%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU619^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 10:45:37 AM UTC 2026
% Result : Theorem 179.53s 30.24s
% Output : CNFRefutation 179.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 139
% Syntax : Number of formulae : 2599 ( 862 unt; 0 typ; 138 def)
% Number of atoms : 20593 (8735 equ; 0 cnn)
% Maximal formula atoms : 136 ( 7 avg)
% Number of connectives : 44641 (9945 ~;8027 |; 161 &;25248 @)
% ( 56 <=>;1204 =>; 0 <=; 0 <~>)
% Maximal formula depth : 145 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1704 (1704 >; 0 *; 0 +; 0 <<)
% Number of symbols : 277 ( 274 usr; 141 con; 0-4 aty)
% Number of variables : 9952 ( 534 ^;9253 !; 165 ?;9952 :)
% 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_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_SY1046,type,
sK100_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK101_SY1191,type,
sK101_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK102_SY1046,type,
sK102_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK103_SY1191,type,
sK103_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK104_SY1046,type,
sK104_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK105_SY1191,type,
sK105_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK106_SY1046,type,
sK106_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK107_SY1191,type,
sK107_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK108_SY1046,type,
sK108_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK109_SY1191,type,
sK109_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK10_SY1158,type,
sK10_SY1158: $i > $i > $i ).
thf(tp_sK110_SY1046,type,
sK110_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK111_SY1367,type,
sK111_SY1367: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK112_SY1369,type,
sK112_SY1369: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK113_SY1370,type,
sK113_SY1370: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK114_SY1371,type,
sK114_SY1371: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK115_SY1375,type,
sK115_SY1375: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK116_SY1376,type,
sK116_SY1376: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK117_SY1377,type,
sK117_SY1377: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK118_SY1384,type,
sK118_SY1384: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY1178,type,
sK11_SY1178: $i > $i > $i ).
thf(tp_sK12_SY1187,type,
sK12_SY1187: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK13_SY1204,type,
sK13_SY1204: ( $i > $o ) > $i > $i ).
thf(tp_sK14_SY1210,type,
sK14_SY1210: $i > $i > $i ).
thf(tp_sK15_SY1258,type,
sK15_SY1258: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK16_SY965,type,
sK16_SY965: $i > $i ).
thf(tp_sK17_SY1270,type,
sK17_SY1270: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK18_SY1053,type,
sK18_SY1053: $i > $i ).
thf(tp_sK19_SY1267,type,
sK19_SY1267: $i > ( $i > $o ) > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY1180,type,
sK20_SY1180: $i > $i > $i ).
thf(tp_sK21_SY1197,type,
sK21_SY1197: ( $i > $o ) > $i > $i ).
thf(tp_sK22_SY1221,type,
sK22_SY1221: ( $i > $o ) > $i > $i ).
thf(tp_sK23_SY911,type,
sK23_SY911: $i > $i ).
thf(tp_sK24_SY1259,type,
sK24_SY1259: $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_SY951,type,
sK27_SY951: $i > $i > $i ).
thf(tp_sK28_SY1225,type,
sK28_SY1225: $i > $i > $i ).
thf(tp_sK29_SY1121,type,
sK29_SY1121: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK2_SY860,type,
sK2_SY860: $i > $i ).
thf(tp_sK30_SY928,type,
sK30_SY928: $i > ( $i > $o ) > $i ).
thf(tp_sK31_SY1276,type,
sK31_SY1276: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK32_SY1159,type,
sK32_SY1159: $i > $i > $i ).
thf(tp_sK33_SY1170,type,
sK33_SY1170: $i > $i > $i ).
thf(tp_sK34_SY1130,type,
sK34_SY1130: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK35_SY1292,type,
sK35_SY1292: $i > ( $i > $o ) > $i ).
thf(tp_sK36_SY1159,type,
sK36_SY1159: $i > $i > $i ).
thf(tp_sK37_SY1177,type,
sK37_SY1177: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK38_SY1254,type,
sK38_SY1254: $i > ( $i > $o ) > $i ).
thf(tp_sK39_SY1257,type,
sK39_SY1257: $i > ( $i > $o ) > $i ).
thf(tp_sK3_SY1200,type,
sK3_SY1200: $i ).
thf(tp_sK40_SY1260,type,
sK40_SY1260: $i > ( $i > $o ) > $i ).
thf(tp_sK41_SY1293,type,
sK41_SY1293: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK42_SY1268,type,
sK42_SY1268: $i > ( $i > $o ) > $i ).
thf(tp_sK43_SY1269,type,
sK43_SY1269: $i > ( $i > $o ) > $i ).
thf(tp_sK44_SY1272,type,
sK44_SY1272: $i > ( $i > $o ) > $i ).
thf(tp_sK45_SY1274,type,
sK45_SY1274: $i > ( $i > $o ) > $i ).
thf(tp_sK46_SY1280,type,
sK46_SY1280: $i > $i > $i ).
thf(tp_sK47_SY882,type,
sK47_SY882: $i > ( $i > $o ) > $i ).
thf(tp_sK48_SY1287,type,
sK48_SY1287: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK49_SY896,type,
sK49_SY896: $i > ( $i > $o ) > $i ).
thf(tp_sK4_SY1011,type,
sK4_SY1011: $i > $i ).
thf(tp_sK50_SY1134,type,
sK50_SY1134: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK51_SY930,type,
sK51_SY930: $i > ( $i > $o ) > $i ).
thf(tp_sK52_SY930,type,
sK52_SY930: $i > ( $i > $o ) > $i ).
thf(tp_sK53_SY1019,type,
sK53_SY1019: $i > ( $i > $o ) > $i ).
thf(tp_sK54_SY1064,type,
sK54_SY1064: $i > ( $i > $o ) > $i ).
thf(tp_sK55_SY882,type,
sK55_SY882: $i > ( $i > $o ) > $i ).
thf(tp_sK56_SY896,type,
sK56_SY896: $i > ( $i > $o ) > $i ).
thf(tp_sK57_SY930,type,
sK57_SY930: $i > ( $i > $o ) > $i ).
thf(tp_sK58_SY995,type,
sK58_SY995: $i > ( $i > $o ) > $i ).
thf(tp_sK59_SY1019,type,
sK59_SY1019: $i > ( $i > $o ) > $i ).
thf(tp_sK5_SY1013,type,
sK5_SY1013: $i > $i ).
thf(tp_sK60_SY1064,type,
sK60_SY1064: $i > ( $i > $o ) > $i ).
thf(tp_sK61_SY995,type,
sK61_SY995: $i > ( $i > $o ) > $i ).
thf(tp_sK62_SY995,type,
sK62_SY995: $i > ( $i > $o ) > $i ).
thf(tp_sK63_SY1121,type,
sK63_SY1121: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK64_SY995,type,
sK64_SY995: $i > ( $i > $o ) > $i ).
thf(tp_sK65_SY1297,type,
sK65_SY1297: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK66_SY1121,type,
sK66_SY1121: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK67_SY1301,type,
sK67_SY1301: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK68_SY1282,type,
sK68_SY1282: $i > $i > $i > $i ).
thf(tp_sK69_SY1319,type,
sK69_SY1319: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK6_SY1118,type,
sK6_SY1118: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK70_SY1320,type,
sK70_SY1320: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK71_SY1282,type,
sK71_SY1282: $i > $i > $i > $i ).
thf(tp_sK72_SY1327,type,
sK72_SY1327: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK73_SY1314,type,
sK73_SY1314: $i > $i > $i > $i ).
thf(tp_sK74_SY1341,type,
sK74_SY1341: $i > $i > $i > $i ).
thf(tp_sK75_SY1332,type,
sK75_SY1332: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK76_SY1333,type,
sK76_SY1333: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK77_SY1191,type,
sK77_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK78_SY1046,type,
sK78_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK79_SY1349,type,
sK79_SY1349: $i > $i > $i > $i ).
thf(tp_sK7_SY1135,type,
sK7_SY1135: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK80_SY1336,type,
sK80_SY1336: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK81_SY1191,type,
sK81_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK82_SY1046,type,
sK82_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK83_SY1334,type,
sK83_SY1334: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK84_SY1339,type,
sK84_SY1339: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK85_SY1340,type,
sK85_SY1340: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK86_SY1337,type,
sK86_SY1337: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK87_SY1345,type,
sK87_SY1345: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY1346,type,
sK88_SY1346: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY1347,type,
sK89_SY1347: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY1143,type,
sK8_SY1143: $i > $i > $i ).
thf(tp_sK90_SY1348,type,
sK90_SY1348: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK91_SY1353,type,
sK91_SY1353: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK92_SY1354,type,
sK92_SY1354: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK93_SY1355,type,
sK93_SY1355: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK94_SY1191,type,
sK94_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK95_SY1046,type,
sK95_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK96_SY1359,type,
sK96_SY1359: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK97_SY1191,type,
sK97_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK98_SY1046,type,
sK98_SY1046: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK99_SY1191,type,
sK99_SY1191: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK9_SY1153,type,
sK9_SY1153: $i > $i > $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_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/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(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/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(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
=> ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
=> ( ! [SY21: $i > $i > $o,SY22: $i] :
( ! [SY23: $i] :
( ( in @ SY23 @ SY22 )
=> ? [SY25: $i] :
( ( SY21 @ SY23 @ SY25 )
& ! [SY26: $i] :
( ( SY21 @ SY23 @ SY26 )
=> ( SY25 = SY26 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY22 )
& ( SY21 @ 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 ) ) ) ) ) )
=> ( ! [SY53: $i > $o] :
( ? [SY55: $i] :
( ( SY53 @ SY55 )
& ! [SY56: $i] :
( ( SY53 @ SY56 )
=> ( SY55 = SY56 ) ) )
=> ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ 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 ) )
=> ( ! [SY70: $i > $o] :
( ? [SY72: $i] :
( ( SY70 @ SY72 )
& ! [SY73: $i] :
( ( SY70 @ SY73 )
=> ( SY72 = SY73 ) ) )
=> ? [Xx: $i] :
( ( SY70 @ Xx )
& ! [Xy: $i] :
( ( SY70 @ 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 )
=> ( ! [SY82: $i > $o] :
( ? [SY84: $i] :
( ( SY82 @ SY84 )
& ! [SY85: $i] :
( ( SY82 @ SY85 )
=> ( SY84 = SY85 ) ) )
=> ? [Xx: $i] : ( SY82 @ 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 ) ) )
=> ( ! [SY99: $i] :
( ( SY99 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY99 ) )
=> ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ( in @ SY103 @ SY101 )
=> ( ( SY102 @ SY103 )
=> ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY105: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY105 )
=> ( SY105 != 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 ) ) ) )
=> ( ! [SY138: $i > $o] :
( ? [SY140: $i] :
( ( SY138 @ SY140 )
& ! [SY141: $i] :
( ( SY138 @ SY141 )
=> ( SY140 = SY141 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY138 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY144: $i] :
( ( SY144 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY144 )
& $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 ) ) )
=> ( ! [SY193: $i > $o] :
( ? [Xx: $i] :
( ( SY193 @ Xx )
& ! [Xy: $i] :
( ( SY193 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY197: $i] :
( ( SY193 @ SY197 )
& ! [SY198: $i] :
( ( SY193 @ SY198 )
=> ( SY197 = SY198 ) ) ) )
=> ( ! [SY199: $i > $o] :
( ? [Xx: $i] : ( SY199 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY199 @ Xx )
=> ( ( SY199 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY204: $i] :
( ( SY199 @ SY204 )
& ! [SY205: $i] :
( ( SY199 @ SY205 )
=> ( SY204 = SY205 ) ) ) ) )
=> ( ! [SY206: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY206 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY210: $i] :
( ( SY206 @ SY210 )
& ! [SY211: $i] :
( ( SY206 @ SY211 )
=> ( SY210 = SY211 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [SY220: $i > $o] :
( ? [SY222: $i] :
( ( SY220 @ SY222 )
& ! [SY223: $i] :
( ( SY220 @ SY223 )
=> ( SY222 = SY223 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY220 @ Xx )
=> ( ( SY220 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY226: $i > $o,SY227: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY226 @ Xx )
<=> ( SY227 @ Xy ) ) )
=> ( ? [SY231: $i] :
( ( SY226 @ SY231 )
& ! [SY232: $i] :
( ( SY226 @ SY232 )
=> ( SY231 = SY232 ) ) )
<=> ? [SY234: $i] :
( ( SY227 @ SY234 )
& ! [SY235: $i] :
( ( SY227 @ SY235 )
=> ( SY234 = SY235 ) ) ) ) )
=> ( ( 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 )
=> ( ! [SY244: $i > $o] :
( ? [SY246: $i] :
( ( SY244 @ SY246 )
& ! [SY247: $i] :
( ( SY244 @ SY247 )
=> ( SY246 = SY247 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY244 @ Xx )
=> ( ( SY244 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY250: $i > $o,SY251: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY250 @ Xx )
<=> ( SY251 @ Xy ) ) )
=> ( ? [SY255: $i] :
( ( SY250 @ SY255 )
& ! [SY256: $i] :
( ( SY250 @ SY256 )
=> ( SY255 = SY256 ) ) )
=> ( ? [SY258: $i] :
( ( SY251 @ SY258 )
& ! [SY259: $i] :
( ( SY251 @ SY259 )
=> ( SY258 = SY259 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY251 @ 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 ) ) ) )
=> ! [SY0: $i,SY1: $i] :
? [SY2: $i] :
( ( in @ SY2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY3: $i] :
( ( in @ SY3 @ ( 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 @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,
( ( ! [SY21: $i > $i > $o,SY22: $i] :
( ! [SY23: $i] :
( ( in @ SY23 @ SY22 )
=> ? [SY25: $i] :
( ( SY21 @ SY23 @ SY25 )
& ! [SY26: $i] :
( ( SY21 @ SY23 @ SY26 )
=> ( SY25 = SY26 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY22 )
& ( SY21 @ 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,
( ( ! [SY53: $i > $o] :
( ? [SY55: $i] :
( ( SY53 @ SY55 )
& ! [SY56: $i] :
( ( SY53 @ SY56 )
=> ( SY55 = SY56 ) ) )
=> ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ 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,
( ( ! [SY70: $i > $o] :
( ? [SY72: $i] :
( ( SY70 @ SY72 )
& ! [SY73: $i] :
( ( SY70 @ SY73 )
=> ( SY72 = SY73 ) ) )
=> ? [Xx: $i] :
( ( SY70 @ Xx )
& ! [Xy: $i] :
( ( SY70 @ 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,
( ( ! [SY82: $i > $o] :
( ? [SY84: $i] :
( ( SY82 @ SY84 )
& ! [SY85: $i] :
( ( SY82 @ SY85 )
=> ( SY84 = SY85 ) ) )
=> ? [Xx: $i] : ( SY82 @ 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,
( ( ! [SY99: $i] :
( ( SY99 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY99 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ( in @ SY103 @ SY101 )
=> ( ( SY102 @ SY103 )
=> ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY105: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY105 )
=> ( SY105 != 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,
( ( ! [SY138: $i > $o] :
( ? [SY140: $i] :
( ( SY138 @ SY140 )
& ! [SY141: $i] :
( ( SY138 @ SY141 )
=> ( SY140 = SY141 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY138 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY144: $i] :
( ( SY144 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY144 )
& $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,
( ( ! [SY193: $i > $o] :
( ? [Xx: $i] :
( ( SY193 @ Xx )
& ! [Xy: $i] :
( ( SY193 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY197: $i] :
( ( SY193 @ SY197 )
& ! [SY198: $i] :
( ( SY193 @ SY198 )
=> ( SY197 = SY198 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY199: $i > $o] :
( ? [Xx: $i] : ( SY199 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY199 @ Xx )
=> ( ( SY199 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY204: $i] :
( ( SY199 @ SY204 )
& ! [SY205: $i] :
( ( SY199 @ SY205 )
=> ( SY204 = SY205 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY206: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY206 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY210: $i] :
( ( SY206 @ SY210 )
& ! [SY211: $i] :
( ( SY206 @ SY211 )
=> ( SY210 = SY211 ) ) ) ) )
= $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,
( ( ! [SY220: $i > $o] :
( ? [SY222: $i] :
( ( SY220 @ SY222 )
& ! [SY223: $i] :
( ( SY220 @ SY223 )
=> ( SY222 = SY223 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY220 @ Xx )
=> ( ( SY220 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY226: $i > $o,SY227: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY226 @ Xx )
<=> ( SY227 @ Xy ) ) )
=> ( ? [SY231: $i] :
( ( SY226 @ SY231 )
& ! [SY232: $i] :
( ( SY226 @ SY232 )
=> ( SY231 = SY232 ) ) )
<=> ? [SY234: $i] :
( ( SY227 @ SY234 )
& ! [SY235: $i] :
( ( SY227 @ SY235 )
=> ( SY234 = SY235 ) ) ) ) ) )
= $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,
( ( ! [SY244: $i > $o] :
( ? [SY246: $i] :
( ( SY244 @ SY246 )
& ! [SY247: $i] :
( ( SY244 @ SY247 )
=> ( SY246 = SY247 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY244 @ Xx )
=> ( ( SY244 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY250: $i > $o,SY251: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY250 @ Xx )
<=> ( SY251 @ Xy ) ) )
=> ( ? [SY255: $i] :
( ( SY250 @ SY255 )
& ! [SY256: $i] :
( ( SY250 @ SY256 )
=> ( SY255 = SY256 ) ) )
=> ( ? [SY258: $i] :
( ( SY251 @ SY258 )
& ! [SY259: $i] :
( ( SY251 @ SY259 )
=> ( SY258 = SY259 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY251 @ 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,
( ( ! [SY0: $i,SY1: $i] :
? [SY2: $i] :
( ( in @ SY2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY3: $i] :
( ( in @ SY3 @ ( 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 @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(140,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
? [SY2: $i] :
( ( in @ SY2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY3: $i] :
( ( in @ SY3 @ ( 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 @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[139]) ).
thf(141,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(142,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(143,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(144,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(145,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(146,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(147,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(148,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(149,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(150,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(153,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(154,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(155,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(156,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(157,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(158,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(159,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(160,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(163,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(164,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(166,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(167,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(168,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(169,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(170,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(171,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(172,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(173,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(174,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(175,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(176,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(177,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(178,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(179,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(181,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(184,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(187,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(188,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(189,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(190,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(191,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(192,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(193,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(194,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(195,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(196,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(197,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(198,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(201,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(202,plain,
( ( ! [SY250: $i > $o,SY251: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY250 @ Xx )
<=> ( SY251 @ Xy ) ) )
=> ( ? [SY255: $i] :
( ( SY250 @ SY255 )
& ! [SY256: $i] :
( ( SY250 @ SY256 )
=> ( SY255 = SY256 ) ) )
=> ( ? [SY258: $i] :
( ( SY251 @ SY258 )
& ! [SY259: $i] :
( ( SY251 @ SY259 )
=> ( SY258 = SY259 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(203,plain,
( ( ! [SY244: $i > $o] :
( ? [SY246: $i] :
( ( SY244 @ SY246 )
& ! [SY247: $i] :
( ( SY244 @ SY247 )
=> ( SY246 = SY247 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY244 @ Xx )
=> ( ( SY244 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(205,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(206,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(207,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(209,plain,
( ( ! [SY226: $i > $o,SY227: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY226 @ Xx )
<=> ( SY227 @ Xy ) ) )
=> ( ? [SY231: $i] :
( ( SY226 @ SY231 )
& ! [SY232: $i] :
( ( SY226 @ SY232 )
=> ( SY231 = SY232 ) ) )
<=> ? [SY234: $i] :
( ( SY227 @ SY234 )
& ! [SY235: $i] :
( ( SY227 @ SY235 )
=> ( SY234 = SY235 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(210,plain,
( ( ! [SY220: $i > $o] :
( ? [SY222: $i] :
( ( SY220 @ SY222 )
& ! [SY223: $i] :
( ( SY220 @ SY223 )
=> ( SY222 = SY223 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY220 @ Xx )
=> ( ( SY220 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(211,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(212,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(213,plain,
( ( ! [SY206: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY206 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY210: $i] :
( ( SY206 @ SY210 )
& ! [SY211: $i] :
( ( SY206 @ SY211 )
=> ( SY210 = SY211 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(214,plain,
( ( ! [SY199: $i > $o] :
( ? [Xx: $i] : ( SY199 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY199 @ Xx )
=> ( ( SY199 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY204: $i] :
( ( SY199 @ SY204 )
& ! [SY205: $i] :
( ( SY199 @ SY205 )
=> ( SY204 = SY205 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(215,plain,
( ( ! [SY193: $i > $o] :
( ? [Xx: $i] :
( ( SY193 @ Xx )
& ! [Xy: $i] :
( ( SY193 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY197: $i] :
( ( SY193 @ SY197 )
& ! [SY198: $i] :
( ( SY193 @ SY198 )
=> ( SY197 = SY198 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(216,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(217,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(218,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(219,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(220,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(221,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(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)],[57]) ).
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)],[56]) ).
thf(224,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(225,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(226,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(227,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(228,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(229,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(230,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(231,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(232,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(233,plain,
( ( ! [SY144: $i] :
( ( SY144 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY144 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(234,plain,
( ( ! [SY138: $i > $o] :
( ? [SY140: $i] :
( ( SY138 @ SY140 )
& ! [SY141: $i] :
( ( SY138 @ SY141 )
=> ( SY140 = SY141 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY138 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(235,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(236,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(237,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(238,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(239,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(240,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(241,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(242,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(243,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(244,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(245,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(246,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(247,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(248,plain,
( ( ! [SY105: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY105 )
=> ( SY105 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(249,plain,
( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ( in @ SY103 @ SY101 )
=> ( ( SY102 @ SY103 )
=> ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(250,plain,
( ( ! [SY99: $i] :
( ( SY99 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY99 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(251,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(252,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(253,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(254,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(255,plain,
( ( ! [SY82: $i > $o] :
( ? [SY84: $i] :
( ( SY82 @ SY84 )
& ! [SY85: $i] :
( ( SY82 @ SY85 )
=> ( SY84 = SY85 ) ) )
=> ? [Xx: $i] : ( SY82 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(256,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(257,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(258,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(259,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(260,plain,
( ( ! [SY70: $i > $o] :
( ? [SY72: $i] :
( ( SY70 @ SY72 )
& ! [SY73: $i] :
( ( SY70 @ SY73 )
=> ( SY72 = SY73 ) ) )
=> ? [Xx: $i] :
( ( SY70 @ Xx )
& ! [Xy: $i] :
( ( SY70 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(261,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(262,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(263,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(264,plain,
( ( ! [SY53: $i > $o] :
( ? [SY55: $i] :
( ( SY53 @ SY55 )
& ! [SY56: $i] :
( ( SY53 @ SY56 )
=> ( SY55 = SY56 ) ) )
=> ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(265,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(266,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(267,plain,
( ( ! [SY21: $i > $i > $o,SY22: $i] :
( ! [SY23: $i] :
( ( in @ SY23 @ SY22 )
=> ? [SY25: $i] :
( ( SY21 @ SY23 @ SY25 )
& ! [SY26: $i] :
( ( SY21 @ SY23 @ SY26 )
=> ( SY25 = SY26 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY22 )
& ( SY21 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(268,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(269,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(270,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(271,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(273,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(274,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(276,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
? [SY2: $i] :
( ( in @ SY2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY3: $i] :
( ( in @ SY3 @ ( 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 @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(277,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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(278,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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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(279,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 )
| ~ ( subset @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ~ ( ~ ( 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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX1 @ SX3 )
| ~ ( in @ SX3 @ SX0 )
| SX2 )
| 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 )
| ! [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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ SX0 )
| ( in @ SX2 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX2: $i,SX3: $o] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) )
= $true ),
inference(unfold_def,[status(thm)],[174,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ( ( setadjoin @ SX0 @ SX2 )
= ( setadjoin @ SX1 @ SX3 ) ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,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)],[244,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= emptyset )
| $false ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[258,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 )
| ( 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[210,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
~ ! [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)],[276,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 )
| ~ ( ~ ( ~ ( 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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,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)],[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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ 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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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 > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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] :
~ ( ~ ( ~ ( 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)],[272,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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $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,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,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,
! [SV1: $i] :
( ( ! [SY830: $i] : ( in @ SY830 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY830 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(386,plain,
! [SV2: $i] :
( ( ! [SY831: $i] : ( in @ SV2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY831 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(387,plain,
! [SV3: $i] :
( ( ! [SY832: $i] : ( in @ SY832 @ ( setadjoin @ SV3 @ ( setadjoin @ SY832 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(388,plain,
! [SV4: $i] :
( ( ! [SY833: $i] : ( subset @ ( setminus @ SV4 @ SY833 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(389,plain,
! [SV5: $i] :
( ( ! [SY834: $i,SY835: $i] :
( ( binintersect @ SV5 @ ( binunion @ SY834 @ SY835 ) )
= ( binunion @ ( binintersect @ SV5 @ SY834 ) @ ( binintersect @ SV5 @ SY835 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(390,plain,
! [SV6: $i] :
( ( ! [SY836: $i] : ( subset @ ( binintersect @ SV6 @ SY836 ) @ SY836 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(391,plain,
! [SV7: $i] :
( ( ! [SY837: $i] : ( subset @ ( binintersect @ SV7 @ SY837 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(392,plain,
! [SV8: $i] :
( ( ! [SY838: $i] : ( subset @ SY838 @ ( binunion @ SV8 @ SY838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(393,plain,
! [SV9: $i] :
( ( ! [SY839: $i] : ( subset @ SV9 @ ( binunion @ SV9 @ SY839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(394,plain,
! [SV10: $i] :
( ( ! [SY840: $i] : ( in @ SY840 @ ( setadjoin @ SV10 @ ( setadjoin @ SY840 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(395,plain,
! [SV11: $i] :
( ( ! [SY841: $i > $o] :
( subset
@ ( dsetconstr @ SV11
@ ^ [Xx: $i] : ( SY841 @ Xx ) )
@ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(396,plain,
! [SV12: $i] :
( ( ! [SY843: $i > $o] :
( in
@ ( dsetconstr @ SV12
@ ^ [Xx: $i] : ( SY843 @ Xx ) )
@ ( powerset @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(397,plain,
! [SV13: $i] :
( ( in @ SV13 @ ( powerset @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(398,plain,
! [SV14: $i] :
( ( ! [SY845: $i] : ( subset @ SY845 @ ( setadjoin @ SV14 @ SY845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(399,plain,
! [SV15: $i] :
( ( subset @ SV15 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(400,plain,
! [SV16: $i] :
( ( subset @ emptyset @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(401,plain,
! [SV17: $i] :
( ( ! [SY846: $i] : ( in @ SY846 @ ( setadjoin @ SV17 @ ( setadjoin @ SY846 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(402,plain,
! [SV18: $i] :
( ( ! [SY847: $i] : ( in @ SV18 @ ( setadjoin @ SV18 @ ( setadjoin @ SY847 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(403,plain,
! [SV19: $i] :
( ( in @ emptyset @ ( powerset @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(404,plain,
! [SV20: $i] :
( ( in @ emptyset @ ( powerset @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(405,plain,
! [SV21: $i] :
( ( ( dsetconstr @ SV21
@ ^ [Xx: $i] : $true )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(406,plain,
! [SV22: $i] :
( ( ! [SY849: $i] : ( in @ SV22 @ ( setadjoin @ SV22 @ SY849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(407,plain,
! [SV23: $i] :
( ( ~ ( in @ SV23 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(408,plain,
! [SV24: $i] :
( ( ~ ( in @ SV24 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(409,plain,
! [SV25: $i] :
( ( ! [SY850: $i,SY851: $i] :
( ~ ( in @ SY850 @ ( powerset @ SV25 ) )
| ~ ( in @ SY851 @ SY850 )
| ( in @ SY851 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(410,plain,
! [SV26: $i] :
( ( ! [SY852: $i > $o,SY853: $i] :
( ~ ( in @ SY853 @ SV26 )
| ~ ( SY852 @ SY853 )
| ( in @ SY853
@ ( dsetconstr @ SV26
@ ^ [SX3: $i] : ( SY852 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(411,plain,
! [SV27: $i] :
( ( ! [SY855: $i,SY856: $i] :
( ~ ( in @ SY856 @ SV27 )
| ( in @ SY856 @ ( binunion @ SV27 @ SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(412,plain,
! [SV28: $i] :
( ( ! [SY857: $i] :
( ~ ( in @ SV28 @ ( setadjoin @ SY857 @ emptyset ) )
| ( SV28 = SY857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(413,plain,
! [SV29: $i] :
( ( ! [SY858: $i] :
( ( SV29 != SY858 )
| ( subset @ SV29 @ SY858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(414,plain,
! [SV30: $i] :
( ( ~ ~ ! [SY859: $i] :
~ ( in @ SY859 @ SV30 )
| ( SV30 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(415,plain,
! [SV31: $i] :
( ( ~ ! [SY860: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY861: $i] :
( ~ ( in @ SY861 @ SY860 )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY861 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY863: $i,SY864: $i] :
( ~ ~ ( ~ ( in @ SY863 @ SV31 )
| ~ ( in @ SY864 @ SV31 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY860 )
| ~ ( ~ ( ~ ( in @ SY863 @ SX4 )
| ( in @ SY864 @ SX4 ) )
| ~ ( ~ ( in @ SY864 @ SX4 )
| ( in @ SY863 @ SX4 ) ) ) )
| ( SY863 = SY864 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY860 )
| ~ ( in @ SX3 @ SY860 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY870: $i] :
( ~ ~ ( ~ ! [SY871: $i] :
( ~ ( in @ SY871 @ SY870 )
| ( in @ SY871 @ SV31 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY870 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY860 )
| ~ ( in @ SX4 @ SY870 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY870 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY860 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(416,plain,
! [SV32: $i] :
( ( ! [SY878: $i,SY879: $i] :
( ~ ( in @ SY879 @ SV32 )
| ~ ~ ( in @ SY879 @ SY878 )
| ( SV32 != SY878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(417,plain,
! [SV33: $i > $o] :
( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV33 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV33 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(418,plain,
! [SV34: $i] :
( ( ! [SY884: $i,SY885: $i] :
( ~ ( in @ SY885 @ ( binunion @ SV34 @ SY884 ) )
| ( in @ SY885 @ SV34 )
| ( in @ SY885 @ SY884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(419,plain,
! [SV35: $i > $i > $o] :
( ( ! [SY886: $i] :
( ~ ! [SY887: $i] :
( ~ ( in @ SY887 @ SY886 )
| ~ ! [SY888: $i] :
~ ~ ( ~ ( SV35 @ SY887 @ SY888 )
| ~ ! [SY889: $i] :
( ~ ( SV35 @ SY887 @ SY889 )
| ( SY888 = SY889 ) ) ) )
| ~ ! [SY890: $i] :
~ ! [SY891: $i] :
~ ( ~ ( ~ ( in @ SY891 @ SY890 )
| ~ ! [SY892: $i] :
~ ~ ( ~ ( in @ SY892 @ SY886 )
| ~ ( SV35 @ SY892 @ SY891 ) ) )
| ~ ( ~ ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ SY893 @ SY886 )
| ~ ( SV35 @ SY893 @ SY891 ) )
| ( in @ SY891 @ SY890 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(420,plain,
! [SV36: $i > $o] :
( ( ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( SV36 @ SY894 )
| ~ ! [SY895: $i] :
( ~ ( SV36 @ SY895 )
| ( SY894 = SY895 ) ) )
| ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(421,plain,
! [SV37: $i] :
( ( ! [SY897: $i,SY898: $i] :
( ~ ( in @ SY898 @ SV37 )
| ~ ( in @ SY898 @ SY897 )
| ( in @ SY898 @ ( binintersect @ SV37 @ SY897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(422,plain,
! [SV38: $i] :
( ( ! [SY899: $i,SY900: $i] :
( ~ ( in @ SY900 @ SV38 )
| ~ ~ ( in @ SY900 @ SY899 )
| ( in @ SY900 @ ( setminus @ SV38 @ SY899 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(423,plain,
! [SV39: $i] :
( ( ! [SY901: $i,SY902: $i] :
( ~ ( in @ SY902 @ SY901 )
| ~ ( in @ SY902 @ ( setminus @ SV39 @ SY901 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(424,plain,
! [SV40: $i] :
( ( ! [SY903: $i,SY904: $i] :
( ~ ~ ( in @ SY904 @ ( setminus @ SV40 @ SY903 ) )
| ~ ( in @ SY904 @ SV40 )
| ( in @ SY904 @ SY903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(425,plain,
! [SV41: $i] :
( ( ! [SY905: $i > $o] :
( ~ ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV41 )
| ( SY905 @ SY906 ) )
| ~ ! [SY907: $i] :
~ ~ ( ~ ( in @ SY907 @ SV41 )
| ~ ~ ( SY905 @ SY907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(426,plain,
! [SV42: $i] :
( ( ! [SY908: $i] :
( ( ( binintersect @ SV42 @ SY908 )
!= SY908 )
| ( subset @ SY908 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(427,plain,
! [SV43: $i] :
( ( ! [SY909: $i,SY910: $i] :
( ~ ( in @ SY910 @ SV43 )
| ~ ~ ( in @ SY910 @ SY909 )
| ~ ( subset @ SV43 @ SY909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(428,plain,
! [SV44: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV44 )
| ~ ! [SY911: $i] :
( ~ ~ ( ~ ( in @ SY911 @ omega )
| ~ ( in @ SY911 @ SV44 ) )
| ( in @ ( setadjoin @ SY911 @ SY911 ) @ SV44 ) ) )
| ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(429,plain,
! [SV45: $i] :
( ( ! [SY913: $i,SY914: $i] :
( ~ ~ ( in @ SY914 @ SV45 )
| ~ ( in @ SY914 @ SY913 )
| ( in @ SY914 @ ( symdiff @ SV45 @ SY913 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(430,plain,
! [SV46: $i] :
( ( ! [SY915: $i > $o] :
( ~ ~ ! [SY916: $i] :
~ ~ ( ~ ( in @ SY916 @ SV46 )
| ~ ~ ( SY915 @ SY916 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ SV46 )
| ( SY915 @ SY917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(431,plain,
! [SV47: $i > $o] :
( ( ! [SY918: $i > $o] :
( ~ ! [SY919: $i,SY920: $i] :
( ( SY919 != SY920 )
| ~ ( ~ ( ~ ( SV47 @ SY919 )
| ( SY918 @ SY920 ) )
| ~ ( ~ ( SY918 @ SY920 )
| ( SV47 @ SY919 ) ) ) )
| ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY918 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY918 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SX2: $i] : ( SY918 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(432,plain,
! [SV48: $i > $o] :
( ( ~ ~ ! [SY927: $i] :
~ ( SV48 @ SY927 )
| ~ ! [SY928: $i,SY929: $i] :
( ~ ( SV48 @ SY928 )
| ~ ( SV48 @ SY929 )
| ( SY928 = SY929 ) )
| ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(433,plain,
! [SV49: $i] :
( ( ! [SY932: $i] :
( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ SV49 )
| ( in @ SY933 @ SY932 ) )
| ( subset @ SV49 @ SY932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(434,plain,
! [SV50: $i] :
( ( ! [SY934: $i] :
( ~ ( in @ SY934 @ ( setunion @ SV50 ) )
| ! [SY935: $o] :
( ~ ! [SY936: $i] :
( ~ ( in @ SY934 @ SY936 )
| ~ ( in @ SY936 @ SV50 )
| SY935 )
| SY935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(435,plain,
! [SV51: $i > $o] :
( ( ~ ~ ! [SY937: $i] :
~ ~ ( ~ ( SV51 @ SY937 )
| ~ ! [SY938: $i] :
( ~ ( SV51 @ SY938 )
| ( SY937 = SY938 ) ) )
| ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(436,plain,
! [SV52: $i] :
( ( ! [SY941: $i] :
( ( SV52 != SY941 )
| ! [SY942: $i > $o,SY943: $i > $o] :
( ~ ! [SY944: $i] :
( ~ ( in @ SY944 @ SV52 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY941 )
| ( SY944 != SX5 )
| ~ ( ~ ( ~ ( SY942 @ SY944 )
| ( SY943 @ SX5 ) )
| ~ ( ~ ( SY943 @ SX5 )
| ( SY942 @ SY944 ) ) ) ) )
| ( ( dsetconstr @ SV52
@ ^ [SX4: $i] : ( SY942 @ SX4 ) )
= ( dsetconstr @ SY941
@ ^ [SX4: $i] : ( SY943 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(437,plain,
! [SV53: $i] :
( ( ! [SY948: $i,SY949: $i] :
( ~ ( in @ SY949 @ ( binintersect @ SV53 @ SY948 ) )
| ( in @ SY949 @ SY948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(438,plain,
! [SV54: $i] :
( ( ~ ~ ! [SY950: $i] :
~ ( in @ SY950 @ SV54 )
| ~ ! [SY951: $i] :
~ ~ ( ~ ( in @ SY951 @ SV54 )
| ~ ~ ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(439,plain,
! [SV55: $i] :
( ( ! [SY953: $i] :
( ~ ! [SY954: $i] :
( ~ ( in @ SY954 @ SV55 )
| ( in @ SY954 @ SY953 ) )
| ( subset @ SV55 @ SY953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(440,plain,
! [SV56: $i] :
( ( ! [SY955: $i] :
( ~ ( subset @ SV56 @ SY955 )
| ( ( binintersect @ SV56 @ SY955 )
= SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(441,plain,
! [SV57: $i] :
( ( ! [SY956: $i,SY957: $i,SY958: $o] :
( ~ ( in @ SY957 @ ( binunion @ SV57 @ SY956 ) )
| ~ ( ~ ( in @ SY957 @ SV57 )
| SY958 )
| ~ ( ~ ( in @ SY957 @ SY956 )
| SY958 )
| SY958 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(442,plain,
! [SV58: $i] :
( ( ! [SY959: $i] :
( ( SV58 != SY959 )
| ! [SY960: $i,SY961: $i] :
( ( SY960 != SY961 )
| ( ( setadjoin @ SV58 @ SY960 )
= ( setadjoin @ SY959 @ SY961 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(443,plain,
! [SV59: $i] :
( ( ! [SY962: $i] :
( ~ ! [SY963: $i] :
( ~ ( in @ SY963 @ SV59 )
| ( in @ SY963 @ SY962 ) )
| ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ SY962 )
| ( in @ SY964 @ SV59 ) )
| ( SV59 = SY962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(444,plain,
! [SV60: $i] :
( ( ~ ( ( SV60 != emptyset ) )
| ~ ! [SY965: $i] :
~ ~ ( ~ ( in @ SY965 @ SV60 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(445,plain,
! [SV61: $i] :
( ( ! [SY966: $i > $o,SY967: $i] :
( ~ ( in @ SY967
@ ( dsetconstr @ SV61
@ ^ [SX3: $i] : ( SY966 @ SX3 ) ) )
| ( SY966 @ SY967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(446,plain,
! [SV62: $i] :
( ( ~ ( subset @ SV62 @ emptyset )
| ( SV62 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(447,plain,
! [SV63: $i] :
( ( ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY970 @ ( symdiff @ SV63 @ SY969 ) )
| ! [SY971: $o] :
( ~ ( ~ ( in @ SY970 @ SV63 )
| ~ ~ ( in @ SY970 @ SY969 )
| SY971 )
| ~ ( ~ ~ ( in @ SY970 @ SV63 )
| ~ ( in @ SY970 @ SY969 )
| SY971 )
| SY971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(448,plain,
! [SV64: $i] :
( ( ! [SY972: $i] :
( ~ ( subset @ SY972 @ SV64 )
| ( in @ SY972 @ ( powerset @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(449,plain,
! [SV65: $i] :
( ( ! [SY973: $i,SY974: $i] :
( ~ ( subset @ SV65 @ SY973 )
| ~ ~ ( in @ SY974 @ SY973 )
| ~ ( in @ SY974 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(450,plain,
! [SV66: $i] :
( ( ! [SY975: $i,SY976: $i] :
( ~ ( in @ SY976 @ ( setadjoin @ SV66 @ SY975 ) )
| ( SY976 = SV66 )
| ( in @ SY976 @ SY975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(451,plain,
! [SV67: $i] :
( ( ! [SY977: $i,SY978: $i] :
( ~ ~ ( in @ SY978 @ SV67 )
| ~ ~ ( in @ SY978 @ SY977 )
| ~ ( in @ SY978 @ ( symdiff @ SV67 @ SY977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(452,plain,
! [SV68: $i] :
( ( ! [SY979: $i] :
( ~ ( subset @ SY979 @ SV68 )
| ( ( binintersect @ SV68 @ SY979 )
= SY979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(453,plain,
! [SV69: $i] :
( ( ! [SY980: $i,SY981: $i] :
( ~ ( in @ SY981 @ ( setadjoin @ SV69 @ SY980 ) )
| ! [SY982: $o] :
( ~ ( ( SY981 != SV69 )
| SY982 )
| ~ ( ~ ( in @ SY981 @ SY980 )
| SY982 )
| SY982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(454,plain,
! [SV70: $i] :
( ( ~ ( in @ SV70 @ omega )
| ( in @ ( setadjoin @ SV70 @ SV70 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(455,plain,
! [SV71: $i] :
( ( ! [SY983: $i,SY984: $i] :
( ~ ( in @ SY984 @ ( setadjoin @ SV71 @ ( setadjoin @ SY983 @ emptyset ) ) )
| ( SY984 = SV71 )
| ( SY984 = SY983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(456,plain,
! [SV72: $i] :
( ( ! [SY985: $i] :
~ ( ~ ( ~ ( in @ SY985 @ ( setunion @ SV72 ) )
| ~ ! [SY986: $i] :
~ ~ ( ~ ( in @ SY985 @ SY986 )
| ~ ( in @ SY986 @ SV72 ) ) )
| ~ ( ~ ~ ! [SY987: $i] :
~ ~ ( ~ ( in @ SY985 @ SY987 )
| ~ ( in @ SY987 @ SV72 ) )
| ( in @ SY985 @ ( setunion @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(457,plain,
! [SV73: $o] :
( ( ! [SY988: $i] :
( ~ ( in @ SY988 @ ( prop2set @ SV73 ) )
| SV73 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[325]) ).
thf(459,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[325]) ).
thf(460,plain,
! [SV74: $i] :
( ( ! [SY989: $i] :
( ~ ~ ( subset @ SV74 @ SY989 )
| ( SV74 != SY989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(461,plain,
! [SV75: $i] :
( ( ! [SY990: $i > $o] :
( ~ ~ ! [SY991: $i] :
~ ~ ( ~ ( in @ SY991 @ SV75 )
| ~ ( SY990 @ SY991 ) )
| ( ( dsetconstr @ SV75
@ ^ [SX2: $i] : ( SY990 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(462,plain,
! [SV76: $i > $o] :
( ( ~ ~ ! [SY993: $i] :
~ ! [SY994: $i] :
~ ( ~ ( ~ ( SV76 @ SY994 )
| ( SY994 = SY993 ) )
| ~ ( ( SY994 != SY993 )
| ( SV76 @ SY994 ) ) )
| ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(463,plain,
! [SV77: $i] :
( ( ! [SY997: $i,SY998: $i] :
( ~ ( subset @ SV77 @ SY997 )
| ~ ( in @ SY998 @ SV77 )
| ( in @ SY998 @ SY997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(464,plain,
! [SV78: $i] :
( ( ! [SY999: $i,SY1000: $i] :
( ~ ( in @ SY1000 @ ( binintersect @ SV78 @ SY999 ) )
| ( in @ SY1000 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(465,plain,
! [SV79: $i] :
( ( ! [SY1001: $i > $o] :
( ~ ~ ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV79 )
| ( SY1001 @ SY1002 ) )
| ~ ! [SY1003: $i] :
~ ~ ( ~ ( in @ SY1003 @ SV79 )
| ~ ~ ( SY1001 @ SY1003 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(466,plain,
! [SV80: $i] :
( ( ! [SY1004: $i] :
( ~ ! [SY1005: $i] :
~ ( ~ ( ~ ( in @ SY1005 @ SV80 )
| ( in @ SY1005 @ SY1004 ) )
| ~ ( ~ ( in @ SY1005 @ SY1004 )
| ( in @ SY1005 @ SV80 ) ) )
| ( SV80 = SY1004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(467,plain,
! [SV81: $i] :
( ( ! [SY1006: $i] :
( ~ ( subset @ SV81 @ SY1006 )
| ( subset @ ( powerset @ SV81 ) @ ( powerset @ SY1006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(468,plain,
! [SV82: $i] :
( ( ! [SY1007: $i,SY1008: $i] :
( ~ ( subset @ SV82 @ SY1007 )
| ~ ( subset @ SY1007 @ SY1008 )
| ( subset @ SV82 @ SY1008 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(469,plain,
! [SV83: $i] :
( ( ~ ( in @ SV83 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(470,plain,
! [SV84: $i] :
( ( ! [SY1010: $i] :
( ~ ( in @ SV84 @ ( setadjoin @ SY1010 @ emptyset ) )
| ( in @ SY1010 @ ( setadjoin @ SV84 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(471,plain,
! [SV85: $i] :
( ( ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV85 )
| ( SV85 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(472,plain,
! [SV86: $i] :
( ( ! [SY1012: $i] :
( ( ( setminus @ SV86 @ SY1012 )
!= emptyset )
| ( subset @ SV86 @ SY1012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(473,plain,
! [SV87: $i] :
( ( ~ ! [SY1013: $i] :
~ ( in @ SY1013 @ SV87 )
| ( SV87 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(474,plain,
! [SV88: $i] :
( ( ! [SY1014: $i] :
( ( SV88 != SY1014 )
| ( in @ SV88 @ ( setadjoin @ SY1014 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(475,plain,
! [SV89: $i] :
( ( ! [SY1015: $i] :
( ~ ~ ~ ! [SY1016: $i] :
~ ~ ( ~ ( in @ SY1016 @ SV89 )
| ~ ( in @ SY1016 @ SY1015 ) )
| ( ( binintersect @ SV89 @ SY1015 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(476,plain,
! [SV90: $o] :
( ( ~ SV90
| ( set2prop @ ( prop2set @ SV90 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[342]) ).
thf(477,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[342]) ).
thf(479,plain,
! [SV91: $i > $o] :
( ( ~ ~ ! [SY1017: $i] :
~ ~ ( ~ ( SV91 @ SY1017 )
| ~ ! [SY1018: $i] :
( ~ ( SV91 @ SY1018 )
| ( SY1017 = SY1018 ) ) )
| ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(480,plain,
! [SV92: $i] :
( ( ! [SY1021: $i,SY1022: $i] :
( ~ ( in @ SY1022 @ SV92 )
| ~ ~ ( in @ SY1022 @ SY1021 )
| ( in @ SY1022 @ ( symdiff @ SV92 @ SY1021 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(481,plain,
! [SV93: $i] :
( ( ! [SY1023: $i] :
( ~ ( subset @ SV93 @ SY1023 )
| ( ( setminus @ SV93 @ SY1023 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(482,plain,
! [SV94: $i > $o] :
( ( ~ ~ ! [SY1024: $i] :
~ ~ ( ~ ( SV94 @ SY1024 )
| ~ ! [SY1025: $i] :
( ~ ( SV94 @ SY1025 )
| ( SY1024 = SY1025 ) ) )
| ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(483,plain,
! [SV95: $i] :
( ( ! [SY1028: $i > $o,SY1029: $i] :
( ~ ( in @ SY1029 @ SV95 )
| ~ ( SY1028 @ SY1029 )
| ( ( dsetconstr @ SV95
@ ^ [SX3: $i] : ( SY1028 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(484,plain,
! [SV96: $i] :
( ( ~ ( in @ SV96 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(485,plain,
! [SV97: $i] :
( ( ! [SY1031: $i,SY1032: $i] :
( ~ ( in @ SY1032 @ ( setminus @ SV97 @ SY1031 ) )
| ~ ( in @ SY1032 @ SY1031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(486,plain,
! [SV98: $i] :
( ( ! [SY1033: $i,SY1034: $i] :
( ~ ( in @ SY1034 @ SY1033 )
| ( in @ SY1034 @ ( setadjoin @ SV98 @ SY1033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(487,plain,
! [SV99: $i] :
( ( ! [SY1035: $i,SY1036: $i] :
~ ( ~ ( ~ ( in @ SY1036 @ ( setadjoin @ SV99 @ SY1035 ) )
| ( SY1036 = SV99 )
| ( in @ SY1036 @ SY1035 ) )
| ~ ( ~ ( ( SY1036 = SV99 )
| ( in @ SY1036 @ SY1035 ) )
| ( in @ SY1036 @ ( setadjoin @ SV99 @ SY1035 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(488,plain,
! [SV100: $i > $o] :
( ( ! [SY1037: $i > $o] :
( ~ ! [SY1038: $i,SY1039: $i] :
( ( SY1038 != SY1039 )
| ~ ( ~ ( ~ ( SV100 @ SY1038 )
| ( SY1037 @ SY1039 ) )
| ~ ( ~ ( SY1037 @ SY1039 )
| ( SV100 @ SY1038 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1037 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1037 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1037 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1037 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(489,plain,
! [SV101: $i] :
( ( ! [SY1048: $i > $o] :
( ~ ~ ~ ! [SY1049: $i] :
~ ~ ( ~ ( in @ SY1049 @ SV101 )
| ~ ( SY1048 @ SY1049 ) )
| ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV101 )
| ~ ( SY1048 @ SY1050 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(490,plain,
! [SV102: $i] :
( ( ! [SY1051: $i] :
( ( SV102 != SY1051 )
| ( ( powerset @ SV102 )
= ( powerset @ SY1051 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(491,plain,
! [SV103: $i] :
( ( ! [SY1052: $i] :
( ~ ( subset @ SV103 @ SY1052 )
| ~ ( subset @ SY1052 @ SV103 )
| ( SV103 = SY1052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(492,plain,
! [SV104: $i] :
( ( ~ ( ( SV104 != emptyset ) )
| ~ ! [SY1053: $i] :
~ ( in @ SY1053 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(493,plain,
! [SV105: $i] :
( ( ! [SY1054: $i,SY1055: $i] :
( ~ ~ ( in @ SY1055 @ ( setminus @ SV105 @ SY1054 ) )
| ~ ~ ( in @ SY1055 @ SY1054 )
| ~ ( in @ SY1055 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(494,plain,
! [SV106: $i > $o] :
( ( ! [SY1056: $i] :
( ~ ( in @ SY1056 @ emptyset )
| ( SV106 @ SY1056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(495,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)],[359]) ).
thf(496,plain,
! [SV107: $i] :
( ( ! [SY1057: $i,SY1058: $i] :
( ~ ( in @ SY1058 @ SY1057 )
| ( in @ SY1058 @ ( binunion @ SV107 @ SY1057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(497,plain,
! [SV108: $i] :
( ( ! [SY1059: $i > $o] :
( ~ ! [SY1060: $i] :
( ~ ( in @ SY1060 @ SV108 )
| ~ ( SY1059 @ SY1060 ) )
| ~ ~ ! [SY1061: $i] :
~ ~ ( ~ ( in @ SY1061 @ SV108 )
| ~ ( SY1059 @ SY1061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(498,plain,
! [SV109: $i > $o] :
( ( ~ ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV109 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV109 @ SY1063 )
| ( SY1062 = SY1063 ) ) )
| ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(499,plain,
! [SV110: $i] :
( ( ! [SY1066: $i,SY1067: $i] :
( ~ ( subset @ SY1067 @ SV110 )
| ~ ( subset @ SY1067 @ SY1066 )
| ( subset @ SY1067 @ ( binintersect @ SV110 @ SY1066 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(500,plain,
! [SV111: $i] :
( ( ! [SY1068: $i > $o,SY1069: $i] :
( ~ ( in @ SY1069 @ SV111 )
| ~ ( ~ ( ~ ( in @ SY1069
@ ( dsetconstr @ SV111
@ ^ [SX3: $i] : ( SY1068 @ SX3 ) ) )
| ( SY1068 @ SY1069 ) )
| ~ ( ~ ( SY1068 @ SY1069 )
| ( in @ SY1069
@ ( dsetconstr @ SV111
@ ^ [SX3: $i] : ( SY1068 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(501,plain,
! [SV112: $i] :
( ( ! [SY1072: $i] :
( ~ ! [SY1073: $i] :
( ~ ( in @ SY1073 @ SY1072 )
| ( in @ SY1073 @ SV112 ) )
| ( in @ SY1072 @ ( powerset @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(502,plain,
! [SV113: $i] :
( ( ! [SY1074: $i] :
( ( SV113 != SY1074 )
| ! [SY1075: $i,SY1076: $i] :
( ( SY1075 != SY1076 )
| ~ ( in @ SY1075 @ SV113 )
| ( in @ SY1076 @ SY1074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(503,plain,
! [SV114: $i] :
( ( ! [SY1077: $i,SY1078: $i] :
( ~ ( in @ SY1078 @ ( setminus @ SV114 @ SY1077 ) )
| ( in @ SY1078 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(504,plain,
! [SV115: $i] :
( ( ! [SY1079: $i > $o,SY1080: $i] :
( ~ ( in @ SY1080
@ ( dsetconstr @ SV115
@ ^ [SX3: $i] : ( SY1079 @ SX3 ) ) )
| ( in @ SY1080 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(505,plain,
! [SV116: $i] :
( ( ! [SY1082: $i,SY1083: $i] :
( ~ ( subset @ SV116 @ SY1083 )
| ( subset @ SV116 @ ( setadjoin @ SY1082 @ SY1083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(506,plain,
! [SV117: $i > $o] :
( ( ~ ~ ! [SY1084: $i] :
~ ~ ( ~ ( SV117 @ SY1084 )
| ~ ! [SY1085: $i] :
( ~ ( SV117 @ SY1085 )
| ( SY1084 = SY1085 ) ) )
| ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(507,plain,
! [SV118: $i] :
( ( ! [SY1087: $i] :
( ( SV118 != SY1087 )
| ( subset @ SY1087 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(508,plain,
! [SV119: $i] :
( ( ! [SY1088: $i] :
( ( SV119 != SY1088 )
| ! [SY1089: $i,SY1090: $i] :
( ( SY1089 != SY1090 )
| ~ ( ~ ( ~ ( in @ SY1089 @ SV119 )
| ( in @ SY1090 @ SY1088 ) )
| ~ ( ~ ( in @ SY1090 @ SY1088 )
| ( in @ SY1089 @ SV119 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(509,plain,
! [SV120: $i] :
( ( ! [SY1091: $i] :
( ~ ( subset @ SV120 @ SY1091 )
| ( in @ SV120 @ ( powerset @ SY1091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(510,plain,
! [SV121: $i] :
( ( ! [SY1092: $i,SY1093: $i] :
( ~ ( in @ SY1092 @ SY1093 )
| ~ ( in @ SY1093 @ SV121 )
| ( in @ SY1092 @ ( setunion @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(511,plain,
! [SV122: $i] :
( ( ! [SY1094: $i] :
( ~ ( ( SV122 != SY1094 ) )
| ~ ( in @ SY1094 @ ( setadjoin @ SV122 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(512,plain,
! [SV123: $i] :
( ( ! [SY1095: $i] :
( ~ ( in @ SY1095 @ SV123 )
| ( in @ SY1095 @ ( powerset @ ( setunion @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(513,plain,
! [SV124: $i] :
( ( ! [SY1096: $i] :
( ( ( binintersect @ SV124 @ SY1096 )
!= SV124 )
| ( subset @ SV124 @ SY1096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(514,plain,
! [SV125: $i] :
( ( ! [SY1097: $i] :
( ( SV125 != SY1097 )
| ( ( setunion @ SV125 )
= ( setunion @ SY1097 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(515,plain,
! [SV126: $i] :
( ( ! [SY1098: $i,SY1099: $i] :
( ~ ~ ( in @ SY1099 @ SV126 )
| ~ ( in @ SY1099 @ ( setminus @ SV126 @ SY1098 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(516,plain,
! [SV127: $i] :
( ( ! [SY1100: $i > $o] :
( ~ ~ ~ ! [SY1101: $i] :
~ ~ ( ~ ( in @ SY1101 @ SV127 )
| ~ ( SY1100 @ SY1101 ) )
| ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV127 )
| ~ ( SY1100 @ SY1102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(517,plain,
! [SV128: $i] :
( ( ! [SY1103: $i,SY1104: $i] :
( ~ ( in @ SY1104 @ SV128 )
| ~ ( in @ SY1104 @ SY1103 )
| ~ ( in @ SY1104 @ ( symdiff @ SV128 @ SY1103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(518,plain,
! [SV129: $i] :
( ( ! [SY1105: $i] :
~ ( ~ ( ~ ( in @ SY1105 @ ( powerset @ SV129 ) )
| ! [SY1106: $i] :
( ~ ( in @ SY1106 @ SY1105 )
| ( in @ SY1106 @ SV129 ) ) )
| ~ ( ~ ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SY1105 )
| ( in @ SY1107 @ SV129 ) )
| ( in @ SY1105 @ ( powerset @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(519,plain,
! [SV130: $o] :
( ( ~ SV130
| ( in @ emptyset @ ( prop2set @ SV130 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[383]) ).
