%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU768^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:02 AM UTC 2026
% Result : Theorem 182.78s 27.32s
% Output : Refutation 182.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 6081 (1709 equ; 0 cnn)
% Maximal formula atoms : 291 ( 66 avg)
% Number of connectives : 3393 ( 140 ~; 109 |;1197 &; 753 @)
% ( 10 <=>;1184 =>; 0 <=; 0 <~>)
% Maximal formula depth : 300 ( 30 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 549 ( 546 usr; 301 con; 0-4 aty)
% Number of variables : 258 ( 30 ^; 170 !; 58 ?; 258 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_323,type,
breln1: $i > $i > $o ).
thf(func_def_337,type,
sP0: $i > $i > $i > $o ).
thf(func_def_338,type,
sP1: $i > $i > $o ).
thf(func_def_342,type,
sP5: $i > ( $i > $o ) > $o ).
thf(func_def_355,type,
sP18: $i > $i > $i > $i > $o ).
thf(func_def_357,type,
sP20: $i > $o > $i > $i > $o ).
thf(func_def_359,type,
sP22: $i > $i > $i > $i > $o ).
thf(func_def_360,type,
sP23: $i > $i > $i > $o ).
thf(func_def_361,type,
sP24: $i > $i > $i > $o ).
thf(func_def_362,type,
sP25: $i > $i > $i > $o ).
thf(func_def_363,type,
sP26: $i > $i > $o ).
thf(func_def_364,type,
sP27: $i > $o ).
thf(func_def_365,type,
sP28: $i > $i > $o ).
thf(func_def_366,type,
sP29: $i > $i > $o ).
thf(func_def_370,type,
sP33: ( $i > $i > $o ) > $i > $o ).
thf(func_def_375,type,
sP38: $i > ( $i > $o ) > $o ).
thf(func_def_388,type,
sK51: $i > $i > $i ).
thf(func_def_389,type,
sK52: $i > $i > $i > $i ).
thf(func_def_390,type,
sK53: $i > $i > $i > $i ).
thf(func_def_409,type,
sK72: $i > $o ).
thf(func_def_411,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_412,type,
sK75: $i > $o ).
thf(func_def_414,type,
sK77: $i > ( $i > $o ) > $i ).
thf(func_def_422,type,
sK85: $i > $o ).
thf(func_def_452,type,
sK115: $i > $i ).
thf(func_def_456,type,
sK119: $i > $o ).
thf(func_def_458,type,
sK121: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_459,type,
sK122: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_467,type,
sK130: $i > $o ).
thf(func_def_470,type,
sK133: $i > $o ).
thf(func_def_478,type,
sK141: $i > $i > $i > $i > $i ).
thf(func_def_483,type,
sK146: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_484,type,
sK147: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_485,type,
sK148: $i > $o ).
thf(func_def_486,type,
sK149: $i > $o ).
thf(func_def_503,type,
sK166: $i > $o ).
thf(func_def_504,type,
sK167: $i > ( $i > $o ) > $i ).
thf(func_def_505,type,
sK168: $i > ( $i > $o ) > $i ).
thf(func_def_507,type,
sK170: $i > $o ).
thf(func_def_526,type,
sK189: $i > $i ).
thf(func_def_532,type,
sK195: $i > $o ).
thf(func_def_534,type,
sK197: ( $i > $o ) > $i > $i ).
thf(func_def_555,type,
sK218: $i > $o ).
thf(func_def_557,type,
sK220: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_558,type,
sK221: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_563,type,
sK226: $i > $i > $i ).
thf(func_def_564,type,
sK227: $i > $i > $i ).
thf(func_def_567,type,
sK230: $i > $o ).
thf(func_def_568,type,
sK231: $i > $o ).
thf(func_def_569,type,
sK232: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_570,type,
sK233: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_572,type,
sK235: $i > $o ).
thf(func_def_576,type,
sK239: $i > $i > $i ).
thf(func_def_589,type,
sK252: $i > $i ).
thf(func_def_592,type,
sK255: $i > ( $i > $i ) > $i > $i ).
thf(func_def_610,type,
sK273: $i > $o ).
thf(func_def_611,type,
sK274: $i > $o ).
thf(func_def_614,type,
sK277: $i > $i > $o ).
thf(func_def_622,type,
sK285: ( $i > $o ) > $i ).
thf(func_def_623,type,
sK286: $i > $o ).
thf(func_def_628,type,
sK291: $i > $o ).
thf(func_def_636,type,
sK299: $i > $i > $i ).
thf(func_def_647,type,
sK310: $i > $i > $i ).
thf(func_def_672,type,
sK335: $i > $o ).
