 @ SV38 )
= $false )
| ( ( in @ ( sK20_SY1138 @ SV159 @ SV38 ) @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1737,plain,
! [SV38: $i,SV316: $i,SV159: $i > $o] :
( ( ( SV159 @ SV316 )
= $false )
| ( ( in @ SV316 @ SV38 )
= $false )
| ( ( SV159 @ ( sK20_SY1138 @ SV159 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1738,plain,
! [SV41: $i,SV279: $i,SV331: $i] :
( ( ( ~ ~ ( ~ ( in @ SV331 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SV331 @ SV41 ) ) )
= $true )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1739,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ~ ! [SY1330: $i] :
~ ( ~ ( ~ ( SV47 @ SY1330 )
| ( SY1330
= ( sK57_SY921 @ SV281 @ SV47 ) ) )
| ~ ( ( SY1330
!= ( sK57_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SY1330 ) ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1654]) ).
thf(1740,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ! [SY1322: $i] :
~ ( ~ ( ~ ( SV47 @ SY1322 )
| ( SY1322
= ( sK49_SY921 @ SV281 @ SV47 ) ) )
| ~ ( ( SY1322
!= ( sK49_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SY1322 ) ) ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1741,plain,
! [SV48: $i,SV166: $i,SV295: $i > $o,SV282: $i > $o] :
( ( ( ~ ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
| ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1743,plain,
! [SV64: $i,SV296: $o,SV182: $i,SV251: $i] :
( ( ( in @ SV251 @ SV182 )
= $true )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1744,plain,
! [SV182: $i,SV296: $o,SV64: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV64 ) )
= $false )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1755,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( in @ SV251 @ SV182 )
= $true )
| ( $false = $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1756,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ~ ( in @ SV251 @ SV64 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1760,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) ) )
= $true )
| ( ( ~ ! [SY1312: $i] :
~ ~ ( ~ ( in @ SY1312 @ SV184 )
| ~ ( SV66 @ SY1312 @ SV312 ) ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1761,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ~ ! [SY1313: $i] :
~ ~ ( ~ ( in @ SY1313 @ SV184 )
| ~ ( SV66 @ SY1313 @ SV312 ) ) )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1762,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( ~ ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1763,plain,
! [SV66: $i > $i > $o,SV184: $i,SV306: $i] :
( ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1764,plain,
! [SV71: $i,SV298: $i,SV187: $i > $o] :
( ( ( SV187 @ ( sK35_SY1173 @ SV298 @ SV187 @ SV71 ) )
= $false )
| ( ( SV187 @ SV298 )
= $true )
| ( ( in @ SV298 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1765,plain,
! [SV190: $i > $o,SV317: $i,SV74: $i > $o] :
( ( ( ~ ( SV74 @ SV317 ) )
= $true )
| ( ( ~ ! [SY1316: $i] :
( ~ ( SV74 @ SY1316 )
| ( SV317 = SY1316 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1766,plain,
! [SV74: $i > $o,SV190: $i > $o] :
( ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) )
| ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1685]) ).
thf(1769,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1770,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( SV76 @ ( sK51_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1323: $i] :
( ~ ( SV76 @ SY1323 )
| ( ( sK51_SY992 @ SV285 @ SV76 )
= SY1323 ) ) ) )
= $true )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1771,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ~ ( ~ ( SV76 @ ( sK58_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1331: $i] :
( ~ ( SV76 @ SY1331 )
| ( ( sK58_SY992 @ SV285 @ SV76 )
= SY1331 ) ) ) )
= $false )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1690]) ).
thf(1772,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( SV76 @ ( sK52_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1324: $i] :
( ~ ( SV76 @ SY1324 )
| ( ( sK52_SY992 @ SV285 @ SV76 )
= SY1324 ) ) ) )
= $true )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1773,plain,
! [SV85: $i,SV300: $i,SV199: $i > $o] :
( ( ( SV199 @ ( sK37_SY1194 @ SV300 @ SV199 @ SV85 ) )
= $false )
| ( ( SV199 @ SV300 )
= $true )
| ( ( in @ SV300 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1774,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( ~ ( SV92 @ ( sK59_SY1027 @ SV286 @ SV92 ) ) )
= $false )
| ( ( SV92 @ SV286 )
= $false )
| ( ( SV92 @ ( sK43_SY1283 @ SV286 @ SV92 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1694]) ).
thf(1775,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( SV92 @ ( sK53_SY1027 @ SV286 @ SV92 ) )
= $true )
| ( ( SV92 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1283 @ SV286 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1776,plain,
! [SV98: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ omega ) )
= $true )
| ( ( in @ SV324 @ SV98 )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( sK29_SY1039 @ SV98 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1777,plain,
! [SV98: $i,SV325: $i] :
( ( ( ~ ( in @ SV325 @ omega ) )
= $true )
| ( ( in @ SV325 @ SV98 )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1778,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ~ ( ~ ( SV99 @ ( sK60_SY1043 @ SV288 @ SV99 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV99 @ SY1332 )
| ( ( sK60_SY1043 @ SV288 @ SV99 )
= SY1332 ) ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1699]) ).
thf(1779,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( ~ ( SV99 @ ( sK54_SY1043 @ SV288 @ SV99 ) )
| ~ ! [SY1325: $i] :
( ~ ( SV99 @ SY1325 )
| ( ( sK54_SY1043 @ SV288 @ SV99 )
= SY1325 ) ) ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1780,plain,
! [SV104: $i,SV309: $i,SV214: $i > $o] :
( ( ( SV214 @ SV309 )
= $false )
| ( ( in @ SV309 @ SV104 )
= $false )
| ( ( in @ ( sK13_SY1209 @ SV214 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1781,plain,
! [SV104: $i,SV310: $i,SV214: $i > $o] :
( ( ( SV214 @ SV310 )
= $false )
| ( ( in @ SV310 @ SV104 )
= $false )
| ( ( SV214 @ ( sK13_SY1209 @ SV214 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1782,plain,
! [SV107: $i,SV217: $i > $o,SV302: $i] :
( ( ( ~ ( in @ ( sK55_SY1213 @ SV302 @ SV217 @ SV107 ) @ SV107 ) )
= $false )
| ( ( in @ SV302 @ SV107 )
= $false )
| ( ( SV217 @ SV302 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1783,plain,
! [SV107: $i,SV302: $i,SV217: $i > $o] :
( ( ( SV217 @ ( sK55_SY1213 @ SV302 @ SV217 @ SV107 ) )
= $false )
| ( ( in @ SV302 @ SV107 )
= $false )
| ( ( SV217 @ SV302 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1784,plain,
! [SV108: $i > $o,SV290: $i] :
( ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1787,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ~ ( ~ ( SV108 @ ( sK61_SY1062 @ SV290 @ SV108 ) )
| ~ ! [SY1333: $i] :
( ~ ( SV108 @ SY1333 )
| ( ( sK61_SY1062 @ SV290 @ SV108 )
= SY1333 ) ) ) )
= $false )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1707]) ).
thf(1788,plain,
! [SV291: $i,SV332: $i,SV326: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ SV326 )
| ~ ( SV110 @ SV332 )
| ( SV326 = SV332 ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1789,plain,
! [SV291: $i,SV327: $i,SV320: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ SV320 ) )
= $true )
| ( ( ~ ( SV110 @ SV327 )
| ( SV320 = SV327 ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV291
= ( sK45_SY1287 @ SV291 @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1790,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ~ ( ~ ( SV112 @ ( sK62_SY1074 @ SV292 @ SV112 ) )
| ~ ! [SY1334: $i] :
( ~ ( SV112 @ SY1334 )
| ( ( sK62_SY1074 @ SV292 @ SV112 )
= SY1334 ) ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1710]) ).
thf(1791,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( ~ ( SV112 @ ( sK56_SY1074 @ SV292 @ SV112 ) )
| ~ ! [SY1327: $i] :
( ~ ( SV112 @ SY1327 )
| ( ( sK56_SY1074 @ SV292 @ SV112 )
= SY1327 ) ) ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1792,plain,
! [SV225: $i > $o,SV333: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ SV333 )
| ~ ! [SY1335: $i] :
( ~ ( SV118 @ SY1335 )
| ( SV333 = SY1335 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1793,plain,
! [SV118: $i > $o,SV334: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ SV334 )
| ~ ! [SY1336: $i] :
( ~ ( SV225 @ SY1336 )
| ( SV334 = SY1336 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(1794,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1797,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(1798,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(1799,plain,
! [SV293: $i,SV335: $i,SV328: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ SV328 )
| ~ ( SV128 @ SV335 )
| ( SV328 = SV335 ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1800,plain,
! [SV293: $i,SV329: $i,SV321: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ SV321 ) )
= $true )
| ( ( ~ ( SV128 @ SV329 )
| ( SV321 = SV329 ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV293
= ( sK47_SY1290 @ SV293 @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1801,plain,
! [SV130: $i,SV318: $i,SV233: $i > $o] :
( ( ( SV233 @ SV318 )
= $false )
| ( ( in @ SV318 @ SV130 )
= $false )
| ( ( in @ ( sK23_SY1238 @ SV233 @ SV130 ) @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1802,plain,
! [SV130: $i,SV319: $i,SV233: $i > $o] :
( ( ( SV233 @ SV319 )
= $false )
| ( ( in @ SV319 @ SV130 )
= $false )
| ( ( SV233 @ ( sK23_SY1238 @ SV233 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1803,plain,
! [SV32: $i,SV322: $i] :
( ( ( in @ SV322 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( ! [SY1319: $i] :
( ~ ( in @ SY1319 @ SV322 )
| ( in @ SY1319 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1804,plain,
! [SV330: $i,SV32: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( in @ SV323 @ SV32 )
| ~ ( in @ SV330 @ SV32 ) ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) )
| ( SV323 = SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1805,plain,
! [SV313: $i,SV32: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ ( sK2_SY874 @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ SV313 @ ( sK2_SY874 @ SV32 ) ) )
= $true )
| ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV311 )
| ( in @ SY1314 @ SV313 ) )
| ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1806,plain,
! [SV304: $i,SV32: $i] :
( ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( ~ ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1733]) ).
thf(1807,plain,
! [SV32: $i,SV304: $i] :
( ( ( ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1808,plain,
! [SV278: $i,SV314: $i] :
( ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV314 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1809,plain,
! [SV41: $i,SV279: $i,SV331: $i] :
( ( ( ~ ( ~ ( in @ SV331 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SV331 @ SV41 ) ) )
= $false )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1810,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( ! [SY1330: $i] :
~ ( ~ ( ~ ( SV47 @ SY1330 )
| ( SY1330
= ( sK57_SY921 @ SV281 @ SV47 ) ) )
| ~ ( ( SY1330
!= ( sK57_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SY1330 ) ) ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1811,plain,
! [SV281: $i,SV336: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV47 @ SV336 )
| ( SV336
= ( sK49_SY921 @ SV281 @ SV47 ) ) )
| ~ ( ( SV336
!= ( sK49_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SV336 ) ) ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(1812,plain,
! [SV48: $i,SV166: $i,SV295: $i > $o,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
| ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) ) )
= $false )
| ( ( ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1813,plain,
! [SV182: $i,SV296: $o,SV64: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV64 ) )
= $true )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1819,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV64 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1822,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( ~ ! [SY1312: $i] :
~ ~ ( ~ ( in @ SY1312 @ SV184 )
| ~ ( SV66 @ SY1312 @ SV312 ) ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1823,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ! [SY1313: $i] :
~ ~ ( ~ ( in @ SY1313 @ SV184 )
| ~ ( SV66 @ SY1313 @ SV312 ) ) )
= $false )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1824,plain,
! [SV306: $i,SV184: $i,SV66: $i > $i > $o] :
( ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1825,plain,
! [SV306: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1826,plain,
! [SV190: $i > $o,SV317: $i,SV74: $i > $o] :
( ( ( SV74 @ SV317 )
= $false )
| ( ( ~ ! [SY1316: $i] :
( ~ ( SV74 @ SY1316 )
| ( SV317 = SY1316 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1827,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1830,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1831,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK51_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1323: $i] :
( ~ ( SV76 @ SY1323 )
| ( ( sK51_SY992 @ SV285 @ SV76 )
= SY1323 ) ) )
= $false )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1832,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( SV76 @ ( sK58_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1331: $i] :
( ~ ( SV76 @ SY1331 )
| ( ( sK58_SY992 @ SV285 @ SV76 )
= SY1331 ) ) ) )
= $true )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1833,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK52_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1324: $i] :
( ~ ( SV76 @ SY1324 )
| ( ( sK52_SY992 @ SV285 @ SV76 )
= SY1324 ) ) )
= $false )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1834,plain,
! [SV286: $i,SV92: $i > $o] :
( ( ( SV92 @ ( sK59_SY1027 @ SV286 @ SV92 ) )
= $true )
| ( ( SV92 @ SV286 )
= $false )
| ( ( SV92 @ ( sK43_SY1283 @ SV286 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1835,plain,
! [SV98: $i,SV324: $i] :
( ( ( in @ SV324 @ omega )
= $false )
| ( ( in @ SV324 @ SV98 )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( sK29_SY1039 @ SV98 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1836,plain,
! [SV98: $i,SV325: $i] :
( ( ( in @ SV325 @ omega )
= $false )
| ( ( in @ SV325 @ SV98 )
= $true )
| ( ( in @ emptyset @ SV98 )
= $false )
| ( ( in @ ( sK29_SY1039 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1837,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( ~ ( SV99 @ ( sK60_SY1043 @ SV288 @ SV99 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV99 @ SY1332 )
| ( ( sK60_SY1043 @ SV288 @ SV99 )
= SY1332 ) ) ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1838,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ ( sK54_SY1043 @ SV288 @ SV99 ) )
| ~ ! [SY1325: $i] :
( ~ ( SV99 @ SY1325 )
| ( ( sK54_SY1043 @ SV288 @ SV99 )
= SY1325 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1839,plain,
! [SV107: $i,SV217: $i > $o,SV302: $i] :
( ( ( in @ ( sK55_SY1213 @ SV302 @ SV217 @ SV107 ) @ SV107 )
= $true )
| ( ( in @ SV302 @ SV107 )
= $false )
| ( ( SV217 @ SV302 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1782]) ).
thf(1840,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ! [SY1062: $i] :
~ ~ ( ~ ( SV108 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV108 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1843,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( ~ ( SV108 @ ( sK61_SY1062 @ SV290 @ SV108 ) )
| ~ ! [SY1333: $i] :
( ~ ( SV108 @ SY1333 )
| ( ( sK61_SY1062 @ SV290 @ SV108 )
= SY1333 ) ) ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1844,plain,
! [SV291: $i,SV332: $i,SV326: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ SV326 ) )
= $true )
| ( ( ~ ( SV110 @ SV332 )
| ( SV326 = SV332 ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(1845,plain,
! [SV291: $i,SV327: $i,SV320: $i,SV110: $i > $o] :
( ( ( SV110 @ SV320 )
= $false )
| ( ( ~ ( SV110 @ SV327 )
| ( SV320 = SV327 ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV291
= ( sK45_SY1287 @ SV291 @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1846,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( ~ ( SV112 @ ( sK62_SY1074 @ SV292 @ SV112 ) )
| ~ ! [SY1334: $i] :
( ~ ( SV112 @ SY1334 )
| ( ( sK62_SY1074 @ SV292 @ SV112 )
= SY1334 ) ) ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1847,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ ( sK56_SY1074 @ SV292 @ SV112 ) )
| ~ ! [SY1327: $i] :
( ~ ( SV112 @ SY1327 )
| ( ( sK56_SY1074 @ SV292 @ SV112 )
= SY1327 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1848,plain,
! [SV225: $i > $o,SV333: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ SV333 )
| ~ ! [SY1335: $i] :
( ~ ( SV118 @ SY1335 )
| ( SV333 = SY1335 ) ) ) )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1849,plain,
! [SV118: $i > $o,SV334: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ SV334 )
| ~ ! [SY1336: $i] :
( ~ ( SV225 @ SY1336 )
| ( SV334 = SY1336 ) ) ) )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1850,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
| ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(1855,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1856,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1857,plain,
! [SV293: $i,SV335: $i,SV328: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ SV328 ) )
= $true )
| ( ( ~ ( SV128 @ SV335 )
| ( SV328 = SV335 ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1858,plain,
! [SV293: $i,SV329: $i,SV321: $i,SV128: $i > $o] :
( ( ( SV128 @ SV321 )
= $false )
| ( ( ~ ( SV128 @ SV329 )
| ( SV321 = SV329 ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV293
= ( sK47_SY1290 @ SV293 @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1859,plain,
! [SV32: $i,SV322: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ SV322 )
| ( in @ SV337 @ SV32 ) )
= $true )
| ( ( in @ SV322 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(1860,plain,
! [SV330: $i,SV32: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ SV323 @ SV32 )
| ~ ( in @ SV330 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) )
| ( SV323 = SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1861,plain,
! [SV313: $i,SV32: $i,SV311: $i] :
( ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( ~ ( in @ SV313 @ ( sK2_SY874 @ SV32 ) ) )
= $true )
| ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV311 )
| ( in @ SY1314 @ SV313 ) )
| ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1862,plain,
! [SV32: $i,SV304: $i] :
( ( ( ~ ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1863,plain,
! [SV32: $i,SV304: $i] :
( ( ( ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1864,plain,
! [SV314: $i,SV278: $i] :
( ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV314 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1865,plain,
! [SV41: $i,SV279: $i,SV331: $i] :
( ( ( ~ ( in @ SV331 @ ( sK27_SY908 @ SV279 @ SV41 ) )
| ~ ( in @ SV331 @ SV41 ) )
= $true )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1866,plain,
! [SV281: $i,SV338: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV47 @ SV338 )
| ( SV338
= ( sK57_SY921 @ SV281 @ SV47 ) ) )
| ~ ( ( SV338
!= ( sK57_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SV338 ) ) ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(1867,plain,
! [SV281: $i,SV336: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ SV336 )
| ( SV336
= ( sK49_SY921 @ SV281 @ SV47 ) ) )
| ~ ( ( SV336
!= ( sK49_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SV336 ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1868,plain,
! [SV48: $i,SV166: $i,SV295: $i > $o,SV282: $i > $o] :
( ( ( ~ ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) )
= $false )
| ( ( ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1812]) ).
thf(1869,plain,
! [SV166: $i,SV282: $i > $o,SV48: $i,SV295: $i > $o] :
( ( ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
= $false )
| ( ( ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1812]) ).
thf(1870,plain,
! [SV182: $i,SV296: $o,SV64: $i,SV251: $i] :
( ( ( in @ SV251 @ SV64 )
= $false )
| ( SV296 = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1874,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( in @ SV251 @ SV64 )
= $false )
| ( $false = $true )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1876,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1312: $i] :
~ ~ ( ~ ( in @ SY1312 @ SV184 )
| ~ ( SV66 @ SY1312 @ SV312 ) ) )
= $false )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1877,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1313: $i] :
~ ~ ( ~ ( in @ SY1313 @ SV184 )
| ~ ( SV66 @ SY1313 @ SV312 ) ) )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1878,plain,
! [SV306: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1165: $i] :
~ ! [SY1166: $i] :
~ ( ~ ( ~ ( in @ SY1166 @ SY1165 )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1166 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1166 ) )
| ( in @ SY1166 @ SY1165 ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1879,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i] :
( ( ( ~ ! [SY1339: $i] :
~ ( ~ ( ~ ( in @ SY1339 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1339 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1339 ) )
| ( in @ SY1339 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1825]) ).
thf(1880,plain,
! [SV190: $i > $o,SV317: $i,SV74: $i > $o] :
( ( ( ! [SY1316: $i] :
( ~ ( SV74 @ SY1316 )
| ( SV317 = SY1316 ) ) )
= $false )
| ( ( SV74 @ SV317 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1881,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1884,plain,
! [SV190: $i > $o,SV339: $i,SV74: $i > $o] :
( ( ( ~ ~ ( ~ ( SV74 @ SV339 )
| ~ ! [SY1342: $i] :
( ~ ( SV74 @ SY1342 )
| ( SV339 = SY1342 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(1885,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK51_SY992 @ SV285 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1886,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ! [SY1323: $i] :
( ~ ( SV76 @ SY1323 )
| ( ( sK51_SY992 @ SV285 @ SV76 )
= SY1323 ) ) )
= $false )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1887,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK58_SY992 @ SV285 @ SV76 ) )
| ~ ! [SY1331: $i] :
( ~ ( SV76 @ SY1331 )
| ( ( sK58_SY992 @ SV285 @ SV76 )
= SY1331 ) ) )
= $false )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1888,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK52_SY992 @ SV285 @ SV76 ) ) )
= $false )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1833]) ).
thf(1889,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ! [SY1324: $i] :
( ~ ( SV76 @ SY1324 )
| ( ( sK52_SY992 @ SV285 @ SV76 )
= SY1324 ) ) )
= $false )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1833]) ).
thf(1890,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ ( sK60_SY1043 @ SV288 @ SV99 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV99 @ SY1332 )
| ( ( sK60_SY1043 @ SV288 @ SV99 )
= SY1332 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1891,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ ( sK54_SY1043 @ SV288 @ SV99 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1892,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ! [SY1325: $i] :
( ~ ( SV99 @ SY1325 )
| ( ( sK54_SY1043 @ SV288 @ SV99 )
= SY1325 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1893,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ~ ( ~ ( SV108 @ ( sK66_SY1062 @ SV290 @ SV108 ) )
| ~ ! [SY1343: $i] :
( ~ ( SV108 @ SY1343 )
| ( ( sK66_SY1062 @ SV290 @ SV108 )
= SY1343 ) ) ) )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1840]) ).
thf(1896,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ ( sK61_SY1062 @ SV290 @ SV108 ) )
| ~ ! [SY1333: $i] :
( ~ ( SV108 @ SY1333 )
| ( ( sK61_SY1062 @ SV290 @ SV108 )
= SY1333 ) ) )
= $false )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(1897,plain,
! [SV291: $i,SV332: $i,SV326: $i,SV110: $i > $o] :
( ( ( SV110 @ SV326 )
= $false )
| ( ( ~ ( SV110 @ SV332 )
| ( SV326 = SV332 ) )
= $true )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1898,plain,
! [SV291: $i,SV320: $i,SV327: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ SV327 ) )
= $true )
| ( ( SV320 = SV327 )
= $true )
| ( ( SV110 @ SV320 )
= $false )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV291
= ( sK45_SY1287 @ SV291 @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1899,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ ( sK62_SY1074 @ SV292 @ SV112 ) )
| ~ ! [SY1334: $i] :
( ~ ( SV112 @ SY1334 )
| ( ( sK62_SY1074 @ SV292 @ SV112 )
= SY1334 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1900,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ ( sK56_SY1074 @ SV292 @ SV112 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1847]) ).