thf(520,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[383]) ).
thf(522,plain,
! [SV131: $i] :
( ( ! [SY1108: $i] :
( ~ ( in @ SY1108 @ ( powerset @ SV131 ) )
| ( subset @ SY1108 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(523,plain,
! [SV1: $i,SV132: $i] :
( ( in @ SV132 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV132 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(524,plain,
! [SV133: $i,SV2: $i] :
( ( in @ SV2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV133 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(525,plain,
! [SV3: $i,SV134: $i] :
( ( in @ SV134 @ ( setadjoin @ SV3 @ ( setadjoin @ SV134 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(526,plain,
! [SV135: $i,SV4: $i] :
( ( subset @ ( setminus @ SV4 @ SV135 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(527,plain,
! [SV136: $i,SV5: $i] :
( ( ! [SY1109: $i] :
( ( binintersect @ SV5 @ ( binunion @ SV136 @ SY1109 ) )
= ( binunion @ ( binintersect @ SV5 @ SV136 ) @ ( binintersect @ SV5 @ SY1109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(528,plain,
! [SV137: $i,SV6: $i] :
( ( subset @ ( binintersect @ SV6 @ SV137 ) @ SV137 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(529,plain,
! [SV138: $i,SV7: $i] :
( ( subset @ ( binintersect @ SV7 @ SV138 ) @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(530,plain,
! [SV8: $i,SV139: $i] :
( ( subset @ SV139 @ ( binunion @ SV8 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(531,plain,
! [SV140: $i,SV9: $i] :
( ( subset @ SV9 @ ( binunion @ SV9 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(532,plain,
! [SV10: $i,SV141: $i] :
( ( in @ SV141 @ ( setadjoin @ SV10 @ ( setadjoin @ SV141 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(533,plain,
! [SV142: $i > $o,SV11: $i] :
( ( subset
@ ( dsetconstr @ SV11
@ ^ [SY1110: $i] : ( SV142 @ SY1110 ) )
@ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(534,plain,
! [SV143: $i > $o,SV12: $i] :
( ( in
@ ( dsetconstr @ SV12
@ ^ [SY1111: $i] : ( SV143 @ SY1111 ) )
@ ( powerset @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(535,plain,
! [SV14: $i,SV144: $i] :
( ( subset @ SV144 @ ( setadjoin @ SV14 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(536,plain,
! [SV17: $i,SV145: $i] :
( ( in @ SV145 @ ( setadjoin @ SV17 @ ( setadjoin @ SV145 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(537,plain,
! [SV146: $i,SV18: $i] :
( ( in @ SV18 @ ( setadjoin @ SV18 @ ( setadjoin @ SV146 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(538,plain,
! [SV147: $i,SV22: $i] :
( ( in @ SV22 @ ( setadjoin @ SV22 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(539,plain,
! [SV23: $i] :
( ( in @ SV23 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(540,plain,
! [SV24: $i] :
( ( in @ SV24 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(541,plain,
! [SV25: $i,SV148: $i] :
( ( ! [SY1112: $i] :
( ~ ( in @ SV148 @ ( powerset @ SV25 ) )
| ~ ( in @ SY1112 @ SV148 )
| ( in @ SY1112 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(542,plain,
! [SV149: $i > $o,SV26: $i] :
( ( ! [SY1113: $i] :
( ~ ( in @ SY1113 @ SV26 )
| ~ ( SV149 @ SY1113 )
| ( in @ SY1113
@ ( dsetconstr @ SV26
@ ^ [SY1114: $i] : ( SV149 @ SY1114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(543,plain,
! [SV150: $i,SV27: $i] :
( ( ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV27 )
| ( in @ SY1115 @ ( binunion @ SV27 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(544,plain,
! [SV151: $i,SV28: $i] :
( ( ~ ( in @ SV28 @ ( setadjoin @ SV151 @ emptyset ) )
| ( SV28 = SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(545,plain,
! [SV152: $i,SV29: $i] :
( ( ( SV29 != SV152 )
| ( subset @ SV29 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(546,plain,
! [SV30: $i] :
( ( ( ~ ~ ! [SY859: $i] :
~ ( in @ SY859 @ SV30 ) )
= $true )
| ( ( SV30 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(547,plain,
! [SV31: $i] :
( ( ! [SY860: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY861: $i] :
( ~ ( in @ SY861 @ SY860 )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY861 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY863: $i,SY864: $i] :
( ~ ~ ( ~ ( in @ SY863 @ SV31 )
| ~ ( in @ SY864 @ SV31 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY860 )
| ~ ( ~ ( ~ ( in @ SY863 @ SX4 )
| ( in @ SY864 @ SX4 ) )
| ~ ( ~ ( in @ SY864 @ SX4 )
| ( in @ SY863 @ SX4 ) ) ) )
| ( SY863 = SY864 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY860 )
| ~ ( in @ SX3 @ SY860 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY870: $i] :
( ~ ~ ( ~ ! [SY871: $i] :
( ~ ( in @ SY871 @ SY870 )
| ( in @ SY871 @ SV31 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY870 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY860 )
| ~ ( in @ SX4 @ SY870 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY870 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY860 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(548,plain,
! [SV153: $i,SV32: $i] :
( ( ! [SY1116: $i] :
( ~ ( in @ SY1116 @ SV32 )
| ~ ~ ( in @ SY1116 @ SV153 )
| ( SV32 != SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(549,plain,
! [SV33: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV33 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV33 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(550,plain,
! [SV154: $i,SV34: $i] :
( ( ! [SY1117: $i] :
( ~ ( in @ SY1117 @ ( binunion @ SV34 @ SV154 ) )
| ( in @ SY1117 @ SV34 )
| ( in @ SY1117 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(551,plain,
! [SV35: $i > $i > $o,SV155: $i] :
( ( ~ ! [SY1118: $i] :
( ~ ( in @ SY1118 @ SV155 )
| ~ ! [SY888: $i] :
~ ~ ( ~ ( SV35 @ SY1118 @ SY888 )
| ~ ! [SY889: $i] :
( ~ ( SV35 @ SY1118 @ SY889 )
| ( SY888 = SY889 ) ) ) )
| ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(552,plain,
! [SV36: $i > $o] :
( ( ( ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( SV36 @ SY894 )
| ~ ! [SY895: $i] :
( ~ ( SV36 @ SY895 )
| ( SY894 = SY895 ) ) ) )
= $true )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(553,plain,
! [SV156: $i,SV37: $i] :
( ( ! [SY1125: $i] :
( ~ ( in @ SY1125 @ SV37 )
| ~ ( in @ SY1125 @ SV156 )
| ( in @ SY1125 @ ( binintersect @ SV37 @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(554,plain,
! [SV157: $i,SV38: $i] :
( ( ! [SY1126: $i] :
( ~ ( in @ SY1126 @ SV38 )
| ~ ~ ( in @ SY1126 @ SV157 )
| ( in @ SY1126 @ ( setminus @ SV38 @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(555,plain,
! [SV39: $i,SV158: $i] :
( ( ! [SY1127: $i] :
( ~ ( in @ SY1127 @ SV158 )
| ~ ( in @ SY1127 @ ( setminus @ SV39 @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(556,plain,
! [SV159: $i,SV40: $i] :
( ( ! [SY1128: $i] :
( ~ ~ ( in @ SY1128 @ ( setminus @ SV40 @ SV159 ) )
| ~ ( in @ SY1128 @ SV40 )
| ( in @ SY1128 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(557,plain,
! [SV160: $i > $o,SV41: $i] :
( ( ~ ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV41 )
| ( SV160 @ SY1129 ) )
| ~ ! [SY1130: $i] :
~ ~ ( ~ ( in @ SY1130 @ SV41 )
| ~ ~ ( SV160 @ SY1130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(558,plain,
! [SV161: $i,SV42: $i] :
( ( ( ( binintersect @ SV42 @ SV161 )
!= SV161 )
| ( subset @ SV161 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(559,plain,
! [SV162: $i,SV43: $i] :
( ( ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV43 )
| ~ ~ ( in @ SY1131 @ SV162 )
| ~ ( subset @ SV43 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(560,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV44 )
| ~ ! [SY911: $i] :
( ~ ~ ( ~ ( in @ SY911 @ omega )
| ~ ( in @ SY911 @ SV44 ) )
| ( in @ ( setadjoin @ SY911 @ SY911 ) @ SV44 ) ) ) )
= $true )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(561,plain,
! [SV163: $i,SV45: $i] :
( ( ! [SY1132: $i] :
( ~ ~ ( in @ SY1132 @ SV45 )
| ~ ( in @ SY1132 @ SV163 )
| ( in @ SY1132 @ ( symdiff @ SV45 @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(562,plain,
! [SV164: $i > $o,SV46: $i] :
( ( ~ ~ ! [SY1133: $i] :
~ ~ ( ~ ( in @ SY1133 @ SV46 )
| ~ ~ ( SV164 @ SY1133 ) )
| ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(563,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ~ ! [SY1135: $i,SY1136: $i] :
( ( SY1135 != SY1136 )
| ~ ( ~ ( ~ ( SV47 @ SY1135 )
| ( SV165 @ SY1136 ) )
| ~ ( ~ ( SV165 @ SY1136 )
| ( SV47 @ SY1135 ) ) ) )
| ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(564,plain,
! [SV48: $i > $o] :
( ( ( ~ ~ ! [SY927: $i] :
~ ( SV48 @ SY927 ) )
= $true )
| ( ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( SV48 @ SY928 )
| ~ ( SV48 @ SY929 )
| ( SY928 = SY929 ) )
| ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(565,plain,
! [SV166: $i,SV49: $i] :
( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV49 )
| ( in @ SY1143 @ SV166 ) )
| ( subset @ SV49 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(566,plain,
! [SV50: $i,SV167: $i] :
( ( ~ ( in @ SV167 @ ( setunion @ SV50 ) )
| ! [SY1144: $o] :
( ~ ! [SY1145: $i] :
( ~ ( in @ SV167 @ SY1145 )
| ~ ( in @ SY1145 @ SV50 )
| SY1144 )
| SY1144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(567,plain,
! [SV51: $i > $o] :
( ( ( ~ ~ ! [SY937: $i] :
~ ~ ( ~ ( SV51 @ SY937 )
| ~ ! [SY938: $i] :
( ~ ( SV51 @ SY938 )
| ( SY937 = SY938 ) ) ) )
= $true )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(568,plain,
! [SV168: $i,SV52: $i] :
( ( ( SV52 != SV168 )
| ! [SY1146: $i > $o,SY1147: $i > $o] :
( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ SV52 )
| ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV168 )
| ( SY1148 != SY1149 )
| ~ ( ~ ( ~ ( SY1146 @ SY1148 )
| ( SY1147 @ SY1149 ) )
| ~ ( ~ ( SY1147 @ SY1149 )
| ( SY1146 @ SY1148 ) ) ) ) )
| ( ( dsetconstr @ SV52
@ ^ [SX4: $i] : ( SY1146 @ SX4 ) )
= ( dsetconstr @ SV168
@ ^ [SX4: $i] : ( SY1147 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(569,plain,
! [SV169: $i,SV53: $i] :
( ( ! [SY1152: $i] :
( ~ ( in @ SY1152 @ ( binintersect @ SV53 @ SV169 ) )
| ( in @ SY1152 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(570,plain,
! [SV54: $i] :
( ( ( ~ ~ ! [SY950: $i] :
~ ( in @ SY950 @ SV54 ) )
= $true )
| ( ( ~ ! [SY951: $i] :
~ ~ ( ~ ( in @ SY951 @ SV54 )
| ~ ~ ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ SV54 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(571,plain,
! [SV170: $i,SV55: $i] :
( ( ~ ! [SY1153: $i] :
( ~ ( in @ SY1153 @ SV55 )
| ( in @ SY1153 @ SV170 ) )
| ( subset @ SV55 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(572,plain,
! [SV171: $i,SV56: $i] :
( ( ~ ( subset @ SV56 @ SV171 )
| ( ( binintersect @ SV56 @ SV171 )
= SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(573,plain,
! [SV172: $i,SV57: $i] :
( ( ! [SY1154: $i,SY1155: $o] :
( ~ ( in @ SY1154 @ ( binunion @ SV57 @ SV172 ) )
| ~ ( ~ ( in @ SY1154 @ SV57 )
| SY1155 )
| ~ ( ~ ( in @ SY1154 @ SV172 )
| SY1155 )
| SY1155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(574,plain,
! [SV173: $i,SV58: $i] :
( ( ( SV58 != SV173 )
| ! [SY1156: $i,SY1157: $i] :
( ( SY1156 != SY1157 )
| ( ( setadjoin @ SV58 @ SY1156 )
= ( setadjoin @ SV173 @ SY1157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(575,plain,
! [SV174: $i,SV59: $i] :
( ( ~ ! [SY1158: $i] :
( ~ ( in @ SY1158 @ SV59 )
| ( in @ SY1158 @ SV174 ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) )
| ( SV59 = SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(576,plain,
! [SV60: $i] :
( ( ( ~ ( ( SV60 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY965: $i] :
~ ~ ( ~ ( in @ SY965 @ SV60 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(577,plain,
! [SV175: $i > $o,SV61: $i] :
( ( ! [SY1160: $i] :
( ~ ( in @ SY1160
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) )
| ( SV175 @ SY1160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(578,plain,
! [SV62: $i] :
( ( ( ~ ( subset @ SV62 @ emptyset ) )
= $true )
| ( ( SV62 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(579,plain,
! [SV176: $i,SV63: $i] :
( ( ! [SY1162: $i] :
( ~ ( in @ SY1162 @ ( symdiff @ SV63 @ SV176 ) )
| ! [SY1163: $o] :
( ~ ( ~ ( in @ SY1162 @ SV63 )
| ~ ~ ( in @ SY1162 @ SV176 )
| SY1163 )
| ~ ( ~ ~ ( in @ SY1162 @ SV63 )
| ~ ( in @ SY1162 @ SV176 )
| SY1163 )
| SY1163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(580,plain,
! [SV64: $i,SV177: $i] :
( ( ~ ( subset @ SV177 @ SV64 )
| ( in @ SV177 @ ( powerset @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(581,plain,
! [SV178: $i,SV65: $i] :
( ( ! [SY1164: $i] :
( ~ ( subset @ SV65 @ SV178 )
| ~ ~ ( in @ SY1164 @ SV178 )
| ~ ( in @ SY1164 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(582,plain,
! [SV179: $i,SV66: $i] :
( ( ! [SY1165: $i] :
( ~ ( in @ SY1165 @ ( setadjoin @ SV66 @ SV179 ) )
| ( SY1165 = SV66 )
| ( in @ SY1165 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(583,plain,
! [SV180: $i,SV67: $i] :
( ( ! [SY1166: $i] :
( ~ ~ ( in @ SY1166 @ SV67 )
| ~ ~ ( in @ SY1166 @ SV180 )
| ~ ( in @ SY1166 @ ( symdiff @ SV67 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(584,plain,
! [SV68: $i,SV181: $i] :
( ( ~ ( subset @ SV181 @ SV68 )
| ( ( binintersect @ SV68 @ SV181 )
= SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(585,plain,
! [SV182: $i,SV69: $i] :
( ( ! [SY1167: $i] :
( ~ ( in @ SY1167 @ ( setadjoin @ SV69 @ SV182 ) )
| ! [SY1168: $o] :
( ~ ( ( SY1167 != SV69 )
| SY1168 )
| ~ ( ~ ( in @ SY1167 @ SV182 )
| SY1168 )
| SY1168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(586,plain,
! [SV70: $i] :
( ( ( ~ ( in @ SV70 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV70 @ SV70 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(587,plain,
! [SV183: $i,SV71: $i] :
( ( ! [SY1169: $i] :
( ~ ( in @ SY1169 @ ( setadjoin @ SV71 @ ( setadjoin @ SV183 @ emptyset ) ) )
| ( SY1169 = SV71 )
| ( SY1169 = SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(588,plain,
! [SV72: $i,SV184: $i] :
( ( ~ ( ~ ( ~ ( in @ SV184 @ ( setunion @ SV72 ) )
| ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1170 )
| ~ ( in @ SY1170 @ SV72 ) ) )
| ~ ( ~ ~ ! [SY1171: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1171 )
| ~ ( in @ SY1171 @ SV72 ) )
| ( in @ SV184 @ ( setunion @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(589,plain,
! [SV73: $o,SV185: $i] :
( ( ~ ( in @ SV185 @ ( prop2set @ SV73 ) )
| SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(591,plain,
! [SV187: $i] :
( ( ~ ( in @ SV187 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(592,plain,
! [SV188: $i,SV74: $i] :
( ( ~ ~ ( subset @ SV74 @ SV188 )
| ( SV74 != SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(593,plain,
! [SV189: $i > $o,SV75: $i] :
( ( ~ ~ ! [SY1172: $i] :
~ ~ ( ~ ( in @ SY1172 @ SV75 )
| ~ ( SV189 @ SY1172 ) )
| ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(594,plain,
! [SV76: $i > $o] :
( ( ( ~ ~ ! [SY993: $i] :
~ ! [SY994: $i] :
~ ( ~ ( ~ ( SV76 @ SY994 )
| ( SY994 = SY993 ) )
| ~ ( ( SY994 != SY993 )
| ( SV76 @ SY994 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(595,plain,
! [SV190: $i,SV77: $i] :
( ( ! [SY1174: $i] :
( ~ ( subset @ SV77 @ SV190 )
| ~ ( in @ SY1174 @ SV77 )
| ( in @ SY1174 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(596,plain,
! [SV191: $i,SV78: $i] :
( ( ! [SY1175: $i] :
( ~ ( in @ SY1175 @ ( binintersect @ SV78 @ SV191 ) )
| ( in @ SY1175 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(597,plain,
! [SV192: $i > $o,SV79: $i] :
( ( ~ ~ ! [SY1176: $i] :
( ~ ( in @ SY1176 @ SV79 )
| ( SV192 @ SY1176 ) )
| ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ SV79 )
| ~ ~ ( SV192 @ SY1177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(598,plain,
! [SV193: $i,SV80: $i] :
( ( ~ ! [SY1178: $i] :
~ ( ~ ( ~ ( in @ SY1178 @ SV80 )
| ( in @ SY1178 @ SV193 ) )
| ~ ( ~ ( in @ SY1178 @ SV193 )
| ( in @ SY1178 @ SV80 ) ) )
| ( SV80 = SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(599,plain,
! [SV194: $i,SV81: $i] :
( ( ~ ( subset @ SV81 @ SV194 )
| ( subset @ ( powerset @ SV81 ) @ ( powerset @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(600,plain,
! [SV195: $i,SV82: $i] :
( ( ! [SY1179: $i] :
( ~ ( subset @ SV82 @ SV195 )
| ~ ( subset @ SV195 @ SY1179 )
| ( subset @ SV82 @ SY1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(601,plain,
! [SV83: $i] :
( ( ( ~ ( in @ SV83 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(602,plain,
! [SV196: $i,SV84: $i] :
( ( ~ ( in @ SV84 @ ( setadjoin @ SV196 @ emptyset ) )
| ( in @ SV196 @ ( setadjoin @ SV84 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(603,plain,
! [SV85: $i] :
( ( ( ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV85 ) )
= $true )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(604,plain,
! [SV197: $i,SV86: $i] :
( ( ( ( setminus @ SV86 @ SV197 )
!= emptyset )
| ( subset @ SV86 @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(605,plain,
! [SV87: $i] :
( ( ( ~ ! [SY1013: $i] :
~ ( in @ SY1013 @ SV87 ) )
= $true )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(606,plain,
! [SV198: $i,SV88: $i] :
( ( ( SV88 != SV198 )
| ( in @ SV88 @ ( setadjoin @ SV198 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(607,plain,
! [SV199: $i,SV89: $i] :
( ( ~ ~ ~ ! [SY1180: $i] :
~ ~ ( ~ ( in @ SY1180 @ SV89 )
| ~ ( in @ SY1180 @ SV199 ) )
| ( ( binintersect @ SV89 @ SV199 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(608,plain,
! [SV90: $o] :
( ( ( ~ SV90 ) = $true )
| ( ( set2prop @ ( prop2set @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(609,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(611,plain,
! [SV91: $i > $o] :
( ( ( ~ ~ ! [SY1017: $i] :
~ ~ ( ~ ( SV91 @ SY1017 )
| ~ ! [SY1018: $i] :
( ~ ( SV91 @ SY1018 )
| ( SY1017 = SY1018 ) ) ) )
= $true )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(612,plain,
! [SV200: $i,SV92: $i] :
( ( ! [SY1181: $i] :
( ~ ( in @ SY1181 @ SV92 )
| ~ ~ ( in @ SY1181 @ SV200 )
| ( in @ SY1181 @ ( symdiff @ SV92 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(613,plain,
! [SV201: $i,SV93: $i] :
( ( ~ ( subset @ SV93 @ SV201 )
| ( ( setminus @ SV93 @ SV201 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(614,plain,
! [SV94: $i > $o] :
( ( ( ~ ~ ! [SY1024: $i] :
~ ~ ( ~ ( SV94 @ SY1024 )
| ~ ! [SY1025: $i] :
( ~ ( SV94 @ SY1025 )
| ( SY1024 = SY1025 ) ) ) )
= $true )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(615,plain,
! [SV202: $i > $o,SV95: $i] :
( ( ! [SY1182: $i] :
( ~ ( in @ SY1182 @ SV95 )
| ~ ( SV202 @ SY1182 )
| ( ( dsetconstr @ SV95
@ ^ [SY1183: $i] : ( SV202 @ SY1183 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(616,plain,
! [SV96: $i] :
( ( ( ~ ( in @ SV96 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(617,plain,
! [SV203: $i,SV97: $i] :
( ( ! [SY1184: $i] :
( ~ ( in @ SY1184 @ ( setminus @ SV97 @ SV203 ) )
| ~ ( in @ SY1184 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(618,plain,
! [SV98: $i,SV204: $i] :
( ( ! [SY1185: $i] :
( ~ ( in @ SY1185 @ SV204 )
| ( in @ SY1185 @ ( setadjoin @ SV98 @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(619,plain,
! [SV205: $i,SV99: $i] :
( ( ! [SY1186: $i] :
~ ( ~ ( ~ ( in @ SY1186 @ ( setadjoin @ SV99 @ SV205 ) )
| ( SY1186 = SV99 )
| ( in @ SY1186 @ SV205 ) )
| ~ ( ~ ( ( SY1186 = SV99 )
| ( in @ SY1186 @ SV205 ) )
| ( in @ SY1186 @ ( setadjoin @ SV99 @ SV205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(620,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ~ ! [SY1187: $i,SY1188: $i] :
( ( SY1187 != SY1188 )
| ~ ( ~ ( ~ ( SV100 @ SY1187 )
| ( SV206 @ SY1188 ) )
| ~ ( ~ ( SV206 @ SY1188 )
| ( SV100 @ SY1187 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(621,plain,
! [SV207: $i > $o,SV101: $i] :
( ( ~ ~ ~ ! [SY1197: $i] :
~ ~ ( ~ ( in @ SY1197 @ SV101 )
| ~ ( SV207 @ SY1197 ) )
| ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(622,plain,
! [SV208: $i,SV102: $i] :
( ( ( SV102 != SV208 )
| ( ( powerset @ SV102 )
= ( powerset @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(623,plain,
! [SV209: $i,SV103: $i] :
( ( ~ ( subset @ SV103 @ SV209 )
| ~ ( subset @ SV209 @ SV103 )
| ( SV103 = SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(624,plain,
! [SV104: $i] :
( ( ( ~ ( ( SV104 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY1053: $i] :
~ ( in @ SY1053 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(625,plain,
! [SV210: $i,SV105: $i] :
( ( ! [SY1199: $i] :
( ~ ~ ( in @ SY1199 @ ( setminus @ SV105 @ SV210 ) )
| ~ ~ ( in @ SY1199 @ SV210 )
| ~ ( in @ SY1199 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(626,plain,
! [SV106: $i > $o,SV211: $i] :
( ( ~ ( in @ SV211 @ emptyset )
| ( SV106 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(627,plain,
( ( ! [SY1200: $i] :
~ ! [SY1201: $i] :
~ ~ ( ~ ( in @ SY1201 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1202: $i] :
~ ~ ( ~ ( in @ SY1202 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1201 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1201 @ ( setadjoin @ SY1202 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[495]) ).
thf(628,plain,
! [SV107: $i,SV212: $i] :
( ( ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV212 )
| ( in @ SY1203 @ ( binunion @ SV107 @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(629,plain,
! [SV213: $i > $o,SV108: $i] :
( ( ~ ! [SY1204: $i] :
( ~ ( in @ SY1204 @ SV108 )
| ~ ( SV213 @ SY1204 ) )
| ~ ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(630,plain,
! [SV109: $i > $o] :
( ( ( ~ ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV109 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV109 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(631,plain,
! [SV214: $i,SV110: $i] :
( ( ! [SY1206: $i] :
( ~ ( subset @ SY1206 @ SV110 )
| ~ ( subset @ SY1206 @ SV214 )
| ( subset @ SY1206 @ ( binintersect @ SV110 @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(632,plain,
! [SV215: $i > $o,SV111: $i] :
( ( ! [SY1207: $i] :
( ~ ( in @ SY1207 @ SV111 )
| ~ ( ~ ( ~ ( in @ SY1207
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) )
| ( SV215 @ SY1207 ) )
| ~ ( ~ ( SV215 @ SY1207 )
| ( in @ SY1207
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(633,plain,
! [SV112: $i,SV216: $i] :
( ( ~ ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV216 )
| ( in @ SY1210 @ SV112 ) )
| ( in @ SV216 @ ( powerset @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(634,plain,
! [SV217: $i,SV113: $i] :
( ( ( SV113 != SV217 )
| ! [SY1211: $i,SY1212: $i] :
( ( SY1211 != SY1212 )
| ~ ( in @ SY1211 @ SV113 )
| ( in @ SY1212 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(635,plain,
! [SV218: $i,SV114: $i] :
( ( ! [SY1213: $i] :
( ~ ( in @ SY1213 @ ( setminus @ SV114 @ SV218 ) )
| ( in @ SY1213 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(636,plain,
! [SV219: $i > $o,SV115: $i] :
( ( ! [SY1214: $i] :
( ~ ( in @ SY1214
@ ( dsetconstr @ SV115
@ ^ [SY1215: $i] : ( SV219 @ SY1215 ) ) )
| ( in @ SY1214 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(637,plain,
! [SV220: $i,SV116: $i] :
( ( ! [SY1216: $i] :
( ~ ( subset @ SV116 @ SY1216 )
| ( subset @ SV116 @ ( setadjoin @ SV220 @ SY1216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(638,plain,
! [SV117: $i > $o] :
( ( ( ~ ~ ! [SY1084: $i] :
~ ~ ( ~ ( SV117 @ SY1084 )
| ~ ! [SY1085: $i] :
( ~ ( SV117 @ SY1085 )
| ( SY1084 = SY1085 ) ) ) )
= $true )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(639,plain,
! [SV221: $i,SV118: $i] :
( ( ( SV118 != SV221 )
| ( subset @ SV221 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(640,plain,
! [SV222: $i,SV119: $i] :
( ( ( SV119 != SV222 )
| ! [SY1217: $i,SY1218: $i] :
( ( SY1217 != SY1218 )
| ~ ( ~ ( ~ ( in @ SY1217 @ SV119 )
| ( in @ SY1218 @ SV222 ) )
| ~ ( ~ ( in @ SY1218 @ SV222 )
| ( in @ SY1217 @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(641,plain,
! [SV223: $i,SV120: $i] :
( ( ~ ( subset @ SV120 @ SV223 )
| ( in @ SV120 @ ( powerset @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(642,plain,
! [SV121: $i,SV224: $i] :
( ( ! [SY1219: $i] :
( ~ ( in @ SV224 @ SY1219 )
| ~ ( in @ SY1219 @ SV121 )
| ( in @ SV224 @ ( setunion @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(643,plain,
! [SV225: $i,SV122: $i] :
( ( ~ ( ( SV122 != SV225 ) )
| ~ ( in @ SV225 @ ( setadjoin @ SV122 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(644,plain,
! [SV123: $i,SV226: $i] :
( ( ~ ( in @ SV226 @ SV123 )
| ( in @ SV226 @ ( powerset @ ( setunion @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(645,plain,
! [SV227: $i,SV124: $i] :
( ( ( ( binintersect @ SV124 @ SV227 )
!= SV124 )
| ( subset @ SV124 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(646,plain,
! [SV228: $i,SV125: $i] :
( ( ( SV125 != SV228 )
| ( ( setunion @ SV125 )
= ( setunion @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(647,plain,
! [SV229: $i,SV126: $i] :
( ( ! [SY1220: $i] :
( ~ ~ ( in @ SY1220 @ SV126 )
| ~ ( in @ SY1220 @ ( setminus @ SV126 @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(648,plain,
! [SV230: $i > $o,SV127: $i] :
( ( ~ ~ ~ ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV127 )
| ~ ( SV230 @ SY1221 ) )
| ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(649,plain,
! [SV231: $i,SV128: $i] :
( ( ! [SY1223: $i] :
( ~ ( in @ SY1223 @ SV128 )
| ~ ( in @ SY1223 @ SV231 )
| ~ ( in @ SY1223 @ ( symdiff @ SV128 @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(650,plain,
! [SV129: $i,SV232: $i] :
( ( ~ ( ~ ( ~ ( in @ SV232 @ ( powerset @ SV129 ) )
| ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV232 )
| ( in @ SY1224 @ SV129 ) ) )
| ~ ( ~ ! [SY1225: $i] :
( ~ ( in @ SY1225 @ SV232 )
| ( in @ SY1225 @ SV129 ) )
| ( in @ SV232 @ ( powerset @ SV129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(651,plain,
! [SV130: $o] :
( ( ( ~ SV130 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(652,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(654,plain,
! [SV131: $i,SV233: $i] :
( ( ~ ( in @ SV233 @ ( powerset @ SV131 ) )
| ( subset @ SV233 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(655,plain,
! [SV234: $i,SV136: $i,SV5: $i] :
( ( ( binintersect @ SV5 @ ( binunion @ SV136 @ SV234 ) )
= ( binunion @ ( binintersect @ SV5 @ SV136 ) @ ( binintersect @ SV5 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(656,plain,
! [SV235: $i,SV25: $i,SV148: $i] :
( ( ~ ( in @ SV148 @ ( powerset @ SV25 ) )
| ~ ( in @ SV235 @ SV148 )
| ( in @ SV235 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(657,plain,
! [SV149: $i > $o,SV26: $i,SV236: $i] :
( ( ~ ( in @ SV236 @ SV26 )
| ~ ( SV149 @ SV236 )
| ( in @ SV236
@ ( dsetconstr @ SV26
@ ^ [SY1114: $i] : ( SV149 @ SY1114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(658,plain,
! [SV150: $i,SV27: $i,SV237: $i] :
( ( ~ ( in @ SV237 @ SV27 )
| ( in @ SV237 @ ( binunion @ SV27 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(659,plain,
! [SV151: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ ( setadjoin @ SV151 @ emptyset ) ) )
= $true )
| ( ( SV28 = SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(660,plain,
! [SV152: $i,SV29: $i] :
( ( ( SV29 != SV152 )
= $true )
| ( ( subset @ SV29 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(661,plain,
! [SV30: $i] :
( ( ( ~ ! [SY859: $i] :
~ ( in @ SY859 @ SV30 ) )
= $false )
| ( ( SV30 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(662,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
| ~ ! [SY1232: $i,SY1233: $i] :
( ~ ~ ( ~ ( in @ SY1232 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1233 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1232 )
| ( in @ SX4 @ SY1233 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1233 )
| ( in @ SX4 @ SY1232 ) ) ) )
| ~ ! [SY1236: $i] :
( ~ ~ ( ~ ! [SY871: $i] :
( ~ ( in @ SY871 @ SY1236 )
| ( in @ SY871 @ SV31 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1236 ) )
| ~ ! [SY1239: $i] :
~ ~ ! [SY1240: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1239 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1240 @ SY1236 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1239 )
| ~ ( in @ SX5 @ SY1236 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1239 ) )
| ( in @ SY1240 @ SY1242 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[547]) ).
thf(663,plain,
! [SV153: $i,SV32: $i,SV238: $i] :
( ( ~ ( in @ SV238 @ SV32 )
| ~ ~ ( in @ SV238 @ SV153 )
| ( SV32 != SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(664,plain,
! [SV33: $i > $o] :
( ( ( ~ ! [SY880: $i] :
~ ~ ( ~ ( SV33 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV33 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $false )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(665,plain,
! [SV154: $i,SV34: $i,SV239: $i] :
( ( ~ ( in @ SV239 @ ( binunion @ SV34 @ SV154 ) )
| ( in @ SV239 @ SV34 )
| ( in @ SV239 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(666,plain,
! [SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ! [SY1118: $i] :
( ~ ( in @ SY1118 @ SV155 )
| ~ ! [SY888: $i] :
~ ~ ( ~ ( SV35 @ SY1118 @ SY888 )
| ~ ! [SY889: $i] :
( ~ ( SV35 @ SY1118 @ SY889 )
| ( SY888 = SY889 ) ) ) ) )
= $true )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(667,plain,
! [SV36: $i > $o] :
( ( ( ~ ! [SY894: $i] :
~ ~ ( ~ ( SV36 @ SY894 )
| ~ ! [SY895: $i] :
( ~ ( SV36 @ SY895 )
| ( SY894 = SY895 ) ) ) )
= $false )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(668,plain,
! [SV156: $i,SV37: $i,SV240: $i] :
( ( ~ ( in @ SV240 @ SV37 )
| ~ ( in @ SV240 @ SV156 )
| ( in @ SV240 @ ( binintersect @ SV37 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(669,plain,
! [SV157: $i,SV38: $i,SV241: $i] :
( ( ~ ( in @ SV241 @ SV38 )
| ~ ~ ( in @ SV241 @ SV157 )
| ( in @ SV241 @ ( setminus @ SV38 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(670,plain,
! [SV39: $i,SV158: $i,SV242: $i] :
( ( ~ ( in @ SV242 @ SV158 )
| ~ ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(671,plain,
! [SV159: $i,SV40: $i,SV243: $i] :
( ( ~ ~ ( in @ SV243 @ ( setminus @ SV40 @ SV159 ) )
| ~ ( in @ SV243 @ SV40 )
| ( in @ SV243 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(672,plain,
! [SV160: $i > $o,SV41: $i] :
( ( ( ~ ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV41 )
| ( SV160 @ SY1129 ) ) )
= $true )
| ( ( ~ ! [SY1130: $i] :
~ ~ ( ~ ( in @ SY1130 @ SV41 )
| ~ ~ ( SV160 @ SY1130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(673,plain,
! [SV161: $i,SV42: $i] :
( ( ( ( binintersect @ SV42 @ SV161 )
!= SV161 )
= $true )
| ( ( subset @ SV161 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(674,plain,
! [SV162: $i,SV43: $i,SV244: $i] :
( ( ~ ( in @ SV244 @ SV43 )
| ~ ~ ( in @ SV244 @ SV162 )
| ~ ( subset @ SV43 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(675,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV44 )
| ~ ! [SY911: $i] :
( ~ ~ ( ~ ( in @ SY911 @ omega )
| ~ ( in @ SY911 @ SV44 ) )
| ( in @ ( setadjoin @ SY911 @ SY911 ) @ SV44 ) ) ) )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(676,plain,
! [SV163: $i,SV45: $i,SV245: $i] :
( ( ~ ~ ( in @ SV245 @ SV45 )
| ~ ( in @ SV245 @ SV163 )
| ( in @ SV245 @ ( symdiff @ SV45 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(677,plain,
! [SV164: $i > $o,SV46: $i] :
( ( ( ~ ~ ! [SY1133: $i] :
~ ~ ( ~ ( in @ SY1133 @ SV46 )
| ~ ~ ( SV164 @ SY1133 ) ) )
= $true )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(678,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ! [SY1135: $i,SY1136: $i] :
( ( SY1135 != SY1136 )
| ~ ( ~ ( ~ ( SV47 @ SY1135 )
| ( SV165 @ SY1136 ) )
| ~ ( ~ ( SV165 @ SY1136 )
| ( SV47 @ SY1135 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(679,plain,
! [SV48: $i > $o] :
( ( ( ~ ! [SY927: $i] :
~ ( SV48 @ SY927 ) )
= $false )
| ( ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( SV48 @ SY928 )
| ~ ( SV48 @ SY929 )
| ( SY928 = SY929 ) )
| ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(680,plain,
! [SV166: $i,SV49: $i] :
( ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV49 )
| ( in @ SY1143 @ SV166 ) ) )
= $true )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(681,plain,
! [SV50: $i,SV167: $i] :
( ( ( ~ ( in @ SV167 @ ( setunion @ SV50 ) ) )
= $true )
| ( ( ! [SY1144: $o] :
( ~ ! [SY1145: $i] :
( ~ ( in @ SV167 @ SY1145 )
| ~ ( in @ SY1145 @ SV50 )
| SY1144 )
| SY1144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(682,plain,
! [SV51: $i > $o] :
( ( ( ~ ! [SY937: $i] :
~ ~ ( ~ ( SV51 @ SY937 )
| ~ ! [SY938: $i] :
( ~ ( SV51 @ SY938 )
| ( SY937 = SY938 ) ) ) )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(683,plain,
! [SV168: $i,SV52: $i] :
( ( ( SV52 != SV168 )
= $true )
| ( ( ! [SY1146: $i > $o,SY1147: $i > $o] :
( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ SV52 )
| ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV168 )
| ( SY1148 != SY1149 )
| ~ ( ~ ( ~ ( SY1146 @ SY1148 )
| ( SY1147 @ SY1149 ) )
| ~ ( ~ ( SY1147 @ SY1149 )
| ( SY1146 @ SY1148 ) ) ) ) )
| ( ( dsetconstr @ SV52
@ ^ [SX4: $i] : ( SY1146 @ SX4 ) )
= ( dsetconstr @ SV168
@ ^ [SX4: $i] : ( SY1147 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(684,plain,
! [SV169: $i,SV53: $i,SV246: $i] :
( ( ~ ( in @ SV246 @ ( binintersect @ SV53 @ SV169 ) )
| ( in @ SV246 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(685,plain,
! [SV54: $i] :
( ( ( ~ ! [SY950: $i] :
~ ( in @ SY950 @ SV54 ) )
= $false )
| ( ( ~ ! [SY951: $i] :
~ ~ ( ~ ( in @ SY951 @ SV54 )
| ~ ~ ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ SV54 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(686,plain,
! [SV170: $i,SV55: $i] :
( ( ( ~ ! [SY1153: $i] :
( ~ ( in @ SY1153 @ SV55 )
| ( in @ SY1153 @ SV170 ) ) )
= $true )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(687,plain,
! [SV171: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV171 ) )
= $true )
| ( ( ( binintersect @ SV56 @ SV171 )
= SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(688,plain,
! [SV172: $i,SV57: $i,SV247: $i] :
( ( ! [SY1244: $o] :
( ~ ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
| ~ ( ~ ( in @ SV247 @ SV57 )
| SY1244 )
| ~ ( ~ ( in @ SV247 @ SV172 )
| SY1244 )
| SY1244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(689,plain,
! [SV173: $i,SV58: $i] :
( ( ( SV58 != SV173 )
= $true )
| ( ( ! [SY1156: $i,SY1157: $i] :
( ( SY1156 != SY1157 )
| ( ( setadjoin @ SV58 @ SY1156 )
= ( setadjoin @ SV173 @ SY1157 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(690,plain,
! [SV174: $i,SV59: $i] :
( ( ( ~ ! [SY1158: $i] :
( ~ ( in @ SY1158 @ SV59 )
| ( in @ SY1158 @ SV174 ) ) )
= $true )
| ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) )
| ( SV59 = SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(691,plain,
! [SV60: $i] :
( ( ( SV60 != emptyset )
= $false )
| ( ( ~ ! [SY965: $i] :
~ ~ ( ~ ( in @ SY965 @ SV60 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(692,plain,
! [SV175: $i > $o,SV61: $i,SV248: $i] :
( ( ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) )
| ( SV175 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(693,plain,
! [SV62: $i] :
( ( ( subset @ SV62 @ emptyset )
= $false )
| ( ( SV62 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(694,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ~ ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
| ! [SY1246: $o] :
( ~ ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| SY1246 )
| ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SY1246 )
| SY1246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(695,plain,
! [SV64: $i,SV177: $i] :
( ( ( ~ ( subset @ SV177 @ SV64 ) )
= $true )
| ( ( in @ SV177 @ ( powerset @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(696,plain,
! [SV250: $i,SV178: $i,SV65: $i] :
( ( ~ ( subset @ SV65 @ SV178 )
| ~ ~ ( in @ SV250 @ SV178 )
| ~ ( in @ SV250 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(697,plain,
! [SV179: $i,SV66: $i,SV251: $i] :
( ( ~ ( in @ SV251 @ ( setadjoin @ SV66 @ SV179 ) )
| ( SV251 = SV66 )
| ( in @ SV251 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(698,plain,
! [SV180: $i,SV67: $i,SV252: $i] :
( ( ~ ~ ( in @ SV252 @ SV67 )
| ~ ~ ( in @ SV252 @ SV180 )
| ~ ( in @ SV252 @ ( symdiff @ SV67 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(699,plain,
! [SV68: $i,SV181: $i] :
( ( ( ~ ( subset @ SV181 @ SV68 ) )
= $true )
| ( ( ( binintersect @ SV68 @ SV181 )
= SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(700,plain,
! [SV182: $i,SV69: $i,SV253: $i] :
( ( ~ ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
| ! [SY1247: $o] :
( ~ ( ( SV253 != SV69 )
| SY1247 )
| ~ ( ~ ( in @ SV253 @ SV182 )
| SY1247 )
| SY1247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(701,plain,
! [SV70: $i] :
( ( ( in @ SV70 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV70 @ SV70 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(702,plain,
! [SV183: $i,SV71: $i,SV254: $i] :
( ( ~ ( in @ SV254 @ ( setadjoin @ SV71 @ ( setadjoin @ SV183 @ emptyset ) ) )
| ( SV254 = SV71 )
| ( SV254 = SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(703,plain,
! [SV72: $i,SV184: $i] :
( ( ~ ( ~ ( in @ SV184 @ ( setunion @ SV72 ) )
| ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1170 )
| ~ ( in @ SY1170 @ SV72 ) ) )
| ~ ( ~ ~ ! [SY1171: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1171 )
| ~ ( in @ SY1171 @ SV72 ) )
| ( in @ SV184 @ ( setunion @ SV72 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(704,plain,
! [SV73: $o,SV185: $i] :
( ( ( ~ ( in @ SV185 @ ( prop2set @ SV73 ) ) )
= $true )
| ( SV73 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(706,plain,
! [SV187: $i] :
( ( ( ~ ( in @ SV187 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(707,plain,
! [SV188: $i,SV74: $i] :
( ( ( ~ ~ ( subset @ SV74 @ SV188 ) )
= $true )
| ( ( SV74 != SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(708,plain,
! [SV189: $i > $o,SV75: $i] :
( ( ( ~ ~ ! [SY1172: $i] :
~ ~ ( ~ ( in @ SY1172 @ SV75 )
| ~ ( SV189 @ SY1172 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(709,plain,
! [SV76: $i > $o] :
( ( ( ~ ! [SY993: $i] :
~ ! [SY994: $i] :
~ ( ~ ( ~ ( SV76 @ SY994 )
| ( SY994 = SY993 ) )
| ~ ( ( SY994 != SY993 )
| ( SV76 @ SY994 ) ) ) )
= $false )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(710,plain,
! [SV255: $i,SV190: $i,SV77: $i] :
( ( ~ ( subset @ SV77 @ SV190 )
| ~ ( in @ SV255 @ SV77 )
| ( in @ SV255 @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(711,plain,
! [SV191: $i,SV78: $i,SV256: $i] :
( ( ~ ( in @ SV256 @ ( binintersect @ SV78 @ SV191 ) )
| ( in @ SV256 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(712,plain,
! [SV192: $i > $o,SV79: $i] :
( ( ( ~ ~ ! [SY1176: $i] :
( ~ ( in @ SY1176 @ SV79 )
| ( SV192 @ SY1176 ) ) )
= $true )
| ( ( ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ SV79 )
| ~ ~ ( SV192 @ SY1177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(713,plain,
! [SV193: $i,SV80: $i] :
( ( ( ~ ! [SY1178: $i] :
~ ( ~ ( ~ ( in @ SY1178 @ SV80 )
| ( in @ SY1178 @ SV193 ) )
| ~ ( ~ ( in @ SY1178 @ SV193 )
| ( in @ SY1178 @ SV80 ) ) ) )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(714,plain,
! [SV194: $i,SV81: $i] :
( ( ( ~ ( subset @ SV81 @ SV194 ) )
= $true )
| ( ( subset @ ( powerset @ SV81 ) @ ( powerset @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(715,plain,
! [SV257: $i,SV195: $i,SV82: $i] :
( ( ~ ( subset @ SV82 @ SV195 )
| ~ ( subset @ SV195 @ SV257 )
| ( subset @ SV82 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(716,plain,
! [SV83: $i] :
( ( ( in @ SV83 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(717,plain,
! [SV196: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ ( setadjoin @ SV196 @ emptyset ) ) )
= $true )
| ( ( in @ SV196 @ ( setadjoin @ SV84 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(718,plain,
! [SV85: $i] :
( ( ( ! [SY1011: $i] :
~ ( in @ SY1011 @ SV85 ) )
= $false )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(719,plain,
! [SV197: $i,SV86: $i] :
( ( ( ( setminus @ SV86 @ SV197 )
!= emptyset )
= $true )
| ( ( subset @ SV86 @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(720,plain,
! [SV87: $i] :
( ( ( ! [SY1013: $i] :
~ ( in @ SY1013 @ SV87 ) )
= $false )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(721,plain,
! [SV198: $i,SV88: $i] :
( ( ( SV88 != SV198 )
= $true )
| ( ( in @ SV88 @ ( setadjoin @ SV198 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(722,plain,
! [SV199: $i,SV89: $i] :
( ( ( ~ ~ ~ ! [SY1180: $i] :
~ ~ ( ~ ( in @ SY1180 @ SV89 )
| ~ ( in @ SY1180 @ SV199 ) ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(723,plain,
! [SV90: $o] :
( ( SV90 = $false )
| ( ( set2prop @ ( prop2set @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(724,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(726,plain,
! [SV91: $i > $o] :
( ( ( ~ ! [SY1017: $i] :
~ ~ ( ~ ( SV91 @ SY1017 )
| ~ ! [SY1018: $i] :
( ~ ( SV91 @ SY1018 )
| ( SY1017 = SY1018 ) ) ) )
= $false )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(727,plain,
! [SV200: $i,SV92: $i,SV258: $i] :
( ( ~ ( in @ SV258 @ SV92 )
| ~ ~ ( in @ SV258 @ SV200 )
| ( in @ SV258 @ ( symdiff @ SV92 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(728,plain,
! [SV201: $i,SV93: $i] :
( ( ( ~ ( subset @ SV93 @ SV201 ) )
= $true )
| ( ( ( setminus @ SV93 @ SV201 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(729,plain,
! [SV94: $i > $o] :
( ( ( ~ ! [SY1024: $i] :
~ ~ ( ~ ( SV94 @ SY1024 )
| ~ ! [SY1025: $i] :
( ~ ( SV94 @ SY1025 )
| ( SY1024 = SY1025 ) ) ) )
= $false )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(730,plain,
! [SV202: $i > $o,SV95: $i,SV259: $i] :
( ( ~ ( in @ SV259 @ SV95 )
| ~ ( SV202 @ SV259 )
| ( ( dsetconstr @ SV95
@ ^ [SY1183: $i] : ( SV202 @ SY1183 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(731,plain,
! [SV96: $i] :
( ( ( in @ SV96 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(732,plain,
! [SV203: $i,SV97: $i,SV260: $i] :
( ( ~ ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
| ~ ( in @ SV260 @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(733,plain,
! [SV98: $i,SV204: $i,SV261: $i] :
( ( ~ ( in @ SV261 @ SV204 )
| ( in @ SV261 @ ( setadjoin @ SV98 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(734,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ~ ( ~ ( ~ ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
| ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
| ~ ( ~ ( ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
| ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(735,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ! [SY1187: $i,SY1188: $i] :
( ( SY1187 != SY1188 )
| ~ ( ~ ( ~ ( SV100 @ SY1187 )
| ( SV206 @ SY1188 ) )
| ~ ( ~ ( SV206 @ SY1188 )
| ( SV100 @ SY1187 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(736,plain,
! [SV207: $i > $o,SV101: $i] :
( ( ( ~ ~ ~ ! [SY1197: $i] :
~ ~ ( ~ ( in @ SY1197 @ SV101 )
| ~ ( SV207 @ SY1197 ) ) )
= $true )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(737,plain,
! [SV208: $i,SV102: $i] :
( ( ( SV102 != SV208 )
= $true )
| ( ( ( powerset @ SV102 )
= ( powerset @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(738,plain,
! [SV209: $i,SV103: $i] :
( ( ( ~ ( subset @ SV103 @ SV209 ) )
= $true )
| ( ( ~ ( subset @ SV209 @ SV103 )
| ( SV103 = SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(739,plain,
! [SV104: $i] :
( ( ( SV104 != emptyset )
= $false )
| ( ( ~ ! [SY1053: $i] :
~ ( in @ SY1053 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(740,plain,
! [SV210: $i,SV105: $i,SV263: $i] :
( ( ~ ~ ( in @ SV263 @ ( setminus @ SV105 @ SV210 ) )
| ~ ~ ( in @ SV263 @ SV210 )
| ~ ( in @ SV263 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(741,plain,
! [SV106: $i > $o,SV211: $i] :
( ( ( ~ ( in @ SV211 @ emptyset ) )
= $true )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(742,plain,
( ( ~ ! [SY1249: $i] :
~ ~ ( ~ ( in @ SY1249 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1250: $i] :
~ ~ ( ~ ( in @ SY1250 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1249 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1249 @ ( setadjoin @ SY1250 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[627]) ).