thf(func_def_678,type,
sK341: $i > $o ).
thf(func_def_679,type,
sK342: $i > $o ).
thf(func_def_680,type,
sK343: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_681,type,
sK344: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_719,type,
sK382: $i > $i > $i > $i > $i ).
thf(func_def_723,type,
sK386: $i > $i > $i > $i ).
thf(func_def_724,type,
sK387: $i > $i > $i > $i ).
thf(func_def_734,type,
sK397: $i > $i ).
thf(func_def_735,type,
sK398: $i > $i ).
thf(func_def_750,type,
sK413: $i > $o ).
thf(func_def_755,type,
sK418: $i > $i > $i ).
thf(func_def_763,type,
sK426: $i > $o ).
thf(func_def_765,type,
sK428: $i > ( $i > $o ) > $i ).
thf(func_def_781,type,
sK444: $o > $i > $i > $i ).
thf(func_def_787,type,
sK450: $i > $i > $o ).
thf(func_def_798,type,
sK461: $i > $i > $i > $i > $i ).
thf(func_def_799,type,
sK462: $i > $i > $i > $i > $i ).
thf(func_def_800,type,
sK463: $i > $i > $i > $i > $i ).
thf(func_def_835,type,
sK498: $i > $i > $o ).
thf(func_def_843,type,
sK506: $i > $i > $i > $i ).
thf(func_def_844,type,
sK507: $i > $i > $i > $i > $i ).
thf(func_def_845,type,
sK508: $i > $i > $i > $i > $i ).
thf(func_def_846,type,
sK509: $i > $i > $i > $i > $i ).
thf(func_def_847,type,
sK510: $i > $i > $i > $i > $i ).
thf(func_def_855,type,
sK518: $i > ( $i > $i ) > $i > $i ).
thf(func_def_857,type,
sK520: $i > $i ).
thf(func_def_865,type,
sK528: $i > $i > $o ).
thf(func_def_869,type,
sK532: $i > $o ).
thf(func_def_893,type,
sK556: $i > $i > $i > $o ).
thf(func_def_894,type,
sK557: $i > $i > $i > $i ).
thf(func_def_916,type,
sK579: $i > $i ).
thf(func_def_917,type,
sK580: $i > $i ).
thf(func_def_918,type,
sK581: $i > $i ).
thf(func_def_919,type,
sK582: $i > $i > $i ).
thf(func_def_920,type,
sK583: $i > $i > $i ).
thf(func_def_921,type,
sK584: $i > $i > $i ).
thf(func_def_922,type,
sK585: $i > $i > $i ).
thf(func_def_923,type,
sK586: $i > $i > $i ).
thf(func_def_924,type,
sK587: $i > $i > $i > $i ).
thf(func_def_925,type,
sK588: $i > $i ).
thf(func_def_926,type,
sK589: $i > $i ).
thf(func_def_927,type,
sK590: $i > $i ).
thf(func_def_928,type,
sK591: $i > $i ).
thf(func_def_929,type,
sK592: $i > $i > $i ).
thf(func_def_930,type,
sK593: $i > $i > $i ).
thf(func_def_931,type,
sK594: $i > $i > $i ).
thf(func_def_932,type,
sK595: $i > $i > $i > $i ).
thf(func_def_933,type,
sK596: $i > $i > $i > $i ).
thf(func_def_971,type,
sK634: $i > $o ).
thf(func_def_973,type,
sK636: ( $i > $o ) > $i > $i ).
thf(func_def_975,type,
sK638: $i > $i > $o ).
thf(func_def_981,type,
sK644: $i > $i > $i ).
thf(func_def_984,type,
sK647: $i > $o ).
thf(func_def_986,type,
sK649: $i > ( $i > $o ) > $i ).
thf(func_def_991,type,
sK654: $i > $i > $i ).
thf(func_def_996,type,
sK659: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_997,type,
sK660: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_998,type,
sK661: ( $i > $i > $o ) > $i > $i ).
thf(func_def_999,type,
sK662: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1001,type,
sK664: $i > $i > $o ).
thf(func_def_1002,type,
sK665: ( $i > $i > $o ) > $i > $i ).
thf(func_def_1008,type,
sK671: $i > $o ).
thf(func_def_1019,type,
sK682: $i > $o ).
thf(func_def_1020,type,
sK683: $i > $i ).
thf(func_def_1021,type,
sK684: ( $i > $o ) > $i ).
thf(func_def_1041,type,
sK704: $i > $o ).
thf(func_def_1047,type,
sK710: $i > $i > $i > $i ).
thf(func_def_1054,type,
sK717: $i > $i > $i > $i ).
thf(func_def_1060,type,
sK723: $i > $i ).