thf(1901,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ! [SY1327: $i] :
( ~ ( SV112 @ SY1327 )
| ( ( sK56_SY1074 @ SV292 @ SV112 )
= SY1327 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1847]) ).
thf(1902,plain,
! [SV225: $i > $o,SV333: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV333 )
| ~ ! [SY1335: $i] :
( ~ ( SV118 @ SY1335 )
| ( SV333 = SY1335 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1903,plain,
! [SV118: $i > $o,SV334: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV334 )
| ~ ! [SY1336: $i] :
( ~ ( SV225 @ SY1336 )
| ( SV334 = SY1336 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1904,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(1905,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(1910,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(1911,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(1912,plain,
! [SV293: $i,SV335: $i,SV328: $i,SV128: $i > $o] :
( ( ( SV128 @ SV328 )
= $false )
| ( ( ~ ( SV128 @ SV335 )
| ( SV328 = SV335 ) )
= $true )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1913,plain,
! [SV293: $i,SV321: $i,SV329: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ SV329 ) )
= $true )
| ( ( SV321 = SV329 )
= $true )
| ( ( SV128 @ SV321 )
= $false )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV293
= ( sK47_SY1290 @ SV293 @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(1914,plain,
! [SV32: $i,SV322: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ SV322 ) )
= $true )
| ( ( in @ SV337 @ SV32 )
= $true )
| ( ( in @ SV322 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(1915,plain,
! [SV330: $i,SV32: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV32 )
| ~ ( in @ SV330 @ SV32 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) )
| ( SV323 = SV330 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1916,plain,
! [SV311: $i,SV32: $i,SV313: $i] :
( ( ( in @ SV313 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV311 )
| ( in @ SY1314 @ SV313 ) )
| ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1917,plain,
! [SV32: $i,SV304: $i] :
( ( ( ! [SY1296: $i] :
~ ( in @ SY1296 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1918,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1919,plain,
! [SV41: $i,SV279: $i,SV331: $i] :
( ( ( ~ ( in @ SV331 @ ( sK27_SY908 @ SV279 @ SV41 ) ) )
= $true )
| ( ( ~ ( in @ SV331 @ SV41 ) )
= $true )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1920,plain,
! [SV281: $i,SV338: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ SV338 )
| ( SV338
= ( sK57_SY921 @ SV281 @ SV47 ) ) )
| ~ ( ( SV338
!= ( sK57_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SV338 ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1921,plain,
! [SV281: $i,SV336: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ SV336 )
| ( SV336
= ( sK49_SY921 @ SV281 @ SV47 ) ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1922,plain,
! [SV47: $i > $o,SV281: $i,SV336: $i] :
( ( ( ~ ( ( SV336
!= ( sK49_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SV336 ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1923,plain,
! [SV48: $i,SV166: $i,SV295: $i > $o,SV282: $i > $o] :
( ( ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
= $true )
| ( ( ~ ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1868]) ).
thf(1924,plain,
! [SV166: $i,SV282: $i > $o,SV48: $i,SV295: $i > $o] :
( ( ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) )
= $false )
| ( ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1925,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV312 ) ) )
= $false )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1876]) ).
thf(1926,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i,SV341: $i] :
( ( ( ~ ~ ( ~ ( in @ SV341 @ SV184 )
| ~ ( SV66 @ SV341 @ SV312 ) ) )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(1927,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i] :
( ( ( ~ ! [SY1344: $i] :
~ ( ~ ( ~ ( in @ SY1344 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1344 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1344 ) )
| ( in @ SY1344 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1878]) ).
thf(1928,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i] :
( ( ( ! [SY1339: $i] :
~ ( ~ ( ~ ( in @ SY1339 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1339 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1339 ) )
| ( in @ SY1339 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1879]) ).
thf(1929,plain,
! [SV317: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
| ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) ) )
= $false )
| ( ( SV74 @ SV317 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1880]) ).
thf(1930,plain,
! [SV190: $i > $o,SV74: $i > $o] :
( ( ( ! [SY982: $i] :
~ ~ ( ~ ( SV74 @ SY982 )
| ~ ! [SY983: $i] :
( ~ ( SV74 @ SY983 )
| ( SY982 = SY983 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(1933,plain,
! [SV190: $i > $o,SV339: $i,SV74: $i > $o] :
( ( ( ~ ( ~ ( SV74 @ SV339 )
| ~ ! [SY1342: $i] :
( ~ ( SV74 @ SY1342 )
| ( SV339 = SY1342 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1934,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK51_SY992 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(1935,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ! [SY1323: $i] :
( ~ ( SV76 @ SY1323 )
| ( ( sK51_SY992 @ SV285 @ SV76 )
= SY1323 ) ) )
= $true )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1936,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK58_SY992 @ SV285 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(1937,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ~ ! [SY1331: $i] :
( ~ ( SV76 @ SY1331 )
| ( ( sK58_SY992 @ SV285 @ SV76 )
= SY1331 ) ) )
= $false )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1887]) ).
thf(1938,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK52_SY992 @ SV285 @ SV76 ) )
= $true )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1888]) ).
thf(1939,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ! [SY1324: $i] :
( ~ ( SV76 @ SY1324 )
| ( ( sK52_SY992 @ SV285 @ SV76 )
= SY1324 ) ) )
= $true )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1889]) ).
thf(1940,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ ( sK60_SY1043 @ SV288 @ SV99 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1941,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ~ ! [SY1332: $i] :
( ~ ( SV99 @ SY1332 )
| ( ( sK60_SY1043 @ SV288 @ SV99 )
= SY1332 ) ) )
= $false )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1942,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( SV99 @ ( sK54_SY1043 @ SV288 @ SV99 ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1943,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ! [SY1325: $i] :
( ~ ( SV99 @ SY1325 )
| ( ( sK54_SY1043 @ SV288 @ SV99 )
= SY1325 ) ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(1944,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( ~ ( SV108 @ ( sK66_SY1062 @ SV290 @ SV108 ) )
| ~ ! [SY1343: $i] :
( ~ ( SV108 @ SY1343 )
| ( ( sK66_SY1062 @ SV290 @ SV108 )
= SY1343 ) ) ) )
= $true )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(1947,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ ( sK61_SY1062 @ SV290 @ SV108 ) ) )
= $false )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1948,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ! [SY1333: $i] :
( ~ ( SV108 @ SY1333 )
| ( ( sK61_SY1062 @ SV290 @ SV108 )
= SY1333 ) ) )
= $false )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1949,plain,
! [SV291: $i,SV326: $i,SV332: $i,SV110: $i > $o] :
( ( ( ~ ( SV110 @ SV332 ) )
= $true )
| ( ( SV326 = SV332 )
= $true )
| ( ( SV110 @ SV326 )
= $false )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(1950,plain,
! [SV291: $i,SV320: $i,SV327: $i,SV110: $i > $o] :
( ( ( SV110 @ SV327 )
= $false )
| ( ( SV320 = SV327 )
= $true )
| ( ( SV110 @ SV320 )
= $false )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV291
= ( sK45_SY1287 @ SV291 @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(1951,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ ( sK62_SY1074 @ SV292 @ SV112 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1952,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ~ ! [SY1334: $i] :
( ~ ( SV112 @ SY1334 )
| ( ( sK62_SY1074 @ SV292 @ SV112 )
= SY1334 ) ) )
= $false )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(1953,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( SV112 @ ( sK56_SY1074 @ SV292 @ SV112 ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(1954,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ! [SY1327: $i] :
( ~ ( SV112 @ SY1327 )
| ( ( sK56_SY1074 @ SV292 @ SV112 )
= SY1327 ) ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(1955,plain,
! [SV225: $i > $o,SV333: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV333 ) )
= $true )
| ( ( ~ ! [SY1335: $i] :
( ~ ( SV118 @ SY1335 )
| ( SV333 = SY1335 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(1956,plain,
! [SV118: $i > $o,SV334: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV334 ) )
= $true )
| ( ( ~ ! [SY1336: $i] :
( ~ ( SV225 @ SY1336 )
| ( SV334 = SY1336 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(1957,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) )
| ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(1958,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(1963,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1964,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1965,plain,
! [SV293: $i,SV328: $i,SV335: $i,SV128: $i > $o] :
( ( ( ~ ( SV128 @ SV335 ) )
= $true )
| ( ( SV328 = SV335 )
= $true )
| ( ( SV128 @ SV328 )
= $false )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(1966,plain,
! [SV293: $i,SV321: $i,SV329: $i,SV128: $i > $o] :
( ( ( SV128 @ SV329 )
= $false )
| ( ( SV321 = SV329 )
= $true )
| ( ( SV128 @ SV321 )
= $false )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV293
= ( sK47_SY1290 @ SV293 @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1967,plain,
! [SV32: $i,SV322: $i,SV337: $i] :
( ( ( in @ SV337 @ SV322 )
= $false )
| ( ( in @ SV337 @ SV32 )
= $true )
| ( ( in @ SV322 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1968,plain,
! [SV330: $i,SV32: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV32 ) )
= $true )
| ( ( ~ ( in @ SV330 @ SV32 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) )
| ( SV323 = SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(1969,plain,
! [SV32: $i,SV313: $i,SV311: $i] :
( ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV311 )
| ( in @ SY1314 @ SV313 ) ) )
= $true )
| ( ( ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true )
| ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ SV313 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(1970,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ( in @ SV344 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(1971,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( in @ SV340 @ SV304 )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(1972,plain,
! [SV41: $i,SV279: $i,SV331: $i] :
( ( ( in @ SV331 @ ( sK27_SY908 @ SV279 @ SV41 ) )
= $false )
| ( ( ~ ( in @ SV331 @ SV41 ) )
= $true )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1973,plain,
! [SV281: $i,SV338: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ SV338 )
| ( SV338
= ( sK57_SY921 @ SV281 @ SV47 ) ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1920]) ).
thf(1974,plain,
! [SV47: $i > $o,SV281: $i,SV338: $i] :
( ( ( ~ ( ( SV338
!= ( sK57_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SV338 ) ) )
= $false )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1920]) ).
thf(1975,plain,
! [SV281: $i,SV336: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV336 )
| ( SV336
= ( sK49_SY921 @ SV281 @ SV47 ) ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(1976,plain,
! [SV47: $i > $o,SV281: $i,SV336: $i] :
( ( ( ( SV336
!= ( sK49_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SV336 ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1922]) ).
thf(1977,plain,
! [SV166: $i,SV282: $i > $o,SV48: $i,SV295: $i > $o] :
( ( ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
| ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) ) )
= $false )
| ( ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(1979,plain,
! [SV48: $i,SV166: $i,SV295: $i > $o,SV282: $i > $o] :
( ( ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
= $false )
| ( ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
= $false )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(1980,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV312 ) ) )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1981,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i,SV341: $i] :
( ( ( ~ ( ~ ( in @ SV341 @ SV184 )
| ~ ( SV66 @ SV341 @ SV312 ) ) )
= $false )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(1982,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i] :
( ( ( ! [SY1344: $i] :
~ ( ~ ( ~ ( in @ SY1344 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1167: $i] :
~ ~ ( ~ ( in @ SY1167 @ SV184 )
| ~ ( SV66 @ SY1167 @ SY1344 ) ) )
| ~ ( ~ ~ ! [SY1168: $i] :
~ ~ ( ~ ( in @ SY1168 @ SV184 )
| ~ ( SV66 @ SY1168 @ SY1344 ) )
| ( in @ SY1344 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(1983,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV345: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1349: $i] :
~ ~ ( ~ ( in @ SY1349 @ SV184 )
| ~ ( SV66 @ SY1349 @ SV345 ) ) )
| ~ ( ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ SV184 )
| ~ ( SV66 @ SY1350 @ SV345 ) )
| ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(1984,plain,
! [SV317: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) ) )
= $false )
| ( ( SV74 @ SV317 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(1985,plain,
! [SV74: $i > $o,SV190: $i > $o,SV317: $i] :
( ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( SV74 @ SV317 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(1986,plain,
! [SV190: $i > $o,SV346: $i,SV74: $i > $o] :
( ( ( ~ ~ ( ~ ( SV74 @ SV346 )
| ~ ! [SY1351: $i] :
( ~ ( SV74 @ SY1351 )
| ( SV346 = SY1351 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(1989,plain,
! [SV190: $i > $o,SV339: $i,SV74: $i > $o] :
( ( ( ~ ( SV74 @ SV339 )
| ~ ! [SY1342: $i] :
( ~ ( SV74 @ SY1342 )
| ( SV339 = SY1342 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1933]) ).
thf(1990,plain,
! [SV285: $i,SV347: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV347 )
| ( ( sK51_SY992 @ SV285 @ SV76 )
= SV347 ) )
= $true )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(1991,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK58_SY992 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(1992,plain,
! [SV285: $i,SV76: $i > $o] :
( ( ( ! [SY1331: $i] :
( ~ ( SV76 @ SY1331 )
| ( ( sK58_SY992 @ SV285 @ SV76 )
= SY1331 ) ) )
= $true )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(1993,plain,
! [SV285: $i,SV348: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV348 )
| ( ( sK52_SY992 @ SV285 @ SV76 )
= SV348 ) )
= $true )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(1994,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( SV99 @ ( sK60_SY1043 @ SV288 @ SV99 ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(1995,plain,
! [SV288: $i,SV99: $i > $o] :
( ( ( ! [SY1332: $i] :
( ~ ( SV99 @ SY1332 )
| ( ( sK60_SY1043 @ SV288 @ SV99 )
= SY1332 ) ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1941]) ).
thf(1996,plain,
! [SV288: $i,SV349: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ SV349 )
| ( ( sK54_SY1043 @ SV288 @ SV99 )
= SV349 ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(1997,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ ( sK66_SY1062 @ SV290 @ SV108 ) )
| ~ ! [SY1343: $i] :
( ~ ( SV108 @ SY1343 )
| ( ( sK66_SY1062 @ SV290 @ SV108 )
= SY1343 ) ) )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2002,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( SV108 @ ( sK61_SY1062 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1947]) ).
thf(2003,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ! [SY1333: $i] :
( ~ ( SV108 @ SY1333 )
| ( ( sK61_SY1062 @ SV290 @ SV108 )
= SY1333 ) ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2004,plain,
! [SV291: $i,SV326: $i,SV332: $i,SV110: $i > $o] :
( ( ( SV110 @ SV332 )
= $false )
| ( ( SV326 = SV332 )
= $true )
| ( ( SV110 @ SV326 )
= $false )
| ( ( SV110 @ SV291 )
= $false )
| ( ( SV110 @ ( sK45_SY1287 @ SV291 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2005,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( SV112 @ ( sK62_SY1074 @ SV292 @ SV112 ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(2006,plain,
! [SV292: $i,SV112: $i > $o] :
( ( ( ! [SY1334: $i] :
( ~ ( SV112 @ SY1334 )
| ( ( sK62_SY1074 @ SV292 @ SV112 )
= SY1334 ) ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2007,plain,
! [SV292: $i,SV350: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ SV350 )
| ( ( sK56_SY1074 @ SV292 @ SV112 )
= SV350 ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2008,plain,
! [SV225: $i > $o,SV333: $i,SV118: $i > $o] :
( ( ( SV118 @ SV333 )
= $false )
| ( ( ~ ! [SY1335: $i] :
( ~ ( SV118 @ SY1335 )
| ( SV333 = SY1335 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2009,plain,
! [SV118: $i > $o,SV334: $i,SV225: $i > $o] :
( ( ( SV225 @ SV334 )
= $false )
| ( ( ~ ! [SY1336: $i] :
( ~ ( SV225 @ SY1336 )
| ( SV334 = SY1336 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2010,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2011,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2016,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(2017,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1964]) ).
thf(2018,plain,
! [SV293: $i,SV328: $i,SV335: $i,SV128: $i > $o] :
( ( ( SV128 @ SV335 )
= $false )
| ( ( SV328 = SV335 )
= $true )
| ( ( SV128 @ SV328 )
= $false )
| ( ( SV128 @ SV293 )
= $false )
| ( ( SV128 @ ( sK47_SY1290 @ SV293 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2019,plain,
! [SV330: $i,SV32: $i,SV323: $i] :
( ( ( in @ SV323 @ SV32 )
= $false )
| ( ( ~ ( in @ SV330 @ SV32 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) )
| ( SV323 = SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2020,plain,
! [SV32: $i,SV313: $i,SV311: $i,SV351: $i] :
( ( ( ~ ( in @ SV351 @ SV311 )
| ( in @ SV351 @ SV313 ) )
= $true )
| ( ( ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true )
| ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ SV313 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2021,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( in @ SV344 @ SV304 )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2022,plain,
! [SV340: $i,SV304: $i,SV32: $i] :
( ( ( ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1971]) ).
thf(2023,plain,
! [SV279: $i,SV41: $i,SV331: $i] :
( ( ( in @ SV331 @ SV41 )
= $false )
| ( ( in @ SV331 @ ( sK27_SY908 @ SV279 @ SV41 ) )
= $false )
| ( ( in @ SV279 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2024,plain,
! [SV281: $i,SV338: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV338 )
| ( SV338
= ( sK57_SY921 @ SV281 @ SV47 ) ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(2025,plain,
! [SV47: $i > $o,SV281: $i,SV338: $i] :
( ( ( ( SV338
!= ( sK57_SY921 @ SV281 @ SV47 ) )
| ( SV47 @ SV338 ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2026,plain,
! [SV281: $i,SV336: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV336 ) )
= $true )
| ( ( SV336
= ( sK49_SY921 @ SV281 @ SV47 ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2027,plain,
! [SV47: $i > $o,SV281: $i,SV336: $i] :
( ( ( SV336
!= ( sK49_SY921 @ SV281 @ SV47 ) )
= $true )
| ( ( SV47 @ SV336 )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2028,plain,
! [SV166: $i,SV282: $i > $o,SV48: $i,SV295: $i > $o] :
( ( ( ~ ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) ) )
= $false )
| ( ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2031,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ( in @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV312 ) )
= $false )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2032,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV184 )
| ~ ( SV66 @ SV341 @ SV312 ) )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1981]) ).
thf(2033,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV352: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1352: $i] :
~ ~ ( ~ ( in @ SY1352 @ SV184 )
| ~ ( SV66 @ SY1352 @ SV352 ) ) )
| ~ ( ~ ~ ! [SY1353: $i] :
~ ~ ( ~ ( in @ SY1353 @ SV184 )
| ~ ( SV66 @ SY1353 @ SV352 ) )
| ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2034,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV345: $i] :
( ( ( ~ ( ~ ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1349: $i] :
~ ~ ( ~ ( in @ SY1349 @ SV184 )
| ~ ( SV66 @ SY1349 @ SV345 ) ) )
| ~ ( ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ SV184 )
| ~ ( SV66 @ SY1350 @ SV345 ) )
| ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2035,plain,
! [SV317: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2036,plain,
! [SV317: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2037,plain,
! [SV190: $i > $o,SV346: $i,SV74: $i > $o] :
( ( ( ~ ( ~ ( SV74 @ SV346 )
| ~ ! [SY1351: $i] :
( ~ ( SV74 @ SY1351 )
| ( SV346 = SY1351 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2040,plain,
! [SV190: $i > $o,SV339: $i,SV74: $i > $o] :
( ( ( ~ ( SV74 @ SV339 ) )
= $true )
| ( ( ~ ! [SY1342: $i] :
( ~ ( SV74 @ SY1342 )
| ( SV339 = SY1342 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2041,plain,
! [SV285: $i,SV347: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV347 ) )
= $true )
| ( ( ( sK51_SY992 @ SV285 @ SV76 )
= SV347 )
= $true )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2042,plain,
! [SV285: $i,SV353: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV353 )
| ( ( sK58_SY992 @ SV285 @ SV76 )
= SV353 ) )
= $true )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2043,plain,
! [SV285: $i,SV348: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV348 ) )
= $true )
| ( ( ( sK52_SY992 @ SV285 @ SV76 )
= SV348 )
= $true )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2044,plain,
! [SV288: $i,SV354: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ SV354 )
| ( ( sK60_SY1043 @ SV288 @ SV99 )
= SV354 ) )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2045,plain,
! [SV288: $i,SV349: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ SV349 ) )
= $true )
| ( ( ( sK54_SY1043 @ SV288 @ SV99 )
= SV349 )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2046,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ ( sK66_SY1062 @ SV290 @ SV108 ) ) )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2047,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ~ ! [SY1343: $i] :
( ~ ( SV108 @ SY1343 )
| ( ( sK66_SY1062 @ SV290 @ SV108 )
= SY1343 ) ) )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1997]) ).
thf(2052,plain,
! [SV290: $i,SV355: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ SV355 )
| ( ( sK61_SY1062 @ SV290 @ SV108 )
= SV355 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2053,plain,
! [SV292: $i,SV356: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ SV356 )
| ( ( sK62_SY1074 @ SV292 @ SV112 )
= SV356 ) )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2054,plain,
! [SV292: $i,SV350: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ SV350 ) )
= $true )
| ( ( ( sK56_SY1074 @ SV292 @ SV112 )
= SV350 )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2055,plain,
! [SV225: $i > $o,SV333: $i,SV118: $i > $o] :
( ( ( ! [SY1335: $i] :
( ~ ( SV118 @ SY1335 )
| ( SV333 = SY1335 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2056,plain,
! [SV118: $i > $o,SV334: $i,SV225: $i > $o] :
( ( ( ! [SY1336: $i] :
( ~ ( SV225 @ SY1336 )
| ( SV334 = SY1336 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2057,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2058,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2063,plain,
! [SV225: $i > $o,SV357: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ SV357 )
| ~ ! [SY1354: $i] :
( ~ ( SV118 @ SY1354 )
| ( SV357 = SY1354 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2064,plain,
! [SV118: $i > $o,SV358: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ SV358 )
| ~ ! [SY1355: $i] :
( ~ ( SV225 @ SY1355 )
| ( SV358 = SY1355 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2065,plain,
! [SV323: $i,SV32: $i,SV330: $i] :
( ( ( in @ SV330 @ SV32 )
= $false )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) )
| ( SV323 = SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2066,plain,
! [SV32: $i,SV313: $i,SV311: $i,SV351: $i] :
( ( ( ~ ( in @ SV351 @ SV311 ) )
= $true )
| ( ( in @ SV351 @ SV313 )
= $true )
| ( ( ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true )
| ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ SV313 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2067,plain,
! [SV344: $i,SV304: $i,SV32: $i] :
( ( ( ! [SY1297: $i] :
~ ~ ! [SY1298: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1297 @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1298 @ SV304 ) )
| ~ ~ ~ ! [SY1299: $i] :
~ ~ ( ~ ( in @ SY1299 @ SY1297 )
| ~ ( in @ SY1299 @ SV304 ) ) )
| ~ ! [SY1257: $i] :
( ~ ( in @ SY1257 @ ( sK2_SY874 @ SV32 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1257 )
| ( in @ SX6 @ SY1297 ) )
| ( in @ SY1298 @ SY1257 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2068,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ~ ! [SY1356: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1356 @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
| ~ ! [SY1358: $i] :
( ~ ( in @ SY1358 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SY1358 )
| ( in @ SY1359 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ SY1356 @ SY1358 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2022]) ).