thf(743,plain,
! [SV107: $i,SV212: $i,SV264: $i] :
( ( ~ ( in @ SV264 @ SV212 )
| ( in @ SV264 @ ( binunion @ SV107 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(744,plain,
! [SV213: $i > $o,SV108: $i] :
( ( ( ~ ! [SY1204: $i] :
( ~ ( in @ SY1204 @ SV108 )
| ~ ( SV213 @ SY1204 ) ) )
= $true )
| ( ( ~ ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(745,plain,
! [SV109: $i > $o] :
( ( ( ~ ! [SY1062: $i] :
~ ~ ( ~ ( SV109 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV109 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $false )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(746,plain,
! [SV214: $i,SV110: $i,SV265: $i] :
( ( ~ ( subset @ SV265 @ SV110 )
| ~ ( subset @ SV265 @ SV214 )
| ( subset @ SV265 @ ( binintersect @ SV110 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(747,plain,
! [SV215: $i > $o,SV111: $i,SV266: $i] :
( ( ~ ( in @ SV266 @ SV111 )
| ~ ( ~ ( ~ ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) )
| ( SV215 @ SV266 ) )
| ~ ( ~ ( SV215 @ SV266 )
| ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(748,plain,
! [SV112: $i,SV216: $i] :
( ( ( ~ ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV216 )
| ( in @ SY1210 @ SV112 ) ) )
= $true )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(749,plain,
! [SV217: $i,SV113: $i] :
( ( ( SV113 != SV217 )
= $true )
| ( ( ! [SY1211: $i,SY1212: $i] :
( ( SY1211 != SY1212 )
| ~ ( in @ SY1211 @ SV113 )
| ( in @ SY1212 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(750,plain,
! [SV218: $i,SV114: $i,SV267: $i] :
( ( ~ ( in @ SV267 @ ( setminus @ SV114 @ SV218 ) )
| ( in @ SV267 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(751,plain,
! [SV219: $i > $o,SV115: $i,SV268: $i] :
( ( ~ ( in @ SV268
@ ( dsetconstr @ SV115
@ ^ [SY1215: $i] : ( SV219 @ SY1215 ) ) )
| ( in @ SV268 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(752,plain,
! [SV220: $i,SV269: $i,SV116: $i] :
( ( ~ ( subset @ SV116 @ SV269 )
| ( subset @ SV116 @ ( setadjoin @ SV220 @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(753,plain,
! [SV117: $i > $o] :
( ( ( ~ ! [SY1084: $i] :
~ ~ ( ~ ( SV117 @ SY1084 )
| ~ ! [SY1085: $i] :
( ~ ( SV117 @ SY1085 )
| ( SY1084 = SY1085 ) ) ) )
= $false )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(754,plain,
! [SV221: $i,SV118: $i] :
( ( ( SV118 != SV221 )
= $true )
| ( ( subset @ SV221 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(755,plain,
! [SV222: $i,SV119: $i] :
( ( ( SV119 != SV222 )
= $true )
| ( ( ! [SY1217: $i,SY1218: $i] :
( ( SY1217 != SY1218 )
| ~ ( ~ ( ~ ( in @ SY1217 @ SV119 )
| ( in @ SY1218 @ SV222 ) )
| ~ ( ~ ( in @ SY1218 @ SV222 )
| ( in @ SY1217 @ SV119 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(756,plain,
! [SV223: $i,SV120: $i] :
( ( ( ~ ( subset @ SV120 @ SV223 ) )
= $true )
| ( ( in @ SV120 @ ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(757,plain,
! [SV121: $i,SV270: $i,SV224: $i] :
( ( ~ ( in @ SV224 @ SV270 )
| ~ ( in @ SV270 @ SV121 )
| ( in @ SV224 @ ( setunion @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(758,plain,
! [SV225: $i,SV122: $i] :
( ( ( ~ ( ( SV122 != SV225 ) ) )
= $true )
| ( ( ~ ( in @ SV225 @ ( setadjoin @ SV122 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(759,plain,
! [SV123: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ SV123 ) )
= $true )
| ( ( in @ SV226 @ ( powerset @ ( setunion @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(760,plain,
! [SV227: $i,SV124: $i] :
( ( ( ( binintersect @ SV124 @ SV227 )
!= SV124 )
= $true )
| ( ( subset @ SV124 @ SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(761,plain,
! [SV228: $i,SV125: $i] :
( ( ( SV125 != SV228 )
= $true )
| ( ( ( setunion @ SV125 )
= ( setunion @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(762,plain,
! [SV229: $i,SV126: $i,SV271: $i] :
( ( ~ ~ ( in @ SV271 @ SV126 )
| ~ ( in @ SV271 @ ( setminus @ SV126 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(763,plain,
! [SV230: $i > $o,SV127: $i] :
( ( ( ~ ~ ~ ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV127 )
| ~ ( SV230 @ SY1221 ) ) )
= $true )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(764,plain,
! [SV231: $i,SV128: $i,SV272: $i] :
( ( ~ ( in @ SV272 @ SV128 )
| ~ ( in @ SV272 @ SV231 )
| ~ ( in @ SV272 @ ( symdiff @ SV128 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(765,plain,
! [SV129: $i,SV232: $i] :
( ( ~ ( ~ ( in @ SV232 @ ( powerset @ SV129 ) )
| ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV232 )
| ( in @ SY1224 @ SV129 ) ) )
| ~ ( ~ ! [SY1225: $i] :
( ~ ( in @ SY1225 @ SV232 )
| ( in @ SY1225 @ SV129 ) )
| ( in @ SV232 @ ( powerset @ SV129 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(766,plain,
! [SV130: $o] :
( ( SV130 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(767,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(769,plain,
! [SV131: $i,SV233: $i] :
( ( ( ~ ( in @ SV233 @ ( powerset @ SV131 ) ) )
= $true )
| ( ( subset @ SV233 @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(770,plain,
! [SV235: $i,SV25: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ~ ( in @ SV235 @ SV148 )
| ( in @ SV235 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(771,plain,
! [SV149: $i > $o,SV26: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV26 ) )
= $true )
| ( ( ~ ( SV149 @ SV236 )
| ( in @ SV236
@ ( dsetconstr @ SV26
@ ^ [SY1114: $i] : ( SV149 @ SY1114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(772,plain,
! [SV150: $i,SV27: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ SV27 ) )
= $true )
| ( ( in @ SV237 @ ( binunion @ SV27 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(773,plain,
! [SV151: $i,SV28: $i] :
( ( ( in @ SV28 @ ( setadjoin @ SV151 @ emptyset ) )
= $false )
| ( ( SV28 = SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(774,plain,
! [SV152: $i,SV29: $i] :
( ( ( SV29 = SV152 )
= $false )
| ( ( subset @ SV29 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(775,plain,
! [SV30: $i] :
( ( ( ! [SY859: $i] :
~ ( in @ SY859 @ SV30 ) )
= $true )
| ( ( SV30 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(776,plain,
! [SV31: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
| ~ ! [SY1232: $i,SY1233: $i] :
( ~ ~ ( ~ ( in @ SY1232 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1233 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1232 )
| ( in @ SX4 @ SY1233 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1233 )
| ( in @ SX4 @ SY1232 ) ) ) )
| ~ ! [SY1236: $i] :
( ~ ~ ( ~ ! [SY871: $i] :
( ~ ( in @ SY871 @ SY1236 )
| ( in @ SY871 @ SV31 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1236 ) )
| ~ ! [SY1239: $i] :
~ ~ ! [SY1240: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1239 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1240 @ SY1236 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1239 )
| ~ ( in @ SX5 @ SY1236 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1239 ) )
| ( in @ SY1240 @ SY1242 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(777,plain,
! [SV153: $i,SV32: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV32 ) )
= $true )
| ( ( ~ ~ ( in @ SV238 @ SV153 )
| ( SV32 != SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(778,plain,
! [SV33: $i > $o] :
( ( ( ! [SY880: $i] :
~ ~ ( ~ ( SV33 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV33 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[664]) ).
thf(779,plain,
! [SV154: $i,SV34: $i,SV239: $i] :
( ( ( ~ ( in @ SV239 @ ( binunion @ SV34 @ SV154 ) ) )
= $true )
| ( ( ( in @ SV239 @ SV34 )
| ( in @ SV239 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(780,plain,
! [SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1118: $i] :
( ~ ( in @ SY1118 @ SV155 )
| ~ ! [SY888: $i] :
~ ~ ( ~ ( SV35 @ SY1118 @ SY888 )
| ~ ! [SY889: $i] :
( ~ ( SV35 @ SY1118 @ SY889 )
| ( SY888 = SY889 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(781,plain,
! [SV36: $i > $o] :
( ( ( ! [SY894: $i] :
~ ~ ( ~ ( SV36 @ SY894 )
| ~ ! [SY895: $i] :
( ~ ( SV36 @ SY895 )
| ( SY894 = SY895 ) ) ) )
= $true )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(782,plain,
! [SV156: $i,SV37: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV37 ) )
= $true )
| ( ( ~ ( in @ SV240 @ SV156 )
| ( in @ SV240 @ ( binintersect @ SV37 @ SV156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(783,plain,
! [SV157: $i,SV38: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV38 ) )
= $true )
| ( ( ~ ~ ( in @ SV241 @ SV157 )
| ( in @ SV241 @ ( setminus @ SV38 @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(784,plain,
! [SV39: $i,SV158: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV158 ) )
= $true )
| ( ( ~ ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(785,plain,
! [SV159: $i,SV40: $i,SV243: $i] :
( ( ( ~ ~ ( in @ SV243 @ ( setminus @ SV40 @ SV159 ) ) )
= $true )
| ( ( ~ ( in @ SV243 @ SV40 )
| ( in @ SV243 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(786,plain,
! [SV160: $i > $o,SV41: $i] :
( ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV41 )
| ( SV160 @ SY1129 ) ) )
= $false )
| ( ( ~ ! [SY1130: $i] :
~ ~ ( ~ ( in @ SY1130 @ SV41 )
| ~ ~ ( SV160 @ SY1130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(787,plain,
! [SV161: $i,SV42: $i] :
( ( ( ( binintersect @ SV42 @ SV161 )
= SV161 )
= $false )
| ( ( subset @ SV161 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(788,plain,
! [SV162: $i,SV43: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV43 ) )
= $true )
| ( ( ~ ~ ( in @ SV244 @ SV162 )
| ~ ( subset @ SV43 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(789,plain,
! [SV44: $i] :
( ( ( ~ ( in @ emptyset @ SV44 )
| ~ ! [SY911: $i] :
( ~ ~ ( ~ ( in @ SY911 @ omega )
| ~ ( in @ SY911 @ SV44 ) )
| ( in @ ( setadjoin @ SY911 @ SY911 ) @ SV44 ) ) )
= $true )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(790,plain,
! [SV163: $i,SV45: $i,SV245: $i] :
( ( ( ~ ~ ( in @ SV245 @ SV45 ) )
= $true )
| ( ( ~ ( in @ SV245 @ SV163 )
| ( in @ SV245 @ ( symdiff @ SV45 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(791,plain,
! [SV164: $i > $o,SV46: $i] :
( ( ( ~ ! [SY1133: $i] :
~ ~ ( ~ ( in @ SY1133 @ SV46 )
| ~ ~ ( SV164 @ SY1133 ) ) )
= $false )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(792,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ! [SY1135: $i,SY1136: $i] :
( ( SY1135 != SY1136 )
| ~ ( ~ ( ~ ( SV47 @ SY1135 )
| ( SV165 @ SY1136 ) )
| ~ ( ~ ( SV165 @ SY1136 )
| ( SV47 @ SY1135 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(793,plain,
! [SV48: $i > $o] :
( ( ( ! [SY927: $i] :
~ ( SV48 @ SY927 ) )
= $true )
| ( ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( SV48 @ SY928 )
| ~ ( SV48 @ SY929 )
| ( SY928 = SY929 ) )
| ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[679]) ).
thf(794,plain,
! [SV166: $i,SV49: $i] :
( ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV49 )
| ( in @ SY1143 @ SV166 ) ) )
= $false )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(795,plain,
! [SV50: $i,SV167: $i] :
( ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false )
| ( ( ! [SY1144: $o] :
( ~ ! [SY1145: $i] :
( ~ ( in @ SV167 @ SY1145 )
| ~ ( in @ SY1145 @ SV50 )
| SY1144 )
| SY1144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(796,plain,
! [SV51: $i > $o] :
( ( ( ! [SY937: $i] :
~ ~ ( ~ ( SV51 @ SY937 )
| ~ ! [SY938: $i] :
( ~ ( SV51 @ SY938 )
| ( SY937 = SY938 ) ) ) )
= $true )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(797,plain,
! [SV168: $i,SV52: $i] :
( ( ( SV52 = SV168 )
= $false )
| ( ( ! [SY1146: $i > $o,SY1147: $i > $o] :
( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ SV52 )
| ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV168 )
| ( SY1148 != SY1149 )
| ~ ( ~ ( ~ ( SY1146 @ SY1148 )
| ( SY1147 @ SY1149 ) )
| ~ ( ~ ( SY1147 @ SY1149 )
| ( SY1146 @ SY1148 ) ) ) ) )
| ( ( dsetconstr @ SV52
@ ^ [SX4: $i] : ( SY1146 @ SX4 ) )
= ( dsetconstr @ SV168
@ ^ [SX4: $i] : ( SY1147 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(798,plain,
! [SV169: $i,SV53: $i,SV246: $i] :
( ( ( ~ ( in @ SV246 @ ( binintersect @ SV53 @ SV169 ) ) )
= $true )
| ( ( in @ SV246 @ SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(799,plain,
! [SV54: $i] :
( ( ( ! [SY950: $i] :
~ ( in @ SY950 @ SV54 ) )
= $true )
| ( ( ~ ! [SY951: $i] :
~ ~ ( ~ ( in @ SY951 @ SV54 )
| ~ ~ ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ SV54 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(800,plain,
! [SV170: $i,SV55: $i] :
( ( ( ! [SY1153: $i] :
( ~ ( in @ SY1153 @ SV55 )
| ( in @ SY1153 @ SV170 ) ) )
= $false )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(801,plain,
! [SV171: $i,SV56: $i] :
( ( ( subset @ SV56 @ SV171 )
= $false )
| ( ( ( binintersect @ SV56 @ SV171 )
= SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(802,plain,
! [SV273: $o,SV172: $i,SV57: $i,SV247: $i] :
( ( ~ ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
| ~ ( ~ ( in @ SV247 @ SV57 )
| SV273 )
| ~ ( ~ ( in @ SV247 @ SV172 )
| SV273 )
| SV273 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[688]) ).
thf(804,plain,
! [SV172: $i,SV57: $i,SV247: $i] :
( ( ~ ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
| ~ ( ~ ( in @ SV247 @ SV57 )
| $false )
| ~ ( ~ ( in @ SV247 @ SV172 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[688]) ).
thf(805,plain,
! [SV173: $i,SV58: $i] :
( ( ( SV58 = SV173 )
= $false )
| ( ( ! [SY1156: $i,SY1157: $i] :
( ( SY1156 != SY1157 )
| ( ( setadjoin @ SV58 @ SY1156 )
= ( setadjoin @ SV173 @ SY1157 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(806,plain,
! [SV174: $i,SV59: $i] :
( ( ( ! [SY1158: $i] :
( ~ ( in @ SY1158 @ SV59 )
| ( in @ SY1158 @ SV174 ) ) )
= $false )
| ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) )
| ( SV59 = SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(807,plain,
! [SV60: $i] :
( ( ( SV60 = emptyset )
= $true )
| ( ( ~ ! [SY965: $i] :
~ ~ ( ~ ( in @ SY965 @ SV60 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(808,plain,
! [SV175: $i > $o,SV61: $i,SV248: $i] :
( ( ( ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) ) )
= $true )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(809,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) ) )
= $true )
| ( ( ! [SY1246: $o] :
( ~ ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| SY1246 )
| ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SY1246 )
| SY1246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(810,plain,
! [SV64: $i,SV177: $i] :
( ( ( subset @ SV177 @ SV64 )
= $false )
| ( ( in @ SV177 @ ( powerset @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(811,plain,
! [SV250: $i,SV178: $i,SV65: $i] :
( ( ( ~ ( subset @ SV65 @ SV178 ) )
= $true )
| ( ( ~ ~ ( in @ SV250 @ SV178 )
| ~ ( in @ SV250 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(812,plain,
! [SV179: $i,SV66: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ ( setadjoin @ SV66 @ SV179 ) ) )
= $true )
| ( ( ( SV251 = SV66 )
| ( in @ SV251 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(813,plain,
! [SV180: $i,SV67: $i,SV252: $i] :
( ( ( ~ ~ ( in @ SV252 @ SV67 ) )
= $true )
| ( ( ~ ~ ( in @ SV252 @ SV180 )
| ~ ( in @ SV252 @ ( symdiff @ SV67 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(814,plain,
! [SV68: $i,SV181: $i] :
( ( ( subset @ SV181 @ SV68 )
= $false )
| ( ( ( binintersect @ SV68 @ SV181 )
= SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(815,plain,
! [SV182: $i,SV69: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) ) )
= $true )
| ( ( ! [SY1247: $o] :
( ~ ( ( SV253 != SV69 )
| SY1247 )
| ~ ( ~ ( in @ SV253 @ SV182 )
| SY1247 )
| SY1247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(816,plain,
! [SV183: $i,SV71: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ ( setadjoin @ SV71 @ ( setadjoin @ SV183 @ emptyset ) ) ) )
= $true )
| ( ( ( SV254 = SV71 )
| ( SV254 = SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(817,plain,
! [SV72: $i,SV184: $i] :
( ( ~ ( ~ ( in @ SV184 @ ( setunion @ SV72 ) )
| ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1170 )
| ~ ( in @ SY1170 @ SV72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(818,plain,
! [SV72: $i,SV184: $i] :
( ( ~ ( ~ ~ ! [SY1171: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1171 )
| ~ ( in @ SY1171 @ SV72 ) )
| ( in @ SV184 @ ( setunion @ SV72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(819,plain,
! [SV73: $o,SV185: $i] :
( ( ( in @ SV185 @ ( prop2set @ SV73 ) )
= $false )
| ( SV73 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(821,plain,
! [SV187: $i] :
( ( ( in @ SV187 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(822,plain,
! [SV188: $i,SV74: $i] :
( ( ( ~ ( subset @ SV74 @ SV188 ) )
= $false )
| ( ( SV74 != SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(823,plain,
! [SV189: $i > $o,SV75: $i] :
( ( ( ~ ! [SY1172: $i] :
~ ~ ( ~ ( in @ SY1172 @ SV75 )
| ~ ( SV189 @ SY1172 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(824,plain,
! [SV76: $i > $o] :
( ( ( ! [SY993: $i] :
~ ! [SY994: $i] :
~ ( ~ ( ~ ( SV76 @ SY994 )
| ( SY994 = SY993 ) )
| ~ ( ( SY994 != SY993 )
| ( SV76 @ SY994 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(825,plain,
! [SV255: $i,SV190: $i,SV77: $i] :
( ( ( ~ ( subset @ SV77 @ SV190 ) )
= $true )
| ( ( ~ ( in @ SV255 @ SV77 )
| ( in @ SV255 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(826,plain,
! [SV191: $i,SV78: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ ( binintersect @ SV78 @ SV191 ) ) )
= $true )
| ( ( in @ SV256 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(827,plain,
! [SV192: $i > $o,SV79: $i] :
( ( ( ~ ! [SY1176: $i] :
( ~ ( in @ SY1176 @ SV79 )
| ( SV192 @ SY1176 ) ) )
= $false )
| ( ( ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ SV79 )
| ~ ~ ( SV192 @ SY1177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(828,plain,
! [SV193: $i,SV80: $i] :
( ( ( ! [SY1178: $i] :
~ ( ~ ( ~ ( in @ SY1178 @ SV80 )
| ( in @ SY1178 @ SV193 ) )
| ~ ( ~ ( in @ SY1178 @ SV193 )
| ( in @ SY1178 @ SV80 ) ) ) )
= $false )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(829,plain,
! [SV194: $i,SV81: $i] :
( ( ( subset @ SV81 @ SV194 )
= $false )
| ( ( subset @ ( powerset @ SV81 ) @ ( powerset @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(830,plain,
! [SV257: $i,SV195: $i,SV82: $i] :
( ( ( ~ ( subset @ SV82 @ SV195 ) )
= $true )
| ( ( ~ ( subset @ SV195 @ SV257 )
| ( subset @ SV82 @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(831,plain,
! [SV83: $i,SV274: $o] :
( ( SV274 = $true )
| ( ( in @ SV83 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[716]) ).
thf(833,plain,
! [SV83: $i] :
( ( $false = $true )
| ( ( in @ SV83 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[716]) ).
thf(834,plain,
! [SV196: $i,SV84: $i] :
( ( ( in @ SV84 @ ( setadjoin @ SV196 @ emptyset ) )
= $false )
| ( ( in @ SV196 @ ( setadjoin @ SV84 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(835,plain,
! [SV85: $i] :
( ( ( ~ ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 ) )
= $false )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[718]) ).
thf(836,plain,
! [SV197: $i,SV86: $i] :
( ( ( ( setminus @ SV86 @ SV197 )
= emptyset )
= $false )
| ( ( subset @ SV86 @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(837,plain,
! [SV87: $i] :
( ( ( ~ ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 ) )
= $false )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[720]) ).
thf(838,plain,
! [SV198: $i,SV88: $i] :
( ( ( SV88 = SV198 )
= $false )
| ( ( in @ SV88 @ ( setadjoin @ SV198 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(839,plain,
! [SV199: $i,SV89: $i] :
( ( ( ~ ~ ! [SY1180: $i] :
~ ~ ( ~ ( in @ SY1180 @ SV89 )
| ~ ( in @ SY1180 @ SV199 ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(840,plain,
! [SV91: $i > $o] :
( ( ( ! [SY1017: $i] :
~ ~ ( ~ ( SV91 @ SY1017 )
| ~ ! [SY1018: $i] :
( ~ ( SV91 @ SY1018 )
| ( SY1017 = SY1018 ) ) ) )
= $true )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(841,plain,
! [SV200: $i,SV92: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ SV92 ) )
= $true )
| ( ( ~ ~ ( in @ SV258 @ SV200 )
| ( in @ SV258 @ ( symdiff @ SV92 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(842,plain,
! [SV201: $i,SV93: $i] :
( ( ( subset @ SV93 @ SV201 )
= $false )
| ( ( ( setminus @ SV93 @ SV201 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(843,plain,
! [SV94: $i > $o] :
( ( ( ! [SY1024: $i] :
~ ~ ( ~ ( SV94 @ SY1024 )
| ~ ! [SY1025: $i] :
( ~ ( SV94 @ SY1025 )
| ( SY1024 = SY1025 ) ) ) )
= $true )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(844,plain,
! [SV202: $i > $o,SV95: $i,SV259: $i] :
( ( ( ~ ( in @ SV259 @ SV95 ) )
= $true )
| ( ( ~ ( SV202 @ SV259 )
| ( ( dsetconstr @ SV95
@ ^ [SY1183: $i] : ( SV202 @ SY1183 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(845,plain,
! [SV203: $i,SV97: $i,SV260: $i] :
( ( ( ~ ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) ) )
= $true )
| ( ( ~ ( in @ SV260 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(846,plain,
! [SV98: $i,SV204: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ SV204 ) )
= $true )
| ( ( in @ SV261 @ ( setadjoin @ SV98 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(847,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ~ ( ~ ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
| ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
| ~ ( ~ ( ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
| ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(848,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1187: $i,SY1188: $i] :
( ( SY1187 != SY1188 )
| ~ ( ~ ( ~ ( SV100 @ SY1187 )
| ( SV206 @ SY1188 ) )
| ~ ( ~ ( SV206 @ SY1188 )
| ( SV100 @ SY1187 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(849,plain,
! [SV207: $i > $o,SV101: $i] :
( ( ( ~ ~ ! [SY1197: $i] :
~ ~ ( ~ ( in @ SY1197 @ SV101 )
| ~ ( SV207 @ SY1197 ) ) )
= $false )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(850,plain,
! [SV208: $i,SV102: $i] :
( ( ( SV102 = SV208 )
= $false )
| ( ( ( powerset @ SV102 )
= ( powerset @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(851,plain,
! [SV209: $i,SV103: $i] :
( ( ( subset @ SV103 @ SV209 )
= $false )
| ( ( ~ ( subset @ SV209 @ SV103 )
| ( SV103 = SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(852,plain,
! [SV104: $i] :
( ( ( SV104 = emptyset )
= $true )
| ( ( ~ ! [SY1053: $i] :
~ ( in @ SY1053 @ SV104 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(853,plain,
! [SV210: $i,SV105: $i,SV263: $i] :
( ( ( ~ ~ ( in @ SV263 @ ( setminus @ SV105 @ SV210 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV263 @ SV210 )
| ~ ( in @ SV263 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(854,plain,
! [SV106: $i > $o,SV211: $i] :
( ( ( in @ SV211 @ emptyset )
= $false )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(855,plain,
( ( ! [SY1249: $i] :
~ ~ ( ~ ( in @ SY1249 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1250: $i] :
~ ~ ( ~ ( in @ SY1250 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1249 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1249 @ ( setadjoin @ SY1250 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(856,plain,
! [SV107: $i,SV212: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ SV212 ) )
= $true )
| ( ( in @ SV264 @ ( binunion @ SV107 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(857,plain,
! [SV213: $i > $o,SV108: $i] :
( ( ( ! [SY1204: $i] :
( ~ ( in @ SY1204 @ SV108 )
| ~ ( SV213 @ SY1204 ) ) )
= $false )
| ( ( ~ ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(858,plain,
! [SV109: $i > $o] :
( ( ( ! [SY1062: $i] :
~ ~ ( ~ ( SV109 @ SY1062 )
| ~ ! [SY1063: $i] :
( ~ ( SV109 @ SY1063 )
| ( SY1062 = SY1063 ) ) ) )
= $true )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(859,plain,
! [SV214: $i,SV110: $i,SV265: $i] :
( ( ( ~ ( subset @ SV265 @ SV110 ) )
= $true )
| ( ( ~ ( subset @ SV265 @ SV214 )
| ( subset @ SV265 @ ( binintersect @ SV110 @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(860,plain,
! [SV215: $i > $o,SV111: $i,SV266: $i] :
( ( ( ~ ( in @ SV266 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) )
| ( SV215 @ SV266 ) )
| ~ ( ~ ( SV215 @ SV266 )
| ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(861,plain,
! [SV112: $i,SV216: $i] :
( ( ( ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV216 )
| ( in @ SY1210 @ SV112 ) ) )
= $false )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(862,plain,
! [SV217: $i,SV113: $i] :
( ( ( SV113 = SV217 )
= $false )
| ( ( ! [SY1211: $i,SY1212: $i] :
( ( SY1211 != SY1212 )
| ~ ( in @ SY1211 @ SV113 )
| ( in @ SY1212 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(863,plain,
! [SV218: $i,SV114: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( setminus @ SV114 @ SV218 ) ) )
= $true )
| ( ( in @ SV267 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(864,plain,
! [SV219: $i > $o,SV115: $i,SV268: $i] :
( ( ( ~ ( in @ SV268
@ ( dsetconstr @ SV115
@ ^ [SY1215: $i] : ( SV219 @ SY1215 ) ) ) )
= $true )
| ( ( in @ SV268 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(865,plain,
! [SV220: $i,SV269: $i,SV116: $i] :
( ( ( ~ ( subset @ SV116 @ SV269 ) )
= $true )
| ( ( subset @ SV116 @ ( setadjoin @ SV220 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(866,plain,
! [SV117: $i > $o] :
( ( ( ! [SY1084: $i] :
~ ~ ( ~ ( SV117 @ SY1084 )
| ~ ! [SY1085: $i] :
( ~ ( SV117 @ SY1085 )
| ( SY1084 = SY1085 ) ) ) )
= $true )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(867,plain,
! [SV221: $i,SV118: $i] :
( ( ( SV118 = SV221 )
= $false )
| ( ( subset @ SV221 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(868,plain,
! [SV222: $i,SV119: $i] :
( ( ( SV119 = SV222 )
= $false )
| ( ( ! [SY1217: $i,SY1218: $i] :
( ( SY1217 != SY1218 )
| ~ ( ~ ( ~ ( in @ SY1217 @ SV119 )
| ( in @ SY1218 @ SV222 ) )
| ~ ( ~ ( in @ SY1218 @ SV222 )
| ( in @ SY1217 @ SV119 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(869,plain,
! [SV223: $i,SV120: $i] :
( ( ( subset @ SV120 @ SV223 )
= $false )
| ( ( in @ SV120 @ ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(870,plain,
! [SV121: $i,SV270: $i,SV224: $i] :
( ( ( ~ ( in @ SV224 @ SV270 ) )
= $true )
| ( ( ~ ( in @ SV270 @ SV121 )
| ( in @ SV224 @ ( setunion @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(871,plain,
! [SV225: $i,SV122: $i] :
( ( ( SV122 != SV225 )
= $false )
| ( ( ~ ( in @ SV225 @ ( setadjoin @ SV122 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(872,plain,
! [SV123: $i,SV226: $i] :
( ( ( in @ SV226 @ SV123 )
= $false )
| ( ( in @ SV226 @ ( powerset @ ( setunion @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(873,plain,
! [SV227: $i,SV124: $i] :
( ( ( ( binintersect @ SV124 @ SV227 )
= SV124 )
= $false )
| ( ( subset @ SV124 @ SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(874,plain,
! [SV228: $i,SV125: $i] :
( ( ( SV125 = SV228 )
= $false )
| ( ( ( setunion @ SV125 )
= ( setunion @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(875,plain,
! [SV229: $i,SV126: $i,SV271: $i] :
( ( ( ~ ~ ( in @ SV271 @ SV126 ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( setminus @ SV126 @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(876,plain,
! [SV230: $i > $o,SV127: $i] :
( ( ( ~ ~ ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV127 )
| ~ ( SV230 @ SY1221 ) ) )
= $false )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(877,plain,
! [SV231: $i,SV128: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV128 ) )
= $true )
| ( ( ~ ( in @ SV272 @ SV231 )
| ~ ( in @ SV272 @ ( symdiff @ SV128 @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(878,plain,
! [SV129: $i,SV232: $i] :
( ( ~ ( ~ ( in @ SV232 @ ( powerset @ SV129 ) )
| ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV232 )
| ( in @ SY1224 @ SV129 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(879,plain,
! [SV129: $i,SV232: $i] :
( ( ~ ( ~ ! [SY1225: $i] :
( ~ ( in @ SY1225 @ SV232 )
| ( in @ SY1225 @ SV129 ) )
| ( in @ SV232 @ ( powerset @ SV129 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(880,plain,
! [SV131: $i,SV233: $i] :
( ( ( in @ SV233 @ ( powerset @ SV131 ) )
= $false )
| ( ( subset @ SV233 @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(881,plain,
! [SV235: $i,SV25: $i,SV148: $i] :
( ( ( in @ SV148 @ ( powerset @ SV25 ) )
= $false )
| ( ( ~ ( in @ SV235 @ SV148 )
| ( in @ SV235 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(882,plain,
! [SV149: $i > $o,SV26: $i,SV236: $i] :
( ( ( in @ SV236 @ SV26 )
= $false )
| ( ( ~ ( SV149 @ SV236 )
| ( in @ SV236
@ ( dsetconstr @ SV26
@ ^ [SY1114: $i] : ( SV149 @ SY1114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(883,plain,
! [SV150: $i,SV27: $i,SV237: $i] :
( ( ( in @ SV237 @ SV27 )
= $false )
| ( ( in @ SV237 @ ( binunion @ SV27 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(884,plain,
! [SV30: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV30 ) )
= $true )
| ( ( SV30 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(885,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
| ~ ! [SY1232: $i,SY1233: $i] :
( ~ ~ ( ~ ( in @ SY1232 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1233 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1232 )
| ( in @ SX4 @ SY1233 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1233 )
| ( in @ SX4 @ SY1232 ) ) ) )
| ~ ! [SY1236: $i] :
( ~ ~ ( ~ ! [SY871: $i] :
( ~ ( in @ SY871 @ SY1236 )
| ( in @ SY871 @ SV31 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1236 ) )
| ~ ! [SY1239: $i] :
~ ~ ! [SY1240: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1239 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1240 @ SY1236 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1239 )
| ~ ( in @ SX5 @ SY1236 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1239 ) )
| ( in @ SY1240 @ SY1242 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(886,plain,
! [SV153: $i,SV32: $i,SV238: $i] :
( ( ( in @ SV238 @ SV32 )
= $false )
| ( ( ~ ~ ( in @ SV238 @ SV153 )
| ( SV32 != SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(887,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ~ ( ~ ( SV33 @ SV276 )
| ~ ! [SY1254: $i] :
( ~ ( SV33 @ SY1254 )
| ( SV276 = SY1254 ) ) ) )
= $true )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(888,plain,
! [SV154: $i,SV34: $i,SV239: $i] :
( ( ( in @ SV239 @ ( binunion @ SV34 @ SV154 ) )
= $false )
| ( ( ( in @ SV239 @ SV34 )
| ( in @ SV239 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(889,plain,
! [SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
| ~ ! [SY1255: $i] :
~ ~ ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1255 )
| ~ ! [SY1256: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1256 )
| ( SY1255 = SY1256 ) ) ) )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[780]) ).
thf(890,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ~ ~ ( ~ ( SV36 @ SV277 )
| ~ ! [SY1257: $i] :
( ~ ( SV36 @ SY1257 )
| ( SV277 = SY1257 ) ) ) )
= $true )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(891,plain,
! [SV156: $i,SV37: $i,SV240: $i] :
( ( ( in @ SV240 @ SV37 )
= $false )
| ( ( ~ ( in @ SV240 @ SV156 )
| ( in @ SV240 @ ( binintersect @ SV37 @ SV156 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(892,plain,
! [SV157: $i,SV38: $i,SV241: $i] :
( ( ( in @ SV241 @ SV38 )
= $false )
| ( ( ~ ~ ( in @ SV241 @ SV157 )
| ( in @ SV241 @ ( setminus @ SV38 @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(893,plain,
! [SV39: $i,SV158: $i,SV242: $i] :
( ( ( in @ SV242 @ SV158 )
= $false )
| ( ( ~ ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(894,plain,
! [SV159: $i,SV40: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ ( setminus @ SV40 @ SV159 ) ) )
= $false )
| ( ( ~ ( in @ SV243 @ SV40 )
| ( in @ SV243 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(895,plain,
! [SV160: $i > $o,SV41: $i] :
( ( ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV41 )
| ( SV160 @ SY1129 ) ) )
= $true )
| ( ( ~ ! [SY1130: $i] :
~ ~ ( ~ ( in @ SY1130 @ SV41 )
| ~ ~ ( SV160 @ SY1130 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(896,plain,
! [SV162: $i,SV43: $i,SV244: $i] :
( ( ( in @ SV244 @ SV43 )
= $false )
| ( ( ~ ~ ( in @ SV244 @ SV162 )
| ~ ( subset @ SV43 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(897,plain,
! [SV44: $i] :
( ( ( ~ ( in @ emptyset @ SV44 ) )
= $true )
| ( ( ~ ! [SY911: $i] :
( ~ ~ ( ~ ( in @ SY911 @ omega )
| ~ ( in @ SY911 @ SV44 ) )
| ( in @ ( setadjoin @ SY911 @ SY911 ) @ SV44 ) ) )
= $true )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(898,plain,
! [SV163: $i,SV45: $i,SV245: $i] :
( ( ( ~ ( in @ SV245 @ SV45 ) )
= $false )
| ( ( ~ ( in @ SV245 @ SV163 )
| ( in @ SV245 @ ( symdiff @ SV45 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(899,plain,
! [SV164: $i > $o,SV46: $i] :
( ( ( ! [SY1133: $i] :
~ ~ ( ~ ( in @ SY1133 @ SV46 )
| ~ ~ ( SV164 @ SY1133 ) ) )
= $true )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(900,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( ! [SY1258: $i] :
( ( ( sK7_SY1135 @ SV165 @ SV47 )
!= SY1258 )
| ~ ( ~ ( ~ ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
| ( SV165 @ SY1258 ) )
| ~ ( ~ ( SV165 @ SY1258 )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[792]) ).
thf(901,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ SV278 ) )
= $true )
| ( ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( SV48 @ SY928 )
| ~ ( SV48 @ SY929 )
| ( SY928 = SY929 ) )
| ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(902,plain,
! [SV49: $i,SV166: $i] :
( ( ( ~ ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
| ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV166 ) )
= $false )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[794]) ).
thf(903,plain,
! [SV279: $o,SV50: $i,SV167: $i] :
( ( ( ~ ! [SY1259: $i] :
( ~ ( in @ SV167 @ SY1259 )
| ~ ( in @ SY1259 @ SV50 )
| SV279 )
| SV279 )
= $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[795]) ).
thf(905,plain,
! [SV50: $i,SV167: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV167 @ SX0 )
| ~ ( in @ SX0 @ SV50 )
| $false )
| $false )
= $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[795]) ).
thf(906,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( ~ ~ ( ~ ( SV51 @ SV280 )
| ~ ! [SY1260: $i] :
( ~ ( SV51 @ SY1260 )
| ( SV280 = SY1260 ) ) ) )
= $true )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(907,plain,
! [SV281: $i > $o,SV168: $i,SV52: $i] :
( ( ( ! [SY1261: $i > $o] :
( ~ ! [SY1262: $i] :
( ~ ( in @ SY1262 @ SV52 )
| ! [SY1263: $i] :
( ~ ( in @ SY1263 @ SV168 )
| ( SY1262 != SY1263 )
| ~ ( ~ ( ~ ( SV281 @ SY1262 )
| ( SY1261 @ SY1263 ) )
| ~ ( ~ ( SY1261 @ SY1263 )
| ( SV281 @ SY1262 ) ) ) ) )
| ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SX4: $i] : ( SY1261 @ SX4 ) ) ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(908,plain,
! [SV169: $i,SV53: $i,SV246: $i] :
( ( ( in @ SV246 @ ( binintersect @ SV53 @ SV169 ) )
= $false )
| ( ( in @ SV246 @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(909,plain,
! [SV54: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV54 ) )
= $true )
| ( ( ~ ! [SY951: $i] :
~ ~ ( ~ ( in @ SY951 @ SV54 )
| ~ ~ ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ SV54 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(910,plain,
! [SV55: $i,SV170: $i] :
( ( ( ~ ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
| ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV170 ) )
= $false )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[800]) ).
thf(911,plain,
! [SV273: $o,SV172: $i,SV57: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV247 @ SV57 )
| SV273 )
| ~ ( ~ ( in @ SV247 @ SV172 )
| SV273 )
| SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(913,plain,
! [SV172: $i,SV57: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV247 @ SV57 )
| $false )
| ~ ( ~ ( in @ SV247 @ SV172 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(914,plain,
! [SV173: $i,SV58: $i,SV283: $i] :
( ( ( ! [SY1266: $i] :
( ( SV283 != SY1266 )
| ( ( setadjoin @ SV58 @ SV283 )
= ( setadjoin @ SV173 @ SY1266 ) ) ) )
= $true )
| ( ( SV58 = SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(915,plain,
! [SV59: $i,SV174: $i] :
( ( ( ~ ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 )
| ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV174 ) )
= $false )
| ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) )
| ( SV59 = SV174 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[806]) ).
thf(916,plain,
! [SV60: $i] :
( ( ( ! [SY965: $i] :
~ ~ ( ~ ( in @ SY965 @ SV60 )
| ~ $true ) )
= $false )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(917,plain,
! [SV175: $i > $o,SV61: $i,SV248: $i] :
( ( ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) )
= $false )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(918,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false )
| ( ( ! [SY1246: $o] :
( ~ ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| SY1246 )
| ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SY1246 )
| SY1246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(919,plain,
! [SV250: $i,SV178: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV178 )
= $false )
| ( ( ~ ~ ( in @ SV250 @ SV178 )
| ~ ( in @ SV250 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(920,plain,
! [SV179: $i,SV66: $i,SV251: $i] :
( ( ( in @ SV251 @ ( setadjoin @ SV66 @ SV179 ) )
= $false )
| ( ( ( SV251 = SV66 )
| ( in @ SV251 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(921,plain,
! [SV180: $i,SV67: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV67 ) )
= $false )
| ( ( ~ ~ ( in @ SV252 @ SV180 )
| ~ ( in @ SV252 @ ( symdiff @ SV67 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(922,plain,
! [SV182: $i,SV69: $i,SV253: $i] :
( ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false )
| ( ( ! [SY1247: $o] :
( ~ ( ( SV253 != SV69 )
| SY1247 )
| ~ ( ~ ( in @ SV253 @ SV182 )
| SY1247 )
| SY1247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(923,plain,
! [SV183: $i,SV71: $i,SV254: $i] :
( ( ( in @ SV254 @ ( setadjoin @ SV71 @ ( setadjoin @ SV183 @ emptyset ) ) )
= $false )
| ( ( ( SV254 = SV71 )
| ( SV254 = SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(924,plain,
! [SV72: $i,SV184: $i] :
( ( ~ ( in @ SV184 @ ( setunion @ SV72 ) )
| ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1170 )
| ~ ( in @ SY1170 @ SV72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(925,plain,
! [SV72: $i,SV184: $i] :
( ( ~ ~ ! [SY1171: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1171 )
| ~ ( in @ SY1171 @ SV72 ) )
| ( in @ SV184 @ ( setunion @ SV72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(926,plain,
! [SV188: $i,SV74: $i] :
( ( ( subset @ SV74 @ SV188 )
= $true )
| ( ( SV74 != SV188 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(927,plain,
! [SV189: $i > $o,SV75: $i] :
( ( ( ! [SY1172: $i] :
~ ~ ( ~ ( in @ SY1172 @ SV75 )
| ~ ( SV189 @ SY1172 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(928,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV76 @ SY1267 )
| ( SY1267 = SV284 ) )
| ~ ( ( SY1267 != SV284 )
| ( SV76 @ SY1267 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(929,plain,
! [SV255: $i,SV190: $i,SV77: $i] :
( ( ( subset @ SV77 @ SV190 )
= $false )
| ( ( ~ ( in @ SV255 @ SV77 )
| ( in @ SV255 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(930,plain,
! [SV191: $i,SV78: $i,SV256: $i] :
( ( ( in @ SV256 @ ( binintersect @ SV78 @ SV191 ) )
= $false )
| ( ( in @ SV256 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(931,plain,
! [SV192: $i > $o,SV79: $i] :
( ( ( ! [SY1176: $i] :
( ~ ( in @ SY1176 @ SV79 )
| ( SV192 @ SY1176 ) ) )
= $true )
| ( ( ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ SV79 )
| ~ ~ ( SV192 @ SY1177 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(932,plain,
! [SV80: $i,SV193: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 ) )
| ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) ) ) )
= $false )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[828]) ).
thf(933,plain,
! [SV257: $i,SV195: $i,SV82: $i] :
( ( ( subset @ SV82 @ SV195 )
= $false )
| ( ( ~ ( subset @ SV195 @ SV257 )
| ( subset @ SV82 @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(934,plain,
! [SV85: $i] :
( ( ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(935,plain,
! [SV87: $i] :
( ( ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(936,plain,
! [SV199: $i,SV89: $i] :
( ( ( ~ ! [SY1180: $i] :
~ ~ ( ~ ( in @ SY1180 @ SV89 )
| ~ ( in @ SY1180 @ SV199 ) ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(937,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ~ ~ ( ~ ( SV91 @ SV285 )
| ~ ! [SY1268: $i] :
( ~ ( SV91 @ SY1268 )
| ( SV285 = SY1268 ) ) ) )
= $true )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(938,plain,
! [SV200: $i,SV92: $i,SV258: $i] :
( ( ( in @ SV258 @ SV92 )
= $false )
| ( ( ~ ~ ( in @ SV258 @ SV200 )
| ( in @ SV258 @ ( symdiff @ SV92 @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(939,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( ~ ~ ( ~ ( SV94 @ SV286 )
| ~ ! [SY1269: $i] :
( ~ ( SV94 @ SY1269 )
| ( SV286 = SY1269 ) ) ) )
= $true )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(940,plain,
! [SV202: $i > $o,SV95: $i,SV259: $i] :
( ( ( in @ SV259 @ SV95 )
= $false )
| ( ( ~ ( SV202 @ SV259 )
| ( ( dsetconstr @ SV95
@ ^ [SY1183: $i] : ( SV202 @ SY1183 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(941,plain,
! [SV203: $i,SV97: $i,SV260: $i] :
( ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false )
| ( ( ~ ( in @ SV260 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(942,plain,
! [SV98: $i,SV204: $i,SV261: $i] :
( ( ( in @ SV261 @ SV204 )
= $false )
| ( ( in @ SV261 @ ( setadjoin @ SV98 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(943,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ~ ( ~ ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
| ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(944,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ~ ( ~ ( ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
| ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(945,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1270: $i] :
( ( ( sK12_SY1187 @ SV206 @ SV100 )
!= SY1270 )
| ~ ( ~ ( ~ ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
| ( SV206 @ SY1270 ) )
| ~ ( ~ ( SV206 @ SY1270 )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[848]) ).
thf(946,plain,
! [SV207: $i > $o,SV101: $i] :
( ( ( ~ ! [SY1197: $i] :
~ ~ ( ~ ( in @ SY1197 @ SV101 )
| ~ ( SV207 @ SY1197 ) ) )
= $true )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(947,plain,
! [SV103: $i,SV209: $i] :
( ( ( ~ ( subset @ SV209 @ SV103 ) )
= $true )
| ( ( SV103 = SV209 )
= $true )
| ( ( subset @ SV103 @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(948,plain,
! [SV104: $i] :
( ( ( ! [SY1053: $i] :
~ ( in @ SY1053 @ SV104 ) )
= $false )
| ( ( SV104 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(949,plain,
! [SV210: $i,SV105: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ ( setminus @ SV105 @ SV210 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV263 @ SV210 )
| ~ ( in @ SV263 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(950,plain,
! [SV287: $i] :
( ( ~ ~ ( ~ ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1271: $i] :
~ ~ ( ~ ( in @ SY1271 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SY1271 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(951,plain,
! [SV107: $i,SV212: $i,SV264: $i] :
( ( ( in @ SV264 @ SV212 )
= $false )
| ( ( in @ SV264 @ ( binunion @ SV107 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(952,plain,
! [SV108: $i,SV213: $i > $o] :
( ( ( ~ ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
| ~ ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) ) )
= $false )
| ( ( ~ ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[857]) ).
thf(953,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ~ ( ~ ( SV109 @ SV288 )
| ~ ! [SY1272: $i] :
( ~ ( SV109 @ SY1272 )
| ( SV288 = SY1272 ) ) ) )
= $true )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(954,plain,
! [SV214: $i,SV110: $i,SV265: $i] :
( ( ( subset @ SV265 @ SV110 )
= $false )
| ( ( ~ ( subset @ SV265 @ SV214 )
| ( subset @ SV265 @ ( binintersect @ SV110 @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(955,plain,
! [SV215: $i > $o,SV111: $i,SV266: $i] :
( ( ( in @ SV266 @ SV111 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) )
| ( SV215 @ SV266 ) )
| ~ ( ~ ( SV215 @ SV266 )
| ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(956,plain,
! [SV216: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
| ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV112 ) )
= $false )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[861]) ).
thf(957,plain,
! [SV217: $i,SV113: $i,SV289: $i] :
( ( ( ! [SY1273: $i] :
( ( SV289 != SY1273 )
| ~ ( in @ SV289 @ SV113 )
| ( in @ SY1273 @ SV217 ) ) )
= $true )
| ( ( SV113 = SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(958,plain,
! [SV218: $i,SV114: $i,SV267: $i] :
( ( ( in @ SV267 @ ( setminus @ SV114 @ SV218 ) )
= $false )
| ( ( in @ SV267 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(959,plain,
! [SV219: $i > $o,SV115: $i,SV268: $i] :
( ( ( in @ SV268
@ ( dsetconstr @ SV115
@ ^ [SY1215: $i] : ( SV219 @ SY1215 ) ) )
= $false )
| ( ( in @ SV268 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(960,plain,
! [SV220: $i,SV269: $i,SV116: $i] :
( ( ( subset @ SV116 @ SV269 )
= $false )
| ( ( subset @ SV116 @ ( setadjoin @ SV220 @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(961,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( ~ ~ ( ~ ( SV117 @ SV290 )
| ~ ! [SY1274: $i] :
( ~ ( SV117 @ SY1274 )
| ( SV290 = SY1274 ) ) ) )
= $true )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(962,plain,
! [SV222: $i,SV119: $i,SV291: $i] :
( ( ( ! [SY1275: $i] :
( ( SV291 != SY1275 )
| ~ ( ~ ( ~ ( in @ SV291 @ SV119 )
| ( in @ SY1275 @ SV222 ) )
| ~ ( ~ ( in @ SY1275 @ SV222 )
| ( in @ SV291 @ SV119 ) ) ) ) )
= $true )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(963,plain,
! [SV121: $i,SV270: $i,SV224: $i] :
( ( ( in @ SV224 @ SV270 )
= $false )
| ( ( ~ ( in @ SV270 @ SV121 )
| ( in @ SV224 @ ( setunion @ SV121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(964,plain,
! [SV225: $i,SV122: $i] :
( ( ( SV122 = SV225 )
= $true )
| ( ( ~ ( in @ SV225 @ ( setadjoin @ SV122 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(965,plain,
! [SV229: $i,SV126: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV126 ) )
= $false )
| ( ( ~ ( in @ SV271 @ ( setminus @ SV126 @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(966,plain,
! [SV230: $i > $o,SV127: $i] :
( ( ( ~ ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV127 )
| ~ ( SV230 @ SY1221 ) ) )
= $true )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(967,plain,
! [SV231: $i,SV128: $i,SV272: $i] :
( ( ( in @ SV272 @ SV128 )
= $false )
| ( ( ~ ( in @ SV272 @ SV231 )
| ~ ( in @ SV272 @ ( symdiff @ SV128 @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(968,plain,
! [SV129: $i,SV232: $i] :
( ( ~ ( in @ SV232 @ ( powerset @ SV129 ) )
| ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV232 )
| ( in @ SY1224 @ SV129 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(969,plain,
! [SV129: $i,SV232: $i] :
( ( ~ ! [SY1225: $i] :
( ~ ( in @ SY1225 @ SV232 )
| ( in @ SY1225 @ SV129 ) )
| ( in @ SV232 @ ( powerset @ SV129 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(970,plain,
! [SV25: $i,SV148: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ SV148 ) )
= $true )
| ( ( in @ SV235 @ SV25 )
= $true )
| ( ( in @ SV148 @ ( powerset @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(971,plain,
! [SV26: $i,SV236: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ SV236 ) )
= $true )
| ( ( in @ SV236
@ ( dsetconstr @ SV26
@ ^ [SY1114: $i] : ( SV149 @ SY1114 ) ) )
= $true )
| ( ( in @ SV236 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(972,plain,
! [SV30: $i,SV275: $i] :
( ( ( in @ SV275 @ SV30 )
= $false )
| ( ( SV30 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(973,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
| ~ ! [SY1232: $i,SY1233: $i] :
( ~ ~ ( ~ ( in @ SY1232 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1233 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1232 )
| ( in @ SX4 @ SY1233 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1233 )
| ( in @ SX4 @ SY1232 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(974,plain,
! [SV31: $i] :
( ( ~ ! [SY1236: $i] :
( ~ ~ ( ~ ! [SY871: $i] :
( ~ ( in @ SY871 @ SY1236 )
| ( in @ SY871 @ SV31 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1236 ) )
| ~ ! [SY1239: $i] :
~ ~ ! [SY1240: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1239 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1240 @ SY1236 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1239 )
| ~ ( in @ SX5 @ SY1236 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1239 ) )
| ( in @ SY1240 @ SY1242 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(975,plain,
! [SV32: $i,SV153: $i,SV238: $i] :
( ( ( ~ ~ ( in @ SV238 @ SV153 ) )
= $true )
| ( ( SV32 != SV153 )
= $true )
| ( ( in @ SV238 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(976,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( ~ ( SV33 @ SV276 )
| ~ ! [SY1254: $i] :
( ~ ( SV33 @ SY1254 )
| ( SV276 = SY1254 ) ) ) )
= $false )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(977,plain,
! [SV154: $i,SV34: $i,SV239: $i] :
( ( ( in @ SV239 @ SV34 )
= $true )
| ( ( in @ SV239 @ SV154 )
= $true )
| ( ( in @ SV239 @ ( binunion @ SV34 @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(978,plain,
! [SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 ) )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(979,plain,
! [SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ! [SY1255: $i] :
~ ~ ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1255 )
| ~ ! [SY1256: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1256 )
| ( SY1255 = SY1256 ) ) ) )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(980,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ~ ( ~ ( SV36 @ SV277 )
| ~ ! [SY1257: $i] :
( ~ ( SV36 @ SY1257 )
| ( SV277 = SY1257 ) ) ) )
= $false )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(981,plain,
! [SV37: $i,SV156: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV156 ) )
= $true )
| ( ( in @ SV240 @ ( binintersect @ SV37 @ SV156 ) )
= $true )
| ( ( in @ SV240 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(982,plain,
! [SV38: $i,SV157: $i,SV241: $i] :
( ( ( ~ ~ ( in @ SV241 @ SV157 ) )
= $true )
| ( ( in @ SV241 @ ( setminus @ SV38 @ SV157 ) )
= $true )
| ( ( in @ SV241 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(983,plain,
! [SV158: $i,SV39: $i,SV242: $i] :
( ( ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
= $false )
| ( ( in @ SV242 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(984,plain,
! [SV159: $i,SV40: $i,SV243: $i] :
( ( ( in @ SV243 @ ( setminus @ SV40 @ SV159 ) )
= $true )
| ( ( ~ ( in @ SV243 @ SV40 )
| ( in @ SV243 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(985,plain,
! [SV160: $i > $o,SV41: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV41 )
| ( SV160 @ SV292 ) )
= $true )
| ( ( ~ ! [SY1130: $i] :
~ ~ ( ~ ( in @ SY1130 @ SV41 )
| ~ ~ ( SV160 @ SY1130 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(986,plain,
! [SV43: $i,SV162: $i,SV244: $i] :
( ( ( ~ ~ ( in @ SV244 @ SV162 ) )
= $true )
| ( ( ~ ( subset @ SV43 @ SV162 ) )
= $true )
| ( ( in @ SV244 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(987,plain,
! [SV44: $i] :
( ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ~ ! [SY911: $i] :
( ~ ~ ( ~ ( in @ SY911 @ omega )
| ~ ( in @ SY911 @ SV44 ) )
| ( in @ ( setadjoin @ SY911 @ SY911 ) @ SV44 ) ) )
= $true )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(988,plain,
! [SV163: $i,SV45: $i,SV245: $i] :
( ( ( in @ SV245 @ SV45 )
= $true )
| ( ( ~ ( in @ SV245 @ SV163 )
| ( in @ SV245 @ ( symdiff @ SV45 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(989,plain,
! [SV164: $i > $o,SV46: $i,SV293: $i] :
( ( ( ~ ~ ( ~ ( in @ SV293 @ SV46 )
| ~ ~ ( SV164 @ SV293 ) ) )
= $true )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(990,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( ( ( sK7_SY1135 @ SV165 @ SV47 )
!= ( sK15_SY1258 @ SV47 @ SV165 ) )
| ~ ( ~ ( ~ ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
| ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) ) )
| ~ ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[900]) ).