thf(func_def_1073,type,
sK736: $i > $o ).
thf(func_def_1075,type,
sK738: $i > ( $i > $o ) > $i > $i ).
thf(func_def_1083,type,
sK746: $i > ( $i > $o ) > $i ).
thf(func_def_1084,type,
sK747: $i > ( $i > $o ) > $i ).
thf(func_def_1086,type,
sK749: $i > $o ).
thf(func_def_1115,type,
sK778: $i > $o ).
thf(func_def_1118,type,
sK781: $i > ( $i > $o ) > $i ).
thf(func_def_1142,type,
sK805: $i > $i > $i ).
thf(func_def_1145,type,
sK808: $i > $i ).
thf(func_def_1146,type,
sK809: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1147,type,
sK810: $i > $i ).
thf(func_def_1151,type,
sK814: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1158,type,
sK821: $i > $o ).
thf(func_def_1160,type,
sK823: ( $i > $o ) > $i ).
thf(func_def_1161,type,
sK824: ( $i > $o ) > $i ).
thf(func_def_1163,type,
sK826: $i > $o ).
thf(func_def_1164,type,
sK827: $i > $i ).
thf(func_def_1165,type,
sK828: ( $i > $o ) > $i ).
thf(func_def_1170,type,
sK833: $i > $i > $o ).
thf(func_def_1176,type,
sK839: $i > $i > $i ).
thf(func_def_1183,type,
sK846: $i > $i ).
thf(func_def_1185,type,
sK848: $i > $i ).
thf(func_def_1188,type,
sK851: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1204,type,
sK867: $i > $o ).
thf(func_def_1207,type,
sK870: $i > ( $i > $o ) > $i ).
thf(func_def_1229,type,
sK892: $i > $i > $i > $i > $i ).
thf(func_def_1230,type,
sK893: $i > $i > $i > $i > $i ).
thf(func_def_1241,type,
sK904: $i > $i ).
thf(func_def_1257,type,
sK920: $i > $o ).
thf(func_def_1259,type,
sK922: ( $i > $o ) > $i > $i ).
thf(func_def_1265,type,
sK928: $i > $o ).
thf(func_def_1289,type,
sK952: $i > $i > $o ).
thf(func_def_1294,type,
sK957: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1297,type,
sK960: $i > $i ).
thf(func_def_1302,type,
sK965: ( $i > $o ) > $i ).
thf(func_def_1303,type,
sK966: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1304,type,
sK967: ( $i > $o ) > $i > $i ).
thf(func_def_1305,type,
sK968: ( $i > $o ) > $i > $i ).
thf(func_def_1306,type,
sK969: ( $i > $o ) > $i > $i ).
thf(func_def_1307,type,
sK970: ( $i > $o ) > $i ).
thf(func_def_1308,type,
sK971: ( $i > $o ) > $i > $i ).
thf(func_def_1309,type,
sK972: ( $i > $o ) > $i > $i ).
thf(func_def_1310,type,
sK973: ( $i > $o ) > $i ).
thf(func_def_1311,type,
sK974: ( $i > $o ) > $i > $i ).
thf(func_def_1312,type,
sK975: ( $i > $o ) > $i > $i ).
thf(func_def_1313,type,
sK976: $i > $i ).
thf(func_def_1315,type,
sK978: ( $i > $o ) > $i ).
thf(func_def_1316,type,
sK979: ( $i > $o ) > $i > $i ).
thf(func_def_1317,type,
sK980: $i > ( $i > $o ) > $i ).
thf(func_def_1318,type,
sK981: ( $i > $o ) > $i > $i ).
thf(func_def_1319,type,
sK982: $i > ( $i > $o ) > $i ).
thf(func_def_1320,type,
sK983: $i > ( $i > $o ) > $i ).
thf(func_def_1323,type,
sK986: ( $i > $o ) > $i ).
thf(func_def_1324,type,
sK987: ( $i > $o ) > $i ).
thf(func_def_1325,type,
sK988: ( $i > $o ) > $i ).
thf(func_def_1326,type,
sK989: ( $i > $o ) > $i > $i ).
thf(func_def_1327,type,
sK990: ( $i > $o ) > $i > $i ).
thf(func_def_1328,type,
sK991: ( $i > $o ) > $i > $i ).
thf(func_def_1329,type,
sK992: $i > ( $i > $o ) > $i ).
thf(func_def_1330,type,
sK993: $i > ( $i > $o ) > $i ).
thf(func_def_1331,type,
sK994: ( $i > $o ) > $i ).
thf(func_def_1332,type,
sK995: ( $i > $o ) > $i > $i ).
thf(func_def_1333,type,
sK996: ( $i > $o ) > $i ).