thf(2069,plain,
! [SV281: $i,SV338: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV338 ) )
= $true )
| ( ( SV338
= ( sK57_SY921 @ SV281 @ SV47 ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2070,plain,
! [SV47: $i > $o,SV281: $i,SV338: $i] :
( ( ( SV338
!= ( sK57_SY921 @ SV281 @ SV47 ) )
= $true )
| ( ( SV47 @ SV338 )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2071,plain,
! [SV281: $i,SV336: $i,SV47: $i > $o] :
( ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK49_SY921 @ SV281 @ SV47 ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2072,plain,
! [SV47: $i > $o,SV281: $i,SV336: $i] :
( ( ( SV336
= ( sK49_SY921 @ SV281 @ SV47 ) )
= $false )
| ( ( SV47 @ SV336 )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2073,plain,
! [SV166: $i,SV282: $i > $o,SV48: $i,SV295: $i > $o] :
( ( ( SV295 @ ( sK41_SY1304 @ SV48 @ SV282 @ SV295 @ SV166 ) )
= $true )
| ( ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV48 ) )
= $true )
| ( ( ( dsetconstr @ SV48
@ ^ [SY1276: $i] : ( SV282 @ SY1276 ) )
= ( dsetconstr @ SV166
@ ^ [SY1294: $i] : ( SV295 @ SY1294 ) ) )
= $true )
| ( ( SV48 = SV166 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2028]) ).
thf(2074,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( ~ ( in @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV184 ) )
= $false )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2031]) ).
thf(2075,plain,
! [SV184: $i,SV312: $i,SV66: $i > $i > $o] :
( ( ( ~ ( SV66 @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV312 ) )
= $false )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2031]) ).
thf(2076,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV184 ) )
= $true )
| ( ( ~ ( SV66 @ SV341 @ SV312 ) )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2077,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV352: $i] :
( ( ( ~ ( ~ ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1352: $i] :
~ ~ ( ~ ( in @ SY1352 @ SV184 )
| ~ ( SV66 @ SY1352 @ SV352 ) ) )
| ~ ( ~ ~ ! [SY1353: $i] :
~ ~ ( ~ ( in @ SY1353 @ SV184 )
| ~ ( SV66 @ SY1353 @ SV352 ) )
| ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2078,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV345: $i] :
( ( ( ~ ( ~ ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1349: $i] :
~ ~ ( ~ ( in @ SY1349 @ SV184 )
| ~ ( SV66 @ SY1349 @ SV345 ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2034]) ).
thf(2079,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ( ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ SV184 )
| ~ ( SV66 @ SY1350 @ SV345 ) )
| ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2034]) ).
thf(2080,plain,
! [SV317: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2081,plain,
! [SV317: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2082,plain,
! [SV190: $i > $o,SV346: $i,SV74: $i > $o] :
( ( ( ~ ( SV74 @ SV346 )
| ~ ! [SY1351: $i] :
( ~ ( SV74 @ SY1351 )
| ( SV346 = SY1351 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2037]) ).
thf(2085,plain,
! [SV190: $i > $o,SV339: $i,SV74: $i > $o] :
( ( ( SV74 @ SV339 )
= $false )
| ( ( ~ ! [SY1342: $i] :
( ~ ( SV74 @ SY1342 )
| ( SV339 = SY1342 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2086,plain,
! [SV285: $i,SV347: $i,SV76: $i > $o] :
( ( ( SV76 @ SV347 )
= $false )
| ( ( ( sK51_SY992 @ SV285 @ SV76 )
= SV347 )
= $true )
| ( ( SV76 @ ( sK32_SY990 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2087,plain,
! [SV285: $i,SV353: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV353 ) )
= $true )
| ( ( ( sK58_SY992 @ SV285 @ SV76 )
= SV353 )
= $true )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2088,plain,
! [SV285: $i,SV348: $i,SV76: $i > $o] :
( ( ( SV76 @ SV348 )
= $false )
| ( ( ( sK52_SY992 @ SV285 @ SV76 )
= SV348 )
= $true )
| ( ( ( sK32_SY990 @ SV285 @ SV76 )
= ( sK36_SY1308 @ SV285 @ SV76 ) )
= $false )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2089,plain,
! [SV288: $i,SV354: $i,SV99: $i > $o] :
( ( ( ~ ( SV99 @ SV354 ) )
= $true )
| ( ( ( sK60_SY1043 @ SV288 @ SV99 )
= SV354 )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2090,plain,
! [SV288: $i,SV349: $i,SV99: $i > $o] :
( ( ( SV99 @ SV349 )
= $false )
| ( ( ( sK54_SY1043 @ SV288 @ SV99 )
= SV349 )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1285 @ SV288 @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2091,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( SV108 @ ( sK66_SY1062 @ SV290 @ SV108 ) )
= $true )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2046]) ).
thf(2092,plain,
! [SV290: $i,SV108: $i > $o] :
( ( ( ! [SY1343: $i] :
( ~ ( SV108 @ SY1343 )
| ( ( sK66_SY1062 @ SV290 @ SV108 )
= SY1343 ) ) )
= $true )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2095,plain,
! [SV290: $i,SV355: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ SV355 ) )
= $true )
| ( ( ( sK61_SY1062 @ SV290 @ SV108 )
= SV355 )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2096,plain,
! [SV292: $i,SV356: $i,SV112: $i > $o] :
( ( ( ~ ( SV112 @ SV356 ) )
= $true )
| ( ( ( sK62_SY1074 @ SV292 @ SV112 )
= SV356 )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2097,plain,
! [SV292: $i,SV350: $i,SV112: $i > $o] :
( ( ( SV112 @ SV350 )
= $false )
| ( ( ( sK56_SY1074 @ SV292 @ SV112 )
= SV350 )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV292
= ( sK46_SY1288 @ SV292 @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2098,plain,
! [SV333: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
| ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2055]) ).
thf(2099,plain,
! [SV334: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
| ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2056]) ).
thf(2100,plain,
! [SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1089: $i] :
~ ~ ( ~ ( SV118 @ SY1089 )
| ~ ! [SY1090: $i] :
( ~ ( SV118 @ SY1090 )
| ( SY1089 = SY1090 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2101,plain,
! [SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1227: $i] :
~ ~ ( ~ ( SV225 @ SY1227 )
| ~ ! [SY1228: $i] :
( ~ ( SV225 @ SY1228 )
| ( SY1227 = SY1228 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2106,plain,
! [SV225: $i > $o,SV357: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ SV357 )
| ~ ! [SY1354: $i] :
( ~ ( SV118 @ SY1354 )
| ( SV357 = SY1354 ) ) ) )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2107,plain,
! [SV118: $i > $o,SV358: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ SV358 )
| ~ ! [SY1355: $i] :
( ~ ( SV225 @ SY1355 )
| ( SV358 = SY1355 ) ) ) )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2108,plain,
! [SV330: $i,SV323: $i,SV32: $i] :
( ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2065]) ).
thf(2109,plain,
! [SV32: $i,SV313: $i,SV311: $i,SV351: $i] :
( ( ( in @ SV351 @ SV311 )
= $false )
| ( ( in @ SV351 @ SV313 )
= $true )
| ( ( ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV313 )
| ( in @ SY1315 @ SV311 ) ) )
= $true )
| ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ SV313 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2110,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ~ ! [SY1364: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1364 @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
| ~ ! [SY1366: $i] :
( ~ ( in @ SY1366 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SY1366 )
| ( in @ SY1367 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ SY1364 @ SY1366 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2067]) ).
thf(2111,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ! [SY1356: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1356 @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
| ~ ! [SY1358: $i] :
( ~ ( in @ SY1358 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SY1358 )
| ( in @ SY1359 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ SY1356 @ SY1358 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2112,plain,
! [SV281: $i,SV338: $i,SV47: $i > $o] :
( ( ( SV47 @ SV338 )
= $false )
| ( ( SV338
= ( sK57_SY921 @ SV281 @ SV47 ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2113,plain,
! [SV47: $i > $o,SV281: $i,SV338: $i] :
( ( ( SV338
= ( sK57_SY921 @ SV281 @ SV47 ) )
= $false )
| ( ( SV47 @ SV338 )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2114,plain,
! [SV184: $i,SV66: $i > $i > $o,SV312: $i] :
( ( ( in @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV184 )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2115,plain,
! [SV184: $i,SV312: $i,SV66: $i > $i > $o] :
( ( ( SV66 @ ( sK67_SY1312 @ SV312 @ SV66 @ SV184 ) @ SV312 )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $false )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2116,plain,
! [SV312: $i,SV66: $i > $i > $o,SV184: $i,SV341: $i] :
( ( ( in @ SV341 @ SV184 )
= $false )
| ( ( ~ ( SV66 @ SV341 @ SV312 ) )
= $true )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2117,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV352: $i] :
( ( ( ~ ( ~ ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1352: $i] :
~ ~ ( ~ ( in @ SY1352 @ SV184 )
| ~ ( SV66 @ SY1352 @ SV352 ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2118,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ( ~ ~ ! [SY1353: $i] :
~ ~ ( ~ ( in @ SY1353 @ SV184 )
| ~ ( SV66 @ SY1353 @ SV352 ) )
| ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) ) ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2119,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1349: $i] :
~ ~ ( ~ ( in @ SY1349 @ SV184 )
| ~ ( SV66 @ SY1349 @ SV345 ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2120,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ SV184 )
| ~ ( SV66 @ SY1350 @ SV345 ) )
| ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2121,plain,
! [SV317: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2122,plain,
! [SV317: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2081]) ).
thf(2123,plain,
! [SV190: $i > $o,SV346: $i,SV74: $i > $o] :
( ( ( ~ ( SV74 @ SV346 ) )
= $true )
| ( ( ~ ! [SY1351: $i] :
( ~ ( SV74 @ SY1351 )
| ( SV346 = SY1351 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2126,plain,
! [SV190: $i > $o,SV339: $i,SV74: $i > $o] :
( ( ( ! [SY1342: $i] :
( ~ ( SV74 @ SY1342 )
| ( SV339 = SY1342 ) ) )
= $false )
| ( ( SV74 @ SV339 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2127,plain,
! [SV285: $i,SV353: $i,SV76: $i > $o] :
( ( ( SV76 @ SV353 )
= $false )
| ( ( ( sK58_SY992 @ SV285 @ SV76 )
= SV353 )
= $true )
| ( ( SV76 @ ( sK36_SY1308 @ SV285 @ SV76 ) )
= $true )
| ( ( SV76 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2128,plain,
! [SV288: $i,SV354: $i,SV99: $i > $o] :
( ( ( SV99 @ SV354 )
= $false )
| ( ( ( sK60_SY1043 @ SV288 @ SV99 )
= SV354 )
= $true )
| ( ( SV99 @ SV288 )
= $false )
| ( ( SV99 @ ( sK44_SY1285 @ SV288 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2129,plain,
! [SV290: $i,SV365: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ SV365 )
| ( ( sK66_SY1062 @ SV290 @ SV108 )
= SV365 ) )
= $true )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2132,plain,
! [SV290: $i,SV355: $i,SV108: $i > $o] :
( ( ( SV108 @ SV355 )
= $false )
| ( ( ( sK61_SY1062 @ SV290 @ SV108 )
= SV355 )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $false )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2133,plain,
! [SV292: $i,SV356: $i,SV112: $i > $o] :
( ( ( SV112 @ SV356 )
= $false )
| ( ( ( sK62_SY1074 @ SV292 @ SV112 )
= SV356 )
= $true )
| ( ( SV112 @ SV292 )
= $false )
| ( ( SV112 @ ( sK46_SY1288 @ SV292 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2134,plain,
! [SV333: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2135,plain,
! [SV118: $i > $o,SV225: $i > $o,SV333: $i] :
( ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2136,plain,
! [SV334: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2099]) ).
thf(2137,plain,
! [SV225: $i > $o,SV118: $i > $o,SV334: $i] :
( ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2099]) ).
thf(2138,plain,
! [SV225: $i > $o,SV366: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ SV366 )
| ~ ! [SY1368: $i] :
( ~ ( SV118 @ SY1368 )
| ( SV366 = SY1368 ) ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2139,plain,
! [SV118: $i > $o,SV367: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ SV367 )
| ~ ! [SY1369: $i] :
( ~ ( SV225 @ SY1369 )
| ( SV367 = SY1369 ) ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2144,plain,
! [SV225: $i > $o,SV357: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV357 )
| ~ ! [SY1354: $i] :
( ~ ( SV118 @ SY1354 )
| ( SV357 = SY1354 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2106]) ).
thf(2145,plain,
! [SV118: $i > $o,SV358: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV358 )
| ~ ! [SY1355: $i] :
( ~ ( SV225 @ SY1355 )
| ( SV358 = SY1355 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2107]) ).
thf(2146,plain,
! [SV330: $i,SV323: $i,SV32: $i] :
( ( ( ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ SY1329 )
| ( in @ SV330 @ SY1329 ) )
| ~ ( ~ ( in @ SV330 @ SY1329 )
| ( in @ SV323 @ SY1329 ) ) ) ) )
= $false )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2147,plain,
! [SV32: $i,SV351: $i,SV311: $i,SV313: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV313 )
| ( in @ SV368 @ SV311 ) )
= $true )
| ( ( in @ SV351 @ SV313 )
= $true )
| ( ( in @ SV351 @ SV311 )
= $false )
| ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ SV313 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2148,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ! [SY1364: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1364 @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
| ~ ! [SY1366: $i] :
( ~ ( in @ SY1366 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SY1366 )
| ( in @ SY1367 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ SY1364 @ SY1366 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2149,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ! [SY1356: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1356 @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
| ~ ! [SY1358: $i] :
( ~ ( in @ SY1358 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SY1358 )
| ( in @ SY1359 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ SY1356 @ SY1358 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2150,plain,
! [SV184: $i,SV312: $i,SV341: $i,SV66: $i > $i > $o] :
( ( ( SV66 @ SV341 @ SV312 )
= $false )
| ( ( in @ SV341 @ SV184 )
= $false )
| ( ( in @ SV312 @ ( sK31_SY1165 @ SV66 @ SV184 ) )
= $true )
| ( ( in @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2151,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
| ~ ! [SY1352: $i] :
~ ~ ( ~ ( in @ SY1352 @ SV184 )
| ~ ( SV66 @ SY1352 @ SV352 ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2152,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ~ ! [SY1353: $i] :
~ ~ ( ~ ( in @ SY1353 @ SV184 )
| ~ ( SV66 @ SY1353 @ SV352 ) )
| ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2118]) ).
thf(2153,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) ) )
= $true )
| ( ( ~ ! [SY1349: $i] :
~ ~ ( ~ ( in @ SY1349 @ SV184 )
| ~ ( SV66 @ SY1349 @ SV345 ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2119]) ).
thf(2154,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ SV184 )
| ~ ( SV66 @ SY1350 @ SV345 ) ) )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2155,plain,
! [SV317: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2156,plain,
! [SV317: $i,SV74: $i > $o,SV369: $i,SV190: $i > $o] :
( ( ( ~ ~ ( ~ ( SV190 @ SV369 )
| ~ ! [SY1370: $i] :
( ~ ( SV190 @ SY1370 )
| ( SV369 = SY1370 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2157,plain,
! [SV190: $i > $o,SV346: $i,SV74: $i > $o] :
( ( ( SV74 @ SV346 )
= $false )
| ( ( ~ ! [SY1351: $i] :
( ~ ( SV74 @ SY1351 )
| ( SV346 = SY1351 ) ) )
= $true )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2160,plain,
! [SV339: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
| ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) ) )
= $false )
| ( ( SV74 @ SV339 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2126]) ).
thf(2161,plain,
! [SV290: $i,SV365: $i,SV108: $i > $o] :
( ( ( ~ ( SV108 @ SV365 ) )
= $true )
| ( ( ( sK66_SY1062 @ SV290 @ SV108 )
= SV365 )
= $true )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2164,plain,
! [SV333: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2134]) ).
thf(2165,plain,
! [SV333: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2166,plain,
! [SV334: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2167,plain,
! [SV334: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2168,plain,
! [SV225: $i > $o,SV366: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ SV366 )
| ~ ! [SY1368: $i] :
( ~ ( SV118 @ SY1368 )
| ( SV366 = SY1368 ) ) ) )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2169,plain,
! [SV118: $i > $o,SV367: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ SV367 )
| ~ ! [SY1369: $i] :
( ~ ( SV225 @ SY1369 )
| ( SV367 = SY1369 ) ) ) )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2174,plain,
! [SV225: $i > $o,SV357: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV357 ) )
= $true )
| ( ( ~ ! [SY1354: $i] :
( ~ ( SV118 @ SY1354 )
| ( SV357 = SY1354 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2175,plain,
! [SV118: $i > $o,SV358: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV358 ) )
= $true )
| ( ( ~ ! [SY1355: $i] :
( ~ ( SV225 @ SY1355 )
| ( SV358 = SY1355 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2176,plain,
! [SV32: $i,SV323: $i,SV330: $i] :
( ( ( ~ ( in @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( ~ ( ~ ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) )
| ~ ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) ) )
= $false )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2146]) ).
thf(2177,plain,
! [SV32: $i,SV351: $i,SV311: $i,SV313: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV313 ) )
= $true )
| ( ( in @ SV368 @ SV311 )
= $true )
| ( ( in @ SV351 @ SV313 )
= $true )
| ( ( in @ SV351 @ SV311 )
= $false )
| ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ SV313 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2178,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ! [SY1364: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ SY1364 @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
| ~ ! [SY1366: $i] :
( ~ ( in @ SY1366 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SY1366 )
| ( in @ SY1367 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ SY1364 @ SY1366 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2179,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
| ~ ! [SY1372: $i] :
( ~ ( in @ SY1372 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SY1372 )
| ( in @ SY1359 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SY1372 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2149]) ).
thf(2180,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) ) )
= $true )
| ( ( ~ ! [SY1352: $i] :
~ ~ ( ~ ( in @ SY1352 @ SV184 )
| ~ ( SV66 @ SY1352 @ SV352 ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2181,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ~ ! [SY1353: $i] :
~ ~ ( ~ ( in @ SY1353 @ SV184 )
| ~ ( SV66 @ SY1353 @ SV352 ) ) )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2182,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV345: $i] :
( ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( ~ ! [SY1349: $i] :
~ ~ ( ~ ( in @ SY1349 @ SV184 )
| ~ ( SV66 @ SY1349 @ SV345 ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2183,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ SV184 )
| ~ ( SV66 @ SY1350 @ SV345 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2184,plain,
! [SV317: $i,SV74: $i > $o,SV370: $i,SV190: $i > $o] :
( ( ( ~ ~ ( ~ ( SV190 @ SV370 )
| ~ ! [SY1374: $i] :
( ~ ( SV190 @ SY1374 )
| ( SV370 = SY1374 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2185,plain,
! [SV317: $i,SV74: $i > $o,SV369: $i,SV190: $i > $o] :
( ( ( ~ ( ~ ( SV190 @ SV369 )
| ~ ! [SY1370: $i] :
( ~ ( SV190 @ SY1370 )
| ( SV369 = SY1370 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2186,plain,
! [SV190: $i > $o,SV346: $i,SV74: $i > $o] :
( ( ( ! [SY1351: $i] :
( ~ ( SV74 @ SY1351 )
| ( SV346 = SY1351 ) ) )
= $false )
| ( ( SV74 @ SV346 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2189,plain,
! [SV339: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) ) )
= $false )
| ( ( SV74 @ SV339 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2160]) ).
thf(2190,plain,
! [SV74: $i > $o,SV190: $i > $o,SV339: $i] :
( ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV74 @ SV339 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2160]) ).
thf(2191,plain,
! [SV290: $i,SV365: $i,SV108: $i > $o] :
( ( ( SV108 @ SV365 )
= $false )
| ( ( ( sK66_SY1062 @ SV290 @ SV108 )
= SV365 )
= $true )
| ( ( SV108 @ ( sK22_SY1286 @ SV290 @ SV108 ) )
= $true )
| ( ( ( sK22_SY1286 @ SV290 @ SV108 )
= SV290 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2192,plain,
! [SV333: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2193,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ ( sK79_SY1225 @ SV333 @ SV118 @ SV225 ) )
| ~ ! [SY1375: $i] :
( ~ ( SV225 @ SY1375 )
| ( ( sK79_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1375 ) ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2165]) ).
thf(2194,plain,
! [SV334: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2195,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ ( sK80_SY1095 @ SV334 @ SV225 @ SV118 ) )
| ~ ! [SY1376: $i] :
( ~ ( SV118 @ SY1376 )
| ( ( sK80_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1376 ) ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2167]) ).
thf(2196,plain,
! [SV225: $i > $o,SV366: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV366 )
| ~ ! [SY1368: $i] :
( ~ ( SV118 @ SY1368 )
| ( SV366 = SY1368 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2168]) ).
thf(2197,plain,
! [SV118: $i > $o,SV367: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV367 )
| ~ ! [SY1369: $i] :
( ~ ( SV225 @ SY1369 )
| ( SV367 = SY1369 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2169]) ).
thf(2202,plain,
! [SV225: $i > $o,SV357: $i,SV118: $i > $o] :
( ( ( SV118 @ SV357 )
= $false )
| ( ( ~ ! [SY1354: $i] :
( ~ ( SV118 @ SY1354 )
| ( SV357 = SY1354 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2203,plain,
! [SV118: $i > $o,SV358: $i,SV225: $i > $o] :
( ( ( SV225 @ SV358 )
= $false )
| ( ( ~ ! [SY1355: $i] :
( ~ ( SV225 @ SY1355 )
| ( SV358 = SY1355 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2204,plain,
! [SV32: $i,SV323: $i,SV330: $i] :
( ( ( ~ ( in @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) @ ( sK2_SY874 @ SV32 ) ) )
= $false )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2176]) ).