thf(991,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( SV48 @ SV278 )
= $false )
| ( ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( SV48 @ SY928 )
| ~ ( SV48 @ SY929 )
| ( SY928 = SY929 ) )
| ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(992,plain,
! [SV49: $i,SV166: $i] :
( ( ( ~ ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 ) )
= $false )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(993,plain,
! [SV49: $i,SV166: $i] :
( ( ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV166 )
= $false )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(994,plain,
! [SV279: $o,SV50: $i,SV167: $i] :
( ( ( ~ ! [SY1259: $i] :
( ~ ( in @ SV167 @ SY1259 )
| ~ ( in @ SY1259 @ SV50 )
| SV279 ) )
= $true )
| ( SV279 = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(996,plain,
! [SV50: $i,SV167: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV167 @ SX0 )
| ~ ( in @ SX0 @ SV50 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(997,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( ~ ( ~ ( SV51 @ SV280 )
| ~ ! [SY1260: $i] :
( ~ ( SV51 @ SY1260 )
| ( SV280 = SY1260 ) ) ) )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(998,plain,
! [SV294: $i > $o,SV281: $i > $o,SV168: $i,SV52: $i] :
( ( ( ~ ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV52 )
| ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV168 )
| ( SY1276 != SY1277 )
| ~ ( ~ ( ~ ( SV281 @ SY1276 )
| ( SV294 @ SY1277 ) )
| ~ ( ~ ( SV294 @ SY1277 )
| ( SV281 @ SY1276 ) ) ) ) )
| ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(999,plain,
! [SV54: $i,SV282: $i] :
( ( ( in @ SV282 @ SV54 )
= $false )
| ( ( ~ ! [SY951: $i] :
~ ~ ( ~ ( in @ SY951 @ SV54 )
| ~ ~ ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ SV54 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(1000,plain,
! [SV55: $i,SV170: $i] :
( ( ( ~ ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 ) )
= $false )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(1001,plain,
! [SV55: $i,SV170: $i] :
( ( ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV170 )
= $false )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(1002,plain,
! [SV273: $o,SV172: $i,SV57: $i,SV247: $i] :
( ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV247 @ SV57 )
| SV273 )
| ~ ( ~ ( in @ SV247 @ SV172 )
| SV273 )
| SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1004,plain,
! [SV172: $i,SV57: $i,SV247: $i] :
( ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV247 @ SV57 )
| $false )
| ~ ( ~ ( in @ SV247 @ SV172 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(1005,plain,
! [SV173: $i,SV58: $i,SV295: $i,SV283: $i] :
( ( ( ( SV283 != SV295 )
| ( ( setadjoin @ SV58 @ SV283 )
= ( setadjoin @ SV173 @ SV295 ) ) )
= $true )
| ( ( SV58 = SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1006,plain,
! [SV59: $i,SV174: $i] :
( ( ( ~ ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 ) )
= $false )
| ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) )
| ( SV59 = SV174 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(1007,plain,
! [SV59: $i,SV174: $i] :
( ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV174 )
= $false )
| ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) )
| ( SV59 = SV174 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(1008,plain,
! [SV60: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
| ~ $true ) )
= $false )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[916]) ).
thf(1009,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| SV296 )
| ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[918]) ).
thf(1011,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| $false )
| ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[918]) ).
thf(1012,plain,
! [SV65: $i,SV178: $i,SV250: $i] :
( ( ( ~ ~ ( in @ SV250 @ SV178 ) )
= $true )
| ( ( ~ ( in @ SV250 @ SV65 ) )
= $true )
| ( ( subset @ SV65 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1013,plain,
! [SV179: $i,SV66: $i,SV251: $i] :
( ( ( SV251 = SV66 )
= $true )
| ( ( in @ SV251 @ SV179 )
= $true )
| ( ( in @ SV251 @ ( setadjoin @ SV66 @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1014,plain,
! [SV180: $i,SV67: $i,SV252: $i] :
( ( ( in @ SV252 @ SV67 )
= $true )
| ( ( ~ ~ ( in @ SV252 @ SV180 )
| ~ ( in @ SV252 @ ( symdiff @ SV67 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(1015,plain,
! [SV182: $i,SV297: $o,SV69: $i,SV253: $i] :
( ( ( ~ ( ( SV253 != SV69 )
| SV297 )
| ~ ( ~ ( in @ SV253 @ SV182 )
| SV297 )
| SV297 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[922]) ).
thf(1017,plain,
! [SV182: $i,SV69: $i,SV253: $i] :
( ( ( ~ ( ( SV253 != SV69 )
| $false )
| ~ ( ~ ( in @ SV253 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[922]) ).
thf(1018,plain,
! [SV183: $i,SV71: $i,SV254: $i] :
( ( ( SV254 = SV71 )
= $true )
| ( ( SV254 = SV183 )
= $true )
| ( ( in @ SV254 @ ( setadjoin @ SV71 @ ( setadjoin @ SV183 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1019,plain,
! [SV72: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ ( setunion @ SV72 ) ) )
= $true )
| ( ( ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1170 )
| ~ ( in @ SY1170 @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1020,plain,
! [SV72: $i,SV184: $i] :
( ( ( ~ ~ ! [SY1171: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1171 )
| ~ ( in @ SY1171 @ SV72 ) ) )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1021,plain,
! [SV188: $i,SV74: $i] :
( ( ( SV74 = SV188 )
= $false )
| ( ( subset @ SV74 @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1022,plain,
! [SV189: $i > $o,SV75: $i,SV298: $i] :
( ( ( ~ ~ ( ~ ( in @ SV298 @ SV75 )
| ~ ( SV189 @ SV298 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1023,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ! [SY1267: $i] :
~ ( ~ ( ~ ( SV76 @ SY1267 )
| ( SY1267 = SV284 ) )
| ~ ( ( SY1267 != SV284 )
| ( SV76 @ SY1267 ) ) ) )
= $false )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1024,plain,
! [SV190: $i,SV77: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV77 ) )
= $true )
| ( ( in @ SV255 @ SV190 )
= $true )
| ( ( subset @ SV77 @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1025,plain,
! [SV192: $i > $o,SV79: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV79 )
| ( SV192 @ SV299 ) )
= $true )
| ( ( ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ SV79 )
| ~ ~ ( SV192 @ SY1177 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1026,plain,
! [SV80: $i,SV193: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 ) )
| ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(1027,plain,
! [SV82: $i,SV257: $i,SV195: $i] :
( ( ( ~ ( subset @ SV195 @ SV257 ) )
= $true )
| ( ( subset @ SV82 @ SV257 )
= $true )
| ( ( subset @ SV82 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1028,plain,
! [SV199: $i,SV89: $i] :
( ( ( ! [SY1180: $i] :
~ ~ ( ~ ( in @ SY1180 @ SV89 )
| ~ ( in @ SY1180 @ SV199 ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1029,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( SV91 @ SV285 )
| ~ ! [SY1268: $i] :
( ~ ( SV91 @ SY1268 )
| ( SV285 = SY1268 ) ) ) )
= $false )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1030,plain,
! [SV92: $i,SV200: $i,SV258: $i] :
( ( ( ~ ~ ( in @ SV258 @ SV200 ) )
= $true )
| ( ( in @ SV258 @ ( symdiff @ SV92 @ SV200 ) )
= $true )
| ( ( in @ SV258 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1031,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( ~ ( ~ ( SV94 @ SV286 )
| ~ ! [SY1269: $i] :
( ~ ( SV94 @ SY1269 )
| ( SV286 = SY1269 ) ) ) )
= $false )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1032,plain,
! [SV95: $i,SV259: $i,SV202: $i > $o] :
( ( ( ~ ( SV202 @ SV259 ) )
= $true )
| ( ( ( dsetconstr @ SV95
@ ^ [SY1183: $i] : ( SV202 @ SY1183 ) )
!= emptyset )
= $true )
| ( ( in @ SV259 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1033,plain,
! [SV97: $i,SV203: $i,SV260: $i] :
( ( ( in @ SV260 @ SV203 )
= $false )
| ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(1034,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ~ ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
| ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1035,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ~ ( ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
| ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(1036,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ( ( sK12_SY1187 @ SV206 @ SV100 )
!= ( sK17_SY1270 @ SV100 @ SV206 ) )
| ~ ( ~ ( ~ ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
| ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) ) )
| ~ ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[945]) ).
thf(1037,plain,
! [SV207: $i > $o,SV101: $i] :
( ( ( ! [SY1197: $i] :
~ ~ ( ~ ( in @ SY1197 @ SV101 )
| ~ ( SV207 @ SY1197 ) ) )
= $false )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1038,plain,
! [SV103: $i,SV209: $i] :
( ( ( subset @ SV209 @ SV103 )
= $false )
| ( ( SV103 = SV209 )
= $true )
| ( ( subset @ SV103 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1039,plain,
! [SV104: $i] :
( ( ( ~ ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 ) )
= $false )
| ( ( SV104 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[948]) ).
thf(1040,plain,
! [SV210: $i,SV105: $i,SV263: $i] :
( ( ( in @ SV263 @ ( setminus @ SV105 @ SV210 ) )
= $true )
| ( ( ~ ~ ( in @ SV263 @ SV210 )
| ~ ( in @ SV263 @ SV105 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1041,plain,
! [SV287: $i] :
( ( ~ ( ~ ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1271: $i] :
~ ~ ( ~ ( in @ SY1271 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SY1271 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1042,plain,
! [SV108: $i,SV213: $i > $o] :
( ( ( ~ ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 ) )
= $false )
| ( ( ~ ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1043,plain,
! [SV108: $i,SV213: $i > $o] :
( ( ( ~ ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) ) )
= $false )
| ( ( ~ ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1044,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( ~ ( SV109 @ SV288 )
| ~ ! [SY1272: $i] :
( ~ ( SV109 @ SY1272 )
| ( SV288 = SY1272 ) ) ) )
= $false )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1045,plain,
! [SV110: $i,SV214: $i,SV265: $i] :
( ( ( ~ ( subset @ SV265 @ SV214 ) )
= $true )
| ( ( subset @ SV265 @ ( binintersect @ SV110 @ SV214 ) )
= $true )
| ( ( subset @ SV265 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1046,plain,
! [SV215: $i > $o,SV111: $i,SV266: $i] :
( ( ( ~ ( ~ ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) )
| ( SV215 @ SV266 ) )
| ~ ( ~ ( SV215 @ SV266 )
| ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) ) ) )
= $false )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1047,plain,
! [SV216: $i,SV112: $i] :
( ( ( ~ ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 ) )
= $false )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(1048,plain,
! [SV216: $i,SV112: $i] :
( ( ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV112 )
= $false )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(1049,plain,
! [SV217: $i,SV113: $i,SV300: $i,SV289: $i] :
( ( ( ( SV289 != SV300 )
| ~ ( in @ SV289 @ SV113 )
| ( in @ SV300 @ SV217 ) )
= $true )
| ( ( SV113 = SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1050,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( ~ ( ~ ( SV117 @ SV290 )
| ~ ! [SY1274: $i] :
( ~ ( SV117 @ SY1274 )
| ( SV290 = SY1274 ) ) ) )
= $false )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1051,plain,
! [SV222: $i,SV119: $i,SV301: $i,SV291: $i] :
( ( ( ( SV291 != SV301 )
| ~ ( ~ ( ~ ( in @ SV291 @ SV119 )
| ( in @ SV301 @ SV222 ) )
| ~ ( ~ ( in @ SV301 @ SV222 )
| ( in @ SV291 @ SV119 ) ) ) )
= $true )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1052,plain,
! [SV224: $i,SV121: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ SV121 ) )
= $true )
| ( ( in @ SV224 @ ( setunion @ SV121 ) )
= $true )
| ( ( in @ SV224 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1053,plain,
! [SV122: $i,SV225: $i] :
( ( ( in @ SV225 @ ( setadjoin @ SV122 @ emptyset ) )
= $false )
| ( ( SV122 = SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1054,plain,
! [SV229: $i,SV126: $i,SV271: $i] :
( ( ( in @ SV271 @ SV126 )
= $true )
| ( ( ~ ( in @ SV271 @ ( setminus @ SV126 @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1055,plain,
! [SV230: $i > $o,SV127: $i] :
( ( ( ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV127 )
| ~ ( SV230 @ SY1221 ) ) )
= $false )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1056,plain,
! [SV128: $i,SV231: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV231 ) )
= $true )
| ( ( ~ ( in @ SV272 @ ( symdiff @ SV128 @ SV231 ) ) )
= $true )
| ( ( in @ SV272 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1057,plain,
! [SV129: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ ( powerset @ SV129 ) ) )
= $true )
| ( ( ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV232 )
| ( in @ SY1224 @ SV129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1058,plain,
! [SV129: $i,SV232: $i] :
( ( ( ~ ! [SY1225: $i] :
( ~ ( in @ SY1225 @ SV232 )
| ( in @ SY1225 @ SV129 ) ) )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1059,plain,
! [SV25: $i,SV148: $i,SV235: $i] :
( ( ( in @ SV235 @ SV148 )
= $false )
| ( ( in @ SV235 @ SV25 )
= $true )
| ( ( in @ SV148 @ ( powerset @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1060,plain,
! [SV26: $i,SV236: $i,SV149: $i > $o] :
( ( ( SV149 @ SV236 )
= $false )
| ( ( in @ SV236
@ ( dsetconstr @ SV26
@ ^ [SY1114: $i] : ( SV149 @ SY1114 ) ) )
= $true )
| ( ( in @ SV236 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1061,plain,
! [SV275: $i,SV30: $i] :
( ( ( SV30 = emptyset )
= $false )
| ( ( in @ SV275 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1062,plain,
! [SV31: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
| ~ ! [SY1232: $i,SY1233: $i] :
( ~ ~ ( ~ ( in @ SY1232 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1233 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1232 )
| ( in @ SX4 @ SY1233 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1233 )
| ( in @ SX4 @ SY1232 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1063,plain,
! [SV31: $i] :
( ( ! [SY1236: $i] :
( ~ ~ ( ~ ! [SY871: $i] :
( ~ ( in @ SY871 @ SY1236 )
| ( in @ SY871 @ SV31 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1236 ) )
| ~ ! [SY1239: $i] :
~ ~ ! [SY1240: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1239 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1240 @ SY1236 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1239 )
| ~ ( in @ SX5 @ SY1236 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1239 ) )
| ( in @ SY1240 @ SY1242 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1064,plain,
! [SV32: $i,SV153: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV153 ) )
= $false )
| ( ( SV32 != SV153 )
= $true )
| ( ( in @ SV238 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1065,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV276 )
| ~ ! [SY1254: $i] :
( ~ ( SV33 @ SY1254 )
| ( SV276 = SY1254 ) ) )
= $true )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1066,plain,
! [SV155: $i,SV35: $i > $i > $o] :
( ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1067,plain,
! [SV155: $i,SV35: $i > $i > $o] :
( ( ( ! [SY1255: $i] :
~ ~ ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1255 )
| ~ ! [SY1256: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1256 )
| ( SY1255 = SY1256 ) ) ) )
= $true )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1068,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV277 )
| ~ ! [SY1257: $i] :
( ~ ( SV36 @ SY1257 )
| ( SV277 = SY1257 ) ) )
= $true )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1069,plain,
! [SV37: $i,SV156: $i,SV240: $i] :
( ( ( in @ SV240 @ SV156 )
= $false )
| ( ( in @ SV240 @ ( binintersect @ SV37 @ SV156 ) )
= $true )
| ( ( in @ SV240 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1070,plain,
! [SV38: $i,SV157: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV157 ) )
= $false )
| ( ( in @ SV241 @ ( setminus @ SV38 @ SV157 ) )
= $true )
| ( ( in @ SV241 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1071,plain,
! [SV159: $i,SV40: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV40 ) )
= $true )
| ( ( in @ SV243 @ SV159 )
= $true )
| ( ( in @ SV243 @ ( setminus @ SV40 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1072,plain,
! [SV160: $i > $o,SV41: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV41 ) )
= $true )
| ( ( SV160 @ SV292 )
= $true )
| ( ( ~ ! [SY1130: $i] :
~ ~ ( ~ ( in @ SY1130 @ SV41 )
| ~ ~ ( SV160 @ SY1130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1073,plain,
! [SV43: $i,SV162: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV162 ) )
= $false )
| ( ( ~ ( subset @ SV43 @ SV162 ) )
= $true )
| ( ( in @ SV244 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1074,plain,
! [SV44: $i] :
( ( ( ! [SY911: $i] :
( ~ ~ ( ~ ( in @ SY911 @ omega )
| ~ ( in @ SY911 @ SV44 ) )
| ( in @ ( setadjoin @ SY911 @ SY911 ) @ SV44 ) ) )
= $false )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1075,plain,
! [SV45: $i,SV163: $i,SV245: $i] :
( ( ( ~ ( in @ SV245 @ SV163 ) )
= $true )
| ( ( in @ SV245 @ ( symdiff @ SV45 @ SV163 ) )
= $true )
| ( ( in @ SV245 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1076,plain,
! [SV164: $i > $o,SV46: $i,SV293: $i] :
( ( ( ~ ( ~ ( in @ SV293 @ SV46 )
| ~ ~ ( SV164 @ SV293 ) ) )
= $false )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1077,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( ( sK7_SY1135 @ SV165 @ SV47 )
!= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1078,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
| ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) ) )
| ~ ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1079,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ! [SY928: $i,SY929: $i] :
( ~ ( SV48 @ SY928 )
| ~ ( SV48 @ SY929 )
| ( SY928 = SY929 ) ) )
= $true )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1080,plain,
! [SV49: $i,SV166: $i] :
( ( ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
= $true )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1081,plain,
! [SV279: $o,SV50: $i,SV167: $i] :
( ( ( ! [SY1259: $i] :
( ~ ( in @ SV167 @ SY1259 )
| ~ ( in @ SY1259 @ SV50 )
| SV279 ) )
= $false )
| ( SV279 = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1083,plain,
! [SV50: $i,SV167: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV167 @ SX0 )
| ~ ( in @ SX0 @ SV50 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1084,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV280 )
| ~ ! [SY1260: $i] :
( ~ ( SV51 @ SY1260 )
| ( SV280 = SY1260 ) ) )
= $true )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1085,plain,
! [SV294: $i > $o,SV281: $i > $o,SV168: $i,SV52: $i] :
( ( ( ~ ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV52 )
| ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV168 )
| ( SY1276 != SY1277 )
| ~ ( ~ ( ~ ( SV281 @ SY1276 )
| ( SV294 @ SY1277 ) )
| ~ ( ~ ( SV294 @ SY1277 )
| ( SV281 @ SY1276 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1086,plain,
! [SV282: $i,SV54: $i] :
( ( ( ! [SY951: $i] :
~ ~ ( ~ ( in @ SY951 @ SV54 )
| ~ ~ ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ SV54 ) ) ) )
= $false )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1087,plain,
! [SV55: $i,SV170: $i] :
( ( ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
= $true )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1088,plain,
! [SV172: $i,SV273: $o,SV57: $i,SV247: $i] :
( ( ( ~ ( ~ ( in @ SV247 @ SV57 )
| SV273 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| SV273 )
| SV273 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1090,plain,
! [SV172: $i,SV57: $i,SV247: $i] :
( ( ( ~ ( ~ ( in @ SV247 @ SV57 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| $false )
| $false )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1091,plain,
! [SV173: $i,SV58: $i,SV295: $i,SV283: $i] :
( ( ( SV283 != SV295 )
= $true )
| ( ( ( setadjoin @ SV58 @ SV283 )
= ( setadjoin @ SV173 @ SV295 ) )
= $true )
| ( ( SV58 = SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1092,plain,
! [SV59: $i,SV174: $i] :
( ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 )
= $true )
| ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) )
| ( SV59 = SV174 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1093,plain,
! [SV59: $i,SV174: $i] :
( ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) ) )
= $true )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1094,plain,
! [SV60: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
| ~ $true ) )
= $true )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1095,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| SV296 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1097,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1098,plain,
! [SV65: $i,SV178: $i,SV250: $i] :
( ( ( ~ ( in @ SV250 @ SV178 ) )
= $false )
| ( ( ~ ( in @ SV250 @ SV65 ) )
= $true )
| ( ( subset @ SV65 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1099,plain,
! [SV67: $i,SV180: $i,SV252: $i] :
( ( ( ~ ~ ( in @ SV252 @ SV180 ) )
= $true )
| ( ( ~ ( in @ SV252 @ ( symdiff @ SV67 @ SV180 ) ) )
= $true )
| ( ( in @ SV252 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1100,plain,
! [SV182: $i,SV297: $o,SV69: $i,SV253: $i] :
( ( ( ~ ( ( SV253 != SV69 )
| SV297 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| SV297 )
| SV297 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1102,plain,
! [SV182: $i,SV69: $i,SV253: $i] :
( ( ( ~ ( ( SV253 != SV69 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1103,plain,
! [SV72: $i,SV184: $i] :
( ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false )
| ( ( ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1170 )
| ~ ( in @ SY1170 @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1104,plain,
! [SV72: $i,SV184: $i] :
( ( ( ~ ! [SY1171: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1171 )
| ~ ( in @ SY1171 @ SV72 ) ) )
= $false )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1105,plain,
! [SV189: $i > $o,SV75: $i,SV298: $i] :
( ( ( ~ ( ~ ( in @ SV298 @ SV75 )
| ~ ( SV189 @ SV298 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1106,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
| ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 ) )
| ~ ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) ) ) )
= $false )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1023]) ).
thf(1107,plain,
! [SV190: $i,SV77: $i,SV255: $i] :
( ( ( in @ SV255 @ SV77 )
= $false )
| ( ( in @ SV255 @ SV190 )
= $true )
| ( ( subset @ SV77 @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1108,plain,
! [SV192: $i > $o,SV79: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV79 ) )
= $true )
| ( ( SV192 @ SV299 )
= $true )
| ( ( ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ SV79 )
| ~ ~ ( SV192 @ SY1177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1109,plain,
! [SV80: $i,SV193: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1110,plain,
! [SV82: $i,SV257: $i,SV195: $i] :
( ( ( subset @ SV195 @ SV257 )
= $false )
| ( ( subset @ SV82 @ SV257 )
= $true )
| ( ( subset @ SV82 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1111,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
| ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1028]) ).
thf(1112,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV285 )
| ~ ! [SY1268: $i] :
( ~ ( SV91 @ SY1268 )
| ( SV285 = SY1268 ) ) )
= $true )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1113,plain,
! [SV92: $i,SV200: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ SV200 ) )
= $false )
| ( ( in @ SV258 @ ( symdiff @ SV92 @ SV200 ) )
= $true )
| ( ( in @ SV258 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1114,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ SV286 )
| ~ ! [SY1269: $i] :
( ~ ( SV94 @ SY1269 )
| ( SV286 = SY1269 ) ) )
= $true )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1115,plain,
! [SV95: $i,SV259: $i,SV202: $i > $o] :
( ( ( SV202 @ SV259 )
= $false )
| ( ( ( dsetconstr @ SV95
@ ^ [SY1183: $i] : ( SV202 @ SY1183 ) )
!= emptyset )
= $true )
| ( ( in @ SV259 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1116,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ( ~ ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) ) )
= $true )
| ( ( ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1117,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ( ~ ( ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) ) )
= $true )
| ( ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1118,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ( sK12_SY1187 @ SV206 @ SV100 )
!= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1119,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
| ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) ) )
| ~ ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1120,plain,
! [SV101: $i,SV207: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 )
| ~ ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) ) ) )
= $false )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1037]) ).
thf(1121,plain,
! [SV104: $i] :
( ( ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1122,plain,
! [SV105: $i,SV210: $i,SV263: $i] :
( ( ( ~ ~ ( in @ SV263 @ SV210 ) )
= $true )
| ( ( ~ ( in @ SV263 @ SV105 ) )
= $true )
| ( ( in @ SV263 @ ( setminus @ SV105 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1123,plain,
! [SV287: $i] :
( ( ~ ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1271: $i] :
~ ~ ( ~ ( in @ SY1271 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SY1271 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1124,plain,
! [SV108: $i,SV213: $i > $o] :
( ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true )
| ( ( ~ ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1125,plain,
! [SV108: $i,SV213: $i > $o] :
( ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true )
| ( ( ~ ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1126,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ SV288 )
| ~ ! [SY1272: $i] :
( ~ ( SV109 @ SY1272 )
| ( SV288 = SY1272 ) ) )
= $true )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1127,plain,
! [SV110: $i,SV214: $i,SV265: $i] :
( ( ( subset @ SV265 @ SV214 )
= $false )
| ( ( subset @ SV265 @ ( binintersect @ SV110 @ SV214 ) )
= $true )
| ( ( subset @ SV265 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1128,plain,
! [SV215: $i > $o,SV111: $i,SV266: $i] :
( ( ( ~ ( ~ ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) )
| ( SV215 @ SV266 ) ) )
= $false )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1129,plain,
! [SV111: $i,SV266: $i,SV215: $i > $o] :
( ( ( ~ ( ~ ( SV215 @ SV266 )
| ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) ) ) )
= $false )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1130,plain,
! [SV216: $i,SV112: $i] :
( ( ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
= $true )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1131,plain,
! [SV217: $i,SV113: $i,SV300: $i,SV289: $i] :
( ( ( SV289 != SV300 )
= $true )
| ( ( ~ ( in @ SV289 @ SV113 )
| ( in @ SV300 @ SV217 ) )
= $true )
| ( ( SV113 = SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1132,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ SV290 )
| ~ ! [SY1274: $i] :
( ~ ( SV117 @ SY1274 )
| ( SV290 = SY1274 ) ) )
= $true )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1050]) ).
thf(1133,plain,
! [SV222: $i,SV119: $i,SV301: $i,SV291: $i] :
( ( ( SV291 != SV301 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV291 @ SV119 )
| ( in @ SV301 @ SV222 ) )
| ~ ( ~ ( in @ SV301 @ SV222 )
| ( in @ SV291 @ SV119 ) ) ) )
= $true )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1134,plain,
! [SV224: $i,SV121: $i,SV270: $i] :
( ( ( in @ SV270 @ SV121 )
= $false )
| ( ( in @ SV224 @ ( setunion @ SV121 ) )
= $true )
| ( ( in @ SV224 @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1135,plain,
! [SV229: $i,SV126: $i,SV271: $i] :
( ( ( in @ SV271 @ ( setminus @ SV126 @ SV229 ) )
= $false )
| ( ( in @ SV271 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1136,plain,
! [SV127: $i,SV230: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 )
| ~ ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) ) ) )
= $false )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1055]) ).
thf(1137,plain,
! [SV128: $i,SV231: $i,SV272: $i] :
( ( ( in @ SV272 @ SV231 )
= $false )
| ( ( ~ ( in @ SV272 @ ( symdiff @ SV128 @ SV231 ) ) )
= $true )
| ( ( in @ SV272 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1138,plain,
! [SV129: $i,SV232: $i] :
( ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $false )
| ( ( ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV232 )
| ( in @ SY1224 @ SV129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1139,plain,
! [SV129: $i,SV232: $i] :
( ( ( ! [SY1225: $i] :
( ~ ( in @ SY1225 @ SV232 )
| ( in @ SY1225 @ SV129 ) ) )
= $false )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1140,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
| ~ ! [SY1232: $i,SY1233: $i] :
( ~ ~ ( ~ ( in @ SY1232 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1233 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1232 )
| ( in @ SX4 @ SY1233 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1233 )
| ( in @ SX4 @ SY1232 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1141,plain,
! [SV31: $i,SV302: $i] :
( ( ~ ~ ( ~ ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV302 )
| ( in @ SY1280 @ SV31 ) )
| ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
| ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1142,plain,
! [SV32: $i,SV153: $i,SV238: $i] :
( ( ( in @ SV238 @ SV153 )
= $true )
| ( ( SV32 != SV153 )
= $true )
| ( ( in @ SV238 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1143,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV276 ) )
= $true )
| ( ( ~ ! [SY1254: $i] :
( ~ ( SV33 @ SY1254 )
| ( SV276 = SY1254 ) ) )
= $true )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1144,plain,
! [SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1145,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
| ~ ! [SY1287: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1287 )
| ( SV303 = SY1287 ) ) ) )
= $true )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1146,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV277 ) )
= $true )
| ( ( ~ ! [SY1257: $i] :
( ~ ( SV36 @ SY1257 )
| ( SV277 = SY1257 ) ) )
= $true )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1147,plain,
! [SV38: $i,SV157: $i,SV241: $i] :
( ( ( in @ SV241 @ SV157 )
= $true )
| ( ( in @ SV241 @ ( setminus @ SV38 @ SV157 ) )
= $true )
| ( ( in @ SV241 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1148,plain,
! [SV159: $i,SV40: $i,SV243: $i] :
( ( ( in @ SV243 @ SV40 )
= $false )
| ( ( in @ SV243 @ SV159 )
= $true )
| ( ( in @ SV243 @ ( setminus @ SV40 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1149,plain,
! [SV160: $i > $o,SV41: $i,SV292: $i] :
( ( ( in @ SV292 @ SV41 )
= $false )
| ( ( SV160 @ SV292 )
= $true )
| ( ( ~ ! [SY1130: $i] :
~ ~ ( ~ ( in @ SY1130 @ SV41 )
| ~ ~ ( SV160 @ SY1130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1150,plain,
! [SV43: $i,SV162: $i,SV244: $i] :
( ( ( in @ SV244 @ SV162 )
= $true )
| ( ( ~ ( subset @ SV43 @ SV162 ) )
= $true )
| ( ( in @ SV244 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1151,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY911 @ SV44 ) @ omega )
| ~ ( in @ ( sK23_SY911 @ SV44 ) @ SV44 ) )
| ( in @ ( setadjoin @ ( sK23_SY911 @ SV44 ) @ ( sK23_SY911 @ SV44 ) ) @ SV44 ) )
= $false )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1074]) ).
thf(1152,plain,
! [SV45: $i,SV163: $i,SV245: $i] :
( ( ( in @ SV245 @ SV163 )
= $false )
| ( ( in @ SV245 @ ( symdiff @ SV45 @ SV163 ) )
= $true )
| ( ( in @ SV245 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1153,plain,
! [SV164: $i > $o,SV46: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ SV46 )
| ~ ~ ( SV164 @ SV293 ) )
= $true )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1154,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1155,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
| ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) ) )
| ~ ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1156,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ! [SY928: $i,SY929: $i] :
( ~ ( SV48 @ SY928 )
| ~ ( SV48 @ SY929 )
| ( SY928 = SY929 ) ) )
= $false )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1157,plain,
! [SV50: $i,SV279: $o,SV167: $i] :
( ( ( ~ ( in @ SV167 @ ( sK24_SY1259 @ SV279 @ SV50 @ SV167 ) )
| ~ ( in @ ( sK24_SY1259 @ SV279 @ SV50 @ SV167 ) @ SV50 )
| SV279 )
= $false )
| ( SV279 = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1081]) ).
thf(1159,plain,
! [SV50: $i,SV167: $i] :
( ( ( ~ ( in @ SV167 @ ( sK26_SX0 @ SV50 @ SV167 ) )
| ~ ( in @ ( sK26_SX0 @ SV50 @ SV167 ) @ SV50 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1083]) ).
thf(1160,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV280 ) )
= $true )
| ( ( ~ ! [SY1260: $i] :
( ~ ( SV51 @ SY1260 )
| ( SV280 = SY1260 ) ) )
= $true )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1161,plain,
! [SV294: $i > $o,SV281: $i > $o,SV168: $i,SV52: $i] :
( ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV52 )
| ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV168 )
| ( SY1276 != SY1277 )
| ~ ( ~ ( ~ ( SV281 @ SY1276 )
| ( SV294 @ SY1277 ) )
| ~ ( ~ ( SV294 @ SY1277 )
| ( SV281 @ SY1276 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1162,plain,
! [SV54: $i,SV282: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY951 @ SV282 @ SV54 ) @ SV54 )
| ~ ~ ~ ! [SY1288: $i] :
~ ~ ( ~ ( in @ SY1288 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SY1288 @ SV54 ) ) ) )
= $false )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1086]) ).
thf(1163,plain,
! [SV172: $i,SV273: $o,SV57: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV57 )
| SV273 )
= $false )
| ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| SV273 )
| SV273 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1165,plain,
! [SV172: $i,SV57: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV57 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| $false )
| $false )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1166,plain,
! [SV173: $i,SV58: $i,SV295: $i,SV283: $i] :
( ( ( SV283 = SV295 )
= $false )
| ( ( ( setadjoin @ SV58 @ SV283 )
= ( setadjoin @ SV173 @ SV295 ) )
= $true )
| ( ( SV58 = SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1167,plain,
! [SV59: $i,SV174: $i] :
( ( ( ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) ) )
= $true )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1168,plain,
! [SV59: $i,SV174: $i] :
( ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) ) )
= $false )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1169,plain,
! [SV60: $i] :
( ( ( ~ ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
| ~ $true )
= $false )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1170,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| SV296 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1172,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV63 )
| ~ ~ ( in @ SV249 @ SV176 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1173,plain,
! [SV65: $i,SV178: $i,SV250: $i] :
( ( ( in @ SV250 @ SV178 )
= $true )
| ( ( ~ ( in @ SV250 @ SV65 ) )
= $true )
| ( ( subset @ SV65 @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1174,plain,
! [SV67: $i,SV180: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV180 ) )
= $false )
| ( ( ~ ( in @ SV252 @ ( symdiff @ SV67 @ SV180 ) ) )
= $true )
| ( ( in @ SV252 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1175,plain,
! [SV182: $i,SV297: $o,SV69: $i,SV253: $i] :
( ( ( ( SV253 != SV69 )
| SV297 )
= $false )
| ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| SV297 )
| SV297 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1177,plain,
! [SV182: $i,SV69: $i,SV253: $i] :
( ( ( ( SV253 != SV69 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1178,plain,
! [SV72: $i,SV184: $i] :
( ( ( ! [SY1170: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1170 )
| ~ ( in @ SY1170 @ SV72 ) ) )
= $false )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1179,plain,
! [SV72: $i,SV184: $i] :
( ( ( ! [SY1171: $i] :
~ ~ ( ~ ( in @ SV184 @ SY1171 )
| ~ ( in @ SY1171 @ SV72 ) ) )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1180,plain,
! [SV189: $i > $o,SV75: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV75 )
| ~ ( SV189 @ SV298 ) )
= $true )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1181,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
| ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 ) )
| ~ ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1182,plain,
! [SV192: $i > $o,SV79: $i,SV299: $i] :
( ( ( in @ SV299 @ SV79 )
= $false )
| ( ( SV192 @ SV299 )
= $true )
| ( ( ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ SV79 )
| ~ ~ ( SV192 @ SY1177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1183,plain,
! [SV80: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1184,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
| ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 ) ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1185,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV285 ) )
= $true )
| ( ( ~ ! [SY1268: $i] :
( ~ ( SV91 @ SY1268 )
| ( SV285 = SY1268 ) ) )
= $true )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1186,plain,
! [SV92: $i,SV200: $i,SV258: $i] :
( ( ( in @ SV258 @ SV200 )
= $true )
| ( ( in @ SV258 @ ( symdiff @ SV92 @ SV200 ) )
= $true )
| ( ( in @ SV258 @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1187,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ SV286 ) )
= $true )
| ( ( ~ ! [SY1269: $i] :
( ~ ( SV94 @ SY1269 )
| ( SV286 = SY1269 ) ) )
= $true )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1188,plain,
! [SV259: $i,SV202: $i > $o,SV95: $i] :
( ( ( ( dsetconstr @ SV95
@ ^ [SY1183: $i] : ( SV202 @ SY1183 ) )
= emptyset )
= $false )
| ( ( SV202 @ SV259 )
= $false )
| ( ( in @ SV259 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1189,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
= $false )
| ( ( ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1190,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ( ( SV262 = SV99 )
| ( in @ SV262 @ SV205 ) )
= $false )
| ( ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1191,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1192,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
| ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) ) )
| ~ ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1193,plain,
! [SV101: $i,SV207: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 )
| ~ ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) ) ) )
= $true )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1194,plain,
! [SV105: $i,SV210: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV210 ) )
= $false )
| ( ( ~ ( in @ SV263 @ SV105 ) )
= $true )
| ( ( in @ SV263 @ ( setminus @ SV105 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1195,plain,
! [SV287: $i] :
( ( ( ~ ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1271: $i] :
~ ~ ( ~ ( in @ SY1271 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SY1271 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1196,plain,
! [SV213: $i > $o,SV108: $i] :
( ( ( ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $false )
| ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1197,plain,
! [SV213: $i > $o,SV108: $i] :
( ( ( ~ ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $false )
| ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1198,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ SV288 ) )
= $true )
| ( ( ~ ! [SY1272: $i] :
( ~ ( SV109 @ SY1272 )
| ( SV288 = SY1272 ) ) )
= $true )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1199,plain,
! [SV215: $i > $o,SV111: $i,SV266: $i] :
( ( ( ~ ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) )
| ( SV215 @ SV266 ) )
= $true )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1200,plain,
! [SV111: $i,SV266: $i,SV215: $i > $o] :
( ( ( ~ ( SV215 @ SV266 )
| ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) ) )
= $true )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1201,plain,
! [SV217: $i,SV113: $i,SV300: $i,SV289: $i] :
( ( ( SV289 = SV300 )
= $false )
| ( ( ~ ( in @ SV289 @ SV113 )
| ( in @ SV300 @ SV217 ) )
= $true )
| ( ( SV113 = SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1202,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ SV290 ) )
= $true )
| ( ( ~ ! [SY1274: $i] :
( ~ ( SV117 @ SY1274 )
| ( SV290 = SY1274 ) ) )
= $true )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1203,plain,
! [SV222: $i,SV119: $i,SV301: $i,SV291: $i] :
( ( ( SV291 = SV301 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV291 @ SV119 )
| ( in @ SV301 @ SV222 ) )
| ~ ( ~ ( in @ SV301 @ SV222 )
| ( in @ SV291 @ SV119 ) ) ) )
= $true )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1204,plain,
! [SV127: $i,SV230: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 )
| ~ ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) ) ) )
= $true )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1205,plain,
! [SV231: $i,SV128: $i,SV272: $i] :
( ( ( in @ SV272 @ ( symdiff @ SV128 @ SV231 ) )
= $false )
| ( ( in @ SV272 @ SV231 )
= $false )
| ( ( in @ SV272 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1206,plain,
! [SV129: $i,SV232: $i,SV304: $i] :
( ( ( ~ ( in @ SV304 @ SV232 )
| ( in @ SV304 @ SV129 ) )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1207,plain,
! [SV232: $i,SV129: $i] :
( ( ( ~ ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
| ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV129 ) )
= $false )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1139]) ).
thf(1208,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1209,plain,
! [SV31: $i] :
( ( ~ ! [SY1232: $i,SY1233: $i] :
( ~ ~ ( ~ ( in @ SY1232 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1233 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1232 )
| ( in @ SX4 @ SY1233 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1233 )
| ( in @ SX4 @ SY1232 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1210,plain,
! [SV31: $i,SV302: $i] :
( ( ( ~ ~ ( ~ ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV302 )
| ( in @ SY1280 @ SV31 ) )
| ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1211,plain,
! [SV238: $i,SV153: $i,SV32: $i] :
( ( ( SV32 = SV153 )
= $false )
| ( ( in @ SV238 @ SV153 )
= $true )
| ( ( in @ SV238 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1212,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( SV33 @ SV276 )
= $false )
| ( ( ~ ! [SY1254: $i] :
( ~ ( SV33 @ SY1254 )
| ( SV276 = SY1254 ) ) )
= $true )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1213,plain,
! [SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ! [SY1289: $i] :
~ ( ~ ( ~ ( in @ SY1289 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1289 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1289 ) )
| ( in @ SY1289 @ ( sK29_SY1121 @ SV35 @ SV155 ) ) ) ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1144]) ).
thf(1214,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
| ~ ! [SY1287: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1287 )
| ( SV303 = SY1287 ) ) ) )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1215,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( SV36 @ SV277 )
= $false )
| ( ( ~ ! [SY1257: $i] :
( ~ ( SV36 @ SY1257 )
| ( SV277 = SY1257 ) ) )
= $true )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1216,plain,
! [SV292: $i,SV160: $i > $o,SV41: $i] :
( ( ( ! [SY1130: $i] :
~ ~ ( ~ ( in @ SY1130 @ SV41 )
| ~ ~ ( SV160 @ SY1130 ) ) )
= $false )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1217,plain,
! [SV244: $i,SV162: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV162 )
= $false )
| ( ( in @ SV244 @ SV162 )
= $true )
| ( ( in @ SV244 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1218,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY911 @ SV44 ) @ omega )
| ~ ( in @ ( sK23_SY911 @ SV44 ) @ SV44 ) ) )
= $false )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1151]) ).
thf(1219,plain,
! [SV44: $i] :
( ( ( in @ ( setadjoin @ ( sK23_SY911 @ SV44 ) @ ( sK23_SY911 @ SV44 ) ) @ SV44 )
= $false )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1151]) ).
thf(1220,plain,
! [SV164: $i > $o,SV46: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ SV46 ) )
= $true )
| ( ( ~ ~ ( SV164 @ SV293 ) )
= $true )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1221,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1222,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
| ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1223,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ! [SY1292: $i] :
( ~ ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
| ~ ( SV48 @ SY1292 )
| ( ( sK30_SY928 @ SV278 @ SV48 )
= SY1292 ) ) )
= $false )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1156]) ).
thf(1224,plain,
! [SV50: $i,SV279: $o,SV167: $i] :
( ( ( ~ ( in @ SV167 @ ( sK24_SY1259 @ SV279 @ SV50 @ SV167 ) ) )
= $false )
| ( SV279 = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1157]) ).
thf(1225,plain,
! [SV167: $i,SV50: $i,SV279: $o] :
( ( ( ~ ( in @ ( sK24_SY1259 @ SV279 @ SV50 @ SV167 ) @ SV50 )
| SV279 )
= $false )
| ( SV279 = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1157]) ).
thf(1228,plain,
! [SV50: $i,SV167: $i] :
( ( ( ~ ( in @ SV167 @ ( sK26_SX0 @ SV50 @ SV167 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1229,plain,
! [SV167: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK26_SX0 @ SV50 @ SV167 ) @ SV50 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1230,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( SV51 @ SV280 )
= $false )
| ( ( ~ ! [SY1260: $i] :
( ~ ( SV51 @ SY1260 )
| ( SV280 = SY1260 ) ) )
= $true )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1231,plain,
! [SV52: $i,SV168: $i,SV281: $i > $o,SV294: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) @ SV52 )
| ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SV168 )
| ( ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 )
!= SY1293 )
| ~ ( ~ ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
| ( SV294 @ SY1293 ) )
| ~ ( ~ ( SV294 @ SY1293 )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1161]) ).
thf(1232,plain,
! [SV54: $i,SV282: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_SY951 @ SV282 @ SV54 ) @ SV54 )
| ~ ~ ~ ! [SY1288: $i] :
~ ~ ( ~ ( in @ SY1288 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SY1288 @ SV54 ) ) ) )
= $true )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1233,plain,
! [SV273: $o,SV172: $i,SV57: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV57 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| SV273 )
| SV273 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1237,plain,
! [SV172: $i,SV57: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV57 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| $false )
| $false )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1239,plain,
! [SV59: $i,SV174: $i] :
( ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV174 )
| ( in @ SY1159 @ SV59 ) ) )
= $false )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1240,plain,
! [SV174: $i,SV59: $i] :
( ( ( ~ ( in @ ( sK32_SY1159 @ SV59 @ SV174 ) @ SV174 )
| ( in @ ( sK32_SY1159 @ SV59 @ SV174 ) @ SV59 ) )
= $false )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV174 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1168]) ).
thf(1241,plain,
! [SV60: $i] :
( ( ( ~ ( in @ ( sK16_SY965 @ SV60 ) @ SV60 ) )
= $false )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1243,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV63 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1244,plain,
! [SV63: $i,SV296: $o,SV176: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV176 )
| SV296 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1247,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV63 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1172]) ).
thf(1248,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV176 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1172]) ).
thf(1249,plain,
! [SV178: $i,SV65: $i,SV250: $i] :
( ( ( in @ SV250 @ SV65 )
= $false )
| ( ( in @ SV250 @ SV178 )
= $true )
| ( ( subset @ SV65 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1250,plain,
! [SV67: $i,SV180: $i,SV252: $i] :
( ( ( in @ SV252 @ SV180 )
= $true )
| ( ( ~ ( in @ SV252 @ ( symdiff @ SV67 @ SV180 ) ) )
= $true )
| ( ( in @ SV252 @ SV67 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1251,plain,
! [SV297: $o,SV182: $i,SV69: $i,SV253: $i] :
( ( ( SV253 != SV69 )
= $false )
| ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| SV297 )
| SV297 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1255,plain,
! [SV182: $i,SV69: $i,SV253: $i] :
( ( ( SV253 != SV69 )
= $false )
| ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1257,plain,
! [SV72: $i,SV184: $i] :
( ( ( ~ ~ ( ~ ( in @ SV184 @ ( sK33_SY1170 @ SV72 @ SV184 ) )
| ~ ( in @ ( sK33_SY1170 @ SV72 @ SV184 ) @ SV72 ) ) )
= $false )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1178]) ).
thf(1258,plain,
! [SV72: $i,SV305: $i,SV184: $i] :
( ( ( ~ ~ ( ~ ( in @ SV184 @ SV305 )
| ~ ( in @ SV305 @ SV72 ) ) )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1259,plain,
! [SV189: $i > $o,SV75: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV75 ) )
= $true )
| ( ( ~ ( SV189 @ SV298 ) )
= $true )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1260,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
| ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 ) ) )
= $true )
| ( ( ~ ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1261,plain,
! [SV299: $i,SV192: $i > $o,SV79: $i] :
( ( ( ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ SV79 )
| ~ ~ ( SV192 @ SY1177 ) ) )
= $false )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1262,plain,
! [SV80: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1183]) ).
thf(1263,plain,
! [SV80: $i,SV193: $i] :
( ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1183]) ).
thf(1264,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
| ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1265,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( SV91 @ SV285 )
= $false )
| ( ( ~ ! [SY1268: $i] :
( ~ ( SV91 @ SY1268 )
| ( SV285 = SY1268 ) ) )
= $true )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1266,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( SV94 @ SV286 )
= $false )
| ( ( ~ ! [SY1269: $i] :
( ~ ( SV94 @ SY1269 )
| ( SV286 = SY1269 ) ) )
= $true )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1267,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ( SV262 = SV99 )
= $true )
| ( ( in @ SV262 @ SV205 )
= $true )
| ( ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1268,plain,
! [SV205: $i,SV99: $i,SV262: $i] :
( ( ( SV262 = SV99 )
= $false )
| ( ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1190]) ).
thf(1269,plain,
! [SV99: $i,SV205: $i,SV262: $i] :
( ( ( in @ SV262 @ SV205 )
= $false )
| ( ( in @ SV262 @ ( setadjoin @ SV99 @ SV205 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1190]) ).
thf(1270,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1271,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
| ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1272,plain,
! [SV101: $i,SV207: $i > $o] :
( ( ( ~ ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 )
| ~ ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) ) )
= $false )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1273,plain,
! [SV105: $i,SV210: $i,SV263: $i] :
( ( ( in @ SV263 @ SV210 )
= $true )
| ( ( ~ ( in @ SV263 @ SV105 ) )
= $true )
| ( ( in @ SV263 @ ( setminus @ SV105 @ SV210 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1274,plain,
! [SV287: $i] :
( ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1271: $i] :
~ ~ ( ~ ( in @ SY1271 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SY1271 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1275,plain,
! [SV213: $i > $o,SV108: $i] :
( ( ( ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true )
| ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1196]) ).
thf(1276,plain,
! [SV213: $i > $o,SV108: $i] :
( ( ( ! [SY1205: $i] :
~ ~ ( ~ ( in @ SY1205 @ SV108 )
| ~ ( SV213 @ SY1205 ) ) )
= $true )
| ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1277,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( SV109 @ SV288 )
= $false )
| ( ( ~ ! [SY1272: $i] :
( ~ ( SV109 @ SY1272 )
| ( SV288 = SY1272 ) ) )
= $true )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1278,plain,
! [SV215: $i > $o,SV111: $i,SV266: $i] :
( ( ( ~ ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) ) )
= $true )
| ( ( SV215 @ SV266 )
= $true )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1279,plain,
! [SV111: $i,SV266: $i,SV215: $i > $o] :
( ( ( ~ ( SV215 @ SV266 ) )
= $true )
| ( ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) )
= $true )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1280,plain,
! [SV217: $i,SV300: $i,SV113: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ SV113 ) )
= $true )
| ( ( in @ SV300 @ SV217 )
= $true )
| ( ( SV289 = SV300 )
= $false )
| ( ( SV113 = SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1281,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( SV117 @ SV290 )
= $false )
| ( ( ~ ! [SY1274: $i] :
( ~ ( SV117 @ SY1274 )
| ( SV290 = SY1274 ) ) )
= $true )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1282,plain,
! [SV222: $i,SV301: $i,SV119: $i,SV291: $i] :
( ( ( ~ ( ~ ( in @ SV291 @ SV119 )
| ( in @ SV301 @ SV222 ) )
| ~ ( ~ ( in @ SV301 @ SV222 )
| ( in @ SV291 @ SV119 ) ) )
= $false )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1283,plain,
! [SV127: $i,SV230: $i > $o] :
( ( ( ~ ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 )
| ~ ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) ) )
= $false )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1284,plain,
! [SV129: $i,SV232: $i,SV304: $i] :
( ( ( ~ ( in @ SV304 @ SV232 ) )
= $true )
| ( ( in @ SV304 @ SV129 )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1285,plain,
! [SV232: $i,SV129: $i] :
( ( ( ~ ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 ) )
= $false )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1286,plain,
! [SV232: $i,SV129: $i] :
( ( ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV129 )
= $false )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1287,plain,
! [SV31: $i] :
( ( ~ ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1288,plain,
! [SV31: $i] :
( ( ! [SY1232: $i,SY1233: $i] :
( ~ ~ ( ~ ( in @ SY1232 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1233 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1232 )
| ( in @ SX4 @ SY1233 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1233 )
| ( in @ SX4 @ SY1232 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1289,plain,
! [SV31: $i,SV302: $i] :
( ( ( ~ ( ~ ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV302 )
| ( in @ SY1280 @ SV31 ) )
| ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) ) )
= $false )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1290,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ! [SY1254: $i] :
( ~ ( SV33 @ SY1254 )
| ( SV276 = SY1254 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1291,plain,
! [SV155: $i,SV35: $i > $i > $o] :
( ( ( ! [SY1289: $i] :
~ ( ~ ( ~ ( in @ SY1289 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1289 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1289 ) )
| ( in @ SY1289 @ ( sK29_SY1121 @ SV35 @ SV155 ) ) ) ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1292,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
| ~ ! [SY1287: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1287 )
| ( SV303 = SY1287 ) ) )
= $true )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1293,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ! [SY1257: $i] :
( ~ ( SV36 @ SY1257 )
| ( SV277 = SY1257 ) ) )
= $false )
| ( ( SV36 @ SV277 )
= $false )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1294,plain,
! [SV41: $i,SV160: $i > $o,SV292: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) @ SV41 )
| ~ ~ ( SV160 @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) ) ) )
= $false )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1216]) ).
thf(1295,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY911 @ SV44 ) @ omega )
| ~ ( in @ ( sK23_SY911 @ SV44 ) @ SV44 ) ) )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1218]) ).
thf(1296,plain,
! [SV44: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ omega )
| ( in @ SV306 @ SV44 ) )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( setadjoin @ ( sK23_SY911 @ SV44 ) @ ( sK23_SY911 @ SV44 ) ) @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1297,plain,
! [SV164: $i > $o,SV46: $i,SV293: $i] :
( ( ( in @ SV293 @ SV46 )
= $false )
| ( ( ~ ~ ( SV164 @ SV293 ) )
= $true )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1298,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1299,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
| ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) ) )
= $false )
| ( ( ~ ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1300,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
| ~ ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
| ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) ) )
= $false )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1223]) ).
thf(1301,plain,
! [SV50: $i,SV279: $o,SV167: $i] :
( ( ( in @ SV167 @ ( sK24_SY1259 @ SV279 @ SV50 @ SV167 ) )
= $true )
| ( SV279 = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1302,plain,
! [SV167: $i,SV50: $i,SV279: $o] :
( ( ( ~ ( in @ ( sK24_SY1259 @ SV279 @ SV50 @ SV167 ) @ SV50 ) )
= $false )
| ( SV279 = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1225]) ).
thf(1307,plain,
! [SV50: $i,SV167: $i] :
( ( ( in @ SV167 @ ( sK26_SX0 @ SV50 @ SV167 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1308,plain,
! [SV167: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK26_SX0 @ SV50 @ SV167 ) @ SV50 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1229]) ).
thf(1310,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( ! [SY1260: $i] :
( ~ ( SV51 @ SY1260 )
| ( SV280 = SY1260 ) ) )
= $false )
| ( ( SV51 @ SV280 )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1311,plain,
! [SV52: $i,SV168: $i,SV281: $i > $o,SV294: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) @ SV52 ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1312,plain,
! [SV52: $i,SV281: $i > $o,SV294: $i > $o,SV168: $i] :
( ( ( ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SV168 )
| ( ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 )
!= SY1293 )
| ~ ( ~ ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
| ( SV294 @ SY1293 ) )
| ~ ( ~ ( SV294 @ SY1293 )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1313,plain,
! [SV54: $i,SV282: $i] :
( ( ( ~ ( in @ ( sK27_SY951 @ SV282 @ SV54 ) @ SV54 )
| ~ ~ ~ ! [SY1288: $i] :
~ ~ ( ~ ( in @ SY1288 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SY1288 @ SV54 ) ) )
= $false )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1314,plain,
! [SV273: $o,SV172: $i,SV57: $i,SV247: $i] :
( ( ( in @ SV247 @ SV57 )
= $true )
| ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| SV273 )
| SV273 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1318,plain,
! [SV172: $i,SV57: $i,SV247: $i] :
( ( ( in @ SV247 @ SV57 )
= $true )
| ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| $false )
| $false )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1320,plain,
! [SV174: $i,SV59: $i] :
( ( ( ~ ( in @ ( sK36_SY1159 @ SV59 @ SV174 ) @ SV174 )
| ( in @ ( sK36_SY1159 @ SV59 @ SV174 ) @ SV59 ) )
= $false )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1239]) ).
thf(1321,plain,
! [SV174: $i,SV59: $i] :
( ( ( ~ ( in @ ( sK32_SY1159 @ SV59 @ SV174 ) @ SV174 ) )
= $false )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1322,plain,
! [SV174: $i,SV59: $i] :
( ( ( in @ ( sK32_SY1159 @ SV59 @ SV174 ) @ SV59 )
= $false )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1323,plain,
! [SV60: $i] :
( ( ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
= $true )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1325,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( in @ SV249 @ SV63 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1326,plain,
! [SV296: $o,SV63: $i,SV176: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV176 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1244]) ).
thf(1331,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( in @ SV249 @ SV63 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1332,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV176 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1334,plain,
! [SV180: $i,SV67: $i,SV252: $i] :
( ( ( in @ SV252 @ ( symdiff @ SV67 @ SV180 ) )
= $false )
| ( ( in @ SV252 @ SV180 )
= $true )
| ( ( in @ SV252 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1335,plain,
! [SV297: $o,SV182: $i,SV69: $i,SV253: $i] :
( ( ( SV253 = SV69 )
= $true )
| ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| SV297 )
| SV297 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1339,plain,
! [SV182: $i,SV69: $i,SV253: $i] :
( ( ( SV253 = SV69 )
= $true )
| ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| $false )
| $false )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1341,plain,
! [SV72: $i,SV184: $i] :
( ( ( ~ ( ~ ( in @ SV184 @ ( sK33_SY1170 @ SV72 @ SV184 ) )
| ~ ( in @ ( sK33_SY1170 @ SV72 @ SV184 ) @ SV72 ) ) )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1257]) ).