thf(2205,plain,
! [SV32: $i,SV330: $i,SV323: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) )
| ~ ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) ) )
= $false )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2176]) ).
thf(2206,plain,
! [SV32: $i,SV351: $i,SV311: $i,SV313: $i,SV368: $i] :
( ( ( in @ SV368 @ SV313 )
= $false )
| ( ( in @ SV368 @ SV311 )
= $true )
| ( ( in @ SV351 @ SV313 )
= $true )
| ( ( in @ SV351 @ SV311 )
= $false )
| ( ( in @ SV311 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ SV313 @ ( sK2_SY874 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2207,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( in @ SY1378 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SY1378 )
| ( in @ SY1367 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SY1378 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2178]) ).
thf(2208,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
| ~ ! [SY1372: $i] :
( ~ ( in @ SY1372 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SY1372 )
| ( in @ SY1359 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SY1372 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2179]) ).
thf(2209,plain,
! [SV184: $i,SV66: $i > $i > $o,SV306: $i,SV352: $i] :
( ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( ~ ! [SY1352: $i] :
~ ~ ( ~ ( in @ SY1352 @ SV184 )
| ~ ( SV66 @ SY1352 @ SV352 ) ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2210,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ~ ! [SY1353: $i] :
~ ~ ( ~ ( in @ SY1353 @ SV184 )
| ~ ( SV66 @ SY1353 @ SV352 ) ) )
= $false )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2211,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1349: $i] :
~ ~ ( ~ ( in @ SY1349 @ SV184 )
| ~ ( SV66 @ SY1349 @ SV345 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2212,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ SV184 )
| ~ ( SV66 @ SY1350 @ SV345 ) ) )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2213,plain,
! [SV317: $i,SV74: $i > $o,SV370: $i,SV190: $i > $o] :
( ( ( ~ ( ~ ( SV190 @ SV370 )
| ~ ! [SY1374: $i] :
( ~ ( SV190 @ SY1374 )
| ( SV370 = SY1374 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2214,plain,
! [SV317: $i,SV74: $i > $o,SV369: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV369 )
| ~ ! [SY1370: $i] :
( ~ ( SV190 @ SY1370 )
| ( SV369 = SY1370 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2185]) ).
thf(2215,plain,
! [SV346: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
| ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) ) )
= $false )
| ( ( SV74 @ SV346 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2186]) ).
thf(2220,plain,
! [SV339: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2189]) ).
thf(2221,plain,
! [SV339: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2222,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ ( sK83_SY1225 @ SV333 @ SV118 @ SV225 ) )
| ~ ! [SY1380: $i] :
( ~ ( SV225 @ SY1380 )
| ( ( sK83_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1380 ) ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2192]) ).
thf(2223,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ ( sK79_SY1225 @ SV333 @ SV118 @ SV225 ) )
| ~ ! [SY1375: $i] :
( ~ ( SV225 @ SY1375 )
| ( ( sK79_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1375 ) ) ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2193]) ).
thf(2224,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ ( sK84_SY1095 @ SV334 @ SV225 @ SV118 ) )
| ~ ! [SY1381: $i] :
( ~ ( SV118 @ SY1381 )
| ( ( sK84_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1381 ) ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2194]) ).
thf(2225,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK80_SY1095 @ SV334 @ SV225 @ SV118 ) )
| ~ ! [SY1376: $i] :
( ~ ( SV118 @ SY1376 )
| ( ( sK80_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1376 ) ) ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2226,plain,
! [SV225: $i > $o,SV366: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV366 ) )
= $true )
| ( ( ~ ! [SY1368: $i] :
( ~ ( SV118 @ SY1368 )
| ( SV366 = SY1368 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2227,plain,
! [SV118: $i > $o,SV367: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV367 ) )
= $true )
| ( ( ~ ! [SY1369: $i] :
( ~ ( SV225 @ SY1369 )
| ( SV367 = SY1369 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2232,plain,
! [SV225: $i > $o,SV357: $i,SV118: $i > $o] :
( ( ( ! [SY1354: $i] :
( ~ ( SV118 @ SY1354 )
| ( SV357 = SY1354 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2233,plain,
! [SV118: $i > $o,SV358: $i,SV225: $i > $o] :
( ( ( ! [SY1355: $i] :
( ~ ( SV225 @ SY1355 )
| ( SV358 = SY1355 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2234,plain,
! [SV32: $i,SV323: $i,SV330: $i] :
( ( ( in @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2204]) ).
thf(2235,plain,
! [SV32: $i,SV330: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) )
| ~ ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2236,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( in @ SY1378 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SY1378 )
| ( in @ SY1367 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SY1378 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2237,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
| ~ ! [SY1372: $i] :
( ~ ( in @ SY1372 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SY1372 )
| ( in @ SY1359 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SY1372 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2238,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1352: $i] :
~ ~ ( ~ ( in @ SY1352 @ SV184 )
| ~ ( SV66 @ SY1352 @ SV352 ) ) )
= $false )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2239,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i] :
( ( ( ! [SY1353: $i] :
~ ~ ( ~ ( in @ SY1353 @ SV184 )
| ~ ( SV66 @ SY1353 @ SV352 ) ) )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2210]) ).
thf(2240,plain,
! [SV184: $i,SV66: $i > $i > $o,SV345: $i,SV306: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV345 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2211]) ).
thf(2241,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i,SV371: $i] :
( ( ( ~ ~ ( ~ ( in @ SV371 @ SV184 )
| ~ ( SV66 @ SV371 @ SV345 ) ) )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2242,plain,
! [SV317: $i,SV74: $i > $o,SV370: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV370 )
| ~ ! [SY1374: $i] :
( ~ ( SV190 @ SY1374 )
| ( SV370 = SY1374 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2243,plain,
! [SV317: $i,SV74: $i > $o,SV369: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV369 ) )
= $true )
| ( ( ~ ! [SY1370: $i] :
( ~ ( SV190 @ SY1370 )
| ( SV369 = SY1370 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2244,plain,
! [SV346: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( ~ ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) ) )
= $false )
| ( ( SV74 @ SV346 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2245,plain,
! [SV74: $i > $o,SV190: $i > $o,SV346: $i] :
( ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ SV346 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2250,plain,
! [SV339: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2251,plain,
! [SV339: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2221]) ).
thf(2252,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ ( sK83_SY1225 @ SV333 @ SV118 @ SV225 ) )
| ~ ! [SY1380: $i] :
( ~ ( SV225 @ SY1380 )
| ( ( sK83_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1380 ) ) ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2253,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK79_SY1225 @ SV333 @ SV118 @ SV225 ) )
| ~ ! [SY1375: $i] :
( ~ ( SV225 @ SY1375 )
| ( ( sK79_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1375 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2254,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK84_SY1095 @ SV334 @ SV225 @ SV118 ) )
| ~ ! [SY1381: $i] :
( ~ ( SV118 @ SY1381 )
| ( ( sK84_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1381 ) ) ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2224]) ).
thf(2255,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK80_SY1095 @ SV334 @ SV225 @ SV118 ) )
| ~ ! [SY1376: $i] :
( ~ ( SV118 @ SY1376 )
| ( ( sK80_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1376 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2256,plain,
! [SV225: $i > $o,SV366: $i,SV118: $i > $o] :
( ( ( SV118 @ SV366 )
= $false )
| ( ( ~ ! [SY1368: $i] :
( ~ ( SV118 @ SY1368 )
| ( SV366 = SY1368 ) ) )
= $true )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2257,plain,
! [SV118: $i > $o,SV367: $i,SV225: $i > $o] :
( ( ( SV225 @ SV367 )
= $false )
| ( ( ~ ! [SY1369: $i] :
( ~ ( SV225 @ SY1369 )
| ( SV367 = SY1369 ) ) )
= $true )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2262,plain,
! [SV357: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
| ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2232]) ).
thf(2263,plain,
! [SV358: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
| ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2233]) ).
thf(2264,plain,
! [SV32: $i,SV330: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2265,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
| ~ ! [SY1378: $i] :
( ~ ( in @ SY1378 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SY1378 )
| ( in @ SY1367 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SY1378 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2266,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2237]) ).
thf(2267,plain,
! [SV304: $i,SV340: $i,SV32: $i] :
( ( ( ~ ! [SY1372: $i] :
( ~ ( in @ SY1372 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SY1372 )
| ( in @ SY1359 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SY1372 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2237]) ).
thf(2268,plain,
! [SV184: $i,SV66: $i > $i > $o,SV352: $i,SV306: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV352 ) ) )
= $false )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2238]) ).
thf(2269,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i,SV372: $i] :
( ( ( ~ ~ ( ~ ( in @ SV372 @ SV184 )
| ~ ( SV66 @ SV372 @ SV352 ) ) )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2270,plain,
! [SV184: $i,SV66: $i > $i > $o,SV345: $i,SV306: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV345 ) ) )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2271,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i,SV371: $i] :
( ( ( ~ ( ~ ( in @ SV371 @ SV184 )
| ~ ( SV66 @ SV371 @ SV345 ) ) )
= $false )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2272,plain,
! [SV317: $i,SV74: $i > $o,SV370: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV370 ) )
= $true )
| ( ( ~ ! [SY1374: $i] :
( ~ ( SV190 @ SY1374 )
| ( SV370 = SY1374 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2273,plain,
! [SV317: $i,SV74: $i > $o,SV369: $i,SV190: $i > $o] :
( ( ( SV190 @ SV369 )
= $false )
| ( ( ~ ! [SY1370: $i] :
( ~ ( SV190 @ SY1370 )
| ( SV369 = SY1370 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2274,plain,
! [SV346: $i,SV190: $i > $o,SV74: $i > $o] :
( ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) )
| ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2275,plain,
! [SV346: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2280,plain,
! [SV339: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2281,plain,
! [SV339: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2282,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK83_SY1225 @ SV333 @ SV118 @ SV225 ) )
| ~ ! [SY1380: $i] :
( ~ ( SV225 @ SY1380 )
| ( ( sK83_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1380 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2283,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK79_SY1225 @ SV333 @ SV118 @ SV225 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2253]) ).
thf(2284,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ! [SY1375: $i] :
( ~ ( SV225 @ SY1375 )
| ( ( sK79_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1375 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2253]) ).
thf(2285,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK84_SY1095 @ SV334 @ SV225 @ SV118 ) )
| ~ ! [SY1381: $i] :
( ~ ( SV118 @ SY1381 )
| ( ( sK84_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1381 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2286,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK80_SY1095 @ SV334 @ SV225 @ SV118 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2255]) ).
thf(2287,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ! [SY1376: $i] :
( ~ ( SV118 @ SY1376 )
| ( ( sK80_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1376 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2255]) ).
thf(2288,plain,
! [SV225: $i > $o,SV366: $i,SV118: $i > $o] :
( ( ( ! [SY1368: $i] :
( ~ ( SV118 @ SY1368 )
| ( SV366 = SY1368 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2289,plain,
! [SV118: $i > $o,SV367: $i,SV225: $i > $o] :
( ( ( ! [SY1369: $i] :
( ~ ( SV225 @ SY1369 )
| ( SV367 = SY1369 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2294,plain,
! [SV357: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2295,plain,
! [SV118: $i > $o,SV225: $i > $o,SV357: $i] :
( ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2296,plain,
! [SV358: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2263]) ).
thf(2297,plain,
! [SV225: $i > $o,SV118: $i > $o,SV358: $i] :
( ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2263]) ).
thf(2298,plain,
! [SV32: $i,SV330: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2299,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2265]) ).
thf(2300,plain,
! [SV304: $i,SV344: $i,SV32: $i] :
( ( ( ~ ! [SY1378: $i] :
( ~ ( in @ SY1378 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SY1378 )
| ( in @ SY1367 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SY1378 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2265]) ).
thf(2301,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2302,plain,
! [SV304: $i,SV340: $i,SV32: $i] :
( ( ( ! [SY1372: $i] :
( ~ ( in @ SY1372 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SY1372 )
| ( in @ SY1359 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SY1372 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2267]) ).
thf(2303,plain,
! [SV184: $i,SV66: $i > $i > $o,SV352: $i,SV306: $i] :
( ( ( ~ ( ~ ( in @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV352 ) ) )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2268]) ).
thf(2304,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i,SV372: $i] :
( ( ( ~ ( ~ ( in @ SV372 @ SV184 )
| ~ ( SV66 @ SV372 @ SV352 ) ) )
= $false )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2305,plain,
! [SV184: $i,SV66: $i > $i > $o,SV345: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV345 ) )
= $false )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2306,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV184 )
| ~ ( SV66 @ SV371 @ SV345 ) )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2307,plain,
! [SV317: $i,SV74: $i > $o,SV370: $i,SV190: $i > $o] :
( ( ( SV190 @ SV370 )
= $false )
| ( ( ~ ! [SY1374: $i] :
( ~ ( SV190 @ SY1374 )
| ( SV370 = SY1374 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2308,plain,
! [SV317: $i,SV74: $i > $o,SV369: $i,SV190: $i > $o] :
( ( ( ! [SY1370: $i] :
( ~ ( SV190 @ SY1370 )
| ( SV369 = SY1370 ) ) )
= $false )
| ( ( SV190 @ SV369 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2309,plain,
! [SV346: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2310,plain,
! [SV346: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2315,plain,
! [SV339: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2316,plain,
! [SV339: $i,SV74: $i > $o,SV373: $i,SV190: $i > $o] :
( ( ( ~ ~ ( ~ ( SV190 @ SV373 )
| ~ ! [SY1382: $i] :
( ~ ( SV190 @ SY1382 )
| ( SV373 = SY1382 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2317,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK83_SY1225 @ SV333 @ SV118 @ SV225 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2318,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ~ ! [SY1380: $i] :
( ~ ( SV225 @ SY1380 )
| ( ( sK83_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1380 ) ) )
= $false )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2319,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( SV225 @ ( sK79_SY1225 @ SV333 @ SV118 @ SV225 ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2320,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ! [SY1375: $i] :
( ~ ( SV225 @ SY1375 )
| ( ( sK79_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1375 ) ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2284]) ).
thf(2321,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK84_SY1095 @ SV334 @ SV225 @ SV118 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2285]) ).
thf(2322,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ~ ! [SY1381: $i] :
( ~ ( SV118 @ SY1381 )
| ( ( sK84_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1381 ) ) )
= $false )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2285]) ).
thf(2323,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( SV118 @ ( sK80_SY1095 @ SV334 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2286]) ).
thf(2324,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ! [SY1376: $i] :
( ~ ( SV118 @ SY1376 )
| ( ( sK80_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1376 ) ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2287]) ).
thf(2325,plain,
! [SV366: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
| ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2288]) ).
thf(2326,plain,
! [SV367: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
| ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2289]) ).
thf(2335,plain,
! [SV357: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2336,plain,
! [SV357: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2337,plain,
! [SV358: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2296]) ).
thf(2338,plain,
! [SV358: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2339,plain,
! [SV32: $i,SV330: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2340,plain,
! [SV32: $i,SV323: $i,SV330: $i] :
( ( ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2341,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2299]) ).
thf(2342,plain,
! [SV304: $i,SV344: $i,SV32: $i] :
( ( ( ! [SY1378: $i] :
( ~ ( in @ SY1378 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SY1378 )
| ( in @ SY1367 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SY1378 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2300]) ).
thf(2343,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) )
| ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2344,plain,
! [SV304: $i,SV340: $i,SV32: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV374 )
| ( in @ SY1383 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV374 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2345,plain,
! [SV184: $i,SV66: $i > $i > $o,SV352: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV184 )
| ~ ( SV66 @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV352 ) )
= $false )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2346,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ SV184 )
| ~ ( SV66 @ SV372 @ SV352 ) )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2304]) ).
thf(2347,plain,
! [SV184: $i,SV66: $i > $i > $o,SV345: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV184 ) )
= $false )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2348,plain,
! [SV184: $i,SV345: $i,SV306: $i,SV66: $i > $i > $o] :
( ( ( ~ ( SV66 @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV345 ) )
= $false )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2349,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV184 ) )
= $true )
| ( ( ~ ( SV66 @ SV371 @ SV345 ) )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2350,plain,
! [SV317: $i,SV74: $i > $o,SV370: $i,SV190: $i > $o] :
( ( ( ! [SY1374: $i] :
( ~ ( SV190 @ SY1374 )
| ( SV370 = SY1374 ) ) )
= $false )
| ( ( SV190 @ SV370 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2351,plain,
! [SV369: $i,SV74: $i > $o,SV317: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK95_SY1370 @ SV317 @ SV74 @ SV369 @ SV190 ) )
| ( SV369
= ( sK95_SY1370 @ SV317 @ SV74 @ SV369 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV369 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2308]) ).
thf(2352,plain,
! [SV346: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ~ ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2353,plain,
! [SV346: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2310]) ).
thf(2358,plain,
! [SV339: $i,SV74: $i > $o,SV377: $i,SV190: $i > $o] :
( ( ( ~ ~ ( ~ ( SV190 @ SV377 )
| ~ ! [SY1386: $i] :
( ~ ( SV190 @ SY1386 )
| ( SV377 = SY1386 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2359,plain,
! [SV339: $i,SV74: $i > $o,SV373: $i,SV190: $i > $o] :
( ( ( ~ ( ~ ( SV190 @ SV373 )
| ~ ! [SY1382: $i] :
( ~ ( SV190 @ SY1382 )
| ( SV373 = SY1382 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2360,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( SV225 @ ( sK83_SY1225 @ SV333 @ SV118 @ SV225 ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2317]) ).
thf(2361,plain,
! [SV118: $i > $o,SV333: $i,SV225: $i > $o] :
( ( ( ! [SY1380: $i] :
( ~ ( SV225 @ SY1380 )
| ( ( sK83_SY1225 @ SV333 @ SV118 @ SV225 )
= SY1380 ) ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2318]) ).
thf(2362,plain,
! [SV118: $i > $o,SV333: $i,SV378: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV378 )
| ( ( sK79_SY1225 @ SV333 @ SV118 @ SV225 )
= SV378 ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2363,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( SV118 @ ( sK84_SY1095 @ SV334 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2364,plain,
! [SV225: $i > $o,SV334: $i,SV118: $i > $o] :
( ( ( ! [SY1381: $i] :
( ~ ( SV118 @ SY1381 )
| ( ( sK84_SY1095 @ SV334 @ SV225 @ SV118 )
= SY1381 ) ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2322]) ).
thf(2365,plain,
! [SV225: $i > $o,SV334: $i,SV379: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV379 )
| ( ( sK80_SY1095 @ SV334 @ SV225 @ SV118 )
= SV379 ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2366,plain,
! [SV366: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2367,plain,
! [SV118: $i > $o,SV225: $i > $o,SV366: $i] :
( ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2368,plain,
! [SV367: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2326]) ).
thf(2369,plain,
! [SV225: $i > $o,SV118: $i > $o,SV367: $i] :
( ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2326]) ).
thf(2378,plain,
! [SV357: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2379,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ ( sK96_SY1225 @ SV357 @ SV118 @ SV225 ) )
| ~ ! [SY1387: $i] :
( ~ ( SV225 @ SY1387 )
| ( ( sK96_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1387 ) ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2336]) ).
thf(2380,plain,
! [SV358: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2381,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ ( sK97_SY1095 @ SV358 @ SV225 @ SV118 ) )
| ~ ! [SY1388: $i] :
( ~ ( SV118 @ SY1388 )
| ( ( sK97_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1388 ) ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2338]) ).
thf(2382,plain,
! [SV32: $i,SV330: $i,SV323: $i] :
( ( ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2339]) ).
thf(2383,plain,
! [SV32: $i,SV323: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) )
= $false )
| ( ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $false )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2384,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) )
| ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2385,plain,
! [SV304: $i,SV344: $i,SV32: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ ( sK2_SY874 @ SV32 ) )
| ! [SY1389: $i] :
( ~ ( in @ SY1389 @ SV380 )
| ( in @ SY1389 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV380 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2386,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2343]) ).
thf(2387,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2343]) ).
thf(2388,plain,
! [SV304: $i,SV340: $i,SV32: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ ( sK2_SY874 @ SV32 ) ) )
= $true )
| ( ( ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV374 )
| ( in @ SY1383 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV374 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2344]) ).
thf(2389,plain,
! [SV184: $i,SV66: $i > $i > $o,SV352: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV184 ) )
= $false )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2345]) ).
thf(2390,plain,
! [SV184: $i,SV352: $i,SV306: $i,SV66: $i > $i > $o] :
( ( ( ~ ( SV66 @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV352 ) )
= $false )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2345]) ).
thf(2391,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ SV184 ) )
= $true )
| ( ( ~ ( SV66 @ SV372 @ SV352 ) )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2392,plain,
! [SV184: $i,SV66: $i > $i > $o,SV345: $i,SV306: $i] :
( ( ( in @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV184 )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2347]) ).
thf(2393,plain,
! [SV184: $i,SV345: $i,SV306: $i,SV66: $i > $i > $o] :
( ( ( SV66 @ ( sK85_SY1349 @ SV306 @ SV345 @ SV66 @ SV184 ) @ SV345 )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2348]) ).
thf(2394,plain,
! [SV306: $i,SV345: $i,SV66: $i > $i > $o,SV184: $i,SV371: $i] :
( ( ( in @ SV371 @ SV184 )
= $false )
| ( ( ~ ( SV66 @ SV371 @ SV345 ) )
= $true )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2395,plain,
! [SV370: $i,SV74: $i > $o,SV317: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK98_SY1374 @ SV317 @ SV74 @ SV370 @ SV190 ) )
| ( SV370
= ( sK98_SY1374 @ SV317 @ SV74 @ SV370 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV370 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2350]) ).