thf(1342,plain,
! [SV72: $i,SV305: $i,SV184: $i] :
( ( ( ~ ( ~ ( in @ SV184 @ SV305 )
| ~ ( in @ SV305 @ SV72 ) ) )
= $false )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1343,plain,
! [SV189: $i > $o,SV75: $i,SV298: $i] :
( ( ( in @ SV298 @ SV75 )
= $false )
| ( ( ~ ( SV189 @ SV298 ) )
= $true )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1344,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
| ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 ) )
= $false )
| ( ( ~ ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1345,plain,
! [SV79: $i,SV192: $i > $o,SV299: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) @ SV79 )
| ~ ~ ( SV192 @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) ) ) )
= $false )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1261]) ).
thf(1346,plain,
! [SV80: $i,SV193: $i] :
( ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) ) )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1347,plain,
! [SV80: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) )
= $false )
| ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
= $false )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1348,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1349,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1350,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ! [SY1268: $i] :
( ~ ( SV91 @ SY1268 )
| ( SV285 = SY1268 ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1351,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( ! [SY1269: $i] :
( ~ ( SV94 @ SY1269 )
| ( SV286 = SY1269 ) ) )
= $false )
| ( ( SV94 @ SV286 )
= $false )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1352,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1270]) ).
thf(1353,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1270]) ).
thf(1354,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
| ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) ) )
= $false )
| ( ( ~ ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1355,plain,
! [SV101: $i,SV207: $i > $o] :
( ( ( ~ ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 ) )
= $false )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1272]) ).
thf(1356,plain,
! [SV101: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) ) )
= $false )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1272]) ).
thf(1357,plain,
! [SV210: $i,SV105: $i,SV263: $i] :
( ( ( in @ SV263 @ SV105 )
= $false )
| ( ( in @ SV263 @ SV210 )
= $true )
| ( ( in @ SV263 @ ( setminus @ SV105 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1358,plain,
! [SV287: $i] :
( ( ( ~ ! [SY1271: $i] :
~ ~ ( ~ ( in @ SY1271 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SY1271 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1359,plain,
! [SV213: $i > $o,SV108: $i,SV307: $i] :
( ( ( ~ ~ ( ~ ( in @ SV307 @ SV108 )
| ~ ( SV213 @ SV307 ) ) )
= $true )
| ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1360,plain,
! [SV213: $i > $o,SV108: $i,SV308: $i] :
( ( ( ~ ~ ( ~ ( in @ SV308 @ SV108 )
| ~ ( SV213 @ SV308 ) ) )
= $true )
| ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1361,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ! [SY1272: $i] :
( ~ ( SV109 @ SY1272 )
| ( SV288 = SY1272 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1362,plain,
! [SV215: $i > $o,SV111: $i,SV266: $i] :
( ( ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1208: $i] : ( SV215 @ SY1208 ) ) )
= $false )
| ( ( SV215 @ SV266 )
= $true )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1363,plain,
! [SV111: $i,SV266: $i,SV215: $i > $o] :
( ( ( SV215 @ SV266 )
= $false )
| ( ( in @ SV266
@ ( dsetconstr @ SV111
@ ^ [SY1209: $i] : ( SV215 @ SY1209 ) ) )
= $true )
| ( ( in @ SV266 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1364,plain,
! [SV217: $i,SV300: $i,SV113: $i,SV289: $i] :
( ( ( in @ SV289 @ SV113 )
= $false )
| ( ( in @ SV300 @ SV217 )
= $true )
| ( ( SV289 = SV300 )
= $false )
| ( ( SV113 = SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1365,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( ! [SY1274: $i] :
( ~ ( SV117 @ SY1274 )
| ( SV290 = SY1274 ) ) )
= $false )
| ( ( SV117 @ SV290 )
= $false )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1366,plain,
! [SV222: $i,SV301: $i,SV119: $i,SV291: $i] :
( ( ( ~ ( ~ ( in @ SV291 @ SV119 )
| ( in @ SV301 @ SV222 ) ) )
= $false )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1367,plain,
! [SV119: $i,SV291: $i,SV222: $i,SV301: $i] :
( ( ( ~ ( ~ ( in @ SV301 @ SV222 )
| ( in @ SV291 @ SV119 ) ) )
= $false )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1368,plain,
! [SV127: $i,SV230: $i > $o] :
( ( ( ~ ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 ) )
= $false )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1369,plain,
! [SV127: $i,SV230: $i > $o] :
( ( ( ~ ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) ) )
= $false )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1370,plain,
! [SV129: $i,SV232: $i,SV304: $i] :
( ( ( in @ SV304 @ SV232 )
= $false )
| ( ( in @ SV304 @ SV129 )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1371,plain,
! [SV232: $i,SV129: $i] :
( ( ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1372,plain,
! [SV31: $i] :
( ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) )
| ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1373,plain,
! [SV31: $i,SV309: $i] :
( ( ! [SY1294: $i] :
( ~ ~ ( ~ ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1294 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV309 )
| ( in @ SY1295 @ SY1294 ) )
| ! [SY1296: $i] :
( ~ ( in @ SY1296 @ SY1294 )
| ( in @ SY1296 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1374,plain,
! [SV31: $i,SV302: $i] :
( ( ( ~ ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV302 )
| ( in @ SY1280 @ SV31 ) )
| ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1289]) ).
thf(1375,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
| ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1290]) ).
thf(1376,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
| ~ ! [SY1297: $i] :
~ ~ ( ~ ( in @ SY1297 @ SV155 )
| ~ ( SV35 @ SY1297 @ SV310 ) ) )
| ~ ( ~ ~ ! [SY1298: $i] :
~ ~ ( ~ ( in @ SY1298 @ SV155 )
| ~ ( SV35 @ SY1298 @ SV310 ) )
| ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) ) ) ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1377,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 ) )
= $true )
| ( ( ~ ! [SY1287: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1287 )
| ( SV303 = SY1287 ) ) )
= $true )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1378,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK39_SY1257 @ SV277 @ SV36 ) )
| ( SV277
= ( sK39_SY1257 @ SV277 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV277 )
= $false )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1293]) ).
thf(1379,plain,
! [SV41: $i,SV160: $i > $o,SV292: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) @ SV41 )
| ~ ~ ( SV160 @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) ) ) )
= $true )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1380,plain,
! [SV44: $i] :
( ( ( ~ ( in @ ( sK23_SY911 @ SV44 ) @ omega )
| ~ ( in @ ( sK23_SY911 @ SV44 ) @ SV44 ) )
= $false )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1381,plain,
! [SV44: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ omega ) )
= $true )
| ( ( in @ SV306 @ SV44 )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( setadjoin @ ( sK23_SY911 @ SV44 ) @ ( sK23_SY911 @ SV44 ) ) @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1382,plain,
! [SV46: $i,SV293: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ SV293 ) )
= $false )
| ( ( in @ SV293 @ SV46 )
= $false )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1383,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1384,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) )
= $false )
| ( ( ~ ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1385,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( ~ ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1386,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) ) )
= $false )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1387,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
| ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) ) )
= $false )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1300]) ).
thf(1388,plain,
! [SV167: $i,SV50: $i,SV279: $o] :
( ( ( in @ ( sK24_SY1259 @ SV279 @ SV50 @ SV167 ) @ SV50 )
= $true )
| ( SV279 = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1390,plain,
! [SV167: $i,SV50: $i] :
( ( ( in @ ( sK26_SX0 @ SV50 @ SV167 ) @ SV50 )
= $true )
| ( $false = $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1391,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) )
| ( SV280
= ( sK40_SY1260 @ SV280 @ SV51 ) ) )
= $false )
| ( ( SV51 @ SV280 )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1310]) ).
thf(1392,plain,
! [SV52: $i,SV168: $i,SV281: $i > $o,SV294: $i > $o] :
( ( ( in @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) @ SV52 )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1311]) ).
thf(1393,plain,
! [SV168: $i,SV294: $i > $o,SV281: $i > $o,SV52: $i] :
( ( ( ~ ( in @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) @ SV168 )
| ( ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 )
!= ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ~ ( ~ ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
| ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) ) )
| ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1312]) ).
thf(1394,plain,
! [SV54: $i,SV282: $i] :
( ( ( ~ ( in @ ( sK27_SY951 @ SV282 @ SV54 ) @ SV54 ) )
= $false )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1395,plain,
! [SV54: $i,SV282: $i] :
( ( ( ~ ~ ~ ! [SY1288: $i] :
~ ~ ( ~ ( in @ SY1288 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SY1288 @ SV54 ) ) )
= $false )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1396,plain,
! [SV57: $i,SV273: $o,SV172: $i,SV247: $i] :
( ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| SV273 ) )
= $true )
| ( SV273 = $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1400,plain,
! [SV57: $i,SV172: $i,SV247: $i] :
( ( ( ~ ( ~ ( in @ SV247 @ SV172 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1402,plain,
! [SV174: $i,SV59: $i] :
( ( ( ~ ( in @ ( sK36_SY1159 @ SV59 @ SV174 ) @ SV174 ) )
= $false )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1403,plain,
! [SV174: $i,SV59: $i] :
( ( ( in @ ( sK36_SY1159 @ SV59 @ SV174 ) @ SV59 )
= $false )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1404,plain,
! [SV174: $i,SV59: $i] :
( ( ( in @ ( sK32_SY1159 @ SV59 @ SV174 ) @ SV174 )
= $true )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1405,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 ) )
= $true )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1406,plain,
! [SV296: $o,SV63: $i,SV176: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV176 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1411,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1412,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV176 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1414,plain,
! [SV69: $i,SV297: $o,SV182: $i,SV253: $i] :
( ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| SV297 ) )
= $true )
| ( SV297 = $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1418,plain,
! [SV69: $i,SV182: $i,SV253: $i] :
( ( ( ~ ( ~ ( in @ SV253 @ SV182 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1420,plain,
! [SV72: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ ( sK33_SY1170 @ SV72 @ SV184 ) )
| ~ ( in @ ( sK33_SY1170 @ SV72 @ SV184 ) @ SV72 ) )
= $false )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1421,plain,
! [SV72: $i,SV305: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ SV305 )
| ~ ( in @ SV305 @ SV72 ) )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1422,plain,
! [SV75: $i,SV298: $i,SV189: $i > $o] :
( ( ( SV189 @ SV298 )
= $false )
| ( ( in @ SV298 @ SV75 )
= $false )
| ( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1423,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) )
= $false )
| ( ( ~ ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1424,plain,
! [SV76: $i > $o,SV284: $i] :
( ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( ~ ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1425,plain,
! [SV79: $i,SV192: $i > $o,SV299: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) @ SV79 )
| ~ ~ ( SV192 @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) ) ) )
= $true )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1345]) ).
thf(1426,plain,
! [SV80: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
| ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 ) )
= $false )
| ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1428,plain,
! [SV80: $i,SV193: $i] :
( ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
= $false )
| ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
= $false )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1429,plain,
! [SV89: $i,SV199: $i] :
( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1430,plain,
! [SV89: $i,SV199: $i] :
( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1431,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
| ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1350]) ).
thf(1432,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) )
| ( SV286
= ( sK43_SY1269 @ SV286 @ SV94 ) ) )
= $false )
| ( ( SV94 @ SV286 )
= $false )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1351]) ).
thf(1433,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1434,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1435,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) )
= $false )
| ( ( ~ ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1436,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( ~ ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1437,plain,
! [SV101: $i,SV207: $i > $o] :
( ( ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 )
= $true )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1438,plain,
! [SV101: $i,SV207: $i > $o] :
( ( ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) )
= $true )
| ( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV101 )
| ~ ( SV207 @ SY1198 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1439,plain,
! [SV287: $i] :
( ( ( ! [SY1271: $i] :
~ ~ ( ~ ( in @ SY1271 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SY1271 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1440,plain,
! [SV213: $i > $o,SV108: $i,SV307: $i] :
( ( ( ~ ( ~ ( in @ SV307 @ SV108 )
| ~ ( SV213 @ SV307 ) ) )
= $false )
| ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1441,plain,
! [SV213: $i > $o,SV108: $i,SV308: $i] :
( ( ( ~ ( ~ ( in @ SV308 @ SV108 )
| ~ ( SV213 @ SV308 ) ) )
= $false )
| ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1442,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
| ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1361]) ).
thf(1443,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ ( sK45_SY1274 @ SV290 @ SV117 ) )
| ( SV290
= ( sK45_SY1274 @ SV290 @ SV117 ) ) )
= $false )
| ( ( SV117 @ SV290 )
= $false )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1365]) ).
thf(1444,plain,
! [SV222: $i,SV301: $i,SV119: $i,SV291: $i] :
( ( ( ~ ( in @ SV291 @ SV119 )
| ( in @ SV301 @ SV222 ) )
= $true )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1445,plain,
! [SV119: $i,SV291: $i,SV222: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ SV222 )
| ( in @ SV291 @ SV119 ) )
= $true )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1446,plain,
! [SV127: $i,SV230: $i > $o] :
( ( ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 )
= $true )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1368]) ).
thf(1447,plain,
! [SV127: $i,SV230: $i > $o] :
( ( ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) )
= $true )
| ( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV127 )
| ~ ( SV230 @ SY1222 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1448,plain,
! [SV31: $i] :
( ( ~ ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1449,plain,
! [SV31: $i] :
( ( ~ ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1450,plain,
! [SV311: $i,SV31: $i,SV309: $i] :
( ( ~ ~ ( ~ ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SV311 @ ( sK2_SY860 @ SV31 ) ) )
| ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV309 )
| ( in @ SY1299 @ SV311 ) )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1451,plain,
! [SV31: $i,SV302: $i] :
( ( ( ~ ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV302 )
| ( in @ SY1280 @ SV31 ) ) )
= $true )
| ( ( ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1452,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1453,plain,
! [SV33: $i > $o,SV276: $i] :
( ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1454,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ( ~ ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
| ~ ! [SY1297: $i] :
~ ~ ( ~ ( in @ SY1297 @ SV155 )
| ~ ( SV35 @ SY1297 @ SV310 ) ) )
| ~ ( ~ ~ ! [SY1298: $i] :
~ ~ ( ~ ( in @ SY1298 @ SV155 )
| ~ ( SV35 @ SY1298 @ SV310 ) )
| ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1455,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( ~ ! [SY1287: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1287 )
| ( SV303 = SY1287 ) ) )
= $true )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1456,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK39_SY1257 @ SV277 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV277 )
= $false )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1457,plain,
! [SV36: $i > $o,SV277: $i] :
( ( ( SV277
= ( sK39_SY1257 @ SV277 @ SV36 ) )
= $false )
| ( ( SV36 @ SV277 )
= $false )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1458,plain,
! [SV41: $i,SV160: $i > $o,SV292: $i] :
( ( ( ~ ( in @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) @ SV41 )
| ~ ~ ( SV160 @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) ) )
= $false )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1459,plain,
! [SV44: $i] :
( ( ( ~ ( in @ ( sK23_SY911 @ SV44 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1460,plain,
! [SV44: $i] :
( ( ( ~ ( in @ ( sK23_SY911 @ SV44 ) @ SV44 ) )
= $false )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1461,plain,
! [SV44: $i,SV306: $i] :
( ( ( in @ SV306 @ omega )
= $false )
| ( ( in @ SV306 @ SV44 )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( setadjoin @ ( sK23_SY911 @ SV44 ) @ ( sK23_SY911 @ SV44 ) ) @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1462,plain,
! [SV46: $i,SV293: $i,SV164: $i > $o] :
( ( ( SV164 @ SV293 )
= $true )
| ( ( in @ SV293 @ SV46 )
= $false )
| ( ( ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1463,plain,
! [SV165: $i > $o,SV312: $i,SV47: $i > $o] :
( ( ( ~ ~ ( ~ ( SV47 @ SV312 )
| ~ ! [SY1301: $i] :
( ~ ( SV47 @ SY1301 )
| ( SV312 = SY1301 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1464,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( ~ ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1384]) ).
thf(1465,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1466,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1386]) ).
thf(1467,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) ) )
= $false )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1468,plain,
! [SV48: $i > $o,SV278: $i] :
( ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1469,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) ) )
= $false )
| ( ( SV51 @ SV280 )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1391]) ).
thf(1470,plain,
! [SV51: $i > $o,SV280: $i] :
( ( ( SV280
= ( sK40_SY1260 @ SV280 @ SV51 ) )
= $false )
| ( ( SV51 @ SV280 )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1391]) ).
thf(1471,plain,
! [SV168: $i,SV294: $i > $o,SV281: $i > $o,SV52: $i] :
( ( ( ~ ( in @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) @ SV168 ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1472,plain,
! [SV52: $i,SV168: $i,SV281: $i > $o,SV294: $i > $o] :
( ( ( ( ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 )
!= ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ~ ( ~ ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
| ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) ) )
| ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1473,plain,
! [SV54: $i,SV282: $i] :
( ( ( in @ ( sK27_SY951 @ SV282 @ SV54 ) @ SV54 )
= $true )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1474,plain,
! [SV54: $i,SV282: $i] :
( ( ( ~ ~ ! [SY1288: $i] :
~ ~ ( ~ ( in @ SY1288 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SY1288 @ SV54 ) ) )
= $true )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1475,plain,
! [SV57: $i,SV273: $o,SV172: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV172 )
| SV273 )
= $false )
| ( SV273 = $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1481,plain,
! [SV57: $i,SV172: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV172 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1484,plain,
! [SV174: $i,SV59: $i] :
( ( ( in @ ( sK36_SY1159 @ SV59 @ SV174 ) @ SV174 )
= $true )
| ( ( SV59 = SV174 )
= $true )
| ( ( in @ ( sK10_SY1158 @ SV174 @ SV59 ) @ SV59 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1485,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
= $false )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1486,plain,
! [SV296: $o,SV63: $i,SV176: $i,SV249: $i] :
( ( ( in @ SV249 @ SV176 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
| SV296 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1491,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1492,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( in @ SV249 @ SV176 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
| $false )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1494,plain,
! [SV69: $i,SV297: $o,SV182: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV182 )
| SV297 )
= $false )
| ( SV297 = $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1500,plain,
! [SV69: $i,SV182: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV182 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1503,plain,
! [SV72: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ ( sK33_SY1170 @ SV72 @ SV184 ) ) )
= $false )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1504,plain,
! [SV184: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK33_SY1170 @ SV72 @ SV184 ) @ SV72 ) )
= $false )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1505,plain,
! [SV72: $i,SV305: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ SV305 ) )
= $true )
| ( ( ~ ( in @ SV305 @ SV72 ) )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1506,plain,
! [SV298: $i,SV189: $i > $o,SV75: $i] :
( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV298 @ SV75 )
= $false )
| ( ( SV189 @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1507,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ~ ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1508,plain,
! [SV76: $i > $o,SV284: $i] :
( ( ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) )
= $false )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1509,plain,
! [SV79: $i,SV192: $i > $o,SV299: $i] :
( ( ( ~ ( in @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) @ SV79 )
| ~ ~ ( SV192 @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) ) )
= $false )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1510,plain,
! [SV80: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 ) )
= $false )
| ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1513,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1514,plain,
! [SV91: $i > $o,SV285: $i] :
( ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1515,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) ) )
= $false )
| ( ( SV94 @ SV286 )
= $false )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1516,plain,
! [SV94: $i > $o,SV286: $i] :
( ( ( SV286
= ( sK43_SY1269 @ SV286 @ SV94 ) )
= $false )
| ( ( SV94 @ SV286 )
= $false )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1517,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1518,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1519,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( ~ ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1520,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1521,plain,
! [SV207: $i > $o,SV101: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ SV101 )
| ~ ( SV207 @ SV313 ) )
= $true )
| ( ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1522,plain,
! [SV207: $i > $o,SV101: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ SV101 )
| ~ ( SV207 @ SV314 ) )
= $true )
| ( ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1523,plain,
! [SV287: $i,SV315: $i] :
( ( ( ~ ~ ( ~ ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SV315 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1524,plain,
! [SV213: $i > $o,SV108: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ SV108 )
| ~ ( SV213 @ SV307 ) )
= $true )
| ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1525,plain,
! [SV213: $i > $o,SV108: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV108 )
| ~ ( SV213 @ SV308 ) )
= $true )
| ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1441]) ).
thf(1526,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1527,plain,
! [SV109: $i > $o,SV288: $i] :
( ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1528,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ ( sK45_SY1274 @ SV290 @ SV117 ) ) )
= $false )
| ( ( SV117 @ SV290 )
= $false )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1529,plain,
! [SV117: $i > $o,SV290: $i] :
( ( ( SV290
= ( sK45_SY1274 @ SV290 @ SV117 ) )
= $false )
| ( ( SV117 @ SV290 )
= $false )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1530,plain,
! [SV222: $i,SV301: $i,SV119: $i,SV291: $i] :
( ( ( ~ ( in @ SV291 @ SV119 ) )
= $true )
| ( ( in @ SV301 @ SV222 )
= $true )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1531,plain,
! [SV119: $i,SV291: $i,SV222: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ SV222 ) )
= $true )
| ( ( in @ SV291 @ SV119 )
= $true )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1532,plain,
! [SV230: $i > $o,SV127: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ SV127 )
| ~ ( SV230 @ SV316 ) )
= $true )
| ( ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1533,plain,
! [SV230: $i > $o,SV127: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ SV127 )
| ~ ( SV230 @ SV317 ) )
= $true )
| ( ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1534,plain,
! [SV31: $i] :
( ( ! [SY1227: $i] :
( ~ ( in @ SY1227 @ ( sK2_SY860 @ SV31 ) )
| ! [SY862: $i] :
( ~ ( in @ SY862 @ SY1227 )
| ( in @ SY862 @ SV31 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1535,plain,
! [SV31: $i] :
( ( ! [SY1229: $i,SY1230: $i] :
( ~ ~ ( ~ ( in @ SY1229 @ SV31 )
| ~ ( in @ SY1230 @ SV31 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SY1229 @ SY1231 )
| ( in @ SY1230 @ SY1231 ) )
| ~ ( ~ ( in @ SY1230 @ SY1231 )
| ( in @ SY1229 @ SY1231 ) ) ) )
| ( SY1229 = SY1230 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1536,plain,
! [SV311: $i,SV31: $i,SV309: $i] :
( ( ( ~ ~ ( ~ ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SV311 @ ( sK2_SY860 @ SV31 ) ) ) )
= $true )
| ( ( ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV309 )
| ( in @ SY1299 @ SV311 ) )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1537,plain,
! [SV31: $i,SV302: $i] :
( ( ( ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV302 )
| ( in @ SY1280 @ SV31 ) ) )
= $false )
| ( ( ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1538,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( ~ ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1539,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1540,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ( ~ ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
| ~ ! [SY1297: $i] :
~ ~ ( ~ ( in @ SY1297 @ SV155 )
| ~ ( SV35 @ SY1297 @ SV310 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1541,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ( ~ ~ ! [SY1298: $i] :
~ ~ ( ~ ( in @ SY1298 @ SV155 )
| ~ ( SV35 @ SY1298 @ SV310 ) )
| ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) ) ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1542,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( ! [SY1287: $i] :
( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SY1287 )
| ( SV303 = SY1287 ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1543,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK39_SY1257 @ SV277 @ SV36 ) )
= $true )
| ( ( SV36 @ SV277 )
= $false )
| ( ( ~ ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1544,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $false )
| ( ( SV36 @ SV277 )
= $false )
| ( ( SV277
= ( sK39_SY1257 @ SV277 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1545,plain,
! [SV41: $i,SV160: $i > $o,SV292: $i] :
( ( ( ~ ( in @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) @ SV41 ) )
= $false )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1546,plain,
! [SV41: $i,SV292: $i,SV160: $i > $o] :
( ( ( ~ ~ ( SV160 @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) ) )
= $false )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1547,plain,
! [SV44: $i] :
( ( ( in @ ( sK23_SY911 @ SV44 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1548,plain,
! [SV44: $i] :
( ( ( in @ ( sK23_SY911 @ SV44 ) @ SV44 )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ omega )
| ( in @ SY912 @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1549,plain,
! [SV293: $i,SV164: $i > $o,SV46: $i] :
( ( ( ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV46 )
| ( SV164 @ SY1134 ) ) )
= $false )
| ( ( in @ SV293 @ SV46 )
= $false )
| ( ( SV164 @ SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1550,plain,
! [SV165: $i > $o,SV312: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ SV312 )
| ~ ! [SY1301: $i] :
( ~ ( SV47 @ SY1301 )
| ( SV312 = SY1301 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1551,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
| ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1553,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1554,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $false )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1555,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1556,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $false )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1557,plain,
! [SV280: $i,SV51: $i > $o] :
( ( ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( ! [SY939: $i,SY940: $i] :
( ~ ( SV51 @ SY939 )
| ~ ( SV51 @ SY940 )
| ( SY939 = SY940 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1558,plain,
! [SV280: $i,SV318: $i,SV51: $i > $o] :
( ( ( ! [SY1302: $i] :
( ~ ( SV51 @ SV318 )
| ~ ( SV51 @ SY1302 )
| ( SV318 = SY1302 ) ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV280
= ( sK40_SY1260 @ SV280 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1559,plain,
! [SV168: $i,SV294: $i > $o,SV281: $i > $o,SV52: $i] :
( ( ( in @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) @ SV168 )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1560,plain,
! [SV52: $i,SV168: $i,SV281: $i > $o,SV294: $i > $o] :
( ( ( ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 )
!= ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1561,plain,
! [SV52: $i,SV168: $i,SV294: $i > $o,SV281: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
| ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) ) )
| ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1562,plain,
! [SV54: $i,SV282: $i] :
( ( ( ~ ! [SY1288: $i] :
~ ~ ( ~ ( in @ SY1288 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SY1288 @ SV54 ) ) )
= $false )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1563,plain,
! [SV57: $i,SV273: $o,SV172: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV172 ) )
= $false )
| ( SV273 = $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1569,plain,
! [SV57: $i,SV172: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV172 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1573,plain,
! [SV63: $i,SV296: $o,SV176: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV176 )
| SV296 )
= $false )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1574,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 ) )
= $true )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1583,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV176 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1584,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1587,plain,
! [SV69: $i,SV297: $o,SV182: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV182 ) )
= $false )
| ( SV297 = $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1593,plain,
! [SV69: $i,SV182: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV182 ) )
= $false )
| ( $false = $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1596,plain,
! [SV72: $i,SV184: $i] :
( ( ( in @ SV184 @ ( sK33_SY1170 @ SV72 @ SV184 ) )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1597,plain,
! [SV184: $i,SV72: $i] :
( ( ( in @ ( sK33_SY1170 @ SV72 @ SV184 ) @ SV72 )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1598,plain,
! [SV72: $i,SV305: $i,SV184: $i] :
( ( ( in @ SV184 @ SV305 )
= $false )
| ( ( ~ ( in @ SV305 @ SV72 ) )
= $true )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1599,plain,
! [SV298: $i,SV189: $i > $o,SV75: $i] :
( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV298 @ SV75 )
= $false )
| ( ( SV189 @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1600,plain,
! [SV76: $i > $o,SV284: $i] :
( ( ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
| ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1602,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1603,plain,
! [SV79: $i,SV192: $i > $o,SV299: $i] :
( ( ( ~ ( in @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) @ SV79 ) )
= $false )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1509]) ).
thf(1604,plain,
! [SV79: $i,SV299: $i,SV192: $i > $o] :
( ( ( ~ ~ ( SV192 @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) ) )
= $false )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1509]) ).
thf(1605,plain,
! [SV80: $i,SV193: $i] :
( ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV193 )
= $true )
| ( ( in @ ( sK11_SY1178 @ SV193 @ SV80 ) @ SV80 )
= $true )
| ( ( SV80 = SV193 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1606,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( ~ ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1607,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1608,plain,
! [SV286: $i,SV94: $i > $o] :
( ( ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( ! [SY1026: $i,SY1027: $i] :
( ~ ( SV94 @ SY1026 )
| ~ ( SV94 @ SY1027 )
| ( SY1026 = SY1027 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1515]) ).
thf(1609,plain,
! [SV286: $i,SV319: $i,SV94: $i > $o] :
( ( ( ! [SY1303: $i] :
( ~ ( SV94 @ SV319 )
| ~ ( SV94 @ SY1303 )
| ( SV319 = SY1303 ) ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1269 @ SV286 @ SV94 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1610,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1611,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1612,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
| ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1614,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1520]) ).
thf(1615,plain,
! [SV207: $i > $o,SV101: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ SV101 ) )
= $true )
| ( ( ~ ( SV207 @ SV313 ) )
= $true )
| ( ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1616,plain,
! [SV207: $i > $o,SV101: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ SV101 ) )
= $true )
| ( ( ~ ( SV207 @ SV314 ) )
= $true )
| ( ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1617,plain,
! [SV287: $i,SV315: $i] :
( ( ( ~ ( ~ ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SV315 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1618,plain,
! [SV213: $i > $o,SV108: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ SV108 ) )
= $true )
| ( ( ~ ( SV213 @ SV307 ) )
= $true )
| ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1619,plain,
! [SV213: $i > $o,SV108: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV108 ) )
= $true )
| ( ( ~ ( SV213 @ SV308 ) )
= $true )
| ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1620,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( ~ ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1621,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1622,plain,
! [SV290: $i,SV117: $i > $o] :
( ( ( SV117 @ ( sK45_SY1274 @ SV290 @ SV117 ) )
= $true )
| ( ( SV117 @ SV290 )
= $false )
| ( ( SV117
@ ( descr
@ ^ [SY1086: $i] : ( SV117 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1623,plain,
! [SV222: $i,SV301: $i,SV119: $i,SV291: $i] :
( ( ( in @ SV291 @ SV119 )
= $false )
| ( ( in @ SV301 @ SV222 )
= $true )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1624,plain,
! [SV119: $i,SV291: $i,SV222: $i,SV301: $i] :
( ( ( in @ SV301 @ SV222 )
= $false )
| ( ( in @ SV291 @ SV119 )
= $true )
| ( ( SV291 = SV301 )
= $false )
| ( ( SV119 = SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1625,plain,
! [SV230: $i > $o,SV127: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ SV127 ) )
= $true )
| ( ( ~ ( SV230 @ SV316 ) )
= $true )
| ( ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1626,plain,
! [SV230: $i > $o,SV127: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ SV127 ) )
= $true )
| ( ( ~ ( SV230 @ SV317 ) )
= $true )
| ( ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1627,plain,
! [SV31: $i,SV320: $i] :
( ( ~ ( in @ SV320 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV320 )
| ( in @ SY1304 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1628,plain,
! [SV31: $i,SV321: $i] :
( ( ! [SY1305: $i] :
( ~ ~ ( ~ ( in @ SV321 @ SV31 )
| ~ ( in @ SY1305 @ SV31 ) )
| ~ ! [SY1306: $i] :
( ~ ( in @ SY1306 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1306 )
| ( in @ SY1305 @ SY1306 ) )
| ~ ( ~ ( in @ SY1305 @ SY1306 )
| ( in @ SV321 @ SY1306 ) ) ) )
| ( SV321 = SY1305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1629,plain,
! [SV311: $i,SV31: $i,SV309: $i] :
( ( ( ~ ( ~ ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SV311 @ ( sK2_SY860 @ SV31 ) ) ) )
= $false )
| ( ( ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV309 )
| ( in @ SY1299 @ SV311 ) )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1630,plain,
! [SV302: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
| ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 ) )
= $false )
| ( ( ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1537]) ).
thf(1631,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ! [SY882: $i] :
~ ~ ( ~ ( SV33 @ SY882 )
| ~ ! [SY883: $i] :
( ~ ( SV33 @ SY883 )
| ( SY882 = SY883 ) ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1632,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ~ ( ~ ( SV33 @ ( sK47_SY882 @ SV276 @ SV33 ) )
| ~ ! [SY1307: $i] :
( ~ ( SV33 @ SY1307 )
| ( ( sK47_SY882 @ SV276 @ SV33 )
= SY1307 ) ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1539]) ).
thf(1633,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
| ~ ! [SY1297: $i] :
~ ~ ( ~ ( in @ SY1297 @ SV155 )
| ~ ( SV35 @ SY1297 @ SV310 ) ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1634,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ~ ! [SY1298: $i] :
~ ~ ( ~ ( in @ SY1298 @ SV155 )
| ~ ( SV35 @ SY1298 @ SV310 ) )
| ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1635,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
| ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1542]) ).
thf(1636,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ! [SY896: $i] :
~ ( SV36 @ SY896 ) )
= $false )
| ( ( SV36 @ SV277 )
= $false )
| ( ( SV36 @ ( sK39_SY1257 @ SV277 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1637,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK49_SY896 @ SV277 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV277 )
= $false )
| ( ( SV277
= ( sK39_SY1257 @ SV277 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1544]) ).
thf(1638,plain,
! [SV41: $i,SV160: $i > $o,SV292: $i] :
( ( ( in @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) @ SV41 )
= $true )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1639,plain,
! [SV41: $i,SV292: $i,SV160: $i > $o] :
( ( ( ~ ( SV160 @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) ) )
= $true )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1640,plain,
! [SV44: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ omega )
| ( in @ SV322 @ SV44 ) )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( sK23_SY911 @ SV44 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1641,plain,
! [SV44: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ omega )
| ( in @ SV323 @ SV44 ) )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( sK23_SY911 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1642,plain,
! [SV46: $i,SV164: $i > $o,SV293: $i] :
( ( ( ~ ( in @ ( sK50_SY1134 @ SV293 @ SV164 @ SV46 ) @ SV46 )
| ( SV164 @ ( sK50_SY1134 @ SV293 @ SV164 @ SV46 ) ) )
= $false )
| ( ( in @ SV293 @ SV46 )
= $false )
| ( ( SV164 @ SV293 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1549]) ).
thf(1643,plain,
! [SV165: $i > $o,SV312: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV312 )
| ~ ! [SY1301: $i] :
( ~ ( SV47 @ SY1301 )
| ( SV312 = SY1301 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1644,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1551]) ).
thf(1647,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1648,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ~ ( ~ ( SV48 @ ( sK51_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1308: $i] :
( ~ ( SV48 @ SY1308 )
| ( ( sK51_SY930 @ SV278 @ SV48 )
= SY1308 ) ) ) )
= $false )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1554]) ).
thf(1649,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ! [SY930: $i] :
~ ~ ( ~ ( SV48 @ SY930 )
| ~ ! [SY931: $i] :
( ~ ( SV48 @ SY931 )
| ( SY930 = SY931 ) ) ) )
= $false )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1650,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ~ ( ~ ( SV48 @ ( sK52_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1309: $i] :
( ~ ( SV48 @ SY1309 )
| ( ( sK52_SY930 @ SV278 @ SV48 )
= SY1309 ) ) ) )
= $false )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1556]) ).
thf(1651,plain,
! [SV280: $i,SV324: $i,SV51: $i > $o] :
( ( ( ! [SY1310: $i] :
( ~ ( SV51 @ SV324 )
| ~ ( SV51 @ SY1310 )
| ( SV324 = SY1310 ) ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1652,plain,
! [SV280: $i,SV325: $i,SV318: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV318 )
| ~ ( SV51 @ SV325 )
| ( SV318 = SV325 ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV280
= ( sK40_SY1260 @ SV280 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1653,plain,
! [SV52: $i,SV168: $i,SV281: $i > $o,SV294: $i > $o] :
( ( ( ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 )
= ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1654,plain,
! [SV52: $i,SV168: $i,SV294: $i > $o,SV281: $i > $o] :
( ( ( ~ ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
| ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) ) )
| ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1655,plain,
! [SV54: $i,SV282: $i] :
( ( ( ! [SY1288: $i] :
~ ~ ( ~ ( in @ SY1288 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SY1288 @ SV54 ) ) )
= $true )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1656,plain,
! [SV57: $i,SV273: $o,SV172: $i,SV247: $i] :
( ( ( in @ SV247 @ SV172 )
= $true )
| ( SV273 = $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1658,plain,
! [SV57: $i,SV172: $i,SV247: $i] :
( ( ( in @ SV247 @ SV172 )
= $true )
| ( $false = $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1660,plain,
! [SV63: $i,SV296: $o,SV176: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV176 ) )
= $false )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1662,plain,
! [SV296: $o,SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| SV296 )
= $false )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1674,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV176 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1676,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV63 )
| ~ ( in @ SV249 @ SV176 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1680,plain,
! [SV69: $i,SV297: $o,SV182: $i,SV253: $i] :
( ( ( in @ SV253 @ SV182 )
= $true )
| ( SV297 = $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1682,plain,
! [SV69: $i,SV182: $i,SV253: $i] :
( ( ( in @ SV253 @ SV182 )
= $true )
| ( $false = $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1683,plain,
! [SV184: $i,SV72: $i,SV305: $i] :
( ( ( in @ SV305 @ SV72 )
= $false )
| ( ( in @ SV184 @ SV305 )
= $false )
| ( ( in @ SV184 @ ( setunion @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1684,plain,
! [SV76: $i > $o,SV284: $i] :
( ( ( ( sK19_SY1267 @ SV284 @ SV76 )
!= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1687,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $false )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1688,plain,
! [SV79: $i,SV192: $i > $o,SV299: $i] :
( ( ( in @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) @ SV79 )
= $true )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1689,plain,
! [SV79: $i,SV299: $i,SV192: $i > $o] :
( ( ( ~ ( SV192 @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) ) )
= $true )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1690,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ! [SY1019: $i] :
~ ! [SY1020: $i] :
~ ( ~ ( ~ ( SV91 @ SY1020 )
| ( SY1020 = SY1019 ) )
| ~ ( ( SY1020 != SY1019 )
| ( SV91 @ SY1020 ) ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1691,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ~ ! [SY1311: $i] :
~ ( ~ ( ~ ( SV91 @ SY1311 )
| ( SY1311
= ( sK53_SY1019 @ SV285 @ SV91 ) ) )
| ~ ( ( SY1311
!= ( sK53_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SY1311 ) ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1607]) ).
thf(1692,plain,
! [SV286: $i,SV326: $i,SV94: $i > $o] :
( ( ( ! [SY1312: $i] :
( ~ ( SV94 @ SV326 )
| ~ ( SV94 @ SY1312 )
| ( SV326 = SY1312 ) ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1693,plain,
! [SV286: $i,SV327: $i,SV319: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ SV319 )
| ~ ( SV94 @ SV327 )
| ( SV319 = SV327 ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1269 @ SV286 @ SV94 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1694,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1695,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1696,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1699,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1700,plain,
! [SV207: $i > $o,SV101: $i,SV313: $i] :
( ( ( in @ SV313 @ SV101 )
= $false )
| ( ( ~ ( SV207 @ SV313 ) )
= $true )
| ( ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1701,plain,
! [SV207: $i > $o,SV101: $i,SV314: $i] :
( ( ( in @ SV314 @ SV101 )
= $false )
| ( ( ~ ( SV207 @ SV314 ) )
= $true )
| ( ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1702,plain,
! [SV287: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SV315 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1703,plain,
! [SV213: $i > $o,SV108: $i,SV307: $i] :
( ( ( in @ SV307 @ SV108 )
= $false )
| ( ( ~ ( SV213 @ SV307 ) )
= $true )
| ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1704,plain,
! [SV213: $i > $o,SV108: $i,SV308: $i] :
( ( ( in @ SV308 @ SV108 )
= $false )
| ( ( ~ ( SV213 @ SV308 ) )
= $true )
| ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1705,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ! [SY1064: $i] :
~ ~ ( ~ ( SV109 @ SY1064 )
| ~ ! [SY1065: $i] :
( ~ ( SV109 @ SY1065 )
| ( SY1064 = SY1065 ) ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1706,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ~ ( ~ ( SV109 @ ( sK54_SY1064 @ SV288 @ SV109 ) )
| ~ ! [SY1313: $i] :
( ~ ( SV109 @ SY1313 )
| ( ( sK54_SY1064 @ SV288 @ SV109 )
= SY1313 ) ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1621]) ).
thf(1707,plain,
! [SV230: $i > $o,SV127: $i,SV316: $i] :
( ( ( in @ SV316 @ SV127 )
= $false )
| ( ( ~ ( SV230 @ SV316 ) )
= $true )
| ( ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1708,plain,
! [SV230: $i > $o,SV127: $i,SV317: $i] :
( ( ( in @ SV317 @ SV127 )
= $false )
| ( ( ~ ( SV230 @ SV317 ) )
= $true )
| ( ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1709,plain,
! [SV31: $i,SV320: $i] :
( ( ( ~ ( in @ SV320 @ ( sK2_SY860 @ SV31 ) ) )
= $true )
| ( ( ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV320 )
| ( in @ SY1304 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1710,plain,
! [SV328: $i,SV31: $i,SV321: $i] :
( ( ~ ~ ( ~ ( in @ SV321 @ SV31 )
| ~ ( in @ SV328 @ SV31 ) )
| ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) )
| ( SV321 = SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1711,plain,
! [SV311: $i,SV31: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SV311 @ ( sK2_SY860 @ SV31 ) ) )
= $true )
| ( ( ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV309 )
| ( in @ SY1299 @ SV311 ) )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1712,plain,
! [SV302: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 ) )
= $false )
| ( ( ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1713,plain,
! [SV302: $i,SV31: $i] :
( ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1714,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ~ ( ~ ( SV33 @ ( sK55_SY882 @ SV276 @ SV33 ) )
| ~ ! [SY1315: $i] :
( ~ ( SV33 @ SY1315 )
| ( ( sK55_SY882 @ SV276 @ SV33 )
= SY1315 ) ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1631]) ).
thf(1715,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( ~ ( SV33 @ ( sK47_SY882 @ SV276 @ SV33 ) )
| ~ ! [SY1307: $i] :
( ~ ( SV33 @ SY1307 )
| ( ( sK47_SY882 @ SV276 @ SV33 )
= SY1307 ) ) ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1716,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) ) )
= $true )
| ( ( ~ ! [SY1297: $i] :
~ ~ ( ~ ( in @ SY1297 @ SV155 )
| ~ ( SV35 @ SY1297 @ SV310 ) ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1717,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ~ ! [SY1298: $i] :
~ ~ ( ~ ( in @ SY1298 @ SV155 )
| ~ ( SV35 @ SY1298 @ SV310 ) ) )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1718,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( ~ ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1719,plain,
! [SV35: $i > $i > $o,SV155: $i,SV303: $i] :
( ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1720,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK56_SY896 @ SV277 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV277 )
= $false )
| ( ( SV36 @ ( sK39_SY1257 @ SV277 @ SV36 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1636]) ).
thf(1721,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK49_SY896 @ SV277 @ SV36 ) )
= $true )
| ( ( SV36 @ SV277 )
= $false )
| ( ( SV277
= ( sK39_SY1257 @ SV277 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1722,plain,
! [SV41: $i,SV292: $i,SV160: $i > $o] :
( ( ( SV160 @ ( sK34_SY1130 @ SV292 @ SV160 @ SV41 ) )
= $false )
| ( ( SV160 @ SV292 )
= $true )
| ( ( in @ SV292 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1723,plain,
! [SV44: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ omega ) )
= $true )
| ( ( in @ SV322 @ SV44 )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( sK23_SY911 @ SV44 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1724,plain,
! [SV44: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ omega ) )
= $true )
| ( ( in @ SV323 @ SV44 )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( sK23_SY911 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1725,plain,
! [SV46: $i,SV164: $i > $o,SV293: $i] :
( ( ( ~ ( in @ ( sK50_SY1134 @ SV293 @ SV164 @ SV46 ) @ SV46 ) )
= $false )
| ( ( in @ SV293 @ SV46 )
= $false )
| ( ( SV164 @ SV293 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1726,plain,
! [SV46: $i,SV293: $i,SV164: $i > $o] :
( ( ( SV164 @ ( sK50_SY1134 @ SV293 @ SV164 @ SV46 ) )
= $false )
| ( ( in @ SV293 @ SV46 )
= $false )
| ( ( SV164 @ SV293 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1727,plain,
! [SV165: $i > $o,SV312: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV312 ) )
= $true )
| ( ( ~ ! [SY1301: $i] :
( ~ ( SV47 @ SY1301 )
| ( SV312 = SY1301 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1728,plain,
! [SV47: $i > $o,SV165: $i > $o] :
( ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) )
| ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1731,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1732,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( ~ ( SV48 @ ( sK51_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1308: $i] :
( ~ ( SV48 @ SY1308 )
| ( ( sK51_SY930 @ SV278 @ SV48 )
= SY1308 ) ) ) )
= $true )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1733,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ~ ( ~ ( SV48 @ ( sK57_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1316: $i] :
( ~ ( SV48 @ SY1316 )
| ( ( sK57_SY930 @ SV278 @ SV48 )
= SY1316 ) ) ) )
= $false )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1649]) ).
thf(1734,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( ~ ( SV48 @ ( sK52_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1309: $i] :
( ~ ( SV48 @ SY1309 )
| ( ( sK52_SY930 @ SV278 @ SV48 )
= SY1309 ) ) ) )
= $true )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1735,plain,
! [SV280: $i,SV329: $i,SV324: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV324 )
| ~ ( SV51 @ SV329 )
| ( SV324 = SV329 ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1736,plain,
! [SV280: $i,SV325: $i,SV318: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV318 ) )
= $true )
| ( ( ~ ( SV51 @ SV325 )
| ( SV318 = SV325 ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV280
= ( sK40_SY1260 @ SV280 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1737,plain,
! [SV52: $i,SV168: $i,SV294: $i > $o,SV281: $i > $o] :
( ( ( ~ ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
| ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1738,plain,
! [SV54: $i,SV282: $i,SV330: $i] :
( ( ( ~ ~ ( ~ ( in @ SV330 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SV330 @ SV54 ) ) )
= $true )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1740,plain,
! [SV63: $i,SV296: $o,SV176: $i,SV249: $i] :
( ( ( in @ SV249 @ SV176 )
= $true )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1741,plain,
! [SV176: $i,SV296: $o,SV63: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV63 ) )
= $false )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1662]) ).
thf(1752,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( in @ SV249 @ SV176 )
= $true )
| ( $false = $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1753,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ~ ( in @ SV249 @ SV63 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1757,plain,
! [SV76: $i > $o,SV284: $i] :
( ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ~ ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1760,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ~ ( ~ ( SV76 @ ( sK58_SY995 @ SV284 @ SV76 ) )
| ~ ! [SY1317: $i] :
( ~ ( SV76 @ SY1317 )
| ( ( sK58_SY995 @ SV284 @ SV76 )
= SY1317 ) ) ) )
= $false )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1687]) ).
thf(1761,plain,
! [SV79: $i,SV299: $i,SV192: $i > $o] :
( ( ( SV192 @ ( sK37_SY1177 @ SV299 @ SV192 @ SV79 ) )
= $false )
| ( ( SV192 @ SV299 )
= $true )
| ( ( in @ SV299 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1762,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ~ ! [SY1318: $i] :
~ ( ~ ( ~ ( SV91 @ SY1318 )
| ( SY1318
= ( sK59_SY1019 @ SV285 @ SV91 ) ) )
| ~ ( ( SY1318
!= ( sK59_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SY1318 ) ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1690]) ).
thf(1763,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ! [SY1311: $i] :
~ ( ~ ( ~ ( SV91 @ SY1311 )
| ( SY1311
= ( sK53_SY1019 @ SV285 @ SV91 ) ) )
| ~ ( ( SY1311
!= ( sK53_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SY1311 ) ) ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1764,plain,
! [SV286: $i,SV331: $i,SV326: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ SV326 )
| ~ ( SV94 @ SV331 )
| ( SV326 = SV331 ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1765,plain,
! [SV286: $i,SV327: $i,SV319: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ SV319 ) )
= $true )
| ( ( ~ ( SV94 @ SV327 )
| ( SV319 = SV327 ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1269 @ SV286 @ SV94 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1766,plain,
! [SV206: $i > $o,SV332: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ SV332 )
| ~ ! [SY1319: $i] :
( ~ ( SV100 @ SY1319 )
| ( SV332 = SY1319 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(1767,plain,
! [SV100: $i > $o,SV333: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ SV333 )
| ~ ! [SY1320: $i] :
( ~ ( SV206 @ SY1320 )
| ( SV333 = SY1320 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1768,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(1771,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1772,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1773,plain,
! [SV101: $i,SV313: $i,SV207: $i > $o] :
( ( ( SV207 @ SV313 )
= $false )
| ( ( in @ SV313 @ SV101 )
= $false )
| ( ( in @ ( sK21_SY1197 @ SV207 @ SV101 ) @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1774,plain,
! [SV101: $i,SV314: $i,SV207: $i > $o] :
( ( ( SV207 @ SV314 )
= $false )
| ( ( in @ SV314 @ SV101 )
= $false )
| ( ( SV207 @ ( sK21_SY1197 @ SV207 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1775,plain,
! [SV287: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SV315 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1776,plain,
! [SV108: $i,SV307: $i,SV213: $i > $o] :
( ( ( SV213 @ SV307 )
= $false )
| ( ( in @ SV307 @ SV108 )
= $false )
| ( ( in @ ( sK13_SY1204 @ SV213 @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1777,plain,
! [SV108: $i,SV308: $i,SV213: $i > $o] :
( ( ( SV213 @ SV308 )
= $false )
| ( ( in @ SV308 @ SV108 )
= $false )
| ( ( SV213 @ ( sK13_SY1204 @ SV213 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1778,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ~ ( ~ ( SV109 @ ( sK60_SY1064 @ SV288 @ SV109 ) )
| ~ ! [SY1321: $i] :
( ~ ( SV109 @ SY1321 )
| ( ( sK60_SY1064 @ SV288 @ SV109 )
= SY1321 ) ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1705]) ).
thf(1779,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( ~ ( SV109 @ ( sK54_SY1064 @ SV288 @ SV109 ) )
| ~ ! [SY1313: $i] :
( ~ ( SV109 @ SY1313 )
| ( ( sK54_SY1064 @ SV288 @ SV109 )
= SY1313 ) ) ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1780,plain,
! [SV127: $i,SV316: $i,SV230: $i > $o] :
( ( ( SV230 @ SV316 )
= $false )
| ( ( in @ SV316 @ SV127 )
= $false )
| ( ( in @ ( sK22_SY1221 @ SV230 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1781,plain,
! [SV127: $i,SV317: $i,SV230: $i > $o] :
( ( ( SV230 @ SV317 )
= $false )
| ( ( in @ SV317 @ SV127 )
= $false )
| ( ( SV230 @ ( sK22_SY1221 @ SV230 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1782,plain,
! [SV31: $i,SV320: $i] :
( ( ( in @ SV320 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV320 )
| ( in @ SY1304 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1783,plain,
! [SV328: $i,SV31: $i,SV321: $i] :
( ( ( ~ ~ ( ~ ( in @ SV321 @ SV31 )
| ~ ( in @ SV328 @ SV31 ) ) )
= $true )
| ( ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) )
| ( SV321 = SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1784,plain,
! [SV311: $i,SV31: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ ( sK2_SY860 @ SV31 ) ) )
= $true )
| ( ( ~ ( in @ SV311 @ ( sK2_SY860 @ SV31 ) ) )
= $true )
| ( ( ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV309 )
| ( in @ SY1299 @ SV311 ) )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1785,plain,
! [SV302: $i,SV31: $i] :
( ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( ~ ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1786,plain,
! [SV31: $i,SV302: $i] :
( ( ( ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1787,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( ~ ( SV33 @ ( sK55_SY882 @ SV276 @ SV33 ) )
| ~ ! [SY1315: $i] :
( ~ ( SV33 @ SY1315 )
| ( ( sK55_SY882 @ SV276 @ SV33 )
= SY1315 ) ) ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1788,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ ( sK47_SY882 @ SV276 @ SV33 ) )
| ~ ! [SY1307: $i] :
( ~ ( SV33 @ SY1307 )
| ( ( sK47_SY882 @ SV276 @ SV33 )
= SY1307 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1789,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( ~ ! [SY1297: $i] :
~ ~ ( ~ ( in @ SY1297 @ SV155 )
| ~ ( SV35 @ SY1297 @ SV310 ) ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1790,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ! [SY1298: $i] :
~ ~ ( ~ ( in @ SY1298 @ SV155 )
| ~ ( SV35 @ SY1298 @ SV310 ) ) )
= $false )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1791,plain,
! [SV303: $i,SV155: $i,SV35: $i > $i > $o] :
( ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( ~ ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1792,plain,
! [SV303: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1793,plain,
! [SV277: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK56_SY896 @ SV277 @ SV36 ) )
= $true )
| ( ( SV36 @ SV277 )
= $false )
| ( ( SV36 @ ( sK39_SY1257 @ SV277 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1794,plain,
! [SV44: $i,SV322: $i] :
( ( ( in @ SV322 @ omega )
= $false )
| ( ( in @ SV322 @ SV44 )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( sK23_SY911 @ SV44 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1795,plain,
! [SV44: $i,SV323: $i] :
( ( ( in @ SV323 @ omega )
= $false )
| ( ( in @ SV323 @ SV44 )
= $true )
| ( ( in @ emptyset @ SV44 )
= $false )
| ( ( in @ ( sK23_SY911 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1796,plain,
! [SV46: $i,SV164: $i > $o,SV293: $i] :
( ( ( in @ ( sK50_SY1134 @ SV293 @ SV164 @ SV46 ) @ SV46 )
= $true )
| ( ( in @ SV293 @ SV46 )
= $false )
| ( ( SV164 @ SV293 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1797,plain,
! [SV165: $i > $o,SV312: $i,SV47: $i > $o] :
( ( ( SV47 @ SV312 )
= $false )
| ( ( ~ ! [SY1301: $i] :
( ~ ( SV47 @ SY1301 )
| ( SV312 = SY1301 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1798,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(1801,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1802,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK51_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1308: $i] :
( ~ ( SV48 @ SY1308 )
| ( ( sK51_SY930 @ SV278 @ SV48 )
= SY1308 ) ) )
= $false )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1803,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( ~ ( SV48 @ ( sK57_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1316: $i] :
( ~ ( SV48 @ SY1316 )
| ( ( sK57_SY930 @ SV278 @ SV48 )
= SY1316 ) ) ) )
= $true )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1733]) ).
thf(1804,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK52_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1309: $i] :
( ~ ( SV48 @ SY1309 )
| ( ( sK52_SY930 @ SV278 @ SV48 )
= SY1309 ) ) )
= $false )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1805,plain,
! [SV280: $i,SV329: $i,SV324: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV324 ) )
= $true )
| ( ( ~ ( SV51 @ SV329 )
| ( SV324 = SV329 ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(1806,plain,
! [SV280: $i,SV325: $i,SV318: $i,SV51: $i > $o] :
( ( ( SV51 @ SV318 )
= $false )
| ( ( ~ ( SV51 @ SV325 )
| ( SV318 = SV325 ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV280
= ( sK40_SY1260 @ SV280 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1807,plain,
! [SV52: $i,SV168: $i,SV294: $i > $o,SV281: $i > $o] :
( ( ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
| ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) ) )
= $false )
| ( ( ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1808,plain,
! [SV54: $i,SV282: $i,SV330: $i] :
( ( ( ~ ( ~ ( in @ SV330 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SV330 @ SV54 ) ) )
= $false )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1809,plain,
! [SV176: $i,SV296: $o,SV63: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV63 ) )
= $true )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1741]) ).