thf(2396,plain,
! [SV369: $i,SV74: $i > $o,SV317: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK95_SY1370 @ SV317 @ SV74 @ SV369 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV369 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2397,plain,
! [SV190: $i > $o,SV74: $i > $o,SV317: $i,SV369: $i] :
( ( ( SV369
= ( sK95_SY1370 @ SV317 @ SV74 @ SV369 @ SV190 ) )
= $false )
| ( ( SV190 @ SV369 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2398,plain,
! [SV346: $i,SV74: $i > $o,SV190: $i > $o] :
( ( ( ! [SY1181: $i] :
~ ~ ( ~ ( SV190 @ SY1181 )
| ~ ! [SY1182: $i] :
( ~ ( SV190 @ SY1182 )
| ( SY1181 = SY1182 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2399,plain,
! [SV346: $i,SV74: $i > $o,SV381: $i,SV190: $i > $o] :
( ( ( ~ ~ ( ~ ( SV190 @ SV381 )
| ~ ! [SY1390: $i] :
( ~ ( SV190 @ SY1390 )
| ( SV381 = SY1390 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2404,plain,
! [SV339: $i,SV74: $i > $o,SV377: $i,SV190: $i > $o] :
( ( ( ~ ( ~ ( SV190 @ SV377 )
| ~ ! [SY1386: $i] :
( ~ ( SV190 @ SY1386 )
| ( SV377 = SY1386 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2405,plain,
! [SV339: $i,SV74: $i > $o,SV373: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV373 )
| ~ ! [SY1382: $i] :
( ~ ( SV190 @ SY1382 )
| ( SV373 = SY1382 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2406,plain,
! [SV118: $i > $o,SV333: $i,SV384: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV384 )
| ( ( sK83_SY1225 @ SV333 @ SV118 @ SV225 )
= SV384 ) )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2407,plain,
! [SV118: $i > $o,SV333: $i,SV378: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV378 ) )
= $true )
| ( ( ( sK79_SY1225 @ SV333 @ SV118 @ SV225 )
= SV378 )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2408,plain,
! [SV225: $i > $o,SV334: $i,SV385: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV385 )
| ( ( sK84_SY1095 @ SV334 @ SV225 @ SV118 )
= SV385 ) )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2409,plain,
! [SV225: $i > $o,SV334: $i,SV379: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV379 ) )
= $true )
| ( ( ( sK80_SY1095 @ SV334 @ SV225 @ SV118 )
= SV379 )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2410,plain,
! [SV366: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( ~ ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2411,plain,
! [SV366: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2412,plain,
! [SV367: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2413,plain,
! [SV367: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2422,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ ( sK103_SY1225 @ SV357 @ SV118 @ SV225 ) )
| ~ ! [SY1397: $i] :
( ~ ( SV225 @ SY1397 )
| ( ( sK103_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1397 ) ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2378]) ).
thf(2423,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ ( sK96_SY1225 @ SV357 @ SV118 @ SV225 ) )
| ~ ! [SY1387: $i] :
( ~ ( SV225 @ SY1387 )
| ( ( sK96_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1387 ) ) ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2379]) ).
thf(2424,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ ( sK104_SY1095 @ SV358 @ SV225 @ SV118 ) )
| ~ ! [SY1398: $i] :
( ~ ( SV118 @ SY1398 )
| ( ( sK104_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1398 ) ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2380]) ).
thf(2425,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK97_SY1095 @ SV358 @ SV225 @ SV118 ) )
| ~ ! [SY1388: $i] :
( ~ ( SV118 @ SY1388 )
| ( ( sK97_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1388 ) ) ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2426,plain,
! [SV32: $i,SV323: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
| ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) )
= $false )
| ( ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2382]) ).
thf(2428,plain,
! [SV32: $i,SV330: $i,SV323: $i] :
( ( ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $false )
| ( ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $false )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2383]) ).
thf(2429,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2384]) ).
thf(2430,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2384]) ).
thf(2431,plain,
! [SV304: $i,SV344: $i,SV32: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ ( sK2_SY874 @ SV32 ) ) )
= $true )
| ( ( ! [SY1389: $i] :
( ~ ( in @ SY1389 @ SV380 )
| ( in @ SY1389 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV380 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2432,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2386]) ).
thf(2433,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2387]) ).
thf(2434,plain,
! [SV304: $i,SV340: $i,SV32: $i,SV374: $i] :
( ( ( in @ SV374 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV374 )
| ( in @ SY1383 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
| ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV374 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2435,plain,
! [SV184: $i,SV66: $i > $i > $o,SV352: $i,SV306: $i] :
( ( ( in @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV184 )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2389]) ).
thf(2436,plain,
! [SV184: $i,SV352: $i,SV306: $i,SV66: $i > $i > $o] :
( ( ( SV66 @ ( sK88_SY1352 @ SV306 @ SV352 @ SV66 @ SV184 ) @ SV352 )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2390]) ).
thf(2437,plain,
! [SV306: $i,SV352: $i,SV66: $i > $i > $o,SV184: $i,SV372: $i] :
( ( ( in @ SV372 @ SV184 )
= $false )
| ( ( ~ ( SV66 @ SV372 @ SV352 ) )
= $true )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2438,plain,
! [SV306: $i,SV184: $i,SV345: $i,SV371: $i,SV66: $i > $i > $o] :
( ( ( SV66 @ SV371 @ SV345 )
= $false )
| ( ( in @ SV371 @ SV184 )
= $false )
| ( ( in @ SV345 @ ( sK65_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV306
= ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2439,plain,
! [SV370: $i,SV74: $i > $o,SV317: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK98_SY1374 @ SV317 @ SV74 @ SV370 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV370 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2395]) ).
thf(2440,plain,
! [SV190: $i > $o,SV74: $i > $o,SV317: $i,SV370: $i] :
( ( ( SV370
= ( sK98_SY1374 @ SV317 @ SV74 @ SV370 @ SV190 ) )
= $false )
| ( ( SV190 @ SV370 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2395]) ).
thf(2441,plain,
! [SV369: $i,SV74: $i > $o,SV317: $i,SV190: $i > $o] :
( ( ( SV190 @ ( sK95_SY1370 @ SV317 @ SV74 @ SV369 @ SV190 ) )
= $true )
| ( ( SV190 @ SV369 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV317
= ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $false )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2442,plain,
! [SV346: $i,SV74: $i > $o,SV386: $i,SV190: $i > $o] :
( ( ( ~ ~ ( ~ ( SV190 @ SV386 )
| ~ ! [SY1399: $i] :
( ~ ( SV190 @ SY1399 )
| ( SV386 = SY1399 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2443,plain,
! [SV346: $i,SV74: $i > $o,SV381: $i,SV190: $i > $o] :
( ( ( ~ ( ~ ( SV190 @ SV381 )
| ~ ! [SY1390: $i] :
( ~ ( SV190 @ SY1390 )
| ( SV381 = SY1390 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2448,plain,
! [SV339: $i,SV74: $i > $o,SV377: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV377 )
| ~ ! [SY1386: $i] :
( ~ ( SV190 @ SY1386 )
| ( SV377 = SY1386 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2404]) ).
thf(2449,plain,
! [SV339: $i,SV74: $i > $o,SV373: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV373 ) )
= $true )
| ( ( ~ ! [SY1382: $i] :
( ~ ( SV190 @ SY1382 )
| ( SV373 = SY1382 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2450,plain,
! [SV118: $i > $o,SV333: $i,SV384: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV384 ) )
= $true )
| ( ( ( sK83_SY1225 @ SV333 @ SV118 @ SV225 )
= SV384 )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2451,plain,
! [SV118: $i > $o,SV333: $i,SV378: $i,SV225: $i > $o] :
( ( ( SV225 @ SV378 )
= $false )
| ( ( ( sK79_SY1225 @ SV333 @ SV118 @ SV225 )
= SV378 )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV333
= ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2452,plain,
! [SV225: $i > $o,SV334: $i,SV385: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV385 ) )
= $true )
| ( ( ( sK84_SY1095 @ SV334 @ SV225 @ SV118 )
= SV385 )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2453,plain,
! [SV225: $i > $o,SV334: $i,SV379: $i,SV118: $i > $o] :
( ( ( SV118 @ SV379 )
= $false )
| ( ( ( sK80_SY1095 @ SV334 @ SV225 @ SV118 )
= SV379 )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV334
= ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $false )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2454,plain,
! [SV366: $i,SV118: $i > $o,SV225: $i > $o] :
( ( ( ! [SY1225: $i] :
~ ~ ( ~ ( SV225 @ SY1225 )
| ~ ! [SY1226: $i] :
( ~ ( SV225 @ SY1226 )
| ( SY1225 = SY1226 ) ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2455,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ ( sK105_SY1225 @ SV366 @ SV118 @ SV225 ) )
| ~ ! [SY1400: $i] :
( ~ ( SV225 @ SY1400 )
| ( ( sK105_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1400 ) ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2411]) ).
thf(2456,plain,
! [SV367: $i,SV225: $i > $o,SV118: $i > $o] :
( ( ( ! [SY1095: $i] :
~ ~ ( ~ ( SV118 @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV118 @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2457,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ ( sK106_SY1095 @ SV367 @ SV225 @ SV118 ) )
| ~ ! [SY1401: $i] :
( ~ ( SV118 @ SY1401 )
| ( ( sK106_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1401 ) ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2413]) ).
thf(2466,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ ( sK103_SY1225 @ SV357 @ SV118 @ SV225 ) )
| ~ ! [SY1397: $i] :
( ~ ( SV225 @ SY1397 )
| ( ( sK103_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1397 ) ) ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2422]) ).
thf(2467,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK96_SY1225 @ SV357 @ SV118 @ SV225 ) )
| ~ ! [SY1387: $i] :
( ~ ( SV225 @ SY1387 )
| ( ( sK96_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1387 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2468,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK104_SY1095 @ SV358 @ SV225 @ SV118 ) )
| ~ ! [SY1398: $i] :
( ~ ( SV118 @ SY1398 )
| ( ( sK104_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1398 ) ) ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2424]) ).
thf(2469,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK97_SY1095 @ SV358 @ SV225 @ SV118 ) )
| ~ ! [SY1388: $i] :
( ~ ( SV118 @ SY1388 )
| ( ( sK97_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1388 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2470,plain,
! [SV32: $i,SV323: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) ) )
= $false )
| ( ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2426]) ).
thf(2473,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2429]) ).
thf(2474,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2430]) ).
thf(2475,plain,
! [SV304: $i,SV344: $i,SV32: $i,SV380: $i] :
( ( ( in @ SV380 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( ! [SY1389: $i] :
( ~ ( in @ SY1389 @ SV380 )
| ( in @ SY1389 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
| ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV380 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2476,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2477,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2478,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV374: $i] :
( ( ( ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV374 )
| ( in @ SY1383 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) ) )
= $true )
| ( ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV374 )
= $true )
| ( ( in @ SV374 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2479,plain,
! [SV306: $i,SV184: $i,SV352: $i,SV372: $i,SV66: $i > $i > $o] :
( ( ( SV66 @ SV372 @ SV352 )
= $false )
| ( ( in @ SV372 @ SV184 )
= $false )
| ( ( in @ SV352 @ ( sK68_SY1165 @ SV306 @ SV66 @ SV184 ) )
= $true )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ SV306 )
= $false )
| ( ( SV66 @ ( sK9_SY1162 @ SV66 @ SV184 ) @ ( sK50_SY1303 @ SV306 @ SV184 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2480,plain,
! [SV370: $i,SV74: $i > $o,SV317: $i,SV190: $i > $o] :
( ( ( SV190 @ ( sK98_SY1374 @ SV317 @ SV74 @ SV370 @ SV190 ) )
= $true )
| ( ( SV190 @ SV370 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV317 )
= $false )
| ( ( SV74 @ ( sK69_SY1316 @ SV190 @ SV317 @ SV74 ) )
= $true )
| ( ( ( sK10_SY1177 @ SV190 @ SV74 )
= ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2439]) ).
thf(2481,plain,
! [SV346: $i,SV74: $i > $o,SV386: $i,SV190: $i > $o] :
( ( ( ~ ( ~ ( SV190 @ SV386 )
| ~ ! [SY1399: $i] :
( ~ ( SV190 @ SY1399 )
| ( SV386 = SY1399 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2482,plain,
! [SV346: $i,SV74: $i > $o,SV381: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV381 )
| ~ ! [SY1390: $i] :
( ~ ( SV190 @ SY1390 )
| ( SV381 = SY1390 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2487,plain,
! [SV339: $i,SV74: $i > $o,SV377: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV377 ) )
= $true )
| ( ( ~ ! [SY1386: $i] :
( ~ ( SV190 @ SY1386 )
| ( SV377 = SY1386 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2488,plain,
! [SV339: $i,SV74: $i > $o,SV373: $i,SV190: $i > $o] :
( ( ( SV190 @ SV373 )
= $false )
| ( ( ~ ! [SY1382: $i] :
( ~ ( SV190 @ SY1382 )
| ( SV373 = SY1382 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2489,plain,
! [SV118: $i > $o,SV333: $i,SV384: $i,SV225: $i > $o] :
( ( ( SV225 @ SV384 )
= $false )
| ( ( ( sK83_SY1225 @ SV333 @ SV118 @ SV225 )
= SV384 )
= $true )
| ( ( SV118 @ SV333 )
= $false )
| ( ( SV118 @ ( sK71_SY1335 @ SV225 @ SV333 @ SV118 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2490,plain,
! [SV225: $i > $o,SV334: $i,SV385: $i,SV118: $i > $o] :
( ( ( SV118 @ SV385 )
= $false )
| ( ( ( sK84_SY1095 @ SV334 @ SV225 @ SV118 )
= SV385 )
= $true )
| ( ( SV225 @ SV334 )
= $false )
| ( ( SV225 @ ( sK72_SY1336 @ SV118 @ SV334 @ SV225 ) )
= $true )
| ( ( ( sK15_SY1221 @ SV225 @ SV118 )
= ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2491,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ~ ( ~ ( SV225 @ ( sK111_SY1225 @ SV366 @ SV118 @ SV225 ) )
| ~ ! [SY1406: $i] :
( ~ ( SV225 @ SY1406 )
| ( ( sK111_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1406 ) ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2454]) ).
thf(2492,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ ( sK105_SY1225 @ SV366 @ SV118 @ SV225 ) )
| ~ ! [SY1400: $i] :
( ~ ( SV225 @ SY1400 )
| ( ( sK105_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1400 ) ) ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2455]) ).
thf(2493,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ ( sK112_SY1095 @ SV367 @ SV225 @ SV118 ) )
| ~ ! [SY1407: $i] :
( ~ ( SV118 @ SY1407 )
| ( ( sK112_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1407 ) ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2456]) ).
thf(2494,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK106_SY1095 @ SV367 @ SV225 @ SV118 ) )
| ~ ! [SY1401: $i] :
( ~ ( SV118 @ SY1401 )
| ( ( sK106_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1401 ) ) ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2503,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK103_SY1225 @ SV357 @ SV118 @ SV225 ) )
| ~ ! [SY1397: $i] :
( ~ ( SV225 @ SY1397 )
| ( ( sK103_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1397 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2504,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK96_SY1225 @ SV357 @ SV118 @ SV225 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2505,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ! [SY1387: $i] :
( ~ ( SV225 @ SY1387 )
| ( ( sK96_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1387 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2506,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK104_SY1095 @ SV358 @ SV225 @ SV118 ) )
| ~ ! [SY1398: $i] :
( ~ ( SV118 @ SY1398 )
| ( ( sK104_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1398 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2507,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK97_SY1095 @ SV358 @ SV225 @ SV118 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2469]) ).
thf(2508,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ! [SY1388: $i] :
( ~ ( SV118 @ SY1388 )
| ( ( sK97_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1388 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2469]) ).
thf(2509,plain,
! [SV32: $i,SV323: $i,SV330: $i] :
( ( ( in @ SV330 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $true )
| ( ( in @ SV323 @ ( sK75_SY1329 @ SV330 @ SV323 @ SV32 ) )
= $true )
| ( ( SV323 = SV330 )
= $true )
| ( ( in @ SV323 @ SV32 )
= $false )
| ( ( in @ SV330 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2470]) ).
thf(2510,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
| ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2511,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2512,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV380: $i] :
( ( ( ! [SY1389: $i] :
( ~ ( in @ SY1389 @ SV380 )
| ( in @ SY1389 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) ) )
= $true )
| ( ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV380 )
= $true )
| ( ( in @ SV380 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2513,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ~ ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2476]) ).
thf(2514,plain,
! [SV340: $i,SV304: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2476]) ).
thf(2515,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( ! [SY1357: $i] :
~ ~ ( ~ ( in @ SY1357 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SY1357 @ SV304 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2477]) ).
thf(2516,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV374: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV374 )
| ( in @ SV387 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
= $true )
| ( ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV374 )
= $true )
| ( ( in @ SV374 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2517,plain,
! [SV346: $i,SV74: $i > $o,SV386: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV386 )
| ~ ! [SY1399: $i] :
( ~ ( SV190 @ SY1399 )
| ( SV386 = SY1399 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2518,plain,
! [SV346: $i,SV74: $i > $o,SV381: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV381 ) )
= $true )
| ( ( ~ ! [SY1390: $i] :
( ~ ( SV190 @ SY1390 )
| ( SV381 = SY1390 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2523,plain,
! [SV339: $i,SV74: $i > $o,SV377: $i,SV190: $i > $o] :
( ( ( SV190 @ SV377 )
= $false )
| ( ( ~ ! [SY1386: $i] :
( ~ ( SV190 @ SY1386 )
| ( SV377 = SY1386 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2524,plain,
! [SV339: $i,SV74: $i > $o,SV373: $i,SV190: $i > $o] :
( ( ( ! [SY1382: $i] :
( ~ ( SV190 @ SY1382 )
| ( SV373 = SY1382 ) ) )
= $false )
| ( ( SV190 @ SV373 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2525,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ( ~ ( SV225 @ ( sK111_SY1225 @ SV366 @ SV118 @ SV225 ) )
| ~ ! [SY1406: $i] :
( ~ ( SV225 @ SY1406 )
| ( ( sK111_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1406 ) ) ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2491]) ).
thf(2526,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK105_SY1225 @ SV366 @ SV118 @ SV225 ) )
| ~ ! [SY1400: $i] :
( ~ ( SV225 @ SY1400 )
| ( ( sK105_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1400 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2527,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK112_SY1095 @ SV367 @ SV225 @ SV118 ) )
| ~ ! [SY1407: $i] :
( ~ ( SV118 @ SY1407 )
| ( ( sK112_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1407 ) ) ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2493]) ).
thf(2528,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK106_SY1095 @ SV367 @ SV225 @ SV118 ) )
| ~ ! [SY1401: $i] :
( ~ ( SV118 @ SY1401 )
| ( ( sK106_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1401 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2541,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK103_SY1225 @ SV357 @ SV118 @ SV225 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2503]) ).
thf(2542,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ~ ! [SY1397: $i] :
( ~ ( SV225 @ SY1397 )
| ( ( sK103_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1397 ) ) )
= $false )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2503]) ).
thf(2543,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( SV225 @ ( sK96_SY1225 @ SV357 @ SV118 @ SV225 ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2504]) ).
thf(2544,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ! [SY1387: $i] :
( ~ ( SV225 @ SY1387 )
| ( ( sK96_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1387 ) ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2545,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK104_SY1095 @ SV358 @ SV225 @ SV118 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2506]) ).
thf(2546,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ~ ! [SY1398: $i] :
( ~ ( SV118 @ SY1398 )
| ( ( sK104_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1398 ) ) )
= $false )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2506]) ).
thf(2547,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( SV118 @ ( sK97_SY1095 @ SV358 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2548,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ! [SY1388: $i] :
( ~ ( SV118 @ SY1388 )
| ( ( sK97_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1388 ) ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2549,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ~ ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2510]) ).
thf(2550,plain,
! [SV344: $i,SV304: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2510]) ).
thf(2551,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( ! [SY1365: $i] :
~ ~ ( ~ ( in @ SY1365 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SY1365 @ SV304 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2511]) ).
thf(2552,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV380: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV380 )
| ( in @ SV388 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
= $true )
| ( ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV380 )
= $true )
| ( ( in @ SV380 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2553,plain,
! [SV32: $i,SV304: $i,SV340: $i] :
( ( ( in @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2513]) ).
thf(2554,plain,
! [SV340: $i,SV304: $i,SV32: $i] :
( ( ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV304 )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2514]) ).
thf(2555,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV389: $i] :
( ( ( ~ ~ ( ~ ( in @ SV389 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SV389 @ SV304 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2556,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV374: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV374 ) )
= $true )
| ( ( in @ SV387 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
= $true )
| ( ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV374 )
= $true )
| ( ( in @ SV374 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2557,plain,
! [SV346: $i,SV74: $i > $o,SV386: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ SV386 ) )
= $true )
| ( ( ~ ! [SY1399: $i] :
( ~ ( SV190 @ SY1399 )
| ( SV386 = SY1399 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2558,plain,
! [SV346: $i,SV74: $i > $o,SV381: $i,SV190: $i > $o] :
( ( ( SV190 @ SV381 )
= $false )
| ( ( ~ ! [SY1390: $i] :
( ~ ( SV190 @ SY1390 )
| ( SV381 = SY1390 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2563,plain,
! [SV339: $i,SV74: $i > $o,SV377: $i,SV190: $i > $o] :
( ( ( ! [SY1386: $i] :
( ~ ( SV190 @ SY1386 )
| ( SV377 = SY1386 ) ) )
= $false )
| ( ( SV190 @ SV377 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2564,plain,
! [SV373: $i,SV74: $i > $o,SV339: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK113_SY1382 @ SV339 @ SV74 @ SV373 @ SV190 ) )
| ( SV373
= ( sK113_SY1382 @ SV339 @ SV74 @ SV373 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV373 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2524]) ).
thf(2565,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK111_SY1225 @ SV366 @ SV118 @ SV225 ) )
| ~ ! [SY1406: $i] :
( ~ ( SV225 @ SY1406 )
| ( ( sK111_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1406 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2566,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK105_SY1225 @ SV366 @ SV118 @ SV225 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2567,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ! [SY1400: $i] :
( ~ ( SV225 @ SY1400 )
| ( ( sK105_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1400 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2568,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK112_SY1095 @ SV367 @ SV225 @ SV118 ) )
| ~ ! [SY1407: $i] :
( ~ ( SV118 @ SY1407 )
| ( ( sK112_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1407 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2569,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK106_SY1095 @ SV367 @ SV225 @ SV118 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2528]) ).
thf(2570,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ! [SY1401: $i] :
( ~ ( SV118 @ SY1401 )
| ( ( sK106_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1401 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2528]) ).
thf(2587,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( SV225 @ ( sK103_SY1225 @ SV357 @ SV118 @ SV225 ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2541]) ).
thf(2588,plain,
! [SV118: $i > $o,SV357: $i,SV225: $i > $o] :
( ( ( ! [SY1397: $i] :
( ~ ( SV225 @ SY1397 )
| ( ( sK103_SY1225 @ SV357 @ SV118 @ SV225 )
= SY1397 ) ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2542]) ).
thf(2589,plain,
! [SV118: $i > $o,SV357: $i,SV390: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV390 )
| ( ( sK96_SY1225 @ SV357 @ SV118 @ SV225 )
= SV390 ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2590,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( SV118 @ ( sK104_SY1095 @ SV358 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2545]) ).
thf(2591,plain,
! [SV225: $i > $o,SV358: $i,SV118: $i > $o] :
( ( ( ! [SY1398: $i] :
( ~ ( SV118 @ SY1398 )
| ( ( sK104_SY1095 @ SV358 @ SV225 @ SV118 )
= SY1398 ) ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2546]) ).
thf(2592,plain,
! [SV225: $i > $o,SV358: $i,SV391: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV391 )
| ( ( sK97_SY1095 @ SV358 @ SV225 @ SV118 )
= SV391 ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2593,plain,
! [SV32: $i,SV304: $i,SV344: $i] :
( ( ( in @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) @ ( sK2_SY874 @ SV32 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2594,plain,
! [SV344: $i,SV304: $i,SV32: $i] :
( ( ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV304 )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2595,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV392: $i] :
( ( ( ~ ~ ( ~ ( in @ SV392 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SV392 @ SV304 ) ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2596,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV380: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV380 ) )
= $true )
| ( ( in @ SV388 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
= $true )
| ( ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV380 )
= $true )
| ( ( in @ SV380 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2597,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV389: $i] :
( ( ( ~ ( ~ ( in @ SV389 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SV389 @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2598,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV374: $i,SV387: $i] :
( ( ( in @ SV387 @ SV374 )
= $false )
| ( ( in @ SV387 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
= $true )
| ( ( in @ ( sK76_SY1356 @ SV32 @ SV304 @ SV340 ) @ SV374 )
= $true )
| ( ( in @ SV374 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2599,plain,
! [SV346: $i,SV74: $i > $o,SV386: $i,SV190: $i > $o] :
( ( ( SV190 @ SV386 )
= $false )
| ( ( ~ ! [SY1399: $i] :
( ~ ( SV190 @ SY1399 )
| ( SV386 = SY1399 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2600,plain,
! [SV346: $i,SV74: $i > $o,SV381: $i,SV190: $i > $o] :
( ( ( ! [SY1390: $i] :
( ~ ( SV190 @ SY1390 )
| ( SV381 = SY1390 ) ) )
= $false )
| ( ( SV190 @ SV381 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2605,plain,
! [SV377: $i,SV74: $i > $o,SV339: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK116_SY1386 @ SV339 @ SV74 @ SV377 @ SV190 ) )
| ( SV377
= ( sK116_SY1386 @ SV339 @ SV74 @ SV377 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV377 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2563]) ).
thf(2606,plain,
! [SV373: $i,SV74: $i > $o,SV339: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK113_SY1382 @ SV339 @ SV74 @ SV373 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV373 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2564]) ).
thf(2607,plain,
! [SV190: $i > $o,SV74: $i > $o,SV339: $i,SV373: $i] :
( ( ( SV373
= ( sK113_SY1382 @ SV339 @ SV74 @ SV373 @ SV190 ) )
= $false )
| ( ( SV190 @ SV373 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2564]) ).
thf(2608,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ ( sK111_SY1225 @ SV366 @ SV118 @ SV225 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2609,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ~ ! [SY1406: $i] :
( ~ ( SV225 @ SY1406 )
| ( ( sK111_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1406 ) ) )
= $false )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2610,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( SV225 @ ( sK105_SY1225 @ SV366 @ SV118 @ SV225 ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2566]) ).
thf(2611,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ! [SY1400: $i] :
( ~ ( SV225 @ SY1400 )
| ( ( sK105_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1400 ) ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2612,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ ( sK112_SY1095 @ SV367 @ SV225 @ SV118 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2568]) ).
thf(2613,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ~ ! [SY1407: $i] :
( ~ ( SV118 @ SY1407 )
| ( ( sK112_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1407 ) ) )
= $false )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2568]) ).
thf(2614,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( SV118 @ ( sK106_SY1095 @ SV367 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2569]) ).
thf(2615,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ! [SY1401: $i] :
( ~ ( SV118 @ SY1401 )
| ( ( sK106_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1401 ) ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2628,plain,
! [SV118: $i > $o,SV357: $i,SV397: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV397 )
| ( ( sK103_SY1225 @ SV357 @ SV118 @ SV225 )
= SV397 ) )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2629,plain,
! [SV118: $i > $o,SV357: $i,SV390: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV390 ) )
= $true )
| ( ( ( sK96_SY1225 @ SV357 @ SV118 @ SV225 )
= SV390 )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2630,plain,
! [SV225: $i > $o,SV358: $i,SV398: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV398 )
| ( ( sK104_SY1095 @ SV358 @ SV225 @ SV118 )
= SV398 ) )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(2631,plain,
! [SV225: $i > $o,SV358: $i,SV391: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV391 ) )
= $true )
| ( ( ( sK97_SY1095 @ SV358 @ SV225 @ SV118 )
= SV391 )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2632,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV392: $i] :
( ( ( ~ ( ~ ( in @ SV392 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SV392 @ SV304 ) ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2633,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV380: $i,SV388: $i] :
( ( ( in @ SV388 @ SV380 )
= $false )
| ( ( in @ SV388 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
= $true )
| ( ( in @ ( sK81_SY1364 @ SV32 @ SV304 @ SV344 ) @ SV380 )
= $true )
| ( ( in @ SV380 @ ( sK2_SY874 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2634,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
| ~ ( in @ SV389 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2597]) ).
thf(2635,plain,
! [SV346: $i,SV74: $i > $o,SV386: $i,SV190: $i > $o] :
( ( ( ! [SY1399: $i] :
( ~ ( SV190 @ SY1399 )
| ( SV386 = SY1399 ) ) )
= $false )
| ( ( SV190 @ SV386 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2636,plain,
! [SV381: $i,SV74: $i > $o,SV346: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK117_SY1390 @ SV346 @ SV74 @ SV381 @ SV190 ) )
| ( SV381
= ( sK117_SY1390 @ SV346 @ SV74 @ SV381 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV381 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2600]) ).
thf(2643,plain,
! [SV377: $i,SV74: $i > $o,SV339: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK116_SY1386 @ SV339 @ SV74 @ SV377 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV377 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2605]) ).
thf(2644,plain,
! [SV190: $i > $o,SV74: $i > $o,SV339: $i,SV377: $i] :
( ( ( SV377
= ( sK116_SY1386 @ SV339 @ SV74 @ SV377 @ SV190 ) )
= $false )
| ( ( SV190 @ SV377 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2605]) ).
thf(2645,plain,
! [SV373: $i,SV74: $i > $o,SV339: $i,SV190: $i > $o] :
( ( ( SV190 @ ( sK113_SY1382 @ SV339 @ SV74 @ SV373 @ SV190 ) )
= $true )
| ( ( SV190 @ SV373 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV339
= ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $false )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2606]) ).
thf(2646,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( SV225 @ ( sK111_SY1225 @ SV366 @ SV118 @ SV225 ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2608]) ).
thf(2647,plain,
! [SV118: $i > $o,SV366: $i,SV225: $i > $o] :
( ( ( ! [SY1406: $i] :
( ~ ( SV225 @ SY1406 )
| ( ( sK111_SY1225 @ SV366 @ SV118 @ SV225 )
= SY1406 ) ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2648,plain,
! [SV118: $i > $o,SV366: $i,SV399: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV399 )
| ( ( sK105_SY1225 @ SV366 @ SV118 @ SV225 )
= SV399 ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2649,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( SV118 @ ( sK112_SY1095 @ SV367 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2650,plain,
! [SV225: $i > $o,SV367: $i,SV118: $i > $o] :
( ( ( ! [SY1407: $i] :
( ~ ( SV118 @ SY1407 )
| ( ( sK112_SY1095 @ SV367 @ SV225 @ SV118 )
= SY1407 ) ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2613]) ).
thf(2651,plain,
! [SV225: $i > $o,SV367: $i,SV400: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV400 )
| ( ( sK106_SY1095 @ SV367 @ SV225 @ SV118 )
= SV400 ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(2660,plain,
! [SV118: $i > $o,SV357: $i,SV397: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV397 ) )
= $true )
| ( ( ( sK103_SY1225 @ SV357 @ SV118 @ SV225 )
= SV397 )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2661,plain,
! [SV118: $i > $o,SV357: $i,SV390: $i,SV225: $i > $o] :
( ( ( SV225 @ SV390 )
= $false )
| ( ( ( sK96_SY1225 @ SV357 @ SV118 @ SV225 )
= SV390 )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV357
= ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2662,plain,
! [SV225: $i > $o,SV358: $i,SV398: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV398 ) )
= $true )
| ( ( ( sK104_SY1095 @ SV358 @ SV225 @ SV118 )
= SV398 )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2663,plain,
! [SV225: $i > $o,SV358: $i,SV391: $i,SV118: $i > $o] :
( ( ( SV118 @ SV391 )
= $false )
| ( ( ( sK97_SY1095 @ SV358 @ SV225 @ SV118 )
= SV391 )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV358
= ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $false )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2664,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
| ~ ( in @ SV392 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2632]) ).
thf(2665,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ SV389 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2666,plain,
! [SV386: $i,SV74: $i > $o,SV346: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK120_SY1399 @ SV346 @ SV74 @ SV386 @ SV190 ) )
| ( SV386
= ( sK120_SY1399 @ SV346 @ SV74 @ SV386 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV386 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2635]) ).
thf(2667,plain,
! [SV381: $i,SV74: $i > $o,SV346: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK117_SY1390 @ SV346 @ SV74 @ SV381 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV381 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2636]) ).
thf(2668,plain,
! [SV190: $i > $o,SV74: $i > $o,SV346: $i,SV381: $i] :
( ( ( SV381
= ( sK117_SY1390 @ SV346 @ SV74 @ SV381 @ SV190 ) )
= $false )
| ( ( SV190 @ SV381 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2636]) ).
thf(2675,plain,
! [SV377: $i,SV74: $i > $o,SV339: $i,SV190: $i > $o] :
( ( ( SV190 @ ( sK116_SY1386 @ SV339 @ SV74 @ SV377 @ SV190 ) )
= $true )
| ( ( SV190 @ SV377 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV339 )
= $false )
| ( ( SV74 @ ( sK74_SY1342 @ SV190 @ SV339 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2643]) ).
thf(2676,plain,
! [SV118: $i > $o,SV366: $i,SV405: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV405 )
| ( ( sK111_SY1225 @ SV366 @ SV118 @ SV225 )
= SV405 ) )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(2677,plain,
! [SV118: $i > $o,SV366: $i,SV399: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV399 ) )
= $true )
| ( ( ( sK105_SY1225 @ SV366 @ SV118 @ SV225 )
= SV399 )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(2678,plain,
! [SV225: $i > $o,SV367: $i,SV406: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV406 )
| ( ( sK112_SY1095 @ SV367 @ SV225 @ SV118 )
= SV406 ) )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(2679,plain,
! [SV225: $i > $o,SV367: $i,SV400: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV400 ) )
= $true )
| ( ( ( sK106_SY1095 @ SV367 @ SV225 @ SV118 )
= SV400 )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2688,plain,
! [SV118: $i > $o,SV357: $i,SV397: $i,SV225: $i > $o] :
( ( ( SV225 @ SV397 )
= $false )
| ( ( ( sK103_SY1225 @ SV357 @ SV118 @ SV225 )
= SV397 )
= $true )
| ( ( SV118 @ SV357 )
= $false )
| ( ( SV118 @ ( sK86_SY1354 @ SV225 @ SV357 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2689,plain,
! [SV225: $i > $o,SV358: $i,SV398: $i,SV118: $i > $o] :
( ( ( SV118 @ SV398 )
= $false )
| ( ( ( sK104_SY1095 @ SV358 @ SV225 @ SV118 )
= SV398 )
= $true )
| ( ( SV225 @ SV358 )
= $false )
| ( ( SV225 @ ( sK87_SY1355 @ SV118 @ SV358 @ SV225 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2690,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ SV392 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2664]) ).
thf(2691,plain,
! [SV32: $i,SV304: $i,SV340: $i,SV389: $i] :
( ( ( in @ SV389 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
= $false )
| ( ( ~ ( in @ SV389 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2692,plain,
! [SV386: $i,SV74: $i > $o,SV346: $i,SV190: $i > $o] :
( ( ( ~ ( SV190 @ ( sK120_SY1399 @ SV346 @ SV74 @ SV386 @ SV190 ) ) )
= $false )
| ( ( SV190 @ SV386 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2666]) ).
thf(2693,plain,
! [SV190: $i > $o,SV74: $i > $o,SV346: $i,SV386: $i] :
( ( ( SV386
= ( sK120_SY1399 @ SV346 @ SV74 @ SV386 @ SV190 ) )
= $false )
| ( ( SV190 @ SV386 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2666]) ).
thf(2694,plain,
! [SV381: $i,SV74: $i > $o,SV346: $i,SV190: $i > $o] :
( ( ( SV190 @ ( sK117_SY1390 @ SV346 @ SV74 @ SV381 @ SV190 ) )
= $true )
| ( ( SV190 @ SV381 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV346
= ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $false )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2667]) ).
thf(2697,plain,
! [SV118: $i > $o,SV366: $i,SV405: $i,SV225: $i > $o] :
( ( ( ~ ( SV225 @ SV405 ) )
= $true )
| ( ( ( sK111_SY1225 @ SV366 @ SV118 @ SV225 )
= SV405 )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2698,plain,
! [SV118: $i > $o,SV366: $i,SV399: $i,SV225: $i > $o] :
( ( ( SV225 @ SV399 )
= $false )
| ( ( ( sK105_SY1225 @ SV366 @ SV118 @ SV225 )
= SV399 )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV366
= ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2699,plain,
! [SV225: $i > $o,SV367: $i,SV406: $i,SV118: $i > $o] :
( ( ( ~ ( SV118 @ SV406 ) )
= $true )
| ( ( ( sK112_SY1095 @ SV367 @ SV225 @ SV118 )
= SV406 )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(2700,plain,
! [SV225: $i > $o,SV367: $i,SV400: $i,SV118: $i > $o] :
( ( ( SV118 @ SV400 )
= $false )
| ( ( ( sK106_SY1095 @ SV367 @ SV225 @ SV118 )
= SV400 )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV367
= ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $false )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2705,plain,
! [SV32: $i,SV304: $i,SV344: $i,SV392: $i] :
( ( ( in @ SV392 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
= $false )
| ( ( ~ ( in @ SV392 @ SV304 ) )
= $true )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2706,plain,
! [SV32: $i,SV340: $i,SV304: $i,SV389: $i] :
( ( ( in @ SV389 @ SV304 )
= $false )
| ( ( in @ SV389 @ ( sK70_SY1297 @ SV340 @ SV304 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV32 )
= $false )
| ( ( in @ SV340 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2707,plain,
! [SV386: $i,SV74: $i > $o,SV346: $i,SV190: $i > $o] :
( ( ( SV190 @ ( sK120_SY1399 @ SV346 @ SV74 @ SV386 @ SV190 ) )
= $true )
| ( ( SV190 @ SV386 )
= $false )
| ( ( ( descr
@ ^ [SY986: $i] : ( SV74 @ SY986 ) )
= ( descr
@ ^ [SY1184: $i] : ( SV190 @ SY1184 ) ) )
= $true )
| ( ( SV74 @ SV346 )
= $false )
| ( ( SV74 @ ( sK82_SY1351 @ SV190 @ SV346 @ SV74 ) )
= $true )
| ( ( SV74 @ ( sK10_SY1177 @ SV190 @ SV74 ) )
= $true )
| ( ( SV190 @ ( sK16_SY1282 @ SV74 @ SV190 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2708,plain,
! [SV118: $i > $o,SV366: $i,SV405: $i,SV225: $i > $o] :
( ( ( SV225 @ SV405 )
= $false )
| ( ( ( sK111_SY1225 @ SV366 @ SV118 @ SV225 )
= SV405 )
= $true )
| ( ( SV118 @ SV366 )
= $false )
| ( ( SV118 @ ( sK93_SY1368 @ SV225 @ SV366 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2709,plain,
! [SV225: $i > $o,SV367: $i,SV406: $i,SV118: $i > $o] :
( ( ( SV118 @ SV406 )
= $false )
| ( ( ( sK112_SY1095 @ SV367 @ SV225 @ SV118 )
= SV406 )
= $true )
| ( ( SV225 @ SV367 )
= $false )
| ( ( SV225 @ ( sK94_SY1369 @ SV118 @ SV367 @ SV225 ) )
= $true )
| ( ( SV118 @ ( sK15_SY1221 @ SV225 @ SV118 ) )
= $true )
| ( ( SV225 @ ( sK18_SY1289 @ SV118 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2710,plain,
! [SV32: $i,SV344: $i,SV304: $i,SV392: $i] :
( ( ( in @ SV392 @ SV304 )
= $false )
| ( ( in @ SV392 @ ( sK73_SY1297 @ SV344 @ SV304 @ SV32 ) )
= $false )
| ( ( in @ ( sK48_SY1295 @ SV32 @ SV304 ) @ SV304 )
= $true )
| ( ( in @ SV344 @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2711,plain,
! [SV281: $i,SV336: $i] :
( ( ( SV336
= ( sK49_SY921 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) ) )
= $false )
| ( ( SV336 = SV281 )
= $true )
| ( ( SV281 = SV281 )
= $false )
| ( ( SV281
= ( sK40_SY1272 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) ) )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[2072:[bind(SV47,$thf( ^ [SV407: $i] : ( SV407 = SV281 ) ))]]) ).
thf(2712,plain,
! [SV281: $i,SV336: $i] :
( ( ( SV336
= ( sK49_SY921 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) ) )
= $false )
| ( ( SV336 = SV281 )
= $true )
| ( ( SV281
= ( sK40_SY1272 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) ) )
= $false ) ),
inference(sim,[status(thm)],[2711]) ).
thf(2713,plain,
! [SV281: $i,SV338: $i] :
( ( ( SV338
= ( sK57_SY921 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) ) )
= $false )
| ( ( SV338 = SV281 )
= $true )
| ( ( SV281 = SV281 )
= $false )
| ( ( ( sK40_SY1272 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) )
= SV281 )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[2113:[bind(SV47,$thf( ^ [SV408: $i] : ( SV408 = SV281 ) ))]]) ).
thf(2714,plain,
! [SV281: $i,SV338: $i] :
( ( ( SV338
= ( sK57_SY921 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) ) )
= $false )
| ( ( SV338 = SV281 )
= $true )
| ( ( ( sK40_SY1272 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) )
= SV281 )
= $true ) ),
inference(sim,[status(thm)],[2713]) ).
thf(2715,plain,
! [SV43: $o] :
( ( SV43 = $false )
| ( ( SV43
= ( ~ ( set2prop @ ( prop2set @ SV43 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[680]) ).
thf(2716,plain,
! [SV129: $o] :
( ( SV129 = $false )
| ( ( SV129
= ( ~ ( in @ emptyset @ ( prop2set @ SV129 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[770]) ).
thf(2717,plain,
! [SV31: $i,SV275: $o] :
( ( SV275 = $true )
| ( ( SV275
= ( ~ ( in @ SV31 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[782]) ).
thf(2718,plain,
! [SV57: $o,SV173: $i] :
( ( SV57 = $true )
| ( ( SV57
= ( ~ ( in @ SV173 @ ( prop2set @ SV57 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[810]) ).
thf(2719,plain,
! [SV117: $i > $o,SV224: $i] :
( ( ( SV117 @ SV224 )
= $true )
| ( ( ( SV117 @ SV224 )
= ( ~ ( in @ SV224 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[872]) ).
thf(2720,plain,
! [SV150: $i > $o,SV26: $i,SV237: $i] :
( ( ( SV150 @ SV237 )
= $true )
| ( ( ( SV150 @ SV237 )
= ( ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[891]) ).
thf(2721,plain,
! [SV33: $i] :
( ( ( SV33 = emptyset )
= $true )
| ( ( ( in @ ( sK4_SY892 @ SV33 ) @ SV33 )
= ( SV33 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[896]) ).
thf(2722,plain,
! [SV55: $i] :
( ( ( SV55 = emptyset )
= $true )
| ( ( ( in @ ( sK5_SY940 @ SV55 ) @ SV55 )
= ( SV55 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[914]) ).
thf(2723,plain,
! [SV35: $i,SV156: $i,SV242: $i] :
( ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false )
| ( ( ( in @ SV242 @ SV156 )
= ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[986]) ).
thf(2724,plain,
! [SV213: $i,SV103: $i,SV266: $i] :
( ( ( in @ SV266 @ SV213 )
= $false )
| ( ( ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
= ( in @ SV266 @ SV213 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1044]) ).
thf(2725,plain,
! [SV44: $i,SV163: $i] :
( ( ( subset @ SV44 @ SV163 )
= $true )
| ( ( ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
= ( subset @ SV44 @ SV163 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1082]) ).
thf(2726,plain,
! [SV181: $i,SV63: $i] :
( ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true )
| ( ( ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
= ( in @ SV181 @ ( powerset @ SV63 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1092]) ).
thf(2727,plain,
! [SV82: $i] :
( ( ( SV82 = emptyset )
= $true )
| ( ( ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 )
= ( SV82 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1112]) ).
thf(2728,plain,
! [SV289: $i,SV102: $i] :
( ( ( in @ SV289 @ SV102 )
= $false )
| ( ( ( SV102 = emptyset )
= ( in @ SV289 @ SV102 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1128]) ).
thf(2729,plain,
! [SV116: $i,SV223: $i] :
( ( ( subset @ SV116 @ SV223 )
= $true )
| ( ( ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
= ( subset @ SV116 @ SV223 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1138]) ).
thf(2730,plain,
! [SV178: $i,SV60: $i] :
( ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true )
| ( ( ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
= ( in @ SV178 @ ( powerset @ SV60 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1326]) ).
thf(2731,plain,
! [SV126: $i] :
( ( ( SV126 = emptyset )
= $true )
| ( ( ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
= ( SV126 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1382]) ).
thf(2733,plain,
! [SV39: $i,SV160: $i] :
( ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true )
| ( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
= ( ( binintersect @ SV39 @ SV160 )
= emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1396]) ).
thf(2734,plain,
! [SV39: $i,SV160: $i] :
( ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true )
| ( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 )
= ( ( binintersect @ SV39 @ SV160 )
= emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1397]) ).