thf(1815,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV63 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1818,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ! [SY995: $i] :
~ ~ ( ~ ( SV76 @ SY995 )
| ~ ! [SY996: $i] :
( ~ ( SV76 @ SY996 )
| ( SY995 = SY996 ) ) ) )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1821,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( SV76 @ ( sK58_SY995 @ SV284 @ SV76 ) )
| ~ ! [SY1317: $i] :
( ~ ( SV76 @ SY1317 )
| ( ( sK58_SY995 @ SV284 @ SV76 )
= SY1317 ) ) ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(1822,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( ! [SY1318: $i] :
~ ( ~ ( ~ ( SV91 @ SY1318 )
| ( SY1318
= ( sK59_SY1019 @ SV285 @ SV91 ) ) )
| ~ ( ( SY1318
!= ( sK59_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SY1318 ) ) ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1823,plain,
! [SV285: $i,SV334: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV91 @ SV334 )
| ( SV334
= ( sK53_SY1019 @ SV285 @ SV91 ) ) )
| ~ ( ( SV334
!= ( sK53_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SV334 ) ) ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(1824,plain,
! [SV286: $i,SV331: $i,SV326: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ SV326 ) )
= $true )
| ( ( ~ ( SV94 @ SV331 )
| ( SV326 = SV331 ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(1825,plain,
! [SV286: $i,SV327: $i,SV319: $i,SV94: $i > $o] :
( ( ( SV94 @ SV319 )
= $false )
| ( ( ~ ( SV94 @ SV327 )
| ( SV319 = SV327 ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1269 @ SV286 @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1826,plain,
! [SV206: $i > $o,SV332: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ SV332 )
| ~ ! [SY1319: $i] :
( ~ ( SV100 @ SY1319 )
| ( SV332 = SY1319 ) ) ) )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1827,plain,
! [SV100: $i > $o,SV333: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ SV333 )
| ~ ! [SY1320: $i] :
( ~ ( SV206 @ SY1320 )
| ( SV333 = SY1320 ) ) ) )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1828,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
| ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1833,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1834,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1835,plain,
! [SV287: $i,SV315: $i] :
( ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SV315 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1836,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( ~ ( SV109 @ ( sK60_SY1064 @ SV288 @ SV109 ) )
| ~ ! [SY1321: $i] :
( ~ ( SV109 @ SY1321 )
| ( ( sK60_SY1064 @ SV288 @ SV109 )
= SY1321 ) ) ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1837,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ ( sK54_SY1064 @ SV288 @ SV109 ) )
| ~ ! [SY1313: $i] :
( ~ ( SV109 @ SY1313 )
| ( ( sK54_SY1064 @ SV288 @ SV109 )
= SY1313 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1838,plain,
! [SV31: $i,SV320: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ SV320 )
| ( in @ SV335 @ SV31 ) )
= $true )
| ( ( in @ SV320 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(1839,plain,
! [SV328: $i,SV31: $i,SV321: $i] :
( ( ( ~ ( ~ ( in @ SV321 @ SV31 )
| ~ ( in @ SV328 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) )
| ( SV321 = SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1840,plain,
! [SV311: $i,SV31: $i,SV309: $i] :
( ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( ~ ( in @ SV311 @ ( sK2_SY860 @ SV31 ) ) )
= $true )
| ( ( ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV309 )
| ( in @ SY1299 @ SV311 ) )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1841,plain,
! [SV31: $i,SV302: $i] :
( ( ( ~ ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(1842,plain,
! [SV31: $i,SV302: $i] :
( ( ( ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1843,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ ( sK55_SY882 @ SV276 @ SV33 ) )
| ~ ! [SY1315: $i] :
( ~ ( SV33 @ SY1315 )
| ( ( sK55_SY882 @ SV276 @ SV33 )
= SY1315 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1844,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ ( sK47_SY882 @ SV276 @ SV33 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1845,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ! [SY1307: $i] :
( ~ ( SV33 @ SY1307 )
| ( ( sK47_SY882 @ SV276 @ SV33 )
= SY1307 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1846,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1297: $i] :
~ ~ ( ~ ( in @ SY1297 @ SV155 )
| ~ ( SV35 @ SY1297 @ SV310 ) ) )
= $false )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1847,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1298: $i] :
~ ~ ( ~ ( in @ SY1298 @ SV155 )
| ~ ( SV35 @ SY1298 @ SV310 ) ) )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1848,plain,
! [SV303: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1121: $i] :
~ ! [SY1122: $i] :
~ ( ~ ( ~ ( in @ SY1122 @ SY1121 )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1122 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1122 ) )
| ( in @ SY1122 @ SY1121 ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1849,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i] :
( ( ( ~ ! [SY1324: $i] :
~ ( ~ ( ~ ( in @ SY1324 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1324 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1324 ) )
| ( in @ SY1324 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1792]) ).
thf(1850,plain,
! [SV165: $i > $o,SV312: $i,SV47: $i > $o] :
( ( ( ! [SY1301: $i] :
( ~ ( SV47 @ SY1301 )
| ( SV312 = SY1301 ) ) )
= $false )
| ( ( SV47 @ SV312 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1851,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1854,plain,
! [SV165: $i > $o,SV336: $i,SV47: $i > $o] :
( ( ( ~ ~ ( ~ ( SV47 @ SV336 )
| ~ ! [SY1327: $i] :
( ~ ( SV47 @ SY1327 )
| ( SV336 = SY1327 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(1855,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK51_SY930 @ SV278 @ SV48 ) ) )
= $false )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1802]) ).
thf(1856,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ! [SY1308: $i] :
( ~ ( SV48 @ SY1308 )
| ( ( sK51_SY930 @ SV278 @ SV48 )
= SY1308 ) ) )
= $false )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1802]) ).
thf(1857,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK57_SY930 @ SV278 @ SV48 ) )
| ~ ! [SY1316: $i] :
( ~ ( SV48 @ SY1316 )
| ( ( sK57_SY930 @ SV278 @ SV48 )
= SY1316 ) ) )
= $false )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1858,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK52_SY930 @ SV278 @ SV48 ) ) )
= $false )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1804]) ).
thf(1859,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ! [SY1309: $i] :
( ~ ( SV48 @ SY1309 )
| ( ( sK52_SY930 @ SV278 @ SV48 )
= SY1309 ) ) )
= $false )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1804]) ).
thf(1860,plain,
! [SV280: $i,SV329: $i,SV324: $i,SV51: $i > $o] :
( ( ( SV51 @ SV324 )
= $false )
| ( ( ~ ( SV51 @ SV329 )
| ( SV324 = SV329 ) )
= $true )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1861,plain,
! [SV280: $i,SV318: $i,SV325: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV325 ) )
= $true )
| ( ( SV318 = SV325 )
= $true )
| ( ( SV51 @ SV318 )
= $false )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV280
= ( sK40_SY1260 @ SV280 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(1862,plain,
! [SV52: $i,SV168: $i,SV294: $i > $o,SV281: $i > $o] :
( ( ( ~ ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) )
= $false )
| ( ( ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1863,plain,
! [SV168: $i,SV281: $i > $o,SV52: $i,SV294: $i > $o] :
( ( ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1864,plain,
! [SV54: $i,SV282: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ ( sK27_SY951 @ SV282 @ SV54 ) )
| ~ ( in @ SV330 @ SV54 ) )
= $true )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1865,plain,
! [SV176: $i,SV296: $o,SV63: $i,SV249: $i] :
( ( ( in @ SV249 @ SV63 )
= $false )
| ( SV296 = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(1869,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( in @ SV249 @ SV63 )
= $false )
| ( $false = $true )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1871,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ~ ( ~ ( SV76 @ ( sK64_SY995 @ SV284 @ SV76 ) )
| ~ ! [SY1328: $i] :
( ~ ( SV76 @ SY1328 )
| ( ( sK64_SY995 @ SV284 @ SV76 )
= SY1328 ) ) ) )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1818]) ).
thf(1874,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK58_SY995 @ SV284 @ SV76 ) )
| ~ ! [SY1317: $i] :
( ~ ( SV76 @ SY1317 )
| ( ( sK58_SY995 @ SV284 @ SV76 )
= SY1317 ) ) )
= $false )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1875,plain,
! [SV285: $i,SV337: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV91 @ SV337 )
| ( SV337
= ( sK59_SY1019 @ SV285 @ SV91 ) ) )
| ~ ( ( SV337
!= ( sK59_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SV337 ) ) ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(1876,plain,
! [SV285: $i,SV334: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( SV91 @ SV334 )
| ( SV334
= ( sK53_SY1019 @ SV285 @ SV91 ) ) )
| ~ ( ( SV334
!= ( sK53_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SV334 ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1877,plain,
! [SV286: $i,SV331: $i,SV326: $i,SV94: $i > $o] :
( ( ( SV94 @ SV326 )
= $false )
| ( ( ~ ( SV94 @ SV331 )
| ( SV326 = SV331 ) )
= $true )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1878,plain,
! [SV286: $i,SV319: $i,SV327: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ SV327 ) )
= $true )
| ( ( SV319 = SV327 )
= $true )
| ( ( SV94 @ SV319 )
= $false )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1269 @ SV286 @ SV94 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1879,plain,
! [SV206: $i > $o,SV332: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV332 )
| ~ ! [SY1319: $i] :
( ~ ( SV100 @ SY1319 )
| ( SV332 = SY1319 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1880,plain,
! [SV100: $i > $o,SV333: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV333 )
| ~ ! [SY1320: $i] :
( ~ ( SV206 @ SY1320 )
| ( SV333 = SY1320 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1881,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1882,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1887,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1888,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(1889,plain,
! [SV315: $i,SV287: $i] :
( ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV287 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SV315 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1890,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ ( sK60_SY1064 @ SV288 @ SV109 ) )
| ~ ! [SY1321: $i] :
( ~ ( SV109 @ SY1321 )
| ( ( sK60_SY1064 @ SV288 @ SV109 )
= SY1321 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1891,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ ( sK54_SY1064 @ SV288 @ SV109 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1837]) ).
thf(1892,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ! [SY1313: $i] :
( ~ ( SV109 @ SY1313 )
| ( ( sK54_SY1064 @ SV288 @ SV109 )
= SY1313 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1837]) ).
thf(1893,plain,
! [SV31: $i,SV320: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ SV320 ) )
= $true )
| ( ( in @ SV335 @ SV31 )
= $true )
| ( ( in @ SV320 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(1894,plain,
! [SV328: $i,SV31: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ SV31 )
| ~ ( in @ SV328 @ SV31 ) )
= $true )
| ( ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) )
| ( SV321 = SV328 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1895,plain,
! [SV309: $i,SV31: $i,SV311: $i] :
( ( ( in @ SV311 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV309 )
| ( in @ SY1299 @ SV311 ) )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1896,plain,
! [SV31: $i,SV302: $i] :
( ( ( ! [SY1281: $i] :
~ ( in @ SY1281 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(1897,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ( in @ SV338 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(1898,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ ( sK55_SY882 @ SV276 @ SV33 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1899,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ~ ! [SY1315: $i] :
( ~ ( SV33 @ SY1315 )
| ( ( sK55_SY882 @ SV276 @ SV33 )
= SY1315 ) ) )
= $false )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1900,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( SV33 @ ( sK47_SY882 @ SV276 @ SV33 ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(1901,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ! [SY1307: $i] :
( ~ ( SV33 @ SY1307 )
| ( ( sK47_SY882 @ SV276 @ SV33 )
= SY1307 ) ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(1902,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV310 ) ) )
= $false )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1846]) ).
thf(1903,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i,SV339: $i] :
( ( ( ~ ~ ( ~ ( in @ SV339 @ SV155 )
| ~ ( SV35 @ SV339 @ SV310 ) ) )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(1904,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i] :
( ( ( ~ ! [SY1329: $i] :
~ ( ~ ( ~ ( in @ SY1329 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1329 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1329 ) )
| ( in @ SY1329 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1848]) ).
thf(1905,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i] :
( ( ( ! [SY1324: $i] :
~ ( ~ ( ~ ( in @ SY1324 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1324 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1324 ) )
| ( in @ SY1324 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1906,plain,
! [SV312: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
| ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) ) )
= $false )
| ( ( SV47 @ SV312 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1850]) ).
thf(1907,plain,
! [SV165: $i > $o,SV47: $i > $o] :
( ( ( ! [SY921: $i] :
~ ~ ( ~ ( SV47 @ SY921 )
| ~ ! [SY922: $i] :
( ~ ( SV47 @ SY922 )
| ( SY921 = SY922 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1851]) ).
thf(1910,plain,
! [SV165: $i > $o,SV336: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ SV336 )
| ~ ! [SY1327: $i] :
( ~ ( SV47 @ SY1327 )
| ( SV336 = SY1327 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1911,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( SV48 @ ( sK51_SY930 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1912,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ! [SY1308: $i] :
( ~ ( SV48 @ SY1308 )
| ( ( sK51_SY930 @ SV278 @ SV48 )
= SY1308 ) ) )
= $true )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1913,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ ( sK57_SY930 @ SV278 @ SV48 ) ) )
= $false )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1914,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ~ ! [SY1316: $i] :
( ~ ( SV48 @ SY1316 )
| ( ( sK57_SY930 @ SV278 @ SV48 )
= SY1316 ) ) )
= $false )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1915,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( SV48 @ ( sK52_SY930 @ SV278 @ SV48 ) )
= $true )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(1916,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ! [SY1309: $i] :
( ~ ( SV48 @ SY1309 )
| ( ( sK52_SY930 @ SV278 @ SV48 )
= SY1309 ) ) )
= $true )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(1917,plain,
! [SV280: $i,SV324: $i,SV329: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV329 ) )
= $true )
| ( ( SV324 = SV329 )
= $true )
| ( ( SV51 @ SV324 )
= $false )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1918,plain,
! [SV280: $i,SV318: $i,SV325: $i,SV51: $i > $o] :
( ( ( SV51 @ SV325 )
= $false )
| ( ( SV318 = SV325 )
= $true )
| ( ( SV51 @ SV318 )
= $false )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV280
= ( sK40_SY1260 @ SV280 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1919,plain,
! [SV52: $i,SV168: $i,SV294: $i > $o,SV281: $i > $o] :
( ( ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
= $true )
| ( ( ~ ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1920,plain,
! [SV168: $i,SV281: $i > $o,SV52: $i,SV294: $i > $o] :
( ( ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) )
= $false )
| ( ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(1921,plain,
! [SV54: $i,SV282: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ ( sK27_SY951 @ SV282 @ SV54 ) ) )
= $true )
| ( ( ~ ( in @ SV330 @ SV54 ) )
= $true )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(1922,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( SV76 @ ( sK64_SY995 @ SV284 @ SV76 ) )
| ~ ! [SY1328: $i] :
( ~ ( SV76 @ SY1328 )
| ( ( sK64_SY995 @ SV284 @ SV76 )
= SY1328 ) ) ) )
= $true )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1925,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK58_SY995 @ SV284 @ SV76 ) ) )
= $false )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1926,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ! [SY1317: $i] :
( ~ ( SV76 @ SY1317 )
| ( ( sK58_SY995 @ SV284 @ SV76 )
= SY1317 ) ) )
= $false )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1927,plain,
! [SV285: $i,SV337: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( SV91 @ SV337 )
| ( SV337
= ( sK59_SY1019 @ SV285 @ SV91 ) ) )
| ~ ( ( SV337
!= ( sK59_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SV337 ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(1928,plain,
! [SV285: $i,SV334: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( SV91 @ SV334 )
| ( SV334
= ( sK53_SY1019 @ SV285 @ SV91 ) ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1929,plain,
! [SV91: $i > $o,SV285: $i,SV334: $i] :
( ( ( ~ ( ( SV334
!= ( sK53_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SV334 ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(1930,plain,
! [SV286: $i,SV326: $i,SV331: $i,SV94: $i > $o] :
( ( ( ~ ( SV94 @ SV331 ) )
= $true )
| ( ( SV326 = SV331 )
= $true )
| ( ( SV94 @ SV326 )
= $false )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(1931,plain,
! [SV286: $i,SV319: $i,SV327: $i,SV94: $i > $o] :
( ( ( SV94 @ SV327 )
= $false )
| ( ( SV319 = SV327 )
= $true )
| ( ( SV94 @ SV319 )
= $false )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV286
= ( sK43_SY1269 @ SV286 @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1932,plain,
! [SV206: $i > $o,SV332: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV332 ) )
= $true )
| ( ( ~ ! [SY1319: $i] :
( ~ ( SV100 @ SY1319 )
| ( SV332 = SY1319 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(1933,plain,
! [SV100: $i > $o,SV333: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV333 ) )
= $true )
| ( ( ~ ! [SY1320: $i] :
( ~ ( SV206 @ SY1320 )
| ( SV333 = SY1320 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(1934,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) )
| ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(1935,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) )
| ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1882]) ).
thf(1940,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1941,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1942,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ ( sK60_SY1064 @ SV288 @ SV109 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1943,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ~ ! [SY1321: $i] :
( ~ ( SV109 @ SY1321 )
| ( ( sK60_SY1064 @ SV288 @ SV109 )
= SY1321 ) ) )
= $false )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(1944,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( SV109 @ ( sK54_SY1064 @ SV288 @ SV109 ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1945,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ! [SY1313: $i] :
( ~ ( SV109 @ SY1313 )
| ( ( sK54_SY1064 @ SV288 @ SV109 )
= SY1313 ) ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(1946,plain,
! [SV31: $i,SV320: $i,SV335: $i] :
( ( ( in @ SV335 @ SV320 )
= $false )
| ( ( in @ SV335 @ SV31 )
= $true )
| ( ( in @ SV320 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1947,plain,
! [SV328: $i,SV31: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ SV31 ) )
= $true )
| ( ( ~ ( in @ SV328 @ SV31 ) )
= $true )
| ( ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) )
| ( SV321 = SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(1948,plain,
! [SV31: $i,SV311: $i,SV309: $i] :
( ( ( ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV309 )
| ( in @ SY1299 @ SV311 ) ) )
= $true )
| ( ( ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true )
| ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(1949,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(1950,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( in @ SV338 @ SV302 )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(1951,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( SV33 @ ( sK55_SY882 @ SV276 @ SV33 ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(1952,plain,
! [SV276: $i,SV33: $i > $o] :
( ( ( ! [SY1315: $i] :
( ~ ( SV33 @ SY1315 )
| ( ( sK55_SY882 @ SV276 @ SV33 )
= SY1315 ) ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1953,plain,
! [SV276: $i,SV343: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV343 )
| ( ( sK47_SY882 @ SV276 @ SV33 )
= SV343 ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(1954,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV310 ) ) )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1955,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i,SV339: $i] :
( ( ( ~ ( ~ ( in @ SV339 @ SV155 )
| ~ ( SV35 @ SV339 @ SV310 ) ) )
= $false )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(1956,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i] :
( ( ( ! [SY1329: $i] :
~ ( ~ ( ~ ( in @ SY1329 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1123: $i] :
~ ~ ( ~ ( in @ SY1123 @ SV155 )
| ~ ( SV35 @ SY1123 @ SY1329 ) ) )
| ~ ( ~ ~ ! [SY1124: $i] :
~ ~ ( ~ ( in @ SY1124 @ SV155 )
| ~ ( SV35 @ SY1124 @ SY1329 ) )
| ( in @ SY1329 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(1957,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV344: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1334: $i] :
~ ~ ( ~ ( in @ SY1334 @ SV155 )
| ~ ( SV35 @ SY1334 @ SV344 ) ) )
| ~ ( ~ ~ ! [SY1335: $i] :
~ ~ ( ~ ( in @ SY1335 @ SV155 )
| ~ ( SV35 @ SY1335 @ SV344 ) )
| ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(1958,plain,
! [SV312: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) ) )
= $false )
| ( ( SV47 @ SV312 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(1959,plain,
! [SV47: $i > $o,SV165: $i > $o,SV312: $i] :
( ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( SV47 @ SV312 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(1960,plain,
! [SV165: $i > $o,SV345: $i,SV47: $i > $o] :
( ( ( ~ ~ ( ~ ( SV47 @ SV345 )
| ~ ! [SY1336: $i] :
( ~ ( SV47 @ SY1336 )
| ( SV345 = SY1336 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(1963,plain,
! [SV165: $i > $o,SV336: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV336 )
| ~ ! [SY1327: $i] :
( ~ ( SV47 @ SY1327 )
| ( SV336 = SY1327 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(1964,plain,
! [SV278: $i,SV346: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ SV346 )
| ( ( sK51_SY930 @ SV278 @ SV48 )
= SV346 ) )
= $true )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(1965,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( SV48 @ ( sK57_SY930 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1966,plain,
! [SV278: $i,SV48: $i > $o] :
( ( ( ! [SY1316: $i] :
( ~ ( SV48 @ SY1316 )
| ( ( sK57_SY930 @ SV278 @ SV48 )
= SY1316 ) ) )
= $true )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(1967,plain,
! [SV278: $i,SV347: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ SV347 )
| ( ( sK52_SY930 @ SV278 @ SV48 )
= SV347 ) )
= $true )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(1968,plain,
! [SV280: $i,SV324: $i,SV329: $i,SV51: $i > $o] :
( ( ( SV51 @ SV329 )
= $false )
| ( ( SV324 = SV329 )
= $true )
| ( ( SV51 @ SV324 )
= $false )
| ( ( SV51 @ SV280 )
= $false )
| ( ( SV51 @ ( sK40_SY1260 @ SV280 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1969,plain,
! [SV168: $i,SV281: $i > $o,SV52: $i,SV294: $i > $o] :
( ( ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
| ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) ) )
= $false )
| ( ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1971,plain,
! [SV52: $i,SV168: $i,SV294: $i > $o,SV281: $i > $o] :
( ( ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
= $false )
| ( ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
= $false )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1920]) ).
thf(1972,plain,
! [SV54: $i,SV282: $i,SV330: $i] :
( ( ( in @ SV330 @ ( sK27_SY951 @ SV282 @ SV54 ) )
= $false )
| ( ( ~ ( in @ SV330 @ SV54 ) )
= $true )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1973,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK64_SY995 @ SV284 @ SV76 ) )
| ~ ! [SY1328: $i] :
( ~ ( SV76 @ SY1328 )
| ( ( sK64_SY995 @ SV284 @ SV76 )
= SY1328 ) ) )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1978,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK58_SY995 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1979,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ! [SY1317: $i] :
( ~ ( SV76 @ SY1317 )
| ( ( sK58_SY995 @ SV284 @ SV76 )
= SY1317 ) ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(1980,plain,
! [SV285: $i,SV337: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( SV91 @ SV337 )
| ( SV337
= ( sK59_SY1019 @ SV285 @ SV91 ) ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(1981,plain,
! [SV91: $i > $o,SV285: $i,SV337: $i] :
( ( ( ~ ( ( SV337
!= ( sK59_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SV337 ) ) )
= $false )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(1982,plain,
! [SV285: $i,SV334: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV334 )
| ( SV334
= ( sK53_SY1019 @ SV285 @ SV91 ) ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(1983,plain,
! [SV91: $i > $o,SV285: $i,SV334: $i] :
( ( ( ( SV334
!= ( sK53_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SV334 ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(1984,plain,
! [SV286: $i,SV326: $i,SV331: $i,SV94: $i > $o] :
( ( ( SV94 @ SV331 )
= $false )
| ( ( SV326 = SV331 )
= $true )
| ( ( SV94 @ SV326 )
= $false )
| ( ( SV94 @ SV286 )
= $false )
| ( ( SV94 @ ( sK43_SY1269 @ SV286 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1985,plain,
! [SV206: $i > $o,SV332: $i,SV100: $i > $o] :
( ( ( SV100 @ SV332 )
= $false )
| ( ( ~ ! [SY1319: $i] :
( ~ ( SV100 @ SY1319 )
| ( SV332 = SY1319 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(1986,plain,
! [SV100: $i > $o,SV333: $i,SV206: $i > $o] :
( ( ( SV206 @ SV333 )
= $false )
| ( ( ~ ! [SY1320: $i] :
( ~ ( SV206 @ SY1320 )
| ( SV333 = SY1320 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(1987,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(1988,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(1993,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(1994,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1941]) ).
thf(1995,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( SV109 @ ( sK60_SY1064 @ SV288 @ SV109 ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(1996,plain,
! [SV288: $i,SV109: $i > $o] :
( ( ( ! [SY1321: $i] :
( ~ ( SV109 @ SY1321 )
| ( ( sK60_SY1064 @ SV288 @ SV109 )
= SY1321 ) ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(1997,plain,
! [SV288: $i,SV348: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ SV348 )
| ( ( sK54_SY1064 @ SV288 @ SV109 )
= SV348 ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(1998,plain,
! [SV328: $i,SV31: $i,SV321: $i] :
( ( ( in @ SV321 @ SV31 )
= $false )
| ( ( ~ ( in @ SV328 @ SV31 ) )
= $true )
| ( ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) )
| ( SV321 = SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(1999,plain,
! [SV31: $i,SV311: $i,SV309: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ SV309 )
| ( in @ SV349 @ SV311 ) )
= $true )
| ( ( ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true )
| ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2000,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( in @ SV342 @ SV302 )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( ~ ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2001,plain,
! [SV338: $i,SV302: $i,SV31: $i] :
( ( ( ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2002,plain,
! [SV276: $i,SV350: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV350 )
| ( ( sK55_SY882 @ SV276 @ SV33 )
= SV350 ) )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2003,plain,
! [SV276: $i,SV343: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV343 ) )
= $true )
| ( ( ( sK47_SY882 @ SV276 @ SV33 )
= SV343 )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2004,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ( in @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV310 ) )
= $false )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2005,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i,SV339: $i] :
( ( ( ~ ( in @ SV339 @ SV155 )
| ~ ( SV35 @ SV339 @ SV310 ) )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(2006,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV351: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1337: $i] :
~ ~ ( ~ ( in @ SY1337 @ SV155 )
| ~ ( SV35 @ SY1337 @ SV351 ) ) )
| ~ ( ~ ~ ! [SY1338: $i] :
~ ~ ( ~ ( in @ SY1338 @ SV155 )
| ~ ( SV35 @ SY1338 @ SV351 ) )
| ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2007,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1334: $i] :
~ ~ ( ~ ( in @ SY1334 @ SV155 )
| ~ ( SV35 @ SY1334 @ SV344 ) ) )
| ~ ( ~ ~ ! [SY1335: $i] :
~ ~ ( ~ ( in @ SY1335 @ SV155 )
| ~ ( SV35 @ SY1335 @ SV344 ) )
| ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2008,plain,
! [SV312: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1958]) ).
thf(2009,plain,
! [SV312: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2010,plain,
! [SV165: $i > $o,SV345: $i,SV47: $i > $o] :
( ( ( ~ ( ~ ( SV47 @ SV345 )
| ~ ! [SY1336: $i] :
( ~ ( SV47 @ SY1336 )
| ( SV345 = SY1336 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2013,plain,
! [SV165: $i > $o,SV336: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV336 ) )
= $true )
| ( ( ~ ! [SY1327: $i] :
( ~ ( SV47 @ SY1327 )
| ( SV336 = SY1327 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2014,plain,
! [SV278: $i,SV346: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ SV346 ) )
= $true )
| ( ( ( sK51_SY930 @ SV278 @ SV48 )
= SV346 )
= $true )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2015,plain,
! [SV278: $i,SV352: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ SV352 )
| ( ( sK57_SY930 @ SV278 @ SV48 )
= SV352 ) )
= $true )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2016,plain,
! [SV278: $i,SV347: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ SV347 ) )
= $true )
| ( ( ( sK52_SY930 @ SV278 @ SV48 )
= SV347 )
= $true )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(2017,plain,
! [SV168: $i,SV281: $i > $o,SV52: $i,SV294: $i > $o] :
( ( ( ~ ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) ) )
= $false )
| ( ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1969]) ).
thf(2020,plain,
! [SV282: $i,SV54: $i,SV330: $i] :
( ( ( in @ SV330 @ SV54 )
= $false )
| ( ( in @ SV330 @ ( sK27_SY951 @ SV282 @ SV54 ) )
= $false )
| ( ( in @ SV282 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2021,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK64_SY995 @ SV284 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(2022,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ~ ! [SY1328: $i] :
( ~ ( SV76 @ SY1328 )
| ( ( sK64_SY995 @ SV284 @ SV76 )
= SY1328 ) ) )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(2027,plain,
! [SV284: $i,SV353: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV353 )
| ( ( sK58_SY995 @ SV284 @ SV76 )
= SV353 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2028,plain,
! [SV285: $i,SV337: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV337 )
| ( SV337
= ( sK59_SY1019 @ SV285 @ SV91 ) ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1980]) ).
thf(2029,plain,
! [SV91: $i > $o,SV285: $i,SV337: $i] :
( ( ( ( SV337
!= ( sK59_SY1019 @ SV285 @ SV91 ) )
| ( SV91 @ SV337 ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1981]) ).
thf(2030,plain,
! [SV285: $i,SV334: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV334 ) )
= $true )
| ( ( SV334
= ( sK53_SY1019 @ SV285 @ SV91 ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2031,plain,
! [SV91: $i > $o,SV285: $i,SV334: $i] :
( ( ( SV334
!= ( sK53_SY1019 @ SV285 @ SV91 ) )
= $true )
| ( ( SV91 @ SV334 )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1983]) ).
thf(2032,plain,
! [SV206: $i > $o,SV332: $i,SV100: $i > $o] :
( ( ( ! [SY1319: $i] :
( ~ ( SV100 @ SY1319 )
| ( SV332 = SY1319 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2033,plain,
! [SV100: $i > $o,SV333: $i,SV206: $i > $o] :
( ( ( ! [SY1320: $i] :
( ~ ( SV206 @ SY1320 )
| ( SV333 = SY1320 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2034,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2035,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2040,plain,
! [SV206: $i > $o,SV354: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ SV354 )
| ~ ! [SY1339: $i] :
( ~ ( SV100 @ SY1339 )
| ( SV354 = SY1339 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2041,plain,
! [SV100: $i > $o,SV355: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ SV355 )
| ~ ! [SY1340: $i] :
( ~ ( SV206 @ SY1340 )
| ( SV355 = SY1340 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2042,plain,
! [SV288: $i,SV356: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ SV356 )
| ( ( sK60_SY1064 @ SV288 @ SV109 )
= SV356 ) )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2043,plain,
! [SV288: $i,SV348: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ SV348 ) )
= $true )
| ( ( ( sK54_SY1064 @ SV288 @ SV109 )
= SV348 )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2044,plain,
! [SV321: $i,SV31: $i,SV328: $i] :
( ( ( in @ SV328 @ SV31 )
= $false )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) )
| ( SV321 = SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2045,plain,
! [SV31: $i,SV311: $i,SV309: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ SV309 ) )
= $true )
| ( ( in @ SV349 @ SV311 )
= $true )
| ( ( ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true )
| ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1999]) ).
thf(2046,plain,
! [SV342: $i,SV302: $i,SV31: $i] :
( ( ( ! [SY1282: $i] :
~ ~ ! [SY1283: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1282 @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1283 @ SV302 ) )
| ~ ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SY1282 )
| ~ ( in @ SY1284 @ SV302 ) ) )
| ~ ! [SY1242: $i] :
( ~ ( in @ SY1242 @ ( sK2_SY860 @ SV31 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1242 )
| ( in @ SX6 @ SY1282 ) )
| ( in @ SY1283 @ SY1242 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2047,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ~ ! [SY1341: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1341 @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
| ~ ! [SY1343: $i] :
( ~ ( in @ SY1343 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ SY1341 @ SY1343 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2001]) ).
thf(2048,plain,
! [SV276: $i,SV350: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV350 ) )
= $true )
| ( ( ( sK55_SY882 @ SV276 @ SV33 )
= SV350 )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2049,plain,
! [SV276: $i,SV343: $i,SV33: $i > $o] :
( ( ( SV33 @ SV343 )
= $false )
| ( ( ( sK47_SY882 @ SV276 @ SV33 )
= SV343 )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV276
= ( sK38_SY1254 @ SV276 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2050,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( ~ ( in @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV155 ) )
= $false )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2051,plain,
! [SV155: $i,SV310: $i,SV35: $i > $i > $o] :
( ( ( ~ ( SV35 @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV310 ) )
= $false )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2052,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i,SV339: $i] :
( ( ( ~ ( in @ SV339 @ SV155 ) )
= $true )
| ( ( ~ ( SV35 @ SV339 @ SV310 ) )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2053,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV351: $i] :
( ( ( ~ ( ~ ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1337: $i] :
~ ~ ( ~ ( in @ SY1337 @ SV155 )
| ~ ( SV35 @ SY1337 @ SV351 ) ) )
| ~ ( ~ ~ ! [SY1338: $i] :
~ ~ ( ~ ( in @ SY1338 @ SV155 )
| ~ ( SV35 @ SY1338 @ SV351 ) )
| ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2054,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV344: $i] :
( ( ( ~ ( ~ ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1334: $i] :
~ ~ ( ~ ( in @ SY1334 @ SV155 )
| ~ ( SV35 @ SY1334 @ SV344 ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2055,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ( ~ ~ ! [SY1335: $i] :
~ ~ ( ~ ( in @ SY1335 @ SV155 )
| ~ ( SV35 @ SY1335 @ SV344 ) )
| ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2056,plain,
! [SV312: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2057,plain,
! [SV312: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2058,plain,
! [SV165: $i > $o,SV345: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV345 )
| ~ ! [SY1336: $i] :
( ~ ( SV47 @ SY1336 )
| ( SV345 = SY1336 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2061,plain,
! [SV165: $i > $o,SV336: $i,SV47: $i > $o] :
( ( ( SV47 @ SV336 )
= $false )
| ( ( ~ ! [SY1327: $i] :
( ~ ( SV47 @ SY1327 )
| ( SV336 = SY1327 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2062,plain,
! [SV278: $i,SV346: $i,SV48: $i > $o] :
( ( ( SV48 @ SV346 )
= $false )
| ( ( ( sK51_SY930 @ SV278 @ SV48 )
= SV346 )
= $true )
| ( ( SV48 @ ( sK30_SY928 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2063,plain,
! [SV278: $i,SV352: $i,SV48: $i > $o] :
( ( ( ~ ( SV48 @ SV352 ) )
= $true )
| ( ( ( sK57_SY930 @ SV278 @ SV48 )
= SV352 )
= $true )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2064,plain,
! [SV278: $i,SV347: $i,SV48: $i > $o] :
( ( ( SV48 @ SV347 )
= $false )
| ( ( ( sK52_SY930 @ SV278 @ SV48 )
= SV347 )
= $true )
| ( ( ( sK30_SY928 @ SV278 @ SV48 )
= ( sK35_SY1292 @ SV278 @ SV48 ) )
= $false )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2065,plain,
! [SV168: $i,SV281: $i > $o,SV52: $i,SV294: $i > $o] :
( ( ( SV294 @ ( sK41_SY1293 @ SV52 @ SV281 @ SV294 @ SV168 ) )
= $true )
| ( ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV52 ) )
= $true )
| ( ( ( dsetconstr @ SV52
@ ^ [SY1264: $i] : ( SV281 @ SY1264 ) )
= ( dsetconstr @ SV168
@ ^ [SY1279: $i] : ( SV294 @ SY1279 ) ) )
= $true )
| ( ( SV52 = SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2066,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK64_SY995 @ SV284 @ SV76 ) )
= $true )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2067,plain,
! [SV284: $i,SV76: $i > $o] :
( ( ( ! [SY1328: $i] :
( ~ ( SV76 @ SY1328 )
| ( ( sK64_SY995 @ SV284 @ SV76 )
= SY1328 ) ) )
= $true )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2070,plain,
! [SV284: $i,SV353: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV353 ) )
= $true )
| ( ( ( sK58_SY995 @ SV284 @ SV76 )
= SV353 )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2071,plain,
! [SV285: $i,SV337: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV337 ) )
= $true )
| ( ( SV337
= ( sK59_SY1019 @ SV285 @ SV91 ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2072,plain,
! [SV91: $i > $o,SV285: $i,SV337: $i] :
( ( ( SV337
!= ( sK59_SY1019 @ SV285 @ SV91 ) )
= $true )
| ( ( SV91 @ SV337 )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2073,plain,
! [SV285: $i,SV334: $i,SV91: $i > $o] :
( ( ( SV91 @ SV334 )
= $false )
| ( ( SV334
= ( sK53_SY1019 @ SV285 @ SV91 ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2074,plain,
! [SV91: $i > $o,SV285: $i,SV334: $i] :
( ( ( SV334
= ( sK53_SY1019 @ SV285 @ SV91 ) )
= $false )
| ( ( SV91 @ SV334 )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2075,plain,
! [SV332: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
| ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2032]) ).
thf(2076,plain,
! [SV333: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
| ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2033]) ).
thf(2077,plain,
! [SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1040: $i] :
~ ~ ( ~ ( SV100 @ SY1040 )
| ~ ! [SY1041: $i] :
( ~ ( SV100 @ SY1041 )
| ( SY1040 = SY1041 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2078,plain,
! [SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1193: $i] :
~ ~ ( ~ ( SV206 @ SY1193 )
| ~ ! [SY1194: $i] :
( ~ ( SV206 @ SY1194 )
| ( SY1193 = SY1194 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2083,plain,
! [SV206: $i > $o,SV354: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ SV354 )
| ~ ! [SY1339: $i] :
( ~ ( SV100 @ SY1339 )
| ( SV354 = SY1339 ) ) ) )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2084,plain,
! [SV100: $i > $o,SV355: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ SV355 )
| ~ ! [SY1340: $i] :
( ~ ( SV206 @ SY1340 )
| ( SV355 = SY1340 ) ) ) )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2085,plain,
! [SV288: $i,SV356: $i,SV109: $i > $o] :
( ( ( ~ ( SV109 @ SV356 ) )
= $true )
| ( ( ( sK60_SY1064 @ SV288 @ SV109 )
= SV356 )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2086,plain,
! [SV288: $i,SV348: $i,SV109: $i > $o] :
( ( ( SV109 @ SV348 )
= $false )
| ( ( ( sK54_SY1064 @ SV288 @ SV109 )
= SV348 )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV288
= ( sK44_SY1272 @ SV288 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2087,plain,
! [SV328: $i,SV321: $i,SV31: $i] :
( ( ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2088,plain,
! [SV31: $i,SV311: $i,SV309: $i,SV349: $i] :
( ( ( in @ SV349 @ SV309 )
= $false )
| ( ( in @ SV349 @ SV311 )
= $true )
| ( ( ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV311 )
| ( in @ SY1300 @ SV309 ) ) )
= $true )
| ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2089,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ~ ! [SY1349: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1349 @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
| ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SY1351 )
| ( in @ SY1352 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ SY1349 @ SY1351 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2046]) ).
thf(2090,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ! [SY1341: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1341 @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
| ~ ! [SY1343: $i] :
( ~ ( in @ SY1343 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ SY1341 @ SY1343 ) ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2091,plain,
! [SV276: $i,SV350: $i,SV33: $i > $o] :
( ( ( SV33 @ SV350 )
= $false )
| ( ( ( sK55_SY882 @ SV276 @ SV33 )
= SV350 )
= $true )
| ( ( SV33 @ SV276 )
= $false )
| ( ( SV33 @ ( sK38_SY1254 @ SV276 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2092,plain,
! [SV155: $i,SV35: $i > $i > $o,SV310: $i] :
( ( ( in @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV155 )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2093,plain,
! [SV155: $i,SV310: $i,SV35: $i > $i > $o] :
( ( ( SV35 @ ( sK65_SY1297 @ SV310 @ SV35 @ SV155 ) @ SV310 )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $false )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2051]) ).
thf(2094,plain,
! [SV310: $i,SV35: $i > $i > $o,SV155: $i,SV339: $i] :
( ( ( in @ SV339 @ SV155 )
= $false )
| ( ( ~ ( SV35 @ SV339 @ SV310 ) )
= $true )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2095,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV351: $i] :
( ( ( ~ ( ~ ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1337: $i] :
~ ~ ( ~ ( in @ SY1337 @ SV155 )
| ~ ( SV35 @ SY1337 @ SV351 ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2096,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ( ~ ~ ! [SY1338: $i] :
~ ~ ( ~ ( in @ SY1338 @ SV155 )
| ~ ( SV35 @ SY1338 @ SV351 ) )
| ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) ) ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2053]) ).
thf(2097,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV344: $i] :
( ( ( ~ ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1334: $i] :
~ ~ ( ~ ( in @ SY1334 @ SV155 )
| ~ ( SV35 @ SY1334 @ SV344 ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2098,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ~ ! [SY1335: $i] :
~ ~ ( ~ ( in @ SY1335 @ SV155 )
| ~ ( SV35 @ SY1335 @ SV344 ) )
| ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2099,plain,
! [SV312: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2100,plain,
! [SV312: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2101,plain,
! [SV165: $i > $o,SV345: $i,SV47: $i > $o] :
( ( ( ~ ( SV47 @ SV345 ) )
= $true )
| ( ( ~ ! [SY1336: $i] :
( ~ ( SV47 @ SY1336 )
| ( SV345 = SY1336 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2104,plain,
! [SV165: $i > $o,SV336: $i,SV47: $i > $o] :
( ( ( ! [SY1327: $i] :
( ~ ( SV47 @ SY1327 )
| ( SV336 = SY1327 ) ) )
= $false )
| ( ( SV47 @ SV336 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2105,plain,
! [SV278: $i,SV352: $i,SV48: $i > $o] :
( ( ( SV48 @ SV352 )
= $false )
| ( ( ( sK57_SY930 @ SV278 @ SV48 )
= SV352 )
= $true )
| ( ( SV48 @ ( sK35_SY1292 @ SV278 @ SV48 ) )
= $true )
| ( ( SV48 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2106,plain,
! [SV284: $i,SV363: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV363 )
| ( ( sK64_SY995 @ SV284 @ SV76 )
= SV363 ) )
= $true )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2109,plain,
! [SV284: $i,SV353: $i,SV76: $i > $o] :
( ( ( SV76 @ SV353 )
= $false )
| ( ( ( sK58_SY995 @ SV284 @ SV76 )
= SV353 )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $false )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2110,plain,
! [SV285: $i,SV337: $i,SV91: $i > $o] :
( ( ( SV91 @ SV337 )
= $false )
| ( ( SV337
= ( sK59_SY1019 @ SV285 @ SV91 ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2111,plain,
! [SV91: $i > $o,SV285: $i,SV337: $i] :
( ( ( SV337
= ( sK59_SY1019 @ SV285 @ SV91 ) )
= $false )
| ( ( SV91 @ SV337 )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2112,plain,
! [SV332: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2075]) ).
thf(2113,plain,
! [SV100: $i > $o,SV206: $i > $o,SV332: $i] :
( ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2075]) ).
thf(2114,plain,
! [SV333: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2076]) ).
thf(2115,plain,
! [SV206: $i > $o,SV100: $i > $o,SV333: $i] :
( ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2076]) ).
thf(2116,plain,
! [SV206: $i > $o,SV364: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ SV364 )
| ~ ! [SY1353: $i] :
( ~ ( SV100 @ SY1353 )
| ( SV364 = SY1353 ) ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2117,plain,
! [SV100: $i > $o,SV365: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ SV365 )
| ~ ! [SY1354: $i] :
( ~ ( SV206 @ SY1354 )
| ( SV365 = SY1354 ) ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2122,plain,
! [SV206: $i > $o,SV354: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV354 )
| ~ ! [SY1339: $i] :
( ~ ( SV100 @ SY1339 )
| ( SV354 = SY1339 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2123,plain,
! [SV100: $i > $o,SV355: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV355 )
| ~ ! [SY1340: $i] :
( ~ ( SV206 @ SY1340 )
| ( SV355 = SY1340 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2124,plain,
! [SV288: $i,SV356: $i,SV109: $i > $o] :
( ( ( SV109 @ SV356 )
= $false )
| ( ( ( sK60_SY1064 @ SV288 @ SV109 )
= SV356 )
= $true )
| ( ( SV109 @ SV288 )
= $false )
| ( ( SV109 @ ( sK44_SY1272 @ SV288 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2125,plain,
! [SV328: $i,SV321: $i,SV31: $i] :
( ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ SY1314 )
| ( in @ SV328 @ SY1314 ) )
| ~ ( ~ ( in @ SV328 @ SY1314 )
| ( in @ SV321 @ SY1314 ) ) ) ) )
= $false )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2126,plain,
! [SV31: $i,SV349: $i,SV309: $i,SV311: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV311 )
| ( in @ SV366 @ SV309 ) )
= $true )
| ( ( in @ SV349 @ SV311 )
= $true )
| ( ( in @ SV349 @ SV309 )
= $false )
| ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2127,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ! [SY1349: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1349 @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
| ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SY1351 )
| ( in @ SY1352 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ SY1349 @ SY1351 ) ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2128,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ! [SY1341: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1341 @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
| ~ ! [SY1343: $i] :
( ~ ( in @ SY1343 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ SY1341 @ SY1343 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2129,plain,
! [SV155: $i,SV310: $i,SV339: $i,SV35: $i > $i > $o] :
( ( ( SV35 @ SV339 @ SV310 )
= $false )
| ( ( in @ SV339 @ SV155 )
= $false )
| ( ( in @ SV310 @ ( sK29_SY1121 @ SV35 @ SV155 ) )
= $true )
| ( ( in @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2130,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV351: $i] :
( ( ( ~ ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
| ~ ! [SY1337: $i] :
~ ~ ( ~ ( in @ SY1337 @ SV155 )
| ~ ( SV35 @ SY1337 @ SV351 ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2131,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ~ ! [SY1338: $i] :
~ ~ ( ~ ( in @ SY1338 @ SV155 )
| ~ ( SV35 @ SY1338 @ SV351 ) )
| ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2132,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV344: $i] :
( ( ( ~ ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) ) )
= $true )
| ( ( ~ ! [SY1334: $i] :
~ ~ ( ~ ( in @ SY1334 @ SV155 )
| ~ ( SV35 @ SY1334 @ SV344 ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2133,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ~ ! [SY1335: $i] :
~ ~ ( ~ ( in @ SY1335 @ SV155 )
| ~ ( SV35 @ SY1335 @ SV344 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2134,plain,
! [SV312: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2099]) ).
thf(2135,plain,
! [SV312: $i,SV47: $i > $o,SV367: $i,SV165: $i > $o] :
( ( ( ~ ~ ( ~ ( SV165 @ SV367 )
| ~ ! [SY1355: $i] :
( ~ ( SV165 @ SY1355 )
| ( SV367 = SY1355 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2136,plain,
! [SV165: $i > $o,SV345: $i,SV47: $i > $o] :
( ( ( SV47 @ SV345 )
= $false )
| ( ( ~ ! [SY1336: $i] :
( ~ ( SV47 @ SY1336 )
| ( SV345 = SY1336 ) ) )
= $true )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2139,plain,
! [SV336: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
| ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) ) )
= $false )
| ( ( SV47 @ SV336 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2104]) ).
thf(2140,plain,
! [SV284: $i,SV363: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV363 ) )
= $true )
| ( ( ( sK64_SY995 @ SV284 @ SV76 )
= SV363 )
= $true )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2143,plain,
! [SV332: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2144,plain,
! [SV332: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2145,plain,
! [SV333: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2146,plain,
! [SV333: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2147,plain,
! [SV206: $i > $o,SV364: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ SV364 )
| ~ ! [SY1353: $i] :
( ~ ( SV100 @ SY1353 )
| ( SV364 = SY1353 ) ) ) )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2148,plain,
! [SV100: $i > $o,SV365: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ SV365 )
| ~ ! [SY1354: $i] :
( ~ ( SV206 @ SY1354 )
| ( SV365 = SY1354 ) ) ) )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2153,plain,
! [SV206: $i > $o,SV354: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV354 ) )
= $true )
| ( ( ~ ! [SY1339: $i] :
( ~ ( SV100 @ SY1339 )
| ( SV354 = SY1339 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2154,plain,
! [SV100: $i > $o,SV355: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV355 ) )
= $true )
| ( ( ~ ! [SY1340: $i] :
( ~ ( SV206 @ SY1340 )
| ( SV355 = SY1340 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2155,plain,
! [SV31: $i,SV321: $i,SV328: $i] :
( ( ( ~ ( in @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( ~ ( ~ ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) )
| ~ ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) ) )
= $false )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2125]) ).
thf(2156,plain,
! [SV31: $i,SV349: $i,SV309: $i,SV311: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV311 ) )
= $true )
| ( ( in @ SV366 @ SV309 )
= $true )
| ( ( in @ SV349 @ SV311 )
= $true )
| ( ( in @ SV349 @ SV309 )
= $false )
| ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2157,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ! [SY1349: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ SY1349 @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
| ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SY1351 )
| ( in @ SY1352 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ SY1349 @ SY1351 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2158,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SY1357 )
| ( in @ SY1344 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SY1357 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2128]) ).
thf(2159,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV351: $i] :
( ( ( ~ ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) ) )
= $true )
| ( ( ~ ! [SY1337: $i] :
~ ~ ( ~ ( in @ SY1337 @ SV155 )
| ~ ( SV35 @ SY1337 @ SV351 ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2160,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ~ ! [SY1338: $i] :
~ ~ ( ~ ( in @ SY1338 @ SV155 )
| ~ ( SV35 @ SY1338 @ SV351 ) ) )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2161,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV344: $i] :
( ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( ~ ! [SY1334: $i] :
~ ~ ( ~ ( in @ SY1334 @ SV155 )
| ~ ( SV35 @ SY1334 @ SV344 ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2162,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ! [SY1335: $i] :
~ ~ ( ~ ( in @ SY1335 @ SV155 )
| ~ ( SV35 @ SY1335 @ SV344 ) ) )
= $false )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2163,plain,
! [SV312: $i,SV47: $i > $o,SV368: $i,SV165: $i > $o] :
( ( ( ~ ~ ( ~ ( SV165 @ SV368 )
| ~ ! [SY1359: $i] :
( ~ ( SV165 @ SY1359 )
| ( SV368 = SY1359 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2164,plain,
! [SV312: $i,SV47: $i > $o,SV367: $i,SV165: $i > $o] :
( ( ( ~ ( ~ ( SV165 @ SV367 )
| ~ ! [SY1355: $i] :
( ~ ( SV165 @ SY1355 )
| ( SV367 = SY1355 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2165,plain,
! [SV165: $i > $o,SV345: $i,SV47: $i > $o] :
( ( ( ! [SY1336: $i] :
( ~ ( SV47 @ SY1336 )
| ( SV345 = SY1336 ) ) )
= $false )
| ( ( SV47 @ SV345 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2168,plain,
! [SV336: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) ) )
= $false )
| ( ( SV47 @ SV336 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2169,plain,
! [SV47: $i > $o,SV165: $i > $o,SV336: $i] :
( ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV47 @ SV336 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2170,plain,
! [SV284: $i,SV363: $i,SV76: $i > $o] :
( ( ( SV76 @ SV363 )
= $false )
| ( ( ( sK64_SY995 @ SV284 @ SV76 )
= SV363 )
= $true )
| ( ( SV76 @ ( sK19_SY1267 @ SV284 @ SV76 ) )
= $true )
| ( ( ( sK19_SY1267 @ SV284 @ SV76 )
= SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2171,plain,
! [SV332: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2172,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ ( sK77_SY1191 @ SV332 @ SV100 @ SV206 ) )
| ~ ! [SY1360: $i] :
( ~ ( SV206 @ SY1360 )
| ( ( sK77_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1360 ) ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2144]) ).
thf(2173,plain,
! [SV333: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2174,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK78_SY1046 @ SV333 @ SV206 @ SV100 ) )
| ~ ! [SY1361: $i] :
( ~ ( SV100 @ SY1361 )
| ( ( sK78_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1361 ) ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2146]) ).
thf(2175,plain,
! [SV206: $i > $o,SV364: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV364 )
| ~ ! [SY1353: $i] :
( ~ ( SV100 @ SY1353 )
| ( SV364 = SY1353 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2176,plain,
! [SV100: $i > $o,SV365: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV365 )
| ~ ! [SY1354: $i] :
( ~ ( SV206 @ SY1354 )
| ( SV365 = SY1354 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2181,plain,
! [SV206: $i > $o,SV354: $i,SV100: $i > $o] :
( ( ( SV100 @ SV354 )
= $false )
| ( ( ~ ! [SY1339: $i] :
( ~ ( SV100 @ SY1339 )
| ( SV354 = SY1339 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2182,plain,
! [SV100: $i > $o,SV355: $i,SV206: $i > $o] :
( ( ( SV206 @ SV355 )
= $false )
| ( ( ~ ! [SY1340: $i] :
( ~ ( SV206 @ SY1340 )
| ( SV355 = SY1340 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2183,plain,
! [SV31: $i,SV321: $i,SV328: $i] :
( ( ( ~ ( in @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) @ ( sK2_SY860 @ SV31 ) ) )
= $false )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2184,plain,
! [SV31: $i,SV328: $i,SV321: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) )
| ~ ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) ) )
= $false )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2155]) ).
thf(2185,plain,
! [SV31: $i,SV349: $i,SV309: $i,SV311: $i,SV366: $i] :
( ( ( in @ SV366 @ SV311 )
= $false )
| ( ( in @ SV366 @ SV309 )
= $true )
| ( ( in @ SV349 @ SV311 )
= $true )
| ( ( in @ SV349 @ SV309 )
= $false )
| ( ( in @ SV309 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ SV311 @ ( sK2_SY860 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2186,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SY1363 )
| ( in @ SY1352 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SY1363 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2157]) ).
thf(2187,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SY1357 )
| ( in @ SY1344 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SY1357 ) ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2158]) ).
thf(2188,plain,
! [SV155: $i,SV35: $i > $i > $o,SV303: $i,SV351: $i] :
( ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( ~ ! [SY1337: $i] :
~ ~ ( ~ ( in @ SY1337 @ SV155 )
| ~ ( SV35 @ SY1337 @ SV351 ) ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2189,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ~ ! [SY1338: $i] :
~ ~ ( ~ ( in @ SY1338 @ SV155 )
| ~ ( SV35 @ SY1338 @ SV351 ) ) )
= $false )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2190,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1334: $i] :
~ ~ ( ~ ( in @ SY1334 @ SV155 )
| ~ ( SV35 @ SY1334 @ SV344 ) ) )
= $false )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2191,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1335: $i] :
~ ~ ( ~ ( in @ SY1335 @ SV155 )
| ~ ( SV35 @ SY1335 @ SV344 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2162]) ).
thf(2192,plain,
! [SV312: $i,SV47: $i > $o,SV368: $i,SV165: $i > $o] :
( ( ( ~ ( ~ ( SV165 @ SV368 )
| ~ ! [SY1359: $i] :
( ~ ( SV165 @ SY1359 )
| ( SV368 = SY1359 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2193,plain,
! [SV312: $i,SV47: $i > $o,SV367: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV367 )
| ~ ! [SY1355: $i] :
( ~ ( SV165 @ SY1355 )
| ( SV367 = SY1355 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2194,plain,
! [SV345: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
| ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) ) )
= $false )
| ( ( SV47 @ SV345 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2165]) ).
thf(2199,plain,
! [SV336: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2168]) ).
thf(2200,plain,
! [SV336: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2201,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ ( sK81_SY1191 @ SV332 @ SV100 @ SV206 ) )
| ~ ! [SY1365: $i] :
( ~ ( SV206 @ SY1365 )
| ( ( sK81_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1365 ) ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2171]) ).
thf(2202,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ ( sK77_SY1191 @ SV332 @ SV100 @ SV206 ) )
| ~ ! [SY1360: $i] :
( ~ ( SV206 @ SY1360 )
| ( ( sK77_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1360 ) ) ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2172]) ).
thf(2203,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK82_SY1046 @ SV333 @ SV206 @ SV100 ) )
| ~ ! [SY1366: $i] :
( ~ ( SV100 @ SY1366 )
| ( ( sK82_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1366 ) ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2173]) ).
thf(2204,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK78_SY1046 @ SV333 @ SV206 @ SV100 ) )
| ~ ! [SY1361: $i] :
( ~ ( SV100 @ SY1361 )
| ( ( sK78_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1361 ) ) ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2174]) ).
thf(2205,plain,
! [SV206: $i > $o,SV364: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV364 ) )
= $true )
| ( ( ~ ! [SY1353: $i] :
( ~ ( SV100 @ SY1353 )
| ( SV364 = SY1353 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2206,plain,
! [SV100: $i > $o,SV365: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV365 ) )
= $true )
| ( ( ~ ! [SY1354: $i] :
( ~ ( SV206 @ SY1354 )
| ( SV365 = SY1354 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2211,plain,
! [SV206: $i > $o,SV354: $i,SV100: $i > $o] :
( ( ( ! [SY1339: $i] :
( ~ ( SV100 @ SY1339 )
| ( SV354 = SY1339 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2212,plain,
! [SV100: $i > $o,SV355: $i,SV206: $i > $o] :
( ( ( ! [SY1340: $i] :
( ~ ( SV206 @ SY1340 )
| ( SV355 = SY1340 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2213,plain,
! [SV31: $i,SV321: $i,SV328: $i] :
( ( ( in @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2214,plain,
! [SV31: $i,SV328: $i,SV321: $i] :
( ( ( ~ ( ~ ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) )
| ~ ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2184]) ).
thf(2215,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SY1363 )
| ( in @ SY1352 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SY1363 ) ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2186]) ).
thf(2216,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SY1357 )
| ( in @ SY1344 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SY1357 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2217,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1337: $i] :
~ ~ ( ~ ( in @ SY1337 @ SV155 )
| ~ ( SV35 @ SY1337 @ SV351 ) ) )
= $false )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2218,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i] :
( ( ( ! [SY1338: $i] :
~ ~ ( ~ ( in @ SY1338 @ SV155 )
| ~ ( SV35 @ SY1338 @ SV351 ) ) )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2189]) ).
thf(2219,plain,
! [SV155: $i,SV35: $i > $i > $o,SV344: $i,SV303: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV344 ) ) )
= $false )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2190]) ).
thf(2220,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i,SV369: $i] :
( ( ( ~ ~ ( ~ ( in @ SV369 @ SV155 )
| ~ ( SV35 @ SV369 @ SV344 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2221,plain,
! [SV312: $i,SV47: $i > $o,SV368: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV368 )
| ~ ! [SY1359: $i] :
( ~ ( SV165 @ SY1359 )
| ( SV368 = SY1359 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2192]) ).
thf(2222,plain,
! [SV312: $i,SV47: $i > $o,SV367: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV367 ) )
= $true )
| ( ( ~ ! [SY1355: $i] :
( ~ ( SV165 @ SY1355 )
| ( SV367 = SY1355 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2223,plain,
! [SV345: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( ~ ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) ) )
= $false )
| ( ( SV47 @ SV345 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2194]) ).
thf(2224,plain,
! [SV47: $i > $o,SV165: $i > $o,SV345: $i] :
( ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ SV345 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2194]) ).
thf(2229,plain,
! [SV336: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2230,plain,
! [SV336: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2231,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ ( sK81_SY1191 @ SV332 @ SV100 @ SV206 ) )
| ~ ! [SY1365: $i] :
( ~ ( SV206 @ SY1365 )
| ( ( sK81_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1365 ) ) ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2232,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK77_SY1191 @ SV332 @ SV100 @ SV206 ) )
| ~ ! [SY1360: $i] :
( ~ ( SV206 @ SY1360 )
| ( ( sK77_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1360 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2233,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK82_SY1046 @ SV333 @ SV206 @ SV100 ) )
| ~ ! [SY1366: $i] :
( ~ ( SV100 @ SY1366 )
| ( ( sK82_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1366 ) ) ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2203]) ).
thf(2234,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK78_SY1046 @ SV333 @ SV206 @ SV100 ) )
| ~ ! [SY1361: $i] :
( ~ ( SV100 @ SY1361 )
| ( ( sK78_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1361 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2235,plain,
! [SV206: $i > $o,SV364: $i,SV100: $i > $o] :
( ( ( SV100 @ SV364 )
= $false )
| ( ( ~ ! [SY1353: $i] :
( ~ ( SV100 @ SY1353 )
| ( SV364 = SY1353 ) ) )
= $true )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2236,plain,
! [SV100: $i > $o,SV365: $i,SV206: $i > $o] :
( ( ( SV206 @ SV365 )
= $false )
| ( ( ~ ! [SY1354: $i] :
( ~ ( SV206 @ SY1354 )
| ( SV365 = SY1354 ) ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2241,plain,
! [SV354: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
| ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2211]) ).
thf(2242,plain,
! [SV355: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
| ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2212]) ).
thf(2243,plain,
! [SV31: $i,SV328: $i,SV321: $i] :
( ( ( ~ ( ~ ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2244,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SY1363 )
| ( in @ SY1352 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SY1363 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2245,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2246,plain,
! [SV302: $i,SV338: $i,SV31: $i] :
( ( ( ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SY1357 )
| ( in @ SY1344 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SY1357 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2247,plain,
! [SV155: $i,SV35: $i > $i > $o,SV351: $i,SV303: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV351 ) ) )
= $false )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2217]) ).
thf(2248,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ( in @ SV370 @ SV155 )
| ~ ( SV35 @ SV370 @ SV351 ) ) )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2249,plain,
! [SV155: $i,SV35: $i > $i > $o,SV344: $i,SV303: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV344 ) ) )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2219]) ).
thf(2250,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV155 )
| ~ ( SV35 @ SV369 @ SV344 ) ) )
= $false )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2251,plain,
! [SV312: $i,SV47: $i > $o,SV368: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV368 ) )
= $true )
| ( ( ~ ! [SY1359: $i] :
( ~ ( SV165 @ SY1359 )
| ( SV368 = SY1359 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2252,plain,
! [SV312: $i,SV47: $i > $o,SV367: $i,SV165: $i > $o] :
( ( ( SV165 @ SV367 )
= $false )
| ( ( ~ ! [SY1355: $i] :
( ~ ( SV165 @ SY1355 )
| ( SV367 = SY1355 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2253,plain,
! [SV345: $i,SV165: $i > $o,SV47: $i > $o] :
( ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) )
| ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2223]) ).
thf(2254,plain,
! [SV345: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2259,plain,
! [SV336: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2260,plain,
! [SV336: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2230]) ).
thf(2261,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK81_SY1191 @ SV332 @ SV100 @ SV206 ) )
| ~ ! [SY1365: $i] :
( ~ ( SV206 @ SY1365 )
| ( ( sK81_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1365 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2262,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK77_SY1191 @ SV332 @ SV100 @ SV206 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2232]) ).
thf(2263,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ! [SY1360: $i] :
( ~ ( SV206 @ SY1360 )
| ( ( sK77_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1360 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2232]) ).
thf(2264,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK82_SY1046 @ SV333 @ SV206 @ SV100 ) )
| ~ ! [SY1366: $i] :
( ~ ( SV100 @ SY1366 )
| ( ( sK82_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1366 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2265,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK78_SY1046 @ SV333 @ SV206 @ SV100 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2266,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ! [SY1361: $i] :
( ~ ( SV100 @ SY1361 )
| ( ( sK78_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1361 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2267,plain,
! [SV206: $i > $o,SV364: $i,SV100: $i > $o] :
( ( ( ! [SY1353: $i] :
( ~ ( SV100 @ SY1353 )
| ( SV364 = SY1353 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2268,plain,
! [SV100: $i > $o,SV365: $i,SV206: $i > $o] :
( ( ( ! [SY1354: $i] :
( ~ ( SV206 @ SY1354 )
| ( SV365 = SY1354 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2273,plain,
! [SV354: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2241]) ).
thf(2274,plain,
! [SV100: $i > $o,SV206: $i > $o,SV354: $i] :
( ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2241]) ).
thf(2275,plain,
! [SV355: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2242]) ).
thf(2276,plain,
! [SV206: $i > $o,SV100: $i > $o,SV355: $i] :
( ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2242]) ).
thf(2277,plain,
! [SV31: $i,SV328: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2278,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2244]) ).
thf(2279,plain,
! [SV302: $i,SV342: $i,SV31: $i] :
( ( ( ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SY1363 )
| ( in @ SY1352 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SY1363 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2244]) ).
thf(2280,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2281,plain,
! [SV302: $i,SV338: $i,SV31: $i] :
( ( ( ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SY1357 )
| ( in @ SY1344 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SY1357 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2282,plain,
! [SV155: $i,SV35: $i > $i > $o,SV351: $i,SV303: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV351 ) ) )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2283,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i,SV370: $i] :
( ( ( ~ ( ~ ( in @ SV370 @ SV155 )
| ~ ( SV35 @ SV370 @ SV351 ) ) )
= $false )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2284,plain,
! [SV155: $i,SV35: $i > $i > $o,SV344: $i,SV303: $i] :
( ( ( ~ ( in @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV344 ) )
= $false )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2285,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV155 )
| ~ ( SV35 @ SV369 @ SV344 ) )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2286,plain,
! [SV312: $i,SV47: $i > $o,SV368: $i,SV165: $i > $o] :
( ( ( SV165 @ SV368 )
= $false )
| ( ( ~ ! [SY1359: $i] :
( ~ ( SV165 @ SY1359 )
| ( SV368 = SY1359 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2287,plain,
! [SV312: $i,SV47: $i > $o,SV367: $i,SV165: $i > $o] :
( ( ( ! [SY1355: $i] :
( ~ ( SV165 @ SY1355 )
| ( SV367 = SY1355 ) ) )
= $false )
| ( ( SV165 @ SV367 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2288,plain,
! [SV345: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2289,plain,
! [SV345: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2294,plain,
! [SV336: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2259]) ).
thf(2295,plain,
! [SV336: $i,SV47: $i > $o,SV371: $i,SV165: $i > $o] :
( ( ( ~ ~ ( ~ ( SV165 @ SV371 )
| ~ ! [SY1367: $i] :
( ~ ( SV165 @ SY1367 )
| ( SV371 = SY1367 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2296,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK81_SY1191 @ SV332 @ SV100 @ SV206 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2261]) ).
thf(2297,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ~ ! [SY1365: $i] :
( ~ ( SV206 @ SY1365 )
| ( ( sK81_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1365 ) ) )
= $false )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2261]) ).
thf(2298,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( SV206 @ ( sK77_SY1191 @ SV332 @ SV100 @ SV206 ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2299,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ! [SY1360: $i] :
( ~ ( SV206 @ SY1360 )
| ( ( sK77_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1360 ) ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2263]) ).
thf(2300,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK82_SY1046 @ SV333 @ SV206 @ SV100 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2264]) ).
thf(2301,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ~ ! [SY1366: $i] :
( ~ ( SV100 @ SY1366 )
| ( ( sK82_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1366 ) ) )
= $false )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2264]) ).
thf(2302,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK78_SY1046 @ SV333 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2303,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ! [SY1361: $i] :
( ~ ( SV100 @ SY1361 )
| ( ( sK78_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1361 ) ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2304,plain,
! [SV364: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
| ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2267]) ).
thf(2305,plain,
! [SV365: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
| ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2268]) ).
thf(2314,plain,
! [SV354: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2273]) ).
thf(2315,plain,
! [SV354: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2316,plain,
! [SV355: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2275]) ).
thf(2317,plain,
! [SV355: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2318,plain,
! [SV31: $i,SV328: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2277]) ).
thf(2319,plain,
! [SV31: $i,SV321: $i,SV328: $i] :
( ( ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2277]) ).
thf(2320,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2278]) ).
thf(2321,plain,
! [SV302: $i,SV342: $i,SV31: $i] :
( ( ( ! [SY1363: $i] :
( ~ ( in @ SY1363 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SY1363 )
| ( in @ SY1352 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SY1363 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2322,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) )
| ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2280]) ).
thf(2323,plain,
! [SV302: $i,SV338: $i,SV31: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1368: $i] :
( ~ ( in @ SY1368 @ SV372 )
| ( in @ SY1368 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV372 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2324,plain,
! [SV155: $i,SV35: $i > $i > $o,SV351: $i,SV303: $i] :
( ( ( ~ ( in @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV155 )
| ~ ( SV35 @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV351 ) )
= $false )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2325,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV155 )
| ~ ( SV35 @ SV370 @ SV351 ) )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2326,plain,
! [SV155: $i,SV35: $i > $i > $o,SV344: $i,SV303: $i] :
( ( ( ~ ( in @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV155 ) )
= $false )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2327,plain,
! [SV155: $i,SV344: $i,SV303: $i,SV35: $i > $i > $o] :
( ( ( ~ ( SV35 @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV344 ) )
= $false )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2328,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV155 ) )
= $true )
| ( ( ~ ( SV35 @ SV369 @ SV344 ) )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2329,plain,
! [SV312: $i,SV47: $i > $o,SV368: $i,SV165: $i > $o] :
( ( ( ! [SY1359: $i] :
( ~ ( SV165 @ SY1359 )
| ( SV368 = SY1359 ) ) )
= $false )
| ( ( SV165 @ SV368 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2330,plain,
! [SV367: $i,SV47: $i > $o,SV312: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK93_SY1355 @ SV312 @ SV47 @ SV367 @ SV165 ) )
| ( SV367
= ( sK93_SY1355 @ SV312 @ SV47 @ SV367 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV367 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2287]) ).
thf(2331,plain,
! [SV345: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ~ ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2332,plain,
! [SV345: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2289]) ).
thf(2337,plain,
! [SV336: $i,SV47: $i > $o,SV375: $i,SV165: $i > $o] :
( ( ( ~ ~ ( ~ ( SV165 @ SV375 )
| ~ ! [SY1371: $i] :
( ~ ( SV165 @ SY1371 )
| ( SV375 = SY1371 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2338,plain,
! [SV336: $i,SV47: $i > $o,SV371: $i,SV165: $i > $o] :
( ( ( ~ ( ~ ( SV165 @ SV371 )
| ~ ! [SY1367: $i] :
( ~ ( SV165 @ SY1367 )
| ( SV371 = SY1367 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2339,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( SV206 @ ( sK81_SY1191 @ SV332 @ SV100 @ SV206 ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2296]) ).
thf(2340,plain,
! [SV100: $i > $o,SV332: $i,SV206: $i > $o] :
( ( ( ! [SY1365: $i] :
( ~ ( SV206 @ SY1365 )
| ( ( sK81_SY1191 @ SV332 @ SV100 @ SV206 )
= SY1365 ) ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2341,plain,
! [SV100: $i > $o,SV332: $i,SV376: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV376 )
| ( ( sK77_SY1191 @ SV332 @ SV100 @ SV206 )
= SV376 ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2342,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK82_SY1046 @ SV333 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2300]) ).
thf(2343,plain,
! [SV206: $i > $o,SV333: $i,SV100: $i > $o] :
( ( ( ! [SY1366: $i] :
( ~ ( SV100 @ SY1366 )
| ( ( sK82_SY1046 @ SV333 @ SV206 @ SV100 )
= SY1366 ) ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2301]) ).
thf(2344,plain,
! [SV206: $i > $o,SV333: $i,SV377: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV377 )
| ( ( sK78_SY1046 @ SV333 @ SV206 @ SV100 )
= SV377 ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2345,plain,
! [SV364: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2304]) ).
thf(2346,plain,
! [SV100: $i > $o,SV206: $i > $o,SV364: $i] :
( ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2304]) ).
thf(2347,plain,
! [SV365: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2348,plain,
! [SV206: $i > $o,SV100: $i > $o,SV365: $i] :
( ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2357,plain,
! [SV354: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2358,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ ( sK94_SY1191 @ SV354 @ SV100 @ SV206 ) )
| ~ ! [SY1372: $i] :
( ~ ( SV206 @ SY1372 )
| ( ( sK94_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1372 ) ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2315]) ).
thf(2359,plain,
! [SV355: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2360,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK95_SY1046 @ SV355 @ SV206 @ SV100 ) )
| ~ ! [SY1373: $i] :
( ~ ( SV100 @ SY1373 )
| ( ( sK95_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1373 ) ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2317]) ).
thf(2361,plain,
! [SV31: $i,SV328: $i,SV321: $i] :
( ( ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2318]) ).
thf(2362,plain,
! [SV31: $i,SV321: $i,SV328: $i] :
( ( ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) )
= $false )
| ( ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $false )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2363,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) )
| ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2364,plain,
! [SV302: $i,SV342: $i,SV31: $i,SV378: $i] :
( ( ( ~ ( in @ SV378 @ ( sK2_SY860 @ SV31 ) )
| ! [SY1374: $i] :
( ~ ( in @ SY1374 @ SV378 )
| ( in @ SY1374 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV378 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2365,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2322]) ).
thf(2366,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2322]) ).
thf(2367,plain,
! [SV302: $i,SV338: $i,SV31: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ ( sK2_SY860 @ SV31 ) ) )
= $true )
| ( ( ! [SY1368: $i] :
( ~ ( in @ SY1368 @ SV372 )
| ( in @ SY1368 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV372 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2368,plain,
! [SV155: $i,SV35: $i > $i > $o,SV351: $i,SV303: $i] :
( ( ( ~ ( in @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV155 ) )
= $false )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2324]) ).
thf(2369,plain,
! [SV155: $i,SV351: $i,SV303: $i,SV35: $i > $i > $o] :
( ( ( ~ ( SV35 @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV351 ) )
= $false )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2324]) ).
thf(2370,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV155 ) )
= $true )
| ( ( ~ ( SV35 @ SV370 @ SV351 ) )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2371,plain,
! [SV155: $i,SV35: $i > $i > $o,SV344: $i,SV303: $i] :
( ( ( in @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV155 )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2326]) ).
thf(2372,plain,
! [SV155: $i,SV344: $i,SV303: $i,SV35: $i > $i > $o] :
( ( ( SV35 @ ( sK83_SY1334 @ SV303 @ SV344 @ SV35 @ SV155 ) @ SV344 )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2327]) ).
thf(2373,plain,
! [SV303: $i,SV344: $i,SV35: $i > $i > $o,SV155: $i,SV369: $i] :
( ( ( in @ SV369 @ SV155 )
= $false )
| ( ( ~ ( SV35 @ SV369 @ SV344 ) )
= $true )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2374,plain,
! [SV368: $i,SV47: $i > $o,SV312: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK96_SY1359 @ SV312 @ SV47 @ SV368 @ SV165 ) )
| ( SV368
= ( sK96_SY1359 @ SV312 @ SV47 @ SV368 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV368 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2329]) ).
thf(2375,plain,
! [SV367: $i,SV47: $i > $o,SV312: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK93_SY1355 @ SV312 @ SV47 @ SV367 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV367 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2330]) ).
thf(2376,plain,
! [SV165: $i > $o,SV47: $i > $o,SV312: $i,SV367: $i] :
( ( ( SV367
= ( sK93_SY1355 @ SV312 @ SV47 @ SV367 @ SV165 ) )
= $false )
| ( ( SV165 @ SV367 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2330]) ).
thf(2377,plain,
! [SV345: $i,SV47: $i > $o,SV165: $i > $o] :
( ( ( ! [SY1139: $i] :
~ ~ ( ~ ( SV165 @ SY1139 )
| ~ ! [SY1140: $i] :
( ~ ( SV165 @ SY1140 )
| ( SY1139 = SY1140 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2331]) ).
thf(2378,plain,
! [SV345: $i,SV47: $i > $o,SV379: $i,SV165: $i > $o] :
( ( ( ~ ~ ( ~ ( SV165 @ SV379 )
| ~ ! [SY1375: $i] :
( ~ ( SV165 @ SY1375 )
| ( SV379 = SY1375 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2383,plain,
! [SV336: $i,SV47: $i > $o,SV375: $i,SV165: $i > $o] :
( ( ( ~ ( ~ ( SV165 @ SV375 )
| ~ ! [SY1371: $i] :
( ~ ( SV165 @ SY1371 )
| ( SV375 = SY1371 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2384,plain,
! [SV336: $i,SV47: $i > $o,SV371: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV371 )
| ~ ! [SY1367: $i] :
( ~ ( SV165 @ SY1367 )
| ( SV371 = SY1367 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2385,plain,
! [SV100: $i > $o,SV332: $i,SV382: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV382 )
| ( ( sK81_SY1191 @ SV332 @ SV100 @ SV206 )
= SV382 ) )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2386,plain,
! [SV100: $i > $o,SV332: $i,SV376: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV376 ) )
= $true )
| ( ( ( sK77_SY1191 @ SV332 @ SV100 @ SV206 )
= SV376 )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2387,plain,
! [SV206: $i > $o,SV333: $i,SV383: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV383 )
| ( ( sK82_SY1046 @ SV333 @ SV206 @ SV100 )
= SV383 ) )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2388,plain,
! [SV206: $i > $o,SV333: $i,SV377: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV377 ) )
= $true )
| ( ( ( sK78_SY1046 @ SV333 @ SV206 @ SV100 )
= SV377 )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2344]) ).
thf(2389,plain,
! [SV364: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( ~ ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2390,plain,
! [SV364: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2391,plain,
! [SV365: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( ~ ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2347]) ).
thf(2392,plain,
! [SV365: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2401,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ ( sK101_SY1191 @ SV354 @ SV100 @ SV206 ) )
| ~ ! [SY1382: $i] :
( ~ ( SV206 @ SY1382 )
| ( ( sK101_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1382 ) ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2357]) ).
thf(2402,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ ( sK94_SY1191 @ SV354 @ SV100 @ SV206 ) )
| ~ ! [SY1372: $i] :
( ~ ( SV206 @ SY1372 )
| ( ( sK94_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1372 ) ) ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2403,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK102_SY1046 @ SV355 @ SV206 @ SV100 ) )
| ~ ! [SY1383: $i] :
( ~ ( SV100 @ SY1383 )
| ( ( sK102_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1383 ) ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2359]) ).
thf(2404,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK95_SY1046 @ SV355 @ SV206 @ SV100 ) )
| ~ ! [SY1373: $i] :
( ~ ( SV100 @ SY1373 )
| ( ( sK95_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1373 ) ) ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2405,plain,
! [SV31: $i,SV321: $i,SV328: $i] :
( ( ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
| ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) )
= $false )
| ( ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2407,plain,
! [SV31: $i,SV328: $i,SV321: $i] :
( ( ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $false )
| ( ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $false )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2362]) ).
thf(2408,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2409,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2410,plain,
! [SV302: $i,SV342: $i,SV31: $i,SV378: $i] :
( ( ( ~ ( in @ SV378 @ ( sK2_SY860 @ SV31 ) ) )
= $true )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ SV378 )
| ( in @ SY1374 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV378 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2411,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2365]) ).
thf(2412,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2413,plain,
! [SV302: $i,SV338: $i,SV31: $i,SV372: $i] :
( ( ( in @ SV372 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( ! [SY1368: $i] :
( ~ ( in @ SY1368 @ SV372 )
| ( in @ SY1368 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
| ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV372 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2414,plain,
! [SV155: $i,SV35: $i > $i > $o,SV351: $i,SV303: $i] :
( ( ( in @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV155 )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2415,plain,
! [SV155: $i,SV351: $i,SV303: $i,SV35: $i > $i > $o] :
( ( ( SV35 @ ( sK86_SY1337 @ SV303 @ SV351 @ SV35 @ SV155 ) @ SV351 )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2369]) ).
thf(2416,plain,
! [SV303: $i,SV351: $i,SV35: $i > $i > $o,SV155: $i,SV370: $i] :
( ( ( in @ SV370 @ SV155 )
= $false )
| ( ( ~ ( SV35 @ SV370 @ SV351 ) )
= $true )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2417,plain,
! [SV303: $i,SV155: $i,SV344: $i,SV369: $i,SV35: $i > $i > $o] :
( ( ( SV35 @ SV369 @ SV344 )
= $false )
| ( ( in @ SV369 @ SV155 )
= $false )
| ( ( in @ SV344 @ ( sK63_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV303
= ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2418,plain,
! [SV368: $i,SV47: $i > $o,SV312: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK96_SY1359 @ SV312 @ SV47 @ SV368 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV368 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2419,plain,
! [SV165: $i > $o,SV47: $i > $o,SV312: $i,SV368: $i] :
( ( ( SV368
= ( sK96_SY1359 @ SV312 @ SV47 @ SV368 @ SV165 ) )
= $false )
| ( ( SV165 @ SV368 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2420,plain,
! [SV367: $i,SV47: $i > $o,SV312: $i,SV165: $i > $o] :
( ( ( SV165 @ ( sK93_SY1355 @ SV312 @ SV47 @ SV367 @ SV165 ) )
= $true )
| ( ( SV165 @ SV367 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV312
= ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $false )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2375]) ).
thf(2421,plain,
! [SV345: $i,SV47: $i > $o,SV384: $i,SV165: $i > $o] :
( ( ( ~ ~ ( ~ ( SV165 @ SV384 )
| ~ ! [SY1384: $i] :
( ~ ( SV165 @ SY1384 )
| ( SV384 = SY1384 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2422,plain,
! [SV345: $i,SV47: $i > $o,SV379: $i,SV165: $i > $o] :
( ( ( ~ ( ~ ( SV165 @ SV379 )
| ~ ! [SY1375: $i] :
( ~ ( SV165 @ SY1375 )
| ( SV379 = SY1375 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2427,plain,
! [SV336: $i,SV47: $i > $o,SV375: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV375 )
| ~ ! [SY1371: $i] :
( ~ ( SV165 @ SY1371 )
| ( SV375 = SY1371 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2383]) ).
thf(2428,plain,
! [SV336: $i,SV47: $i > $o,SV371: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV371 ) )
= $true )
| ( ( ~ ! [SY1367: $i] :
( ~ ( SV165 @ SY1367 )
| ( SV371 = SY1367 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2429,plain,
! [SV100: $i > $o,SV332: $i,SV382: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV382 ) )
= $true )
| ( ( ( sK81_SY1191 @ SV332 @ SV100 @ SV206 )
= SV382 )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2430,plain,
! [SV100: $i > $o,SV332: $i,SV376: $i,SV206: $i > $o] :
( ( ( SV206 @ SV376 )
= $false )
| ( ( ( sK77_SY1191 @ SV332 @ SV100 @ SV206 )
= SV376 )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV332
= ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2431,plain,
! [SV206: $i > $o,SV333: $i,SV383: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV383 ) )
= $true )
| ( ( ( sK82_SY1046 @ SV333 @ SV206 @ SV100 )
= SV383 )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2432,plain,
! [SV206: $i > $o,SV333: $i,SV377: $i,SV100: $i > $o] :
( ( ( SV100 @ SV377 )
= $false )
| ( ( ( sK78_SY1046 @ SV333 @ SV206 @ SV100 )
= SV377 )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV333
= ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $false )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2433,plain,
! [SV364: $i,SV100: $i > $o,SV206: $i > $o] :
( ( ( ! [SY1191: $i] :
~ ~ ( ~ ( SV206 @ SY1191 )
| ~ ! [SY1192: $i] :
( ~ ( SV206 @ SY1192 )
| ( SY1191 = SY1192 ) ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2434,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ ( sK103_SY1191 @ SV364 @ SV100 @ SV206 ) )
| ~ ! [SY1385: $i] :
( ~ ( SV206 @ SY1385 )
| ( ( sK103_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1385 ) ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2390]) ).
thf(2435,plain,
! [SV365: $i,SV206: $i > $o,SV100: $i > $o] :
( ( ( ! [SY1046: $i] :
~ ~ ( ~ ( SV100 @ SY1046 )
| ~ ! [SY1047: $i] :
( ~ ( SV100 @ SY1047 )
| ( SY1046 = SY1047 ) ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2436,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK104_SY1046 @ SV365 @ SV206 @ SV100 ) )
| ~ ! [SY1386: $i] :
( ~ ( SV100 @ SY1386 )
| ( ( sK104_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1386 ) ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2392]) ).
thf(2445,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ ( sK101_SY1191 @ SV354 @ SV100 @ SV206 ) )
| ~ ! [SY1382: $i] :
( ~ ( SV206 @ SY1382 )
| ( ( sK101_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1382 ) ) ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2401]) ).
thf(2446,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK94_SY1191 @ SV354 @ SV100 @ SV206 ) )
| ~ ! [SY1372: $i] :
( ~ ( SV206 @ SY1372 )
| ( ( sK94_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1372 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2447,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK102_SY1046 @ SV355 @ SV206 @ SV100 ) )
| ~ ! [SY1383: $i] :
( ~ ( SV100 @ SY1383 )
| ( ( sK102_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1383 ) ) ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2403]) ).
thf(2448,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK95_SY1046 @ SV355 @ SV206 @ SV100 ) )
| ~ ! [SY1373: $i] :
( ~ ( SV100 @ SY1373 )
| ( ( sK95_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1373 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2449,plain,
! [SV31: $i,SV321: $i,SV328: $i] :
( ( ( ~ ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) ) )
= $false )
| ( ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2405]) ).
thf(2452,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2408]) ).
thf(2453,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2454,plain,
! [SV302: $i,SV342: $i,SV31: $i,SV378: $i] :
( ( ( in @ SV378 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ SV378 )
| ( in @ SY1374 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
| ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV378 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2455,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2456,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2457,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV372: $i] :
( ( ( ! [SY1368: $i] :
( ~ ( in @ SY1368 @ SV372 )
| ( in @ SY1368 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) ) )
= $true )
| ( ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV372 )
= $true )
| ( ( in @ SV372 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(2458,plain,
! [SV303: $i,SV155: $i,SV351: $i,SV370: $i,SV35: $i > $i > $o] :
( ( ( SV35 @ SV370 @ SV351 )
= $false )
| ( ( in @ SV370 @ SV155 )
= $false )
| ( ( in @ SV351 @ ( sK66_SY1121 @ SV303 @ SV35 @ SV155 ) )
= $true )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ SV303 )
= $false )
| ( ( SV35 @ ( sK6_SY1118 @ SV35 @ SV155 ) @ ( sK48_SY1287 @ SV303 @ SV155 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2459,plain,
! [SV368: $i,SV47: $i > $o,SV312: $i,SV165: $i > $o] :
( ( ( SV165 @ ( sK96_SY1359 @ SV312 @ SV47 @ SV368 @ SV165 ) )
= $true )
| ( ( SV165 @ SV368 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV312 )
= $false )
| ( ( SV47 @ ( sK67_SY1301 @ SV165 @ SV312 @ SV47 ) )
= $true )
| ( ( ( sK7_SY1135 @ SV165 @ SV47 )
= ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2418]) ).
thf(2460,plain,
! [SV345: $i,SV47: $i > $o,SV384: $i,SV165: $i > $o] :
( ( ( ~ ( ~ ( SV165 @ SV384 )
| ~ ! [SY1384: $i] :
( ~ ( SV165 @ SY1384 )
| ( SV384 = SY1384 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2461,plain,
! [SV345: $i,SV47: $i > $o,SV379: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV379 )
| ~ ! [SY1375: $i] :
( ~ ( SV165 @ SY1375 )
| ( SV379 = SY1375 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2422]) ).
thf(2466,plain,
! [SV336: $i,SV47: $i > $o,SV375: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV375 ) )
= $true )
| ( ( ~ ! [SY1371: $i] :
( ~ ( SV165 @ SY1371 )
| ( SV375 = SY1371 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2467,plain,
! [SV336: $i,SV47: $i > $o,SV371: $i,SV165: $i > $o] :
( ( ( SV165 @ SV371 )
= $false )
| ( ( ~ ! [SY1367: $i] :
( ~ ( SV165 @ SY1367 )
| ( SV371 = SY1367 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2468,plain,
! [SV100: $i > $o,SV332: $i,SV382: $i,SV206: $i > $o] :
( ( ( SV206 @ SV382 )
= $false )
| ( ( ( sK81_SY1191 @ SV332 @ SV100 @ SV206 )
= SV382 )
= $true )
| ( ( SV100 @ SV332 )
= $false )
| ( ( SV100 @ ( sK69_SY1319 @ SV206 @ SV332 @ SV100 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2469,plain,
! [SV206: $i > $o,SV333: $i,SV383: $i,SV100: $i > $o] :
( ( ( SV100 @ SV383 )
= $false )
| ( ( ( sK82_SY1046 @ SV333 @ SV206 @ SV100 )
= SV383 )
= $true )
| ( ( SV206 @ SV333 )
= $false )
| ( ( SV206 @ ( sK70_SY1320 @ SV100 @ SV333 @ SV206 ) )
= $true )
| ( ( ( sK12_SY1187 @ SV206 @ SV100 )
= ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2470,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ~ ( ~ ( SV206 @ ( sK109_SY1191 @ SV364 @ SV100 @ SV206 ) )
| ~ ! [SY1391: $i] :
( ~ ( SV206 @ SY1391 )
| ( ( sK109_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1391 ) ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2433]) ).
thf(2471,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ ( sK103_SY1191 @ SV364 @ SV100 @ SV206 ) )
| ~ ! [SY1385: $i] :
( ~ ( SV206 @ SY1385 )
| ( ( sK103_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1385 ) ) ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2434]) ).
thf(2472,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ~ ( ~ ( SV100 @ ( sK110_SY1046 @ SV365 @ SV206 @ SV100 ) )
| ~ ! [SY1392: $i] :
( ~ ( SV100 @ SY1392 )
| ( ( sK110_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1392 ) ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2435]) ).
thf(2473,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK104_SY1046 @ SV365 @ SV206 @ SV100 ) )
| ~ ! [SY1386: $i] :
( ~ ( SV100 @ SY1386 )
| ( ( sK104_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1386 ) ) ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2482,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK101_SY1191 @ SV354 @ SV100 @ SV206 ) )
| ~ ! [SY1382: $i] :
( ~ ( SV206 @ SY1382 )
| ( ( sK101_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1382 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2483,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK94_SY1191 @ SV354 @ SV100 @ SV206 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2446]) ).
thf(2484,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ! [SY1372: $i] :
( ~ ( SV206 @ SY1372 )
| ( ( sK94_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1372 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2446]) ).
thf(2485,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK102_SY1046 @ SV355 @ SV206 @ SV100 ) )
| ~ ! [SY1383: $i] :
( ~ ( SV100 @ SY1383 )
| ( ( sK102_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1383 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2486,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK95_SY1046 @ SV355 @ SV206 @ SV100 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2448]) ).
thf(2487,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ! [SY1373: $i] :
( ~ ( SV100 @ SY1373 )
| ( ( sK95_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1373 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2448]) ).
thf(2488,plain,
! [SV31: $i,SV321: $i,SV328: $i] :
( ( ( in @ SV328 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $true )
| ( ( in @ SV321 @ ( sK73_SY1314 @ SV328 @ SV321 @ SV31 ) )
= $true )
| ( ( SV321 = SV328 )
= $true )
| ( ( in @ SV321 @ SV31 )
= $false )
| ( ( in @ SV328 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2489,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
| ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2490,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2491,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV378: $i] :
( ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ SV378 )
| ( in @ SY1374 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) ) )
= $true )
| ( ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV378 )
= $true )
| ( ( in @ SV378 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2492,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ~ ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2493,plain,
! [SV338: $i,SV302: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2494,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( ! [SY1342: $i] :
~ ~ ( ~ ( in @ SY1342 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SY1342 @ SV302 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2456]) ).
thf(2495,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV372: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV372 )
| ( in @ SV385 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV372 )
= $true )
| ( ( in @ SV372 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2496,plain,
! [SV345: $i,SV47: $i > $o,SV384: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV384 )
| ~ ! [SY1384: $i] :
( ~ ( SV165 @ SY1384 )
| ( SV384 = SY1384 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2460]) ).
thf(2497,plain,
! [SV345: $i,SV47: $i > $o,SV379: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV379 ) )
= $true )
| ( ( ~ ! [SY1375: $i] :
( ~ ( SV165 @ SY1375 )
| ( SV379 = SY1375 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2502,plain,
! [SV336: $i,SV47: $i > $o,SV375: $i,SV165: $i > $o] :
( ( ( SV165 @ SV375 )
= $false )
| ( ( ~ ! [SY1371: $i] :
( ~ ( SV165 @ SY1371 )
| ( SV375 = SY1371 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2503,plain,
! [SV336: $i,SV47: $i > $o,SV371: $i,SV165: $i > $o] :
( ( ( ! [SY1367: $i] :
( ~ ( SV165 @ SY1367 )
| ( SV371 = SY1367 ) ) )
= $false )
| ( ( SV165 @ SV371 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2504,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ( ~ ( SV206 @ ( sK109_SY1191 @ SV364 @ SV100 @ SV206 ) )
| ~ ! [SY1391: $i] :
( ~ ( SV206 @ SY1391 )
| ( ( sK109_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1391 ) ) ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2470]) ).
thf(2505,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK103_SY1191 @ SV364 @ SV100 @ SV206 ) )
| ~ ! [SY1385: $i] :
( ~ ( SV206 @ SY1385 )
| ( ( sK103_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1385 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2506,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ( ~ ( SV100 @ ( sK110_SY1046 @ SV365 @ SV206 @ SV100 ) )
| ~ ! [SY1392: $i] :
( ~ ( SV100 @ SY1392 )
| ( ( sK110_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1392 ) ) ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2472]) ).
thf(2507,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK104_SY1046 @ SV365 @ SV206 @ SV100 ) )
| ~ ! [SY1386: $i] :
( ~ ( SV100 @ SY1386 )
| ( ( sK104_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1386 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2520,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK101_SY1191 @ SV354 @ SV100 @ SV206 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2482]) ).
thf(2521,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ~ ! [SY1382: $i] :
( ~ ( SV206 @ SY1382 )
| ( ( sK101_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1382 ) ) )
= $false )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2482]) ).
thf(2522,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( SV206 @ ( sK94_SY1191 @ SV354 @ SV100 @ SV206 ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2523,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ! [SY1372: $i] :
( ~ ( SV206 @ SY1372 )
| ( ( sK94_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1372 ) ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2484]) ).
thf(2524,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK102_SY1046 @ SV355 @ SV206 @ SV100 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2525,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ~ ! [SY1383: $i] :
( ~ ( SV100 @ SY1383 )
| ( ( sK102_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1383 ) ) )
= $false )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2526,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK95_SY1046 @ SV355 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2527,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ! [SY1373: $i] :
( ~ ( SV100 @ SY1373 )
| ( ( sK95_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1373 ) ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2487]) ).
thf(2528,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ~ ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2529,plain,
! [SV342: $i,SV302: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2530,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( ! [SY1350: $i] :
~ ~ ( ~ ( in @ SY1350 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SY1350 @ SV302 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2490]) ).
thf(2531,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV378: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV378 )
| ( in @ SV386 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV378 )
= $true )
| ( ( in @ SV378 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(2532,plain,
! [SV31: $i,SV302: $i,SV338: $i] :
( ( ( in @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2492]) ).
thf(2533,plain,
! [SV338: $i,SV302: $i,SV31: $i] :
( ( ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV302 )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2493]) ).
thf(2534,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV387: $i] :
( ( ( ~ ~ ( ~ ( in @ SV387 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SV387 @ SV302 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2535,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV372: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV372 ) )
= $true )
| ( ( in @ SV385 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
= $true )
| ( ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV372 )
= $true )
| ( ( in @ SV372 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2536,plain,
! [SV345: $i,SV47: $i > $o,SV384: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ SV384 ) )
= $true )
| ( ( ~ ! [SY1384: $i] :
( ~ ( SV165 @ SY1384 )
| ( SV384 = SY1384 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2537,plain,
! [SV345: $i,SV47: $i > $o,SV379: $i,SV165: $i > $o] :
( ( ( SV165 @ SV379 )
= $false )
| ( ( ~ ! [SY1375: $i] :
( ~ ( SV165 @ SY1375 )
| ( SV379 = SY1375 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2542,plain,
! [SV336: $i,SV47: $i > $o,SV375: $i,SV165: $i > $o] :
( ( ( ! [SY1371: $i] :
( ~ ( SV165 @ SY1371 )
| ( SV375 = SY1371 ) ) )
= $false )
| ( ( SV165 @ SV375 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2543,plain,
! [SV371: $i,SV47: $i > $o,SV336: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK111_SY1367 @ SV336 @ SV47 @ SV371 @ SV165 ) )
| ( SV371
= ( sK111_SY1367 @ SV336 @ SV47 @ SV371 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV371 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2503]) ).
thf(2544,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK109_SY1191 @ SV364 @ SV100 @ SV206 ) )
| ~ ! [SY1391: $i] :
( ~ ( SV206 @ SY1391 )
| ( ( sK109_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1391 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2545,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK103_SY1191 @ SV364 @ SV100 @ SV206 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2505]) ).
thf(2546,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ! [SY1385: $i] :
( ~ ( SV206 @ SY1385 )
| ( ( sK103_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1385 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2505]) ).
thf(2547,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK110_SY1046 @ SV365 @ SV206 @ SV100 ) )
| ~ ! [SY1392: $i] :
( ~ ( SV100 @ SY1392 )
| ( ( sK110_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1392 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2548,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK104_SY1046 @ SV365 @ SV206 @ SV100 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2507]) ).
thf(2549,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ! [SY1386: $i] :
( ~ ( SV100 @ SY1386 )
| ( ( sK104_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1386 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2507]) ).
thf(2566,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( SV206 @ ( sK101_SY1191 @ SV354 @ SV100 @ SV206 ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2520]) ).
thf(2567,plain,
! [SV100: $i > $o,SV354: $i,SV206: $i > $o] :
( ( ( ! [SY1382: $i] :
( ~ ( SV206 @ SY1382 )
| ( ( sK101_SY1191 @ SV354 @ SV100 @ SV206 )
= SY1382 ) ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2521]) ).
thf(2568,plain,
! [SV100: $i > $o,SV354: $i,SV388: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV388 )
| ( ( sK94_SY1191 @ SV354 @ SV100 @ SV206 )
= SV388 ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(2569,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK102_SY1046 @ SV355 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2570,plain,
! [SV206: $i > $o,SV355: $i,SV100: $i > $o] :
( ( ( ! [SY1383: $i] :
( ~ ( SV100 @ SY1383 )
| ( ( sK102_SY1046 @ SV355 @ SV206 @ SV100 )
= SY1383 ) ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2571,plain,
! [SV206: $i > $o,SV355: $i,SV389: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV389 )
| ( ( sK95_SY1046 @ SV355 @ SV206 @ SV100 )
= SV389 ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2572,plain,
! [SV31: $i,SV302: $i,SV342: $i] :
( ( ( in @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) @ ( sK2_SY860 @ SV31 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2528]) ).
thf(2573,plain,
! [SV342: $i,SV302: $i,SV31: $i] :
( ( ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV302 )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2574,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV390: $i] :
( ( ( ~ ~ ( ~ ( in @ SV390 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SV390 @ SV302 ) ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(2575,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV378: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV378 ) )
= $true )
| ( ( in @ SV386 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
= $true )
| ( ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV378 )
= $true )
| ( ( in @ SV378 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2576,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SV387 @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2577,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV372: $i,SV385: $i] :
( ( ( in @ SV385 @ SV372 )
= $false )
| ( ( in @ SV385 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
= $true )
| ( ( in @ ( sK74_SY1341 @ SV31 @ SV302 @ SV338 ) @ SV372 )
= $true )
| ( ( in @ SV372 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2578,plain,
! [SV345: $i,SV47: $i > $o,SV384: $i,SV165: $i > $o] :
( ( ( SV165 @ SV384 )
= $false )
| ( ( ~ ! [SY1384: $i] :
( ~ ( SV165 @ SY1384 )
| ( SV384 = SY1384 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2579,plain,
! [SV345: $i,SV47: $i > $o,SV379: $i,SV165: $i > $o] :
( ( ( ! [SY1375: $i] :
( ~ ( SV165 @ SY1375 )
| ( SV379 = SY1375 ) ) )
= $false )
| ( ( SV165 @ SV379 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2584,plain,
! [SV375: $i,SV47: $i > $o,SV336: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK114_SY1371 @ SV336 @ SV47 @ SV375 @ SV165 ) )
| ( SV375
= ( sK114_SY1371 @ SV336 @ SV47 @ SV375 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV375 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2542]) ).
thf(2585,plain,
! [SV371: $i,SV47: $i > $o,SV336: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK111_SY1367 @ SV336 @ SV47 @ SV371 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV371 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2586,plain,
! [SV165: $i > $o,SV47: $i > $o,SV336: $i,SV371: $i] :
( ( ( SV371
= ( sK111_SY1367 @ SV336 @ SV47 @ SV371 @ SV165 ) )
= $false )
| ( ( SV165 @ SV371 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2587,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ ( sK109_SY1191 @ SV364 @ SV100 @ SV206 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2588,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ~ ! [SY1391: $i] :
( ~ ( SV206 @ SY1391 )
| ( ( sK109_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1391 ) ) )
= $false )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2589,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( SV206 @ ( sK103_SY1191 @ SV364 @ SV100 @ SV206 ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2545]) ).
thf(2590,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ! [SY1385: $i] :
( ~ ( SV206 @ SY1385 )
| ( ( sK103_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1385 ) ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2546]) ).
thf(2591,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ ( sK110_SY1046 @ SV365 @ SV206 @ SV100 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2547]) ).
thf(2592,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ~ ! [SY1392: $i] :
( ~ ( SV100 @ SY1392 )
| ( ( sK110_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1392 ) ) )
= $false )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2547]) ).
thf(2593,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK104_SY1046 @ SV365 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2594,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ! [SY1386: $i] :
( ~ ( SV100 @ SY1386 )
| ( ( sK104_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1386 ) ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2607,plain,
! [SV100: $i > $o,SV354: $i,SV395: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV395 )
| ( ( sK101_SY1191 @ SV354 @ SV100 @ SV206 )
= SV395 ) )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2608,plain,
! [SV100: $i > $o,SV354: $i,SV388: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV388 ) )
= $true )
| ( ( ( sK94_SY1191 @ SV354 @ SV100 @ SV206 )
= SV388 )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2609,plain,
! [SV206: $i > $o,SV355: $i,SV396: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV396 )
| ( ( sK102_SY1046 @ SV355 @ SV206 @ SV100 )
= SV396 ) )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2610,plain,
! [SV206: $i > $o,SV355: $i,SV389: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV389 ) )
= $true )
| ( ( ( sK95_SY1046 @ SV355 @ SV206 @ SV100 )
= SV389 )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2571]) ).
thf(2611,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV390: $i] :
( ( ( ~ ( ~ ( in @ SV390 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SV390 @ SV302 ) ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2612,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV378: $i,SV386: $i] :
( ( ( in @ SV386 @ SV378 )
= $false )
| ( ( in @ SV386 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
= $true )
| ( ( in @ ( sK79_SY1349 @ SV31 @ SV302 @ SV342 ) @ SV378 )
= $true )
| ( ( in @ SV378 @ ( sK2_SY860 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2613,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
| ~ ( in @ SV387 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2576]) ).
thf(2614,plain,
! [SV345: $i,SV47: $i > $o,SV384: $i,SV165: $i > $o] :
( ( ( ! [SY1384: $i] :
( ~ ( SV165 @ SY1384 )
| ( SV384 = SY1384 ) ) )
= $false )
| ( ( SV165 @ SV384 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2615,plain,
! [SV379: $i,SV47: $i > $o,SV345: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK115_SY1375 @ SV345 @ SV47 @ SV379 @ SV165 ) )
| ( SV379
= ( sK115_SY1375 @ SV345 @ SV47 @ SV379 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV379 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2579]) ).
thf(2622,plain,
! [SV375: $i,SV47: $i > $o,SV336: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK114_SY1371 @ SV336 @ SV47 @ SV375 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV375 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2584]) ).
thf(2623,plain,
! [SV165: $i > $o,SV47: $i > $o,SV336: $i,SV375: $i] :
( ( ( SV375
= ( sK114_SY1371 @ SV336 @ SV47 @ SV375 @ SV165 ) )
= $false )
| ( ( SV165 @ SV375 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2584]) ).
thf(2624,plain,
! [SV371: $i,SV47: $i > $o,SV336: $i,SV165: $i > $o] :
( ( ( SV165 @ ( sK111_SY1367 @ SV336 @ SV47 @ SV371 @ SV165 ) )
= $true )
| ( ( SV165 @ SV371 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV336
= ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $false )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2585]) ).
thf(2625,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( SV206 @ ( sK109_SY1191 @ SV364 @ SV100 @ SV206 ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2626,plain,
! [SV100: $i > $o,SV364: $i,SV206: $i > $o] :
( ( ( ! [SY1391: $i] :
( ~ ( SV206 @ SY1391 )
| ( ( sK109_SY1191 @ SV364 @ SV100 @ SV206 )
= SY1391 ) ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2627,plain,
! [SV100: $i > $o,SV364: $i,SV397: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV397 )
| ( ( sK103_SY1191 @ SV364 @ SV100 @ SV206 )
= SV397 ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(2628,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( SV100 @ ( sK110_SY1046 @ SV365 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2629,plain,
! [SV206: $i > $o,SV365: $i,SV100: $i > $o] :
( ( ( ! [SY1392: $i] :
( ~ ( SV100 @ SY1392 )
| ( ( sK110_SY1046 @ SV365 @ SV206 @ SV100 )
= SY1392 ) ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2592]) ).
thf(2630,plain,
! [SV206: $i > $o,SV365: $i,SV398: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV398 )
| ( ( sK104_SY1046 @ SV365 @ SV206 @ SV100 )
= SV398 ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(2639,plain,
! [SV100: $i > $o,SV354: $i,SV395: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV395 ) )
= $true )
| ( ( ( sK101_SY1191 @ SV354 @ SV100 @ SV206 )
= SV395 )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2640,plain,
! [SV100: $i > $o,SV354: $i,SV388: $i,SV206: $i > $o] :
( ( ( SV206 @ SV388 )
= $false )
| ( ( ( sK94_SY1191 @ SV354 @ SV100 @ SV206 )
= SV388 )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV354
= ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2641,plain,
! [SV206: $i > $o,SV355: $i,SV396: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV396 ) )
= $true )
| ( ( ( sK102_SY1046 @ SV355 @ SV206 @ SV100 )
= SV396 )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2642,plain,
! [SV206: $i > $o,SV355: $i,SV389: $i,SV100: $i > $o] :
( ( ( SV100 @ SV389 )
= $false )
| ( ( ( sK95_SY1046 @ SV355 @ SV206 @ SV100 )
= SV389 )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV355
= ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $false )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2643,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
| ~ ( in @ SV390 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2644,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) ) )
= $true )
| ( ( ~ ( in @ SV387 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2645,plain,
! [SV384: $i,SV47: $i > $o,SV345: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK118_SY1384 @ SV345 @ SV47 @ SV384 @ SV165 ) )
| ( SV384
= ( sK118_SY1384 @ SV345 @ SV47 @ SV384 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV384 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2614]) ).
thf(2646,plain,
! [SV379: $i,SV47: $i > $o,SV345: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK115_SY1375 @ SV345 @ SV47 @ SV379 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV379 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2647,plain,
! [SV165: $i > $o,SV47: $i > $o,SV345: $i,SV379: $i] :
( ( ( SV379
= ( sK115_SY1375 @ SV345 @ SV47 @ SV379 @ SV165 ) )
= $false )
| ( ( SV165 @ SV379 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2654,plain,
! [SV375: $i,SV47: $i > $o,SV336: $i,SV165: $i > $o] :
( ( ( SV165 @ ( sK114_SY1371 @ SV336 @ SV47 @ SV375 @ SV165 ) )
= $true )
| ( ( SV165 @ SV375 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV336 )
= $false )
| ( ( SV47 @ ( sK72_SY1327 @ SV165 @ SV336 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2622]) ).
thf(2655,plain,
! [SV100: $i > $o,SV364: $i,SV403: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV403 )
| ( ( sK109_SY1191 @ SV364 @ SV100 @ SV206 )
= SV403 ) )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(2656,plain,
! [SV100: $i > $o,SV364: $i,SV397: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV397 ) )
= $true )
| ( ( ( sK103_SY1191 @ SV364 @ SV100 @ SV206 )
= SV397 )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2627]) ).
thf(2657,plain,
! [SV206: $i > $o,SV365: $i,SV404: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV404 )
| ( ( sK110_SY1046 @ SV365 @ SV206 @ SV100 )
= SV404 ) )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(2658,plain,
! [SV206: $i > $o,SV365: $i,SV398: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV398 ) )
= $true )
| ( ( ( sK104_SY1046 @ SV365 @ SV206 @ SV100 )
= SV398 )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2667,plain,
! [SV100: $i > $o,SV354: $i,SV395: $i,SV206: $i > $o] :
( ( ( SV206 @ SV395 )
= $false )
| ( ( ( sK101_SY1191 @ SV354 @ SV100 @ SV206 )
= SV395 )
= $true )
| ( ( SV100 @ SV354 )
= $false )
| ( ( SV100 @ ( sK84_SY1339 @ SV206 @ SV354 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(2668,plain,
! [SV206: $i > $o,SV355: $i,SV396: $i,SV100: $i > $o] :
( ( ( SV100 @ SV396 )
= $false )
| ( ( ( sK102_SY1046 @ SV355 @ SV206 @ SV100 )
= SV396 )
= $true )
| ( ( SV206 @ SV355 )
= $false )
| ( ( SV206 @ ( sK85_SY1340 @ SV100 @ SV355 @ SV206 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2669,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) ) )
= $true )
| ( ( ~ ( in @ SV390 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2670,plain,
! [SV31: $i,SV302: $i,SV338: $i,SV387: $i] :
( ( ( in @ SV387 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
= $false )
| ( ( ~ ( in @ SV387 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2671,plain,
! [SV384: $i,SV47: $i > $o,SV345: $i,SV165: $i > $o] :
( ( ( ~ ( SV165 @ ( sK118_SY1384 @ SV345 @ SV47 @ SV384 @ SV165 ) ) )
= $false )
| ( ( SV165 @ SV384 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2645]) ).