thf(2735,plain,
! [SV43: $o] :
( ( ( ~ ( SV43
| ~ ( set2prop @ ( prop2set @ SV43 ) ) )
| ~ ( ~ SV43
| ~ ~ ( set2prop @ ( prop2set @ SV43 ) ) ) )
= $false )
| ( SV43 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2715]) ).
thf(2737,plain,
! [SV129: $o] :
( ( ( ~ ( SV129
| ~ ( in @ emptyset @ ( prop2set @ SV129 ) ) )
| ~ ( ~ SV129
| ~ ~ ( in @ emptyset @ ( prop2set @ SV129 ) ) ) )
= $false )
| ( SV129 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2716]) ).
thf(2739,plain,
! [SV31: $i,SV275: $o] :
( ( ( ~ ( SV275
| ~ ( in @ SV31 @ emptyset ) )
| ~ ( ~ SV275
| ~ ~ ( in @ SV31 @ emptyset ) ) )
= $false )
| ( SV275 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2717]) ).
thf(2740,plain,
! [SV31: $i,SV275: $o] :
( ( ( SV275
= ( ~ ( in @ SV31 @ emptyset ) ) )
= $false )
| ( SV275 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2717]) ).
thf(2741,plain,
! [SV173: $i,SV57: $o] :
( ( ( ~ ( SV57
| ~ ( in @ SV173 @ ( prop2set @ SV57 ) ) )
| ~ ( ~ SV57
| ~ ~ ( in @ SV173 @ ( prop2set @ SV57 ) ) ) )
= $false )
| ( SV57 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2718]) ).
thf(2743,plain,
! [SV224: $i,SV117: $i > $o] :
( ( ( ~ ( ( SV117 @ SV224 )
| ~ ( in @ SV224 @ emptyset ) )
| ~ ( ~ ( SV117 @ SV224 )
| ~ ~ ( in @ SV224 @ emptyset ) ) )
= $false )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2719]) ).
thf(2744,plain,
! [SV224: $i,SV117: $i > $o] :
( ( ( ( SV117 @ SV224 )
= ( ~ ( in @ SV224 @ emptyset ) ) )
= $false )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2719]) ).
thf(2745,plain,
! [SV26: $i,SV237: $i,SV150: $i > $o] :
( ( ( ~ ( ( SV150 @ SV237 )
| ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) ) )
| ~ ( ~ ( SV150 @ SV237 )
| ~ ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) ) ) )
= $false )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2720]) ).
thf(2746,plain,
! [SV26: $i,SV237: $i,SV150: $i > $o] :
( ( ( ( SV150 @ SV237 )
= ( ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) ) ) )
= $false )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2720]) ).
thf(2747,plain,
! [SV33: $i] :
( ( ( ~ ( ( in @ ( sK4_SY892 @ SV33 ) @ SV33 )
| ( SV33 = emptyset ) )
| ~ ( ~ ( in @ ( sK4_SY892 @ SV33 ) @ SV33 )
| ( SV33 != emptyset ) ) )
= $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2721]) ).
thf(2749,plain,
! [SV55: $i] :
( ( ( ~ ( ( in @ ( sK5_SY940 @ SV55 ) @ SV55 )
| ( SV55 = emptyset ) )
| ~ ( ~ ( in @ ( sK5_SY940 @ SV55 ) @ SV55 )
| ( SV55 != emptyset ) ) )
= $false )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2722]) ).
thf(2751,plain,
! [SV35: $i,SV156: $i,SV242: $i] :
( ( ( ~ ( ( in @ SV242 @ SV156 )
| ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) ) )
| ~ ( ~ ( in @ SV242 @ SV156 )
| ~ ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) ) ) )
= $false )
| ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2723]) ).
thf(2753,plain,
! [SV213: $i,SV103: $i,SV266: $i] :
( ( ( ~ ( ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
| ( in @ SV266 @ SV213 ) )
| ~ ( ~ ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
| ~ ( in @ SV266 @ SV213 ) ) )
= $false )
| ( ( in @ SV266 @ SV213 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2724]) ).
thf(2755,plain,
! [SV44: $i,SV163: $i] :
( ( ( ~ ( ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
| ( subset @ SV44 @ SV163 ) )
| ~ ( ~ ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
| ~ ( subset @ SV44 @ SV163 ) ) )
= $false )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2725]) ).
thf(2757,plain,
! [SV181: $i,SV63: $i] :
( ( ( ~ ( ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
| ( in @ SV181 @ ( powerset @ SV63 ) ) )
| ~ ( ~ ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
| ~ ( in @ SV181 @ ( powerset @ SV63 ) ) ) )
= $false )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2726]) ).
thf(2759,plain,
! [SV82: $i] :
( ( ( ~ ( ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 )
| ( SV82 = emptyset ) )
| ~ ( ~ ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 )
| ( SV82 != emptyset ) ) )
= $false )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2727]) ).
thf(2761,plain,
! [SV289: $i,SV102: $i] :
( ( ( ~ ( ( SV102 = emptyset )
| ( in @ SV289 @ SV102 ) )
| ~ ( ( SV102 != emptyset )
| ~ ( in @ SV289 @ SV102 ) ) )
= $false )
| ( ( in @ SV289 @ SV102 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2728]) ).
thf(2763,plain,
! [SV116: $i,SV223: $i] :
( ( ( ~ ( ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
| ( subset @ SV116 @ SV223 ) )
| ~ ( ~ ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
| ~ ( subset @ SV116 @ SV223 ) ) )
= $false )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2729]) ).
thf(2765,plain,
! [SV178: $i,SV60: $i] :
( ( ( ~ ( ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
| ( in @ SV178 @ ( powerset @ SV60 ) ) )
| ~ ( ~ ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
| ~ ( in @ SV178 @ ( powerset @ SV60 ) ) ) )
= $false )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2730]) ).
thf(2767,plain,
! [SV126: $i] :
( ( ( ~ ( ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
| ( SV126 = emptyset ) )
| ~ ( ~ ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
| ( SV126 != emptyset ) ) )
= $false )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2731]) ).
thf(2771,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
| ( ( binintersect @ SV39 @ SV160 )
= emptyset ) )
| ~ ( ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
| ( ( binintersect @ SV39 @ SV160 )
!= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2733]) ).
thf(2773,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 )
| ( ( binintersect @ SV39 @ SV160 )
= emptyset ) )
| ~ ( ~ ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 )
| ( ( binintersect @ SV39 @ SV160 )
!= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2734]) ).
thf(2776,plain,
! [SV43: $o] :
( ( ( ~ ( ~ SV43
| ~ ~ ( set2prop @ ( prop2set @ SV43 ) ) ) )
= $false )
| ( SV43 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2778,plain,
! [SV129: $o] :
( ( ( ~ ( ~ SV129
| ~ ~ ( in @ emptyset @ ( prop2set @ SV129 ) ) ) )
= $false )
| ( SV129 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2737]) ).
thf(2779,plain,
! [SV31: $i,SV275: $o] :
( ( ( ~ ( SV275
| ~ ( in @ SV31 @ emptyset ) ) )
= $false )
| ( SV275 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2781,plain,
! [SV173: $i,SV57: $o] :
( ( ( ~ ( SV57
| ~ ( in @ SV173 @ ( prop2set @ SV57 ) ) ) )
= $false )
| ( SV57 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2741]) ).
thf(2783,plain,
! [SV224: $i,SV117: $i > $o] :
( ( ( ~ ( ( SV117 @ SV224 )
| ~ ( in @ SV224 @ emptyset ) ) )
= $false )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2743]) ).
thf(2785,plain,
! [SV26: $i,SV237: $i,SV150: $i > $o] :
( ( ( ~ ( ( SV150 @ SV237 )
| ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) ) ) )
= $false )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2787,plain,
! [SV33: $i] :
( ( ( ~ ( ( in @ ( sK4_SY892 @ SV33 ) @ SV33 )
| ( SV33 = emptyset ) ) )
= $false )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2747]) ).
thf(2789,plain,
! [SV55: $i] :
( ( ( ~ ( ( in @ ( sK5_SY940 @ SV55 ) @ SV55 )
| ( SV55 = emptyset ) ) )
= $false )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2749]) ).
thf(2792,plain,
! [SV35: $i,SV156: $i,SV242: $i] :
( ( ( ~ ( ~ ( in @ SV242 @ SV156 )
| ~ ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) ) ) )
= $false )
| ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2794,plain,
! [SV213: $i,SV103: $i,SV266: $i] :
( ( ( ~ ( ~ ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
| ~ ( in @ SV266 @ SV213 ) ) )
= $false )
| ( ( in @ SV266 @ SV213 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2753]) ).
thf(2795,plain,
! [SV44: $i,SV163: $i] :
( ( ( ~ ( ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
| ( subset @ SV44 @ SV163 ) ) )
= $false )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2755]) ).
thf(2797,plain,
! [SV181: $i,SV63: $i] :
( ( ( ~ ( ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
| ( in @ SV181 @ ( powerset @ SV63 ) ) ) )
= $false )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(2799,plain,
! [SV82: $i] :
( ( ( ~ ( ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 )
| ( SV82 = emptyset ) ) )
= $false )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2759]) ).
thf(2802,plain,
! [SV289: $i,SV102: $i] :
( ( ( ~ ( ( SV102 != emptyset )
| ~ ( in @ SV289 @ SV102 ) ) )
= $false )
| ( ( in @ SV289 @ SV102 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2761]) ).
thf(2803,plain,
! [SV116: $i,SV223: $i] :
( ( ( ~ ( ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
| ( subset @ SV116 @ SV223 ) ) )
= $false )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2763]) ).
thf(2805,plain,
! [SV178: $i,SV60: $i] :
( ( ( ~ ( ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
| ( in @ SV178 @ ( powerset @ SV60 ) ) ) )
= $false )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2765]) ).
thf(2807,plain,
! [SV126: $i] :
( ( ( ~ ( ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
| ( SV126 = emptyset ) ) )
= $false )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2767]) ).
thf(2811,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
| ( ( binintersect @ SV39 @ SV160 )
= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2813,plain,
! [SV39: $i,SV160: $i] :
( ( ( ~ ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 )
| ( ( binintersect @ SV39 @ SV160 )
= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2773]) ).
thf(2816,plain,
! [SV43: $o] :
( ( ( ~ SV43
| ~ ~ ( set2prop @ ( prop2set @ SV43 ) ) )
= $true )
| ( SV43 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2776]) ).
thf(2818,plain,
! [SV129: $o] :
( ( ( ~ SV129
| ~ ~ ( in @ emptyset @ ( prop2set @ SV129 ) ) )
= $true )
| ( SV129 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2778]) ).
thf(2819,plain,
! [SV31: $i,SV275: $o] :
( ( ( SV275
| ~ ( in @ SV31 @ emptyset ) )
= $true )
| ( SV275 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2779]) ).
thf(2821,plain,
! [SV173: $i,SV57: $o] :
( ( ( SV57
| ~ ( in @ SV173 @ ( prop2set @ SV57 ) ) )
= $true )
| ( SV57 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2781]) ).
thf(2823,plain,
! [SV224: $i,SV117: $i > $o] :
( ( ( ( SV117 @ SV224 )
| ~ ( in @ SV224 @ emptyset ) )
= $true )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2783]) ).
thf(2825,plain,
! [SV26: $i,SV237: $i,SV150: $i > $o] :
( ( ( ( SV150 @ SV237 )
| ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) ) )
= $true )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2827,plain,
! [SV33: $i] :
( ( ( ( in @ ( sK4_SY892 @ SV33 ) @ SV33 )
| ( SV33 = emptyset ) )
= $true )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2787]) ).
thf(2829,plain,
! [SV55: $i] :
( ( ( ( in @ ( sK5_SY940 @ SV55 ) @ SV55 )
| ( SV55 = emptyset ) )
= $true )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2789]) ).
thf(2832,plain,
! [SV35: $i,SV156: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV156 )
| ~ ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) ) )
= $true )
| ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2834,plain,
! [SV213: $i,SV103: $i,SV266: $i] :
( ( ( ~ ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
| ~ ( in @ SV266 @ SV213 ) )
= $true )
| ( ( in @ SV266 @ SV213 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2794]) ).
thf(2835,plain,
! [SV44: $i,SV163: $i] :
( ( ( ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
| ( subset @ SV44 @ SV163 ) )
= $true )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2795]) ).
thf(2837,plain,
! [SV181: $i,SV63: $i] :
( ( ( ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
| ( in @ SV181 @ ( powerset @ SV63 ) ) )
= $true )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2797]) ).
thf(2839,plain,
! [SV82: $i] :
( ( ( ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 )
| ( SV82 = emptyset ) )
= $true )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2799]) ).
thf(2842,plain,
! [SV289: $i,SV102: $i] :
( ( ( ( SV102 != emptyset )
| ~ ( in @ SV289 @ SV102 ) )
= $true )
| ( ( in @ SV289 @ SV102 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2802]) ).
thf(2843,plain,
! [SV116: $i,SV223: $i] :
( ( ( ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
| ( subset @ SV116 @ SV223 ) )
= $true )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2845,plain,
! [SV178: $i,SV60: $i] :
( ( ( ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
| ( in @ SV178 @ ( powerset @ SV60 ) ) )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2847,plain,
! [SV126: $i] :
( ( ( ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
| ( SV126 = emptyset ) )
= $true )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2807]) ).
thf(2851,plain,
! [SV39: $i,SV160: $i] :
( ( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
| ( ( binintersect @ SV39 @ SV160 )
= emptyset ) )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2853,plain,
! [SV39: $i,SV160: $i] :
( ( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 )
| ( ( binintersect @ SV39 @ SV160 )
= emptyset ) )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2813]) ).
thf(2856,plain,
! [SV43: $o] :
( ( ( ~ SV43 ) = $true )
| ( ( ~ ~ ( set2prop @ ( prop2set @ SV43 ) ) )
= $true )
| ( SV43 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(2858,plain,
! [SV129: $o] :
( ( ( ~ SV129 ) = $true )
| ( ( ~ ~ ( in @ emptyset @ ( prop2set @ SV129 ) ) )
= $true )
| ( SV129 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(2859,plain,
! [SV31: $i,SV275: $o] :
( ( SV275 = $true )
| ( ( ~ ( in @ SV31 @ emptyset ) )
= $true )
| ( SV275 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2819]) ).
thf(2861,plain,
! [SV173: $i,SV57: $o] :
( ( SV57 = $true )
| ( ( ~ ( in @ SV173 @ ( prop2set @ SV57 ) ) )
= $true )
| ( SV57 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2821]) ).
thf(2863,plain,
! [SV224: $i,SV117: $i > $o] :
( ( ( SV117 @ SV224 )
= $true )
| ( ( ~ ( in @ SV224 @ emptyset ) )
= $true )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(2865,plain,
! [SV26: $i,SV237: $i,SV150: $i > $o] :
( ( ( SV150 @ SV237 )
= $true )
| ( ( ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) ) )
= $true )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(2867,plain,
! [SV33: $i] :
( ( ( in @ ( sK4_SY892 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33 = emptyset )
= $true )
| ( ( SV33 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(2869,plain,
! [SV55: $i] :
( ( ( in @ ( sK5_SY940 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55 = emptyset )
= $true )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2829]) ).
thf(2872,plain,
! [SV35: $i,SV156: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV156 ) )
= $true )
| ( ( ~ ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) ) )
= $true )
| ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(2874,plain,
! [SV213: $i,SV103: $i,SV266: $i] :
( ( ( ~ ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) ) )
= $true )
| ( ( ~ ( in @ SV266 @ SV213 ) )
= $true )
| ( ( in @ SV266 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(2875,plain,
! [SV44: $i,SV163: $i] :
( ( ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
= $true )
| ( ( subset @ SV44 @ SV163 )
= $true )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2835]) ).
thf(2877,plain,
! [SV181: $i,SV63: $i] :
( ( ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
= $true )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(2879,plain,
! [SV82: $i] :
( ( ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82 = emptyset )
= $true )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(2882,plain,
! [SV289: $i,SV102: $i] :
( ( ( SV102 != emptyset )
= $true )
| ( ( ~ ( in @ SV289 @ SV102 ) )
= $true )
| ( ( in @ SV289 @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2842]) ).
thf(2883,plain,
! [SV116: $i,SV223: $i] :
( ( ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
= $true )
| ( ( subset @ SV116 @ SV223 )
= $true )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(2885,plain,
! [SV178: $i,SV60: $i] :
( ( ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(2887,plain,
! [SV126: $i] :
( ( ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126 = emptyset )
= $true )
| ( ( SV126 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2847]) ).
thf(2891,plain,
! [SV39: $i,SV160: $i] :
( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(2893,plain,
! [SV39: $i,SV160: $i] :
( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(2896,plain,
! [SV43: $o] :
( ( SV43 = $false )
| ( ( ~ ~ ( set2prop @ ( prop2set @ SV43 ) ) )
= $true )
| ( SV43 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2898,plain,
! [SV129: $o] :
( ( SV129 = $false )
| ( ( ~ ~ ( in @ emptyset @ ( prop2set @ SV129 ) ) )
= $true )
| ( SV129 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2899,plain,
! [SV275: $o,SV31: $i] :
( ( ( in @ SV31 @ emptyset )
= $false )
| ( SV275 = $true )
| ( SV275 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(2901,plain,
! [SV57: $o,SV173: $i] :
( ( ( in @ SV173 @ ( prop2set @ SV57 ) )
= $false )
| ( SV57 = $true )
| ( SV57 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(2903,plain,
! [SV117: $i > $o,SV224: $i] :
( ( ( in @ SV224 @ emptyset )
= $false )
| ( ( SV117 @ SV224 )
= $true )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2905,plain,
! [SV150: $i > $o,SV26: $i,SV237: $i] :
( ( ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) )
= $false )
| ( ( SV150 @ SV237 )
= $true )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2909,plain,
! [SV35: $i,SV156: $i,SV242: $i] :
( ( ( in @ SV242 @ SV156 )
= $false )
| ( ( ~ ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) ) )
= $true )
| ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(2910,plain,
! [SV213: $i,SV103: $i,SV266: $i] :
( ( ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
= $false )
| ( ( ~ ( in @ SV266 @ SV213 ) )
= $true )
| ( ( in @ SV266 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2914,plain,
! [SV289: $i,SV102: $i] :
( ( ( SV102 = emptyset )
= $false )
| ( ( ~ ( in @ SV289 @ SV102 ) )
= $true )
| ( ( in @ SV289 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2921,plain,
! [SV43: $o] :
( ( ( ~ ( set2prop @ ( prop2set @ SV43 ) ) )
= $false )
| ( SV43 = $false )
| ( SV43 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(2922,plain,
! [SV129: $o] :
( ( ( ~ ( in @ emptyset @ ( prop2set @ SV129 ) ) )
= $false )
| ( SV129 = $false )
| ( SV129 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(2929,plain,
! [SV156: $i,SV35: $i,SV242: $i] :
( ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false )
| ( ( in @ SV242 @ SV156 )
= $false )
| ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(2930,plain,
! [SV103: $i,SV213: $i,SV266: $i] :
( ( ( in @ SV266 @ SV213 )
= $false )
| ( ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
= $false )
| ( ( in @ SV266 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(2934,plain,
! [SV102: $i,SV289: $i] :
( ( ( in @ SV289 @ SV102 )
= $false )
| ( ( SV102 = emptyset )
= $false )
| ( ( in @ SV289 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(2941,plain,
! [SV43: $o] :
( ( ( set2prop @ ( prop2set @ SV43 ) )
= $true )
| ( SV43 = $false )
| ( SV43 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2921]) ).
thf(2942,plain,
! [SV129: $o] :
( ( ( in @ emptyset @ ( prop2set @ SV129 ) )
= $true )
| ( SV129 = $false )
| ( SV129 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2922]) ).
thf(2947,plain,
! [SV31: $i] :
( ( ~ ( in @ SV31 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[2740:[bind(SV275,$thf( ~ ( in @ SV31 @ emptyset ) ))]]) ).
thf(2949,plain,
! [SV415: $i > $i,SV224: $i,SV414: $i > $i] :
( ( ( ~ ( in @ ( SV414 @ SV224 ) @ ( SV415 @ SV224 ) ) )
= $true )
| ( ( in @ ( SV414 @ SV224 ) @ ( SV415 @ SV224 ) )
= $false )
| ( ( in @ SV224 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[2744:[bind(SV117,$thf( ^ [SX0: $i] : ~ ( in @ ( SV414 @ SX0 ) @ ( SV415 @ SX0 ) ) ))]]) ).
thf(2950,plain,
! [SV224: $i,SV411: $i > $o] :
( ( ( ~ ( SV411 @ SV224 ) )
= $true )
| ( ( ~ ( SV411 @ SV224 ) )
= $true )
| ( ( ~ ( in @ SV224 @ emptyset ) )
= $true ) ),
inference(extuni,[status(esa)],[2744:[bind(SV117,$thf( ^ [SX0: $i] : ~ ( SV411 @ SX0 ) ))]]) ).
thf(2953,plain,
! [SV26: $i,SV422: $i > $i,SV237: $i,SV421: $i > $i] :
( ( ( ~ ( in @ ( SV421 @ SV237 ) @ ( SV422 @ SV237 ) ) )
= $true )
| ( ( in @ ( SV421 @ SV237 ) @ ( SV422 @ SV237 ) )
= $false )
| ( ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SX0: $i] :
~ ( in @ ( SV421 @ SX0 ) @ ( SV422 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[2746:[bind(SV150,$thf( ^ [SX0: $i] : ~ ( in @ ( SV421 @ SX0 ) @ ( SV422 @ SX0 ) ) ))]]) ).
thf(2954,plain,
! [SV26: $i,SV237: $i,SV418: $i > $o] :
( ( ( ~ ( SV418 @ SV237 ) )
= $true )
| ( ( ~ ( SV418 @ SV237 ) )
= $true )
| ( ( ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SX0: $i] :
~ ( SV418 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[2746:[bind(SV150,$thf( ^ [SX0: $i] : ~ ( SV418 @ SX0 ) ))]]) ).
thf(2959,plain,
! [SV289: $i] :
( ( ( in @ SV289 @ emptyset )
= $false )
| ( ( in @ SV289 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[2934:[bind(SV102,$thf( emptyset ))]]) ).
thf(2962,plain,
! [SV152: $i] :
( ( in @ SV152 @ ( setadjoin @ SV152 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[779:[bind(SV28,$thf( SV152 ))]]) ).