thf(2672,plain,
! [SV165: $i > $o,SV47: $i > $o,SV345: $i,SV384: $i] :
( ( ( SV384
= ( sK118_SY1384 @ SV345 @ SV47 @ SV384 @ SV165 ) )
= $false )
| ( ( SV165 @ SV384 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2645]) ).
thf(2673,plain,
! [SV379: $i,SV47: $i > $o,SV345: $i,SV165: $i > $o] :
( ( ( SV165 @ ( sK115_SY1375 @ SV345 @ SV47 @ SV379 @ SV165 ) )
= $true )
| ( ( SV165 @ SV379 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV345
= ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $false )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2676,plain,
! [SV100: $i > $o,SV364: $i,SV403: $i,SV206: $i > $o] :
( ( ( ~ ( SV206 @ SV403 ) )
= $true )
| ( ( ( sK109_SY1191 @ SV364 @ SV100 @ SV206 )
= SV403 )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2677,plain,
! [SV100: $i > $o,SV364: $i,SV397: $i,SV206: $i > $o] :
( ( ( SV206 @ SV397 )
= $false )
| ( ( ( sK103_SY1191 @ SV364 @ SV100 @ SV206 )
= SV397 )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV364
= ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(2678,plain,
! [SV206: $i > $o,SV365: $i,SV404: $i,SV100: $i > $o] :
( ( ( ~ ( SV100 @ SV404 ) )
= $true )
| ( ( ( sK110_SY1046 @ SV365 @ SV206 @ SV100 )
= SV404 )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(2679,plain,
! [SV206: $i > $o,SV365: $i,SV398: $i,SV100: $i > $o] :
( ( ( SV100 @ SV398 )
= $false )
| ( ( ( sK104_SY1046 @ SV365 @ SV206 @ SV100 )
= SV398 )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV365
= ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $false )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2684,plain,
! [SV31: $i,SV302: $i,SV342: $i,SV390: $i] :
( ( ( in @ SV390 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
= $false )
| ( ( ~ ( in @ SV390 @ SV302 ) )
= $true )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2685,plain,
! [SV31: $i,SV338: $i,SV302: $i,SV387: $i] :
( ( ( in @ SV387 @ SV302 )
= $false )
| ( ( in @ SV387 @ ( sK68_SY1282 @ SV338 @ SV302 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV31 )
= $false )
| ( ( in @ SV338 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2686,plain,
! [SV384: $i,SV47: $i > $o,SV345: $i,SV165: $i > $o] :
( ( ( SV165 @ ( sK118_SY1384 @ SV345 @ SV47 @ SV384 @ SV165 ) )
= $true )
| ( ( SV165 @ SV384 )
= $false )
| ( ( ( descr
@ ^ [SY925: $i] : ( SV47 @ SY925 ) )
= ( descr
@ ^ [SY1142: $i] : ( SV165 @ SY1142 ) ) )
= $true )
| ( ( SV47 @ SV345 )
= $false )
| ( ( SV47 @ ( sK80_SY1336 @ SV165 @ SV345 @ SV47 ) )
= $true )
| ( ( SV47 @ ( sK7_SY1135 @ SV165 @ SV47 ) )
= $true )
| ( ( SV165 @ ( sK15_SY1258 @ SV47 @ SV165 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2671]) ).
thf(2687,plain,
! [SV100: $i > $o,SV364: $i,SV403: $i,SV206: $i > $o] :
( ( ( SV206 @ SV403 )
= $false )
| ( ( ( sK109_SY1191 @ SV364 @ SV100 @ SV206 )
= SV403 )
= $true )
| ( ( SV100 @ SV364 )
= $false )
| ( ( SV100 @ ( sK91_SY1353 @ SV206 @ SV364 @ SV100 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2688,plain,
! [SV206: $i > $o,SV365: $i,SV404: $i,SV100: $i > $o] :
( ( ( SV100 @ SV404 )
= $false )
| ( ( ( sK110_SY1046 @ SV365 @ SV206 @ SV100 )
= SV404 )
= $true )
| ( ( SV206 @ SV365 )
= $false )
| ( ( SV206 @ ( sK92_SY1354 @ SV100 @ SV365 @ SV206 ) )
= $true )
| ( ( SV100 @ ( sK12_SY1187 @ SV206 @ SV100 ) )
= $true )
| ( ( SV206 @ ( sK17_SY1270 @ SV100 @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2689,plain,
! [SV31: $i,SV342: $i,SV302: $i,SV390: $i] :
( ( ( in @ SV390 @ SV302 )
= $false )
| ( ( in @ SV390 @ ( sK71_SY1282 @ SV342 @ SV302 @ SV31 ) )
= $false )
| ( ( in @ ( sK46_SY1280 @ SV31 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ SV342 @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2690,plain,
! [SV285: $i,SV334: $i] :
( ( ( SV334
= ( sK53_SY1019 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) ) )
= $false )
| ( ( SV334 = SV285 )
= $true )
| ( ( SV285 = SV285 )
= $false )
| ( ( SV285
= ( sK42_SY1268 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) ) )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[2074:[bind(SV91,$thf( ^ [SV405: $i] : ( SV405 = SV285 ) ))]]) ).
thf(2691,plain,
! [SV285: $i,SV334: $i] :
( ( ( SV334
= ( sK53_SY1019 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) ) )
= $false )
| ( ( SV334 = SV285 )
= $true )
| ( ( SV285
= ( sK42_SY1268 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) ) )
= $false ) ),
inference(sim,[status(thm)],[2690]) ).
thf(2692,plain,
! [SV285: $i,SV337: $i] :
( ( ( SV337
= ( sK59_SY1019 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) ) )
= $false )
| ( ( SV337 = SV285 )
= $true )
| ( ( SV285 = SV285 )
= $false )
| ( ( ( sK42_SY1268 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) )
= SV285 )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[2111:[bind(SV91,$thf( ^ [SV406: $i] : ( SV406 = SV285 ) ))]]) ).
thf(2693,plain,
! [SV285: $i,SV337: $i] :
( ( ( SV337
= ( sK59_SY1019 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) ) )
= $false )
| ( ( SV337 = SV285 )
= $true )
| ( ( ( sK42_SY1268 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) )
= SV285 )
= $true ) ),
inference(sim,[status(thm)],[2692]) ).
thf(2694,plain,
! [SV90: $o] :
( ( SV90 = $false )
| ( ( SV90
= ( ~ ( set2prop @ ( prop2set @ SV90 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[723]) ).
thf(2695,plain,
! [SV130: $o] :
( ( SV130 = $false )
| ( ( SV130
= ( ~ ( in @ emptyset @ ( prop2set @ SV130 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[766]) ).
thf(2696,plain,
! [SV73: $o,SV185: $i] :
( ( SV73 = $true )
| ( ( SV73
= ( ~ ( in @ SV185 @ ( prop2set @ SV73 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[819]) ).
thf(2697,plain,
! [SV83: $i,SV274: $o] :
( ( SV274 = $true )
| ( ( SV274
= ( ~ ( in @ SV83 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[831]) ).
thf(2698,plain,
! [SV106: $i > $o,SV211: $i] :
( ( ( SV106 @ SV211 )
= $true )
| ( ( ( SV106 @ SV211 )
= ( ~ ( in @ SV211 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[854]) ).
thf(2699,plain,
! [SV175: $i > $o,SV61: $i,SV248: $i] :
( ( ( SV175 @ SV248 )
= $true )
| ( ( ( SV175 @ SV248 )
= ( ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[917]) ).
thf(2700,plain,
! [SV85: $i] :
( ( ( SV85 = emptyset )
= $true )
| ( ( ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 )
= ( SV85 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[934]) ).
thf(2701,plain,
! [SV87: $i] :
( ( ( SV87 = emptyset )
= $true )
| ( ( ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 )
= ( SV87 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[935]) ).
thf(2702,plain,
! [SV158: $i,SV39: $i,SV242: $i] :
( ( ( in @ SV242 @ SV158 )
= $false )
| ( ( ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
= ( in @ SV242 @ SV158 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[983]) ).
thf(2703,plain,
! [SV97: $i,SV203: $i,SV260: $i] :
( ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false )
| ( ( ( in @ SV260 @ SV203 )
= ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1033]) ).
thf(2704,plain,
! [SV275: $i,SV30: $i] :
( ( ( in @ SV275 @ SV30 )
= $false )
| ( ( ( SV30 = emptyset )
= ( in @ SV275 @ SV30 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1061]) ).
thf(2705,plain,
! [SV49: $i,SV166: $i] :
( ( ( subset @ SV49 @ SV166 )
= $true )
| ( ( ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
= ( subset @ SV49 @ SV166 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1080]) ).
thf(2706,plain,
! [SV55: $i,SV170: $i] :
( ( ( subset @ SV55 @ SV170 )
= $true )
| ( ( ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
= ( subset @ SV55 @ SV170 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1087]) ).
thf(2707,plain,
! [SV104: $i] :
( ( ( SV104 = emptyset )
= $true )
| ( ( ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 )
= ( SV104 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1121]) ).
thf(2708,plain,
! [SV216: $i,SV112: $i] :
( ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true )
| ( ( ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
= ( in @ SV216 @ ( powerset @ SV112 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1130]) ).
thf(2709,plain,
! [SV60: $i] :
( ( ( SV60 = emptyset )
= $true )
| ( ( ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
= ( SV60 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1323]) ).
thf(2711,plain,
! [SV232: $i,SV129: $i] :
( ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true )
| ( ( ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
= ( in @ SV232 @ ( powerset @ SV129 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1371]) ).
thf(2712,plain,
! [SV89: $i,SV199: $i] :
( ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true )
| ( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
= ( ( binintersect @ SV89 @ SV199 )
= emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1429]) ).
thf(2713,plain,
! [SV89: $i,SV199: $i] :
( ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true )
| ( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 )
= ( ( binintersect @ SV89 @ SV199 )
= emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1430]) ).
thf(2714,plain,
! [SV90: $o] :
( ( ( ~ ( SV90
| ~ ( set2prop @ ( prop2set @ SV90 ) ) )
| ~ ( ~ SV90
| ~ ~ ( set2prop @ ( prop2set @ SV90 ) ) ) )
= $false )
| ( SV90 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2694]) ).
thf(2716,plain,
! [SV130: $o] :
( ( ( ~ ( SV130
| ~ ( in @ emptyset @ ( prop2set @ SV130 ) ) )
| ~ ( ~ SV130
| ~ ~ ( in @ emptyset @ ( prop2set @ SV130 ) ) ) )
= $false )
| ( SV130 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2695]) ).
thf(2718,plain,
! [SV185: $i,SV73: $o] :
( ( ( ~ ( SV73
| ~ ( in @ SV185 @ ( prop2set @ SV73 ) ) )
| ~ ( ~ SV73
| ~ ~ ( in @ SV185 @ ( prop2set @ SV73 ) ) ) )
= $false )
| ( SV73 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2696]) ).
thf(2720,plain,
! [SV83: $i,SV274: $o] :
( ( ( ~ ( SV274
| ~ ( in @ SV83 @ emptyset ) )
| ~ ( ~ SV274
| ~ ~ ( in @ SV83 @ emptyset ) ) )
= $false )
| ( SV274 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2697]) ).
thf(2721,plain,
! [SV83: $i,SV274: $o] :
( ( ( SV274
= ( ~ ( in @ SV83 @ emptyset ) ) )
= $false )
| ( SV274 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2697]) ).
thf(2722,plain,
! [SV211: $i,SV106: $i > $o] :
( ( ( ~ ( ( SV106 @ SV211 )
| ~ ( in @ SV211 @ emptyset ) )
| ~ ( ~ ( SV106 @ SV211 )
| ~ ~ ( in @ SV211 @ emptyset ) ) )
= $false )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2698]) ).
thf(2723,plain,
! [SV211: $i,SV106: $i > $o] :
( ( ( ( SV106 @ SV211 )
= ( ~ ( in @ SV211 @ emptyset ) ) )
= $false )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2698]) ).
thf(2724,plain,
! [SV61: $i,SV248: $i,SV175: $i > $o] :
( ( ( ~ ( ( SV175 @ SV248 )
| ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) ) )
| ~ ( ~ ( SV175 @ SV248 )
| ~ ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) ) ) )
= $false )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2699]) ).
thf(2725,plain,
! [SV61: $i,SV248: $i,SV175: $i > $o] :
( ( ( ( SV175 @ SV248 )
= ( ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) ) ) )
= $false )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2699]) ).
thf(2726,plain,
! [SV85: $i] :
( ( ( ~ ( ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 )
| ( SV85 = emptyset ) )
| ~ ( ~ ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 )
| ( SV85 != emptyset ) ) )
= $false )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2700]) ).
thf(2728,plain,
! [SV87: $i] :
( ( ( ~ ( ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 )
| ( SV87 = emptyset ) )
| ~ ( ~ ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 )
| ( SV87 != emptyset ) ) )
= $false )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2701]) ).
thf(2730,plain,
! [SV158: $i,SV39: $i,SV242: $i] :
( ( ( ~ ( ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
| ( in @ SV242 @ SV158 ) )
| ~ ( ~ ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
| ~ ( in @ SV242 @ SV158 ) ) )
= $false )
| ( ( in @ SV242 @ SV158 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2702]) ).
thf(2732,plain,
! [SV97: $i,SV203: $i,SV260: $i] :
( ( ( ~ ( ( in @ SV260 @ SV203 )
| ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) ) )
| ~ ( ~ ( in @ SV260 @ SV203 )
| ~ ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) ) ) )
= $false )
| ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2703]) ).
thf(2734,plain,
! [SV275: $i,SV30: $i] :
( ( ( ~ ( ( SV30 = emptyset )
| ( in @ SV275 @ SV30 ) )
| ~ ( ( SV30 != emptyset )
| ~ ( in @ SV275 @ SV30 ) ) )
= $false )
| ( ( in @ SV275 @ SV30 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[2704]) ).
thf(2736,plain,
! [SV49: $i,SV166: $i] :
( ( ( ~ ( ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
| ( subset @ SV49 @ SV166 ) )
| ~ ( ~ ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
| ~ ( subset @ SV49 @ SV166 ) ) )
= $false )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2705]) ).
thf(2738,plain,
! [SV55: $i,SV170: $i] :
( ( ( ~ ( ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
| ( subset @ SV55 @ SV170 ) )
| ~ ( ~ ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
| ~ ( subset @ SV55 @ SV170 ) ) )
= $false )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2706]) ).
thf(2740,plain,
! [SV104: $i] :
( ( ( ~ ( ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 )
| ( SV104 = emptyset ) )
| ~ ( ~ ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 )
| ( SV104 != emptyset ) ) )
= $false )
| ( ( SV104 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2707]) ).
thf(2742,plain,
! [SV216: $i,SV112: $i] :
( ( ( ~ ( ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
| ( in @ SV216 @ ( powerset @ SV112 ) ) )
| ~ ( ~ ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
| ~ ( in @ SV216 @ ( powerset @ SV112 ) ) ) )
= $false )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2708]) ).
thf(2744,plain,
! [SV60: $i] :
( ( ( ~ ( ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
| ( SV60 = emptyset ) )
| ~ ( ~ ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
| ( SV60 != emptyset ) ) )
= $false )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2709]) ).
thf(2748,plain,
! [SV232: $i,SV129: $i] :
( ( ( ~ ( ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
| ( in @ SV232 @ ( powerset @ SV129 ) ) )
| ~ ( ~ ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
| ~ ( in @ SV232 @ ( powerset @ SV129 ) ) ) )
= $false )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2711]) ).
thf(2750,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
| ( ( binintersect @ SV89 @ SV199 )
= emptyset ) )
| ~ ( ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
| ( ( binintersect @ SV89 @ SV199 )
!= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2712]) ).
thf(2752,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 )
| ( ( binintersect @ SV89 @ SV199 )
= emptyset ) )
| ~ ( ~ ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 )
| ( ( binintersect @ SV89 @ SV199 )
!= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[2713]) ).
thf(2755,plain,
! [SV90: $o] :
( ( ( ~ ( ~ SV90
| ~ ~ ( set2prop @ ( prop2set @ SV90 ) ) ) )
= $false )
| ( SV90 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2714]) ).
thf(2757,plain,
! [SV130: $o] :
( ( ( ~ ( ~ SV130
| ~ ~ ( in @ emptyset @ ( prop2set @ SV130 ) ) ) )
= $false )
| ( SV130 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2716]) ).
thf(2758,plain,
! [SV185: $i,SV73: $o] :
( ( ( ~ ( SV73
| ~ ( in @ SV185 @ ( prop2set @ SV73 ) ) ) )
= $false )
| ( SV73 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2760,plain,
! [SV83: $i,SV274: $o] :
( ( ( ~ ( SV274
| ~ ( in @ SV83 @ emptyset ) ) )
= $false )
| ( SV274 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2720]) ).
thf(2762,plain,
! [SV211: $i,SV106: $i > $o] :
( ( ( ~ ( ( SV106 @ SV211 )
| ~ ( in @ SV211 @ emptyset ) ) )
= $false )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2722]) ).
thf(2764,plain,
! [SV61: $i,SV248: $i,SV175: $i > $o] :
( ( ( ~ ( ( SV175 @ SV248 )
| ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) ) ) )
= $false )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2724]) ).
thf(2766,plain,
! [SV85: $i] :
( ( ( ~ ( ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 )
| ( SV85 = emptyset ) ) )
= $false )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2768,plain,
! [SV87: $i] :
( ( ( ~ ( ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 )
| ( SV87 = emptyset ) ) )
= $false )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2728]) ).
thf(2771,plain,
! [SV158: $i,SV39: $i,SV242: $i] :
( ( ( ~ ( ~ ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
| ~ ( in @ SV242 @ SV158 ) ) )
= $false )
| ( ( in @ SV242 @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2730]) ).
thf(2773,plain,
! [SV97: $i,SV203: $i,SV260: $i] :
( ( ( ~ ( ~ ( in @ SV260 @ SV203 )
| ~ ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) ) ) )
= $false )
| ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2775,plain,
! [SV275: $i,SV30: $i] :
( ( ( ~ ( ( SV30 != emptyset )
| ~ ( in @ SV275 @ SV30 ) ) )
= $false )
| ( ( in @ SV275 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2734]) ).
thf(2776,plain,
! [SV49: $i,SV166: $i] :
( ( ( ~ ( ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
| ( subset @ SV49 @ SV166 ) ) )
= $false )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2778,plain,
! [SV55: $i,SV170: $i] :
( ( ( ~ ( ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
| ( subset @ SV55 @ SV170 ) ) )
= $false )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2738]) ).
thf(2780,plain,
! [SV104: $i] :
( ( ( ~ ( ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 )
| ( SV104 = emptyset ) ) )
= $false )
| ( ( SV104 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2782,plain,
! [SV216: $i,SV112: $i] :
( ( ( ~ ( ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
| ( in @ SV216 @ ( powerset @ SV112 ) ) ) )
= $false )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2742]) ).
thf(2784,plain,
! [SV60: $i] :
( ( ( ~ ( ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
| ( SV60 = emptyset ) ) )
= $false )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2788,plain,
! [SV232: $i,SV129: $i] :
( ( ( ~ ( ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
| ( in @ SV232 @ ( powerset @ SV129 ) ) ) )
= $false )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2790,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
| ( ( binintersect @ SV89 @ SV199 )
= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2750]) ).
thf(2792,plain,
! [SV89: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 )
| ( ( binintersect @ SV89 @ SV199 )
= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2752]) ).
thf(2795,plain,
! [SV90: $o] :
( ( ( ~ SV90
| ~ ~ ( set2prop @ ( prop2set @ SV90 ) ) )
= $true )
| ( SV90 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2755]) ).
thf(2797,plain,
! [SV130: $o] :
( ( ( ~ SV130
| ~ ~ ( in @ emptyset @ ( prop2set @ SV130 ) ) )
= $true )
| ( SV130 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2757]) ).
thf(2798,plain,
! [SV185: $i,SV73: $o] :
( ( ( SV73
| ~ ( in @ SV185 @ ( prop2set @ SV73 ) ) )
= $true )
| ( SV73 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2758]) ).
thf(2800,plain,
! [SV83: $i,SV274: $o] :
( ( ( SV274
| ~ ( in @ SV83 @ emptyset ) )
= $true )
| ( SV274 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2760]) ).
thf(2802,plain,
! [SV211: $i,SV106: $i > $o] :
( ( ( ( SV106 @ SV211 )
| ~ ( in @ SV211 @ emptyset ) )
= $true )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2762]) ).
thf(2804,plain,
! [SV61: $i,SV248: $i,SV175: $i > $o] :
( ( ( ( SV175 @ SV248 )
| ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) ) )
= $true )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2764]) ).
thf(2806,plain,
! [SV85: $i] :
( ( ( ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 )
| ( SV85 = emptyset ) )
= $true )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2808,plain,
! [SV87: $i] :
( ( ( ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 )
| ( SV87 = emptyset ) )
= $true )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2811,plain,
! [SV158: $i,SV39: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
| ~ ( in @ SV242 @ SV158 ) )
= $true )
| ( ( in @ SV242 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2771]) ).
thf(2813,plain,
! [SV97: $i,SV203: $i,SV260: $i] :
( ( ( ~ ( in @ SV260 @ SV203 )
| ~ ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) ) )
= $true )
| ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2773]) ).
thf(2815,plain,
! [SV275: $i,SV30: $i] :
( ( ( ( SV30 != emptyset )
| ~ ( in @ SV275 @ SV30 ) )
= $true )
| ( ( in @ SV275 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2775]) ).
thf(2816,plain,
! [SV49: $i,SV166: $i] :
( ( ( ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
| ( subset @ SV49 @ SV166 ) )
= $true )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2776]) ).
thf(2818,plain,
! [SV55: $i,SV170: $i] :
( ( ( ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
| ( subset @ SV55 @ SV170 ) )
= $true )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2778]) ).
thf(2820,plain,
! [SV104: $i] :
( ( ( ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 )
| ( SV104 = emptyset ) )
= $true )
| ( ( SV104 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2780]) ).
thf(2822,plain,
! [SV216: $i,SV112: $i] :
( ( ( ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
| ( in @ SV216 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2782]) ).
thf(2824,plain,
! [SV60: $i] :
( ( ( ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
| ( SV60 = emptyset ) )
= $true )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2784]) ).
thf(2828,plain,
! [SV232: $i,SV129: $i] :
( ( ( ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
| ( in @ SV232 @ ( powerset @ SV129 ) ) )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2788]) ).
thf(2830,plain,
! [SV89: $i,SV199: $i] :
( ( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
| ( ( binintersect @ SV89 @ SV199 )
= emptyset ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2832,plain,
! [SV89: $i,SV199: $i] :
( ( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 )
| ( ( binintersect @ SV89 @ SV199 )
= emptyset ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2835,plain,
! [SV90: $o] :
( ( ( ~ SV90 ) = $true )
| ( ( ~ ~ ( set2prop @ ( prop2set @ SV90 ) ) )
= $true )
| ( SV90 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(2837,plain,
! [SV130: $o] :
( ( ( ~ SV130 ) = $true )
| ( ( ~ ~ ( in @ emptyset @ ( prop2set @ SV130 ) ) )
= $true )
| ( SV130 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2838,plain,
! [SV185: $i,SV73: $o] :
( ( SV73 = $true )
| ( ( ~ ( in @ SV185 @ ( prop2set @ SV73 ) ) )
= $true )
| ( SV73 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2798]) ).
thf(2840,plain,
! [SV83: $i,SV274: $o] :
( ( SV274 = $true )
| ( ( ~ ( in @ SV83 @ emptyset ) )
= $true )
| ( SV274 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2800]) ).
thf(2842,plain,
! [SV211: $i,SV106: $i > $o] :
( ( ( SV106 @ SV211 )
= $true )
| ( ( ~ ( in @ SV211 @ emptyset ) )
= $true )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(2844,plain,
! [SV61: $i,SV248: $i,SV175: $i > $o] :
( ( ( SV175 @ SV248 )
= $true )
| ( ( ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) ) )
= $true )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(2846,plain,
! [SV85: $i] :
( ( ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85 = emptyset )
= $true )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(2848,plain,
! [SV87: $i] :
( ( ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87 = emptyset )
= $true )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2808]) ).
thf(2851,plain,
! [SV158: $i,SV39: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) ) )
= $true )
| ( ( ~ ( in @ SV242 @ SV158 ) )
= $true )
| ( ( in @ SV242 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(2853,plain,
! [SV97: $i,SV203: $i,SV260: $i] :
( ( ( ~ ( in @ SV260 @ SV203 ) )
= $true )
| ( ( ~ ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) ) )
= $true )
| ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2813]) ).
thf(2855,plain,
! [SV275: $i,SV30: $i] :
( ( ( SV30 != emptyset )
= $true )
| ( ( ~ ( in @ SV275 @ SV30 ) )
= $true )
| ( ( in @ SV275 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(2856,plain,
! [SV49: $i,SV166: $i] :
( ( ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
= $true )
| ( ( subset @ SV49 @ SV166 )
= $true )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(2858,plain,
! [SV55: $i,SV170: $i] :
( ( ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
= $true )
| ( ( subset @ SV55 @ SV170 )
= $true )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(2860,plain,
! [SV104: $i] :
( ( ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104 = emptyset )
= $true )
| ( ( SV104 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(2862,plain,
! [SV216: $i,SV112: $i] :
( ( ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
= $true )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(2864,plain,
! [SV60: $i] :
( ( ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
= $true )
| ( ( SV60 = emptyset )
= $true )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(2868,plain,
! [SV232: $i,SV129: $i] :
( ( ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2828]) ).
thf(2870,plain,
! [SV89: $i,SV199: $i] :
( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2830]) ).
thf(2872,plain,
! [SV89: $i,SV199: $i] :
( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(2875,plain,
! [SV90: $o] :
( ( SV90 = $false )
| ( ( ~ ~ ( set2prop @ ( prop2set @ SV90 ) ) )
= $true )
| ( SV90 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(2877,plain,
! [SV130: $o] :
( ( SV130 = $false )
| ( ( ~ ~ ( in @ emptyset @ ( prop2set @ SV130 ) ) )
= $true )
| ( SV130 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2878,plain,
! [SV73: $o,SV185: $i] :
( ( ( in @ SV185 @ ( prop2set @ SV73 ) )
= $false )
| ( SV73 = $true )
| ( SV73 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2880,plain,
! [SV274: $o,SV83: $i] :
( ( ( in @ SV83 @ emptyset )
= $false )
| ( SV274 = $true )
| ( SV274 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2882,plain,
! [SV106: $i > $o,SV211: $i] :
( ( ( in @ SV211 @ emptyset )
= $false )
| ( ( SV106 @ SV211 )
= $true )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2884,plain,
! [SV175: $i > $o,SV61: $i,SV248: $i] :
( ( ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) )
= $false )
| ( ( SV175 @ SV248 )
= $true )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(2888,plain,
! [SV158: $i,SV39: $i,SV242: $i] :
( ( ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
= $false )
| ( ( ~ ( in @ SV242 @ SV158 ) )
= $true )
| ( ( in @ SV242 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2889,plain,
! [SV97: $i,SV203: $i,SV260: $i] :
( ( ( in @ SV260 @ SV203 )
= $false )
| ( ( ~ ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) ) )
= $true )
| ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(2890,plain,
! [SV275: $i,SV30: $i] :
( ( ( SV30 = emptyset )
= $false )
| ( ( ~ ( in @ SV275 @ SV30 ) )
= $true )
| ( ( in @ SV275 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2900,plain,
! [SV90: $o] :
( ( ( ~ ( set2prop @ ( prop2set @ SV90 ) ) )
= $false )
| ( SV90 = $false )
| ( SV90 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(2901,plain,
! [SV130: $o] :
( ( ( ~ ( in @ emptyset @ ( prop2set @ SV130 ) ) )
= $false )
| ( SV130 = $false )
| ( SV130 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(2908,plain,
! [SV39: $i,SV158: $i,SV242: $i] :
( ( ( in @ SV242 @ SV158 )
= $false )
| ( ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
= $false )
| ( ( in @ SV242 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(2909,plain,
! [SV203: $i,SV97: $i,SV260: $i] :
( ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false )
| ( ( in @ SV260 @ SV203 )
= $false )
| ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2910,plain,
! [SV30: $i,SV275: $i] :
( ( ( in @ SV275 @ SV30 )
= $false )
| ( ( SV30 = emptyset )
= $false )
| ( ( in @ SV275 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(2920,plain,
! [SV90: $o] :
( ( ( set2prop @ ( prop2set @ SV90 ) )
= $true )
| ( SV90 = $false )
| ( SV90 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2900]) ).
thf(2921,plain,
! [SV130: $o] :
( ( ( in @ emptyset @ ( prop2set @ SV130 ) )
= $true )
| ( SV130 = $false )
| ( SV130 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2901]) ).
thf(2926,plain,
! [SV83: $i] :
( ( ~ ( in @ SV83 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[2721:[bind(SV274,$thf( ~ ( in @ SV83 @ emptyset ) ))]]) ).
thf(2928,plain,
! [SV413: $i > $i,SV211: $i,SV412: $i > $i] :
( ( ( ~ ( in @ ( SV412 @ SV211 ) @ ( SV413 @ SV211 ) ) )
= $true )
| ( ( in @ ( SV412 @ SV211 ) @ ( SV413 @ SV211 ) )
= $false )
| ( ( in @ SV211 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[2723:[bind(SV106,$thf( ^ [SX0: $i] : ~ ( in @ ( SV412 @ SX0 ) @ ( SV413 @ SX0 ) ) ))]]) ).
thf(2929,plain,
! [SV211: $i,SV409: $i > $o] :
( ( ( ~ ( SV409 @ SV211 ) )
= $true )
| ( ( ~ ( SV409 @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV211 @ emptyset ) )
= $true ) ),
inference(extuni,[status(esa)],[2723:[bind(SV106,$thf( ^ [SX0: $i] : ~ ( SV409 @ SX0 ) ))]]) ).
thf(2932,plain,
! [SV61: $i,SV420: $i > $i,SV248: $i,SV419: $i > $i] :
( ( ( ~ ( in @ ( SV419 @ SV248 ) @ ( SV420 @ SV248 ) ) )
= $true )
| ( ( in @ ( SV419 @ SV248 ) @ ( SV420 @ SV248 ) )
= $false )
| ( ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SX0: $i] :
~ ( in @ ( SV419 @ SX0 ) @ ( SV420 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[2725:[bind(SV175,$thf( ^ [SX0: $i] : ~ ( in @ ( SV419 @ SX0 ) @ ( SV420 @ SX0 ) ) ))]]) ).
thf(2933,plain,
! [SV61: $i,SV248: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV248 ) )
= $true )
| ( ( ~ ( SV416 @ SV248 ) )
= $true )
| ( ( ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SX0: $i] :
~ ( SV416 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[2725:[bind(SV175,$thf( ^ [SX0: $i] : ~ ( SV416 @ SX0 ) ))]]) ).
thf(2937,plain,
! [SV275: $i] :
( ( ( in @ SV275 @ emptyset )
= $false )
| ( ( in @ SV275 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[2910:[bind(SV30,$thf( emptyset ))]]) ).
thf(2941,plain,
! [SV152: $i] :
( ( subset @ SV152 @ SV152 )
= $true ),
inference(extuni,[status(esa)],[774:[bind(SV29,$thf( SV152 ))]]) ).
thf(2942,plain,
! [SV198: $i] :
( ( in @ SV198 @ ( setadjoin @ SV198 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[838:[bind(SV88,$thf( SV198 ))]]) ).
thf(2944,plain,
! [SV221: $i] :
( ( subset @ SV221 @ SV221 )
= $true ),
inference(extuni,[status(esa)],[867:[bind(SV118,$thf( SV221 ))]]) ).
thf(2946,plain,
! [SV188: $i] :
( ( subset @ SV188 @ SV188 )
= $true ),
inference(extuni,[status(esa)],[1021:[bind(SV74,$thf( SV188 ))]]) ).
thf(2947,plain,
! [SV275: $i] :
( ( in @ SV275 @ emptyset )
= $false ),
inference(extuni,[status(esa)],[1061:[bind(SV30,$thf( emptyset ))]]) ).
thf(2950,plain,
! [SV205: $i,SV99: $i] :
( ( in @ SV99 @ ( setadjoin @ SV99 @ SV205 ) )
= $true ),
inference(extuni,[status(esa)],[1268:[bind(SV262,$thf( SV99 ))]]) ).
thf(2952,plain,
! [SV294: $i > $o,SV281: $i > $o,SV168: $i] :
( ( ( ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV281 @ SX0 ) )
= ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV294 @ SX0 ) ) )
= $true )
| ( ( in @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV168 ) @ SV168 )
= $true ) ),
inference(extuni,[status(esa)],[1392:[bind(SV52,$thf( SV168 ))]]) ).
thf(2953,plain,
! [SV294: $i > $o,SV281: $i > $o,SV168: $i] :
( ( ( ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV281 @ SX0 ) )
= ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV294 @ SX0 ) ) )
= $true )
| ( ( in @ ( sK41_SY1293 @ SV168 @ SV281 @ SV294 @ SV168 ) @ SV168 )
= $true ) ),
inference(extuni,[status(esa)],[1559:[bind(SV52,$thf( SV168 ))]]) ).
thf(2956,plain,
! [SV294: $i > $o,SV281: $i > $o,SV168: $i] :
( ( ( ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV281 @ SX0 ) )
= ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV294 @ SX0 ) ) )
= $true )
| ( ( ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV168 )
= ( sK41_SY1293 @ SV168 @ SV281 @ SV294 @ SV168 ) )
= $true ) ),
inference(extuni,[status(esa)],[1653:[bind(SV52,$thf( SV168 ))]]) ).
thf(2957,plain,
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ sK3_SY1200 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[1889:[bind(SV315,$thf( sK3_SY1200 )),bind(SV287,$thf( sK1_SX0 ))]]) ).
thf(2958,plain,
! [SV315: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK3_SY1200 @ emptyset )
= ( setadjoin @ SV315 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1889:[bind(SV287,$thf( sK1_SX0 ))]]) ).
thf(2959,plain,
! [SV315: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) )
= ( setadjoin @ sK1_SX0 @ ( setadjoin @ SV315 @ emptyset ) ) )
= $false ) ),
inference(extuni,[status(esa)],[1889:[bind(SV287,$thf( sK1_SX0 ))]]) ).
thf(2960,plain,
! [SV315: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset )
= ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SV315 @ emptyset ) ) @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1889:[bind(SV287,$thf( sK1_SX0 ))]]) ).
thf(2961,plain,
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ sK3_SY1200 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ emptyset )
= ( setadjoin @ sK1_SX0 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1889:[bind(SV315,$thf( sK3_SY1200 )),bind(SV287,$thf( sK1_SX0 ))]]) ).
thf(2962,plain,
! [SV315: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK3_SY1200 @ emptyset )
= ( setadjoin @ SV315 @ emptyset ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ emptyset )
= ( setadjoin @ sK1_SX0 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1889:[bind(SV287,$thf( sK1_SX0 ))]]) ).
thf(2963,plain,
! [SV315: $i,SV287: $i] :
( ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) )
= ( setadjoin @ SV287 @ ( setadjoin @ SV315 @ emptyset ) ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ emptyset )
= ( setadjoin @ SV287 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1889]) ).
thf(2964,plain,
! [SV315: $i,SV287: $i] :
( ( ( in @ SV287 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset )
= ( setadjoin @ ( setadjoin @ SV287 @ ( setadjoin @ SV315 @ emptyset ) ) @ emptyset ) )
= $false )
| ( ( ( setadjoin @ sK1_SX0 @ emptyset )
= ( setadjoin @ SV287 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1889]) ).
thf(2965,plain,
! [SV294: $i > $o,SV281: $i > $o,SV168: $i] :
( ( ( ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV281 @ SX0 ) )
= ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV294 @ SX0 ) ) )
= $true )
| ( ( SV294 @ ( sK41_SY1293 @ SV168 @ SV281 @ SV294 @ SV168 ) )
= $false )
| ( ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV168 ) )
= $false ) ),
inference(extuni,[status(esa)],[1971:[bind(SV52,$thf( SV168 ))]]) ).
thf(2968,plain,
! [SV294: $i > $o,SV281: $i > $o,SV168: $i] :
( ( ( ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV281 @ SX0 ) )
= ( dsetconstr @ SV168
@ ^ [SX0: $i] : ( SV294 @ SX0 ) ) )
= $true )
| ( ( SV281 @ ( sK31_SY1276 @ SV294 @ SV281 @ SV168 @ SV168 ) )
= $true )
| ( ( SV294 @ ( sK41_SY1293 @ SV168 @ SV281 @ SV294 @ SV168 ) )
= $true ) ),
inference(extuni,[status(esa)],[2065:[bind(SV52,$thf( SV168 ))]]) ).
thf(2969,plain,
! [SV285: $i,SV91: $i > $o] :
( ( ( SV91 @ ( sK42_SY1268 @ SV285 @ SV91 ) )
= $true )
| ( ( SV91 @ SV285 )
= $false )
| ( ( SV91 @ ( sK59_SY1019 @ SV285 @ SV91 ) )
= $true ) ),
inference(extuni,[status(esa)],[2111:[bind(SV337,$thf( sK59_SY1019 @ SV285 @ SV91 ))]]) ).
thf(2970,plain,
! [SV285: $i] :
( ( ( ( sK42_SY1268 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) )
= SV285 )
= $true )
| ( ( ( sK59_SY1019 @ SV285
@ ^ [SX0: $i] : ( SX0 = SV285 ) )
= SV285 )
= $true ) ),
inference(extuni,[status(esa)],[2693:[bind(SV337,$thf( sK59_SY1019 @ SV285 @ ^ [SX0: $i] : ( SX0 = SV285 ) ))]]) ).
thf(2971,plain,
! [SV83: $i] :
( ( in @ SV83 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(2973,plain,
! [SV211: $i,SV409: $i > $o] :
( ( ( SV409 @ SV211 )
= $false )
| ( ( ~ ( SV409 @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV211 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(2974,plain,
! [SV413: $i > $i,SV211: $i,SV412: $i > $i] :
( ( ( in @ ( SV412 @ SV211 ) @ ( SV413 @ SV211 ) )
= $false )
| ( ( in @ ( SV412 @ SV211 ) @ ( SV413 @ SV211 ) )
= $false )
| ( ( in @ SV211 @ emptyset )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(2977,plain,
! [SV61: $i,SV248: $i,SV416: $i > $o] :
( ( ( SV416 @ SV248 )
= $false )
| ( ( ~ ( SV416 @ SV248 ) )
= $true )
| ( ( ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SX0: $i] :
~ ( SV416 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2933]) ).
thf(2978,plain,
! [SV61: $i,SV420: $i > $i,SV248: $i,SV419: $i > $i] :
( ( ( in @ ( SV419 @ SV248 ) @ ( SV420 @ SV248 ) )
= $false )
| ( ( in @ ( SV419 @ SV248 ) @ ( SV420 @ SV248 ) )
= $false )
| ( ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SX0: $i] :
~ ( in @ ( SV419 @ SX0 ) @ ( SV420 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(2981,plain,
! [SV211: $i,SV409: $i > $o] :
( ( ( SV409 @ SV211 )
= $false )
| ( ( SV409 @ SV211 )
= $false )
| ( ( ~ ( in @ SV211 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(2983,plain,
! [SV61: $i,SV248: $i,SV416: $i > $o] :
( ( ( SV416 @ SV248 )
= $false )
| ( ( SV416 @ SV248 )
= $false )
| ( ( ~ ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SX0: $i] :
~ ( SV416 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(2985,plain,
! [SV409: $i > $o,SV211: $i] :
( ( ( in @ SV211 @ emptyset )
= $false )
| ( ( SV409 @ SV211 )
= $false )
| ( ( SV409 @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(2987,plain,
! [SV416: $i > $o,SV61: $i,SV248: $i] :
( ( ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SX0: $i] :
~ ( SV416 @ SX0 ) ) )
= $false )
| ( ( SV416 @ SV248 )
= $false )
| ( ( SV416 @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(2988,plain,
( ( set2prop @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[724]) ).
thf(2989,plain,
! [SV96: $i] :
( ( in @ SV96 @ emptyset )
= $false ),
inference(sim,[status(thm)],[731]) ).
thf(2990,plain,
( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[767]) ).
thf(2991,plain,
! [SV187: $i] :
( ( in @ SV187 @ ( prop2set @ $false ) )
= $false ),
inference(sim,[status(thm)],[821]) ).
thf(2992,plain,
! [SV83: $i] :
( ( in @ SV83 @ emptyset )
= $false ),
inference(sim,[status(thm)],[833]) ).
thf(2993,plain,
! [SV50: $i,SV167: $i] :
( ( ( in @ SV167 @ ( sK26_SX0 @ SV50 @ SV167 ) )
= $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(sim,[status(thm)],[1307]) ).
thf(2994,plain,
! [SV167: $i,SV50: $i] :
( ( ( in @ ( sK26_SX0 @ SV50 @ SV167 ) @ SV50 )
= $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(sim,[status(thm)],[1390]) ).
thf(2995,plain,
! [SV298: $i,SV189: $i > $o,SV75: $i] :
( ( ( ( dsetconstr @ SV75
@ ^ [SY1173: $i] : ( SV189 @ SY1173 ) )
= emptyset )
= $false )
| ( ( in @ SV298 @ SV75 )
= $false )
| ( ( SV189 @ SV298 )
= $false ) ),
inference(sim,[status(thm)],[1599]) ).
thf(2996,plain,
! [SV57: $i,SV172: $i,SV247: $i] :
( ( ( in @ SV247 @ SV172 )
= $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(sim,[status(thm)],[1658]) ).
thf(2997,plain,
! [SV69: $i,SV182: $i,SV253: $i] :
( ( ( in @ SV253 @ SV182 )
= $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(sim,[status(thm)],[1682]) ).
thf(2998,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( in @ SV249 @ SV176 )
= $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(sim,[status(thm)],[1752]) ).
thf(2999,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( in @ SV249 @ SV63 )
= $false )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(sim,[status(thm)],[1869]) ).
thf(3000,plain,
! [SV90: $o] :
( ( ( set2prop @ ( prop2set @ SV90 ) )
= $true )
| ( SV90 = $false ) ),
inference(sim,[status(thm)],[2920]) ).
thf(3001,plain,
! [SV130: $o] :
( ( ( in @ emptyset @ ( prop2set @ SV130 ) )
= $true )
| ( SV130 = $false ) ),
inference(sim,[status(thm)],[2921]) ).
thf(3002,plain,
! [SV73: $o,SV185: $i] :
( ( ( in @ SV185 @ ( prop2set @ SV73 ) )
= $false )
| ( SV73 = $true ) ),
inference(sim,[status(thm)],[2878]) ).
thf(3003,plain,
! [SV274: $o,SV83: $i] :
( ( ( in @ SV83 @ emptyset )
= $false )
| ( SV274 = $true ) ),
inference(sim,[status(thm)],[2880]) ).
thf(3004,plain,
! [SV106: $i > $o,SV211: $i] :
( ( ( in @ SV211 @ emptyset )
= $false )
| ( ( SV106 @ SV211 )
= $true ) ),
inference(sim,[status(thm)],[2882]) ).
thf(3005,plain,
! [SV409: $i > $o,SV211: $i] :
( ( ( in @ SV211 @ emptyset )
= $false )
| ( ( SV409 @ SV211 )
= $false ) ),
inference(sim,[status(thm)],[2985]) ).
thf(3006,plain,
! [SV413: $i > $i,SV211: $i,SV412: $i > $i] :
( ( ( in @ ( SV412 @ SV211 ) @ ( SV413 @ SV211 ) )
= $false )
| ( ( in @ SV211 @ emptyset )
= $false ) ),
inference(sim,[status(thm)],[2974]) ).
thf(3007,plain,
! [SV175: $i > $o,SV61: $i,SV248: $i] :
( ( ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SY1161: $i] : ( SV175 @ SY1161 ) ) )
= $false )
| ( ( SV175 @ SV248 )
= $true ) ),
inference(sim,[status(thm)],[2884]) ).
thf(3008,plain,
! [SV416: $i > $o,SV61: $i,SV248: $i] :
( ( ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SX0: $i] :
~ ( SV416 @ SX0 ) ) )
= $false )
| ( ( SV416 @ SV248 )
= $false ) ),
inference(sim,[status(thm)],[2987]) ).
thf(3009,plain,
! [SV61: $i,SV420: $i > $i,SV248: $i,SV419: $i > $i] :
( ( ( in @ ( SV419 @ SV248 ) @ ( SV420 @ SV248 ) )
= $false )
| ( ( in @ SV248
@ ( dsetconstr @ SV61
@ ^ [SX0: $i] :
~ ( in @ ( SV419 @ SX0 ) @ ( SV420 @ SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[2978]) ).
thf(3010,plain,
! [SV85: $i] :
( ( ( in @ ( sK4_SY1011 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[2846]) ).
thf(3011,plain,
! [SV87: $i] :
( ( ( in @ ( sK5_SY1013 @ SV87 ) @ SV87 )
= $true )
| ( ( SV87 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[2848]) ).
thf(3012,plain,
! [SV39: $i,SV158: $i,SV242: $i] :
( ( ( in @ SV242 @ SV158 )
= $false )
| ( ( in @ SV242 @ ( setminus @ SV39 @ SV158 ) )
= $false ) ),
inference(sim,[status(thm)],[2908]) ).
thf(3013,plain,
! [SV203: $i,SV97: $i,SV260: $i] :
( ( ( in @ SV260 @ ( setminus @ SV97 @ SV203 ) )
= $false )
| ( ( in @ SV260 @ SV203 )
= $false ) ),
inference(sim,[status(thm)],[2909]) ).
thf(3014,plain,
! [SV275: $i] :
( ( in @ SV275 @ emptyset )
= $false ),
inference(sim,[status(thm)],[2937]) ).
thf(3015,plain,
! [SV49: $i,SV166: $i] :
( ( ( in @ ( sK8_SY1143 @ SV166 @ SV49 ) @ SV49 )
= $true )
| ( ( subset @ SV49 @ SV166 )
= $true ) ),
inference(sim,[status(thm)],[2856]) ).
thf(3016,plain,
! [SV55: $i,SV170: $i] :
( ( ( in @ ( sK9_SY1153 @ SV170 @ SV55 ) @ SV55 )
= $true )
| ( ( subset @ SV55 @ SV170 )
= $true ) ),
inference(sim,[status(thm)],[2858]) ).
thf(3017,plain,
! [SV104: $i] :
( ( ( in @ ( sK18_SY1053 @ SV104 ) @ SV104 )
= $true )
| ( ( SV104 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[2860]) ).
thf(3018,plain,
! [SV216: $i,SV112: $i] :
( ( ( in @ ( sK14_SY1210 @ SV112 @ SV216 ) @ SV216 )
= $true )
| ( ( in @ SV216 @ ( powerset @ SV112 ) )
= $true ) ),
inference(sim,[status(thm)],[2862]) ).
thf(3019,plain,
! [SV60: $i] :
( ( ( in @ ( sK16_SY965 @ SV60 ) @ SV60 )
= $true )
| ( ( SV60 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[2864]) ).
thf(3020,plain,
! [SV232: $i,SV129: $i] :
( ( ( in @ ( sK28_SY1225 @ SV129 @ SV232 ) @ SV232 )
= $true )
| ( ( in @ SV232 @ ( powerset @ SV129 ) )
= $true ) ),
inference(sim,[status(thm)],[2868]) ).
thf(3021,plain,
! [SV89: $i,SV199: $i] :
( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV89 )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(sim,[status(thm)],[2870]) ).
thf(3022,plain,
! [SV89: $i,SV199: $i] :
( ( ( in @ ( sK20_SY1180 @ SV199 @ SV89 ) @ SV199 )
= $true )
| ( ( ( binintersect @ SV89 @ SV199 )
= emptyset )
= $true ) ),
inference(sim,[status(thm)],[2872]) ).
thf(3023,plain,
( ( set2prop @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[724]) ).
thf(3024,plain,
! [SV96: $i] :
( ( in @ SV96 @ emptyset )
= $false ),
inference(sim,[status(thm)],[731]) ).
thf(3025,plain,
( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[767]) ).
thf(3026,plain,
! [SV187: $i] :
( ( in @ SV187 @ ( prop2set @ $false ) )
= $false ),
inference(sim,[status(thm)],[821]) ).
thf(3027,plain,
! [SV83: $i] :
( ( in @ SV83 @ emptyset )
= $false ),
inference(sim,[status(thm)],[833]) ).
thf(3028,plain,
! [SV50: $i,SV167: $i] :
( ( ( in @ SV167 @ ( sK26_SX0 @ SV50 @ SV167 ) )
= $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(sim,[status(thm)],[1307]) ).
thf(3029,plain,
! [SV167: $i,SV50: $i] :
( ( ( in @ ( sK26_SX0 @ SV50 @ SV167 ) @ SV50 )
= $true )
| ( ( in @ SV167 @ ( setunion @ SV50 ) )
= $false ) ),
inference(sim,[status(thm)],[1390]) ).
thf(3030,plain,
! [SV57: $i,SV172: $i,SV247: $i] :
( ( ( in @ SV247 @ SV172 )
= $true )
| ( ( in @ SV247 @ SV57 )
= $true )
| ( ( in @ SV247 @ ( binunion @ SV57 @ SV172 ) )
= $false ) ),
inference(sim,[status(thm)],[1658]) ).
thf(3031,plain,
! [SV69: $i,SV182: $i,SV253: $i] :
( ( ( in @ SV253 @ SV182 )
= $true )
| ( ( SV253 = SV69 )
= $true )
| ( ( in @ SV253 @ ( setadjoin @ SV69 @ SV182 ) )
= $false ) ),
inference(sim,[status(thm)],[1682]) ).
thf(3032,plain,
! [SV63: $i,SV176: $i,SV249: $i] :
( ( ( in @ SV249 @ SV176 )
= $true )
| ( ( in @ SV249 @ SV63 )
= $true )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(sim,[status(thm)],[1752]) ).
thf(3033,plain,
! [SV176: $i,SV63: $i,SV249: $i] :
( ( ( in @ SV249 @ SV63 )
= $false )
| ( ( in @ SV249 @ SV176 )
= $false )
| ( ( in @ SV249 @ ( symdiff @ SV63 @ SV176 ) )
= $false ) ),
inference(sim,[status(thm)],[1869]) ).
thf(3034,plain,
! [SV315: $i] :
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV315 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( setadjoin @ sK3_SY1200 @ emptyset )
= ( setadjoin @ SV315 @ emptyset ) )
= $false ) ),
inference(sim,[status(thm)],[2962]) ).
thf(3035,plain,
( ( ( in @ sK1_SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ sK3_SY1200 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1200 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[2961]) ).
thf(3036,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[246,3035,3034,3033,3032,3031,3030,3029,3028,3027,3026,3025,3024,3023,3022,3021,3020,3019,3018,3017,3016,3015,3014,3013,3012,3011,3010,3009,3008,3007,3006,3005,3004,3003,3002,3001,3000,2999,2998,2997,2996,2995,2994,2993,2992,2991,2990,2989,2988,2971,2970,2969,2968,2965,2964,2963,2960,2959,2958,2957,2956,2953,2952,2950,2947,2946,2944,2942,2941,2693,2691,2689,2688,2687,2686,2685,2679,2677,2673,2672,2668,2667,2654,2647,2642,2640,2628,2625,2624,2623,2612,2593,2589,2586,2577,2573,2572,2569,2566,2533,2532,2526,2522,2488,2469,2468,2459,2458,2432,2430,2420,2419,2417,2415,2414,2407,2376,2372,2371,2342,2339,2302,2298,2213,2185,2170,2129,2124,2111,2110,2109,2105,2093,2092,2091,2086,2074,2073,2066,2065,2064,2062,2049,2020,1995,1984,1978,1971,1968,1965,1951,1946,1944,1931,1918,1915,1911,1900,1889,1865,1796,1795,1794,1793,1781,1780,1777,1776,1774,1773,1761,1740,1726,1722,1721,1688,1683,1680,1656,1653,1638,1624,1623,1622,1605,1597,1596,1559,1529,1484,1473,1461,1430,1429,1428,1404,1403,1392,1388,1371,1370,1364,1363,1362,1357,1334,1323,1322,1301,1286,1269,1268,1267,1249,1217,1211,1205,1188,1186,1166,1152,1148,1147,1135,1134,1130,1127,1121,1110,1107,1087,1080,1069,1061,1060,1059,1053,1048,1038,1033,1021,1018,1013,1001,993,983,977,960,959,958,951,942,935,934,930,917,908,883,880,874,873,872,869,867,854,850,842,838,836,834,831,829,819,814,810,801,787,774,773,766,723,701,693,655,540,539,538,537,536,535,534,533,532,531,530,529,528,526,525,524,523,405,404,403,400,399,397,270]) ).
thf(3037,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU619^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.20 % Computer : n006.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 15:29:07 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 179.53/30.24
% 179.53/30.24 No.of.Axioms: 0
% 179.53/30.24
% 179.53/30.24 Length.of.Defs: 27989
% 179.53/30.24
% 179.53/30.24 Contains.Choice.Funs: true
% 179.53/30.24 ............................................................................................eprover: CPU time limit exceeded, terminating
% 179.53/30.24 ..........................
% 179.53/30.24
% 179.53/30.24 ********************************
% 179.53/30.24 * All subproblems solved! *
% 179.53/30.24 ********************************
% 179.53/30.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:135,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:3036,loop_count:0,foatp_calls:2,translation:fof_full)
% 179.53/30.24
% 179.53/30.24 %**** Beginning of derivation protocol ****
% 179.53/30.24 % SZS output start CNFRefutation
% See solution above
% 179.53/30.29
% 179.53/30.29 %**** End of derivation protocol ****
% 179.53/30.29 %**** no. of clauses in derivation: 2461 ****
% 179.53/30.29 %**** clause counter: 3036 ****
% 179.53/30.29
% 179.53/30.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:135,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:3036,loop_count:0,foatp_calls:2,translation:fof_full)
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