thf(2963,plain,
! [SV167: $i] :
( ( subset @ SV167 @ SV167 )
= $true ),
inference(extuni,[status(esa)],[802:[bind(SV49,$thf( SV167 ))]]) ).
thf(2964,plain,
! [SV168: $i] :
( ( subset @ SV168 @ SV168 )
= $true ),
inference(extuni,[status(esa)],[804:[bind(SV51,$thf( SV168 ))]]) ).
thf(2967,plain,
! [SV180: $i] :
( ( subset @ SV180 @ SV180 )
= $true ),
inference(extuni,[status(esa)],[1005:[bind(SV62,$thf( SV180 ))]]) ).
thf(2968,plain,
! [SV289: $i] :
( ( in @ SV289 @ emptyset )
= $false ),
inference(extuni,[status(esa)],[1128:[bind(SV102,$thf( emptyset ))]]) ).
thf(2971,plain,
! [SV192: $i,SV77: $i] :
( ( in @ SV77 @ ( setadjoin @ SV77 @ SV192 ) )
= $true ),
inference(extuni,[status(esa)],[1259:[bind(SV254,$thf( SV77 ))]]) ).
thf(2973,plain,
! [SV295: $i > $o,SV282: $i > $o,SV166: $i] :
( ( ( ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV282 @ SX0 ) )
= ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV295 @ SX0 ) ) )
= $true )
| ( ( in @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV166 ) @ SV166 )
= $true ) ),
inference(extuni,[status(esa)],[1401:[bind(SV48,$thf( SV166 ))]]) ).
thf(2974,plain,
! [SV295: $i > $o,SV282: $i > $o,SV166: $i] :
( ( ( ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV282 @ SX0 ) )
= ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV295 @ SX0 ) ) )
= $true )
| ( ( in @ ( sK41_SY1304 @ SV166 @ SV282 @ SV295 @ SV166 ) @ SV166 )
= $true ) ),
inference(extuni,[status(esa)],[1561:[bind(SV48,$thf( SV166 ))]]) ).
thf(2977,plain,
! [SV295: $i > $o,SV282: $i > $o,SV166: $i] :
( ( ( ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV282 @ SX0 ) )
= ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV295 @ SX0 ) ) )
= $true )
| ( ( ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV166 )
= ( sK41_SY1304 @ SV166 @ SV282 @ SV295 @ SV166 ) )
= $true ) ),
inference(extuni,[status(esa)],[1656:[bind(SV48,$thf( SV166 ))]]) ).
thf(2978,plain,
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ sK3_SY1133 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[1864:[bind(SV314,$thf( sK3_SY1133 )),bind(SV278,$thf( sK1_SX0 ))]]) ).
thf(2979,plain,
! [SV314: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK3_SY1133 @ emptyset )
= ( setadjoin @ SV314 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1864:[bind(SV278,$thf( sK1_SX0 ))]]) ).
thf(2980,plain,
! [SV314: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) )
= ( setadjoin @ sK1_SX0 @ ( setadjoin @ SV314 @ emptyset ) ) )
= $false ) ),
inference(extuni,[status(esa)],[1864:[bind(SV278,$thf( sK1_SX0 ))]]) ).
thf(2981,plain,
! [SV314: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset )
= ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SV314 @ emptyset ) ) @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1864:[bind(SV278,$thf( sK1_SX0 ))]]) ).
thf(2982,plain,
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ sK3_SY1133 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ emptyset )
= ( setadjoin @ sK1_SX0 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1864:[bind(SV314,$thf( sK3_SY1133 )),bind(SV278,$thf( sK1_SX0 ))]]) ).
thf(2983,plain,
! [SV314: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK3_SY1133 @ emptyset )
= ( setadjoin @ SV314 @ emptyset ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ emptyset )
= ( setadjoin @ sK1_SX0 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1864:[bind(SV278,$thf( sK1_SX0 ))]]) ).
thf(2984,plain,
! [SV314: $i,SV278: $i] :
( ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) )
= ( setadjoin @ SV278 @ ( setadjoin @ SV314 @ emptyset ) ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ emptyset )
= ( setadjoin @ SV278 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1864]) ).
thf(2985,plain,
! [SV314: $i,SV278: $i] :
( ( ( in @ SV278 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset )
= ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV314 @ emptyset ) ) @ emptyset ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ emptyset )
= ( setadjoin @ SV278 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1864]) ).
thf(2986,plain,
! [SV295: $i > $o,SV282: $i > $o,SV166: $i] :
( ( ( ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV282 @ SX0 ) )
= ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV295 @ SX0 ) ) )
= $true )
| ( ( SV295 @ ( sK41_SY1304 @ SV166 @ SV282 @ SV295 @ SV166 ) )
= $false )
| ( ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV166 ) )
= $false ) ),
inference(extuni,[status(esa)],[1979:[bind(SV48,$thf( SV166 ))]]) ).
thf(2989,plain,
! [SV295: $i > $o,SV282: $i > $o,SV166: $i] :
( ( ( ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV282 @ SX0 ) )
= ( dsetconstr @ SV166
@ ^ [SX0: $i] : ( SV295 @ SX0 ) ) )
= $true )
| ( ( SV282 @ ( sK30_SY1291 @ SV295 @ SV282 @ SV166 @ SV166 ) )
= $true )
| ( ( SV295 @ ( sK41_SY1304 @ SV166 @ SV282 @ SV295 @ SV166 ) )
= $true ) ),
inference(extuni,[status(esa)],[2073:[bind(SV48,$thf( SV166 ))]]) ).
thf(2990,plain,
! [SV281: $i,SV47: $i > $o] :
( ( ( SV47 @ ( sK40_SY1272 @ SV281 @ SV47 ) )
= $true )
| ( ( SV47 @ SV281 )
= $false )
| ( ( SV47 @ ( sK57_SY921 @ SV281 @ SV47 ) )
= $true ) ),
inference(extuni,[status(esa)],[2113:[bind(SV338,$thf( sK57_SY921 @ SV281 @ SV47 ))]]) ).
thf(2991,plain,
! [SV281: $i] :
( ( ( ( sK40_SY1272 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) )
= SV281 )
= $true )
| ( ( ( sK57_SY921 @ SV281
@ ^ [SX0: $i] : ( SX0 = SV281 ) )
= SV281 )
= $true ) ),
inference(extuni,[status(esa)],[2714:[bind(SV338,$thf( sK57_SY921 @ SV281 @ ^ [SX0: $i] : ( SX0 = SV281 ) ))]]) ).
thf(2992,plain,
! [SV31: $i] :
( ( in @ SV31 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(2994,plain,
! [SV224: $i,SV411: $i > $o] :
( ( ( SV411 @ SV224 )
= $false )
| ( ( ~ ( SV411 @ SV224 ) )
= $true )
| ( ( ~ ( in @ SV224 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(2995,plain,
! [SV415: $i > $i,SV224: $i,SV414: $i > $i] :
( ( ( in @ ( SV414 @ SV224 ) @ ( SV415 @ SV224 ) )
= $false )
| ( ( in @ ( SV414 @ SV224 ) @ ( SV415 @ SV224 ) )
= $false )
| ( ( in @ SV224 @ emptyset )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(2998,plain,
! [SV26: $i,SV237: $i,SV418: $i > $o] :
( ( ( SV418 @ SV237 )
= $false )
| ( ( ~ ( SV418 @ SV237 ) )
= $true )
| ( ( ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SX0: $i] :
~ ( SV418 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(2999,plain,
! [SV26: $i,SV422: $i > $i,SV237: $i,SV421: $i > $i] :
( ( ( in @ ( SV421 @ SV237 ) @ ( SV422 @ SV237 ) )
= $false )
| ( ( in @ ( SV421 @ SV237 ) @ ( SV422 @ SV237 ) )
= $false )
| ( ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SX0: $i] :
~ ( in @ ( SV421 @ SX0 ) @ ( SV422 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(3002,plain,
! [SV224: $i,SV411: $i > $o] :
( ( ( SV411 @ SV224 )
= $false )
| ( ( SV411 @ SV224 )
= $false )
| ( ( ~ ( in @ SV224 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3004,plain,
! [SV26: $i,SV237: $i,SV418: $i > $o] :
( ( ( SV418 @ SV237 )
= $false )
| ( ( SV418 @ SV237 )
= $false )
| ( ( ~ ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SX0: $i] :
~ ( SV418 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3006,plain,
! [SV411: $i > $o,SV224: $i] :
( ( ( in @ SV224 @ emptyset )
= $false )
| ( ( SV411 @ SV224 )
= $false )
| ( ( SV411 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3008,plain,
! [SV418: $i > $o,SV26: $i,SV237: $i] :
( ( ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SX0: $i] :
~ ( SV418 @ SX0 ) ) )
= $false )
| ( ( SV418 @ SV237 )
= $false )
| ( ( SV418 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3009,plain,
( ( set2prop @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[681]) ).
thf(3010,plain,
! [SV70: $i] :
( ( in @ SV70 @ emptyset )
= $false ),
inference(sim,[status(thm)],[711]) ).
thf(3011,plain,
( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[771]) ).
thf(3012,plain,
! [SV31: $i] :
( ( in @ SV31 @ emptyset )
= $false ),
inference(sim,[status(thm)],[784]) ).
thf(3013,plain,
! [SV175: $i] :
( ( in @ SV175 @ ( prop2set @ $false ) )
= $false ),
inference(sim,[status(thm)],[812]) ).
thf(3014,plain,
! [SV25: $i,SV149: $i] :
( ( ( in @ SV149 @ ( sK26_SX0 @ SV25 @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(sim,[status(thm)],[1307]) ).
thf(3015,plain,
! [SV149: $i,SV25: $i] :
( ( ( in @ ( sK26_SX0 @ SV25 @ SV149 ) @ SV25 )
= $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(sim,[status(thm)],[1389]) ).
thf(3016,plain,
! [SV297: $i,SV186: $i > $o,SV68: $i] :
( ( ( ( dsetconstr @ SV68
@ ^ [SY1171: $i] : ( SV186 @ SY1171 ) )
= emptyset )
= $false )
| ( ( in @ SV297 @ SV68 )
= $false )
| ( ( SV186 @ SV297 )
= $false ) ),
inference(sim,[status(thm)],[1583]) ).
thf(3017,plain,
! [SV120: $i,SV226: $i,SV270: $i] :
( ( ( in @ SV270 @ SV226 )
= $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(sim,[status(thm)],[1722]) ).
thf(3018,plain,
! [SV125: $i,SV231: $i,SV273: $i] :
( ( ( in @ SV273 @ SV231 )
= $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(sim,[status(thm)],[1725]) ).
thf(3019,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( in @ SV251 @ SV182 )
= $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(sim,[status(thm)],[1755]) ).
thf(3020,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( in @ SV251 @ SV64 )
= $false )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(sim,[status(thm)],[1874]) ).
thf(3021,plain,
! [SV43: $o] :
( ( ( set2prop @ ( prop2set @ SV43 ) )
= $true )
| ( SV43 = $false ) ),
inference(sim,[status(thm)],[2941]) ).
thf(3022,plain,
! [SV129: $o] :
( ( ( in @ emptyset @ ( prop2set @ SV129 ) )
= $true )
| ( SV129 = $false ) ),
inference(sim,[status(thm)],[2942]) ).
thf(3023,plain,
! [SV275: $o,SV31: $i] :
( ( ( in @ SV31 @ emptyset )
= $false )
| ( SV275 = $true ) ),
inference(sim,[status(thm)],[2899]) ).
thf(3024,plain,
! [SV57: $o,SV173: $i] :
( ( ( in @ SV173 @ ( prop2set @ SV57 ) )
= $false )
| ( SV57 = $true ) ),
inference(sim,[status(thm)],[2901]) ).
thf(3025,plain,
! [SV117: $i > $o,SV224: $i] :
( ( ( in @ SV224 @ emptyset )
= $false )
| ( ( SV117 @ SV224 )
= $true ) ),
inference(sim,[status(thm)],[2903]) ).
thf(3026,plain,
! [SV411: $i > $o,SV224: $i] :
( ( ( in @ SV224 @ emptyset )
= $false )
| ( ( SV411 @ SV224 )
= $false ) ),
inference(sim,[status(thm)],[3006]) ).
thf(3027,plain,
! [SV415: $i > $i,SV224: $i,SV414: $i > $i] :
( ( ( in @ ( SV414 @ SV224 ) @ ( SV415 @ SV224 ) )
= $false )
| ( ( in @ SV224 @ emptyset )
= $false ) ),
inference(sim,[status(thm)],[2995]) ).
thf(3028,plain,
! [SV150: $i > $o,SV26: $i,SV237: $i] :
( ( ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SY1127: $i] : ( SV150 @ SY1127 ) ) )
= $false )
| ( ( SV150 @ SV237 )
= $true ) ),
inference(sim,[status(thm)],[2905]) ).
thf(3029,plain,
! [SV418: $i > $o,SV26: $i,SV237: $i] :
( ( ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SX0: $i] :
~ ( SV418 @ SX0 ) ) )
= $false )
| ( ( SV418 @ SV237 )
= $false ) ),
inference(sim,[status(thm)],[3008]) ).
thf(3030,plain,
! [SV26: $i,SV422: $i > $i,SV237: $i,SV421: $i > $i] :
( ( ( in @ ( SV421 @ SV237 ) @ ( SV422 @ SV237 ) )
= $false )
| ( ( in @ SV237
@ ( dsetconstr @ SV26
@ ^ [SX0: $i] :
~ ( in @ ( SV421 @ SX0 ) @ ( SV422 @ SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[2999]) ).
thf(3031,plain,
! [SV33: $i] :
( ( ( in @ ( sK4_SY892 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[2867]) ).
thf(3032,plain,
! [SV55: $i] :
( ( ( in @ ( sK5_SY940 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[2869]) ).
thf(3033,plain,
! [SV156: $i,SV35: $i,SV242: $i] :
( ( ( in @ SV242 @ ( setminus @ SV35 @ SV156 ) )
= $false )
| ( ( in @ SV242 @ SV156 )
= $false ) ),
inference(sim,[status(thm)],[2929]) ).
thf(3034,plain,
! [SV103: $i,SV213: $i,SV266: $i] :
( ( ( in @ SV266 @ SV213 )
= $false )
| ( ( in @ SV266 @ ( setminus @ SV103 @ SV213 ) )
= $false ) ),
inference(sim,[status(thm)],[2930]) ).
thf(3035,plain,
! [SV44: $i,SV163: $i] :
( ( ( in @ ( sK7_SY1143 @ SV163 @ SV44 ) @ SV44 )
= $true )
| ( ( subset @ SV44 @ SV163 )
= $true ) ),
inference(sim,[status(thm)],[2875]) ).
thf(3036,plain,
! [SV181: $i,SV63: $i] :
( ( ( in @ ( sK8_SY1159 @ SV63 @ SV181 ) @ SV181 )
= $true )
| ( ( in @ SV181 @ ( powerset @ SV63 ) )
= $true ) ),
inference(sim,[status(thm)],[2877]) ).
thf(3037,plain,
! [SV82: $i] :
( ( ( in @ ( sK17_SY1006 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[2879]) ).
thf(3038,plain,
! [SV289: $i] :
( ( in @ SV289 @ emptyset )
= $false ),
inference(sim,[status(thm)],[2959]) ).
thf(3039,plain,
! [SV116: $i,SV223: $i] :
( ( ( in @ ( sK14_SY1220 @ SV223 @ SV116 ) @ SV116 )
= $true )
| ( ( subset @ SV116 @ SV223 )
= $true ) ),
inference(sim,[status(thm)],[2883]) ).
thf(3040,plain,
! [SV178: $i,SV60: $i] :
( ( ( in @ ( sK28_SY1157 @ SV60 @ SV178 ) @ SV178 )
= $true )
| ( ( in @ SV178 @ ( powerset @ SV60 ) )
= $true ) ),
inference(sim,[status(thm)],[2885]) ).
thf(3041,plain,
! [SV126: $i] :
( ( ( in @ ( sK19_SY1109 @ SV126 ) @ SV126 )
= $true )
| ( ( SV126 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[2887]) ).
thf(3042,plain,
! [SV39: $i,SV160: $i] :
( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV39 )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(sim,[status(thm)],[2891]) ).
thf(3043,plain,
! [SV39: $i,SV160: $i] :
( ( ( in @ ( sK21_SY1140 @ SV160 @ SV39 ) @ SV160 )
= $true )
| ( ( ( binintersect @ SV39 @ SV160 )
= emptyset )
= $true ) ),
inference(sim,[status(thm)],[2893]) ).
thf(3044,plain,
( ( set2prop @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[681]) ).
thf(3045,plain,
! [SV70: $i] :
( ( in @ SV70 @ emptyset )
= $false ),
inference(sim,[status(thm)],[711]) ).
thf(3046,plain,
( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[771]) ).
thf(3047,plain,
! [SV31: $i] :
( ( in @ SV31 @ emptyset )
= $false ),
inference(sim,[status(thm)],[784]) ).
thf(3048,plain,
! [SV175: $i] :
( ( in @ SV175 @ ( prop2set @ $false ) )
= $false ),
inference(sim,[status(thm)],[812]) ).
thf(3049,plain,
! [SV25: $i,SV149: $i] :
( ( ( in @ SV149 @ ( sK26_SX0 @ SV25 @ SV149 ) )
= $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(sim,[status(thm)],[1307]) ).
thf(3050,plain,
! [SV149: $i,SV25: $i] :
( ( ( in @ ( sK26_SX0 @ SV25 @ SV149 ) @ SV25 )
= $true )
| ( ( in @ SV149 @ ( setunion @ SV25 ) )
= $false ) ),
inference(sim,[status(thm)],[1389]) ).
thf(3051,plain,
! [SV120: $i,SV226: $i,SV270: $i] :
( ( ( in @ SV270 @ SV226 )
= $true )
| ( ( in @ SV270 @ SV120 )
= $true )
| ( ( in @ SV270 @ ( binunion @ SV120 @ SV226 ) )
= $false ) ),
inference(sim,[status(thm)],[1722]) ).
thf(3052,plain,
! [SV125: $i,SV231: $i,SV273: $i] :
( ( ( in @ SV273 @ SV231 )
= $true )
| ( ( SV273 = SV125 )
= $true )
| ( ( in @ SV273 @ ( setadjoin @ SV125 @ SV231 ) )
= $false ) ),
inference(sim,[status(thm)],[1725]) ).
thf(3053,plain,
! [SV64: $i,SV182: $i,SV251: $i] :
( ( ( in @ SV251 @ SV182 )
= $true )
| ( ( in @ SV251 @ SV64 )
= $true )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(sim,[status(thm)],[1755]) ).
thf(3054,plain,
! [SV314: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV314 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK3_SY1133 @ emptyset )
= ( setadjoin @ SV314 @ emptyset ) )
= $false ) ),
inference(sim,[status(thm)],[2983]) ).
thf(3055,plain,
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ sK3_SY1133 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1133 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[2982]) ).
thf(3056,plain,
! [SV182: $i,SV64: $i,SV251: $i] :
( ( ( in @ SV251 @ SV64 )
= $false )
| ( ( in @ SV251 @ SV182 )
= $false )
| ( ( in @ SV251 @ ( symdiff @ SV64 @ SV182 ) )
= $false ) ),
inference(sim,[status(thm)],[1874]) ).
thf(3057,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[248,3056,3055,3054,3053,3052,3051,3050,3049,3048,3047,3046,3045,3044,3043,3042,3041,3040,3039,3038,3037,3036,3035,3034,3033,3032,3031,3030,3029,3028,3027,3026,3025,3024,3023,3022,3021,3020,3019,3018,3017,3016,3015,3014,3013,3012,3011,3010,3009,2992,2991,2990,2989,2986,2985,2984,2981,2980,2979,2978,2977,2974,2973,2971,2968,2967,2964,2963,2962,2714,2712,2710,2709,2708,2707,2706,2700,2698,2694,2693,2689,2688,2675,2668,2663,2661,2649,2646,2645,2644,2633,2614,2610,2607,2598,2594,2593,2590,2587,2554,2553,2547,2543,2509,2490,2489,2480,2479,2453,2451,2441,2440,2438,2436,2435,2428,2397,2393,2392,2363,2360,2323,2319,2234,2206,2191,2150,2133,2132,2128,2127,2115,2114,2113,2112,2097,2091,2090,2088,2086,2073,2072,2071,2023,2018,2005,2004,2002,1994,1991,1979,1967,1966,1953,1950,1942,1938,1934,1870,1864,1839,1836,1835,1834,1802,1801,1783,1781,1780,1775,1773,1764,1743,1737,1736,1723,1720,1713,1712,1696,1692,1682,1656,1606,1600,1599,1587,1586,1564,1561,1509,1501,1478,1471,1436,1427,1426,1401,1397,1396,1387,1382,1351,1350,1346,1345,1326,1325,1320,1319,1301,1267,1260,1259,1258,1254,1242,1233,1218,1207,1204,1196,1193,1187,1185,1166,1138,1128,1114,1112,1108,1098,1092,1091,1084,1082,1076,1072,1071,1056,1054,1047,1044,1036,1026,1007,1005,1000,994,986,972,971,965,933,914,913,912,897,896,892,891,887,886,879,878,872,866,861,856,849,841,838,829,821,813,810,807,804,802,790,782,779,770,760,710,680,660,544,543,542,541,540,539,538,537,536,535,534,533,532,530,529,528,527,408,407,406,403,402,400,272]) ).
thf(3058,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU620^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n016.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 15:34:29 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 187.14/31.95
% 187.14/31.95 No.of.Axioms: 0
% 187.14/31.95
% 187.14/31.95 Length.of.Defs: 28326
% 187.14/31.95
% 187.14/31.95 Contains.Choice.Funs: true
% 187.14/31.95 ..............................................................................................eprover: CPU time limit exceeded, terminating
% 187.14/31.95 ..........................
% 187.14/31.95
% 187.14/31.95 ********************************
% 187.14/31.95 * All subproblems solved! *
% 187.14/31.95 ********************************
% 187.14/31.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:136,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:3057,loop_count:0,foatp_calls:2,translation:fof_full)
% 187.14/31.95
% 187.14/31.95 %**** Beginning of derivation protocol ****
% 187.14/31.95 % SZS output start CNFRefutation
% See solution above
% 187.14/32.00
% 187.14/32.00 %**** End of derivation protocol ****
% 187.14/32.00 %**** no. of clauses in derivation: 2482 ****
% 187.14/32.00 %**** clause counter: 3057 ****
% 187.14/32.00
% 187.14/32.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:136,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:3057,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------