thf(func_def_1334,type,
sK997: ( $i > $o ) > $i ).
thf(func_def_1335,type,
sK998: ( $i > $o ) > $i ).
thf(func_def_1336,type,
sK999: ( $i > $o ) > $i > $i ).
thf(func_def_1337,type,
sK1000: ( $i > $o ) > $i ).
thf(func_def_1338,type,
sK1001: ( $i > $o ) > $i > $i ).
thf(func_def_1339,type,
sK1002: ( $i > $o ) > $i > $i ).
thf(func_def_1340,type,
sK1003: ( $i > $o ) > $i ).
thf(func_def_1341,type,
sK1004: ( $i > $o ) > $i > $i ).
thf(func_def_1342,type,
sK1005: ( $i > $o ) > $i > $i ).
thf(func_def_1344,type,
sK1007: ( $i > $o ) > $i ).
thf(func_def_1345,type,
sK1008: $i > ( $i > $o ) > $i ).
thf(func_def_1346,type,
sK1009: ( $i > $o ) > $i > $i ).
thf(func_def_1347,type,
sK1010: $i > $i ).
thf(func_def_1348,type,
sK1011: $i > $i ).
thf(func_def_1349,type,
ph1012:
!>[X0: $tType] : X0 ).
thf(f25328,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f25327,f24431]) ).
thf(f24431,plain,
( ( in @ ( kfst @ sK86 ) @ sK84 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f24382]) ).
thf(f24382,plain,
( ( ( in @ ( kfst @ sK86 ) @ sK84 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f5620,f24365]) ).
thf(f24365,plain,
( $true
= ( in @ sK86 @ ( cartprod @ sK84 @ sK84 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f24350]) ).
thf(f24350,plain,
( ( $true != $true )
| ( $true
= ( in @ sK86 @ ( cartprod @ sK84 @ sK84 ) ) ) ),
inference(superposition,[status(thm)],[f7075,f3077]) ).
thf(f3077,plain,
( $true
= ( in @ sK86 @ sK83 ) ),
inference(cnf_transformation,[status(thm)],[f1414]) ).
thf(f1414,plain,
( ( setminusELneg = $true )
& ( lamProp = $true )
& ( kpairp = $true )
& ( setextT = $true )
& ( setminusEL = $true )
& ( cartprodsndin = $true )
& ( setukpairinjR11 = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrI = $true )
& ( emptyinPowerset = $true )
& ( singletoninpowunion = $true )
& ( setminusSubset2 = $true )
& ( contrasubsetT2 = $true )
& ( doubleComplementI1 = $true )
& ( binunionLsub = $true )
& ( cartprodpairin = $true )
& ( setminusT_lem = $true )
& ( setadjoinIL = $true )
& ( dsetconstrEL = $true )
& ( funcImageSingleton = $true )
& ( prop2setE = $true )
& ( powersetE1 = $true )
& ( complementTE1 = $true )
& ( demorgan2a = $true )
& ( symdiffI1 = $true )
& ( exuI1 = $true )
& ( prop2set2propI = $true )
& ( binunionTEcontra = $true )
& ( binunionRsub = $true )
& ( setextAx = $true )
& ( eta2 = $true )
& ( contraSubsetComplement = $true )
& ( setext = $true )
& ( iftrueProp1 = $true )
& ( cartprodpairsurjEq = $true )
& ( descrp = $true )
& ( singletonsubset = $true )
& ( cartprodmempair1 = $true )
& ( subsetI2 = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( woz1_2 = $true )
& ( vacuousDall = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subbreln = $true )
& ( omega__Cong = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjR = $true )
& ( demorgan1a = $true )
& ( setunionsingleton1 = $true )
& ( apProp = $true )
& ( binintersectLsub = $true )
& ( cartprodmempair = $true )
& ( setukpairIR = $true )
& ( subsetI1 = $true )
& ( uniqinunit = $true )
& ( upairsetIL = $true )
& ( brelnall2 = $true )
& ( dpsetconstrERa = $true )
& ( binintersectSubset1 = $true )
& ( binunionE = $true )
& ( iffalse = $true )
& ( funcGraphProp2 = $true )
& ( iftrueProp2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( infuncsetfunc = $true )
& ( eqbreln = $true )
& ( powersetI = $true )
& ( upairsetE = $true )
& ( setukpairIL = $true )
& ( subsetTrans = $true )
& ( ap2p = $true )
& ( powersetTE1 = $true )
& ( powerset__Cong = $true )
& ( funcext2 = $true )
& ( $true
= ( breln1 @ sK84 @ sK83 ) )
& ( ( sK85 @ sK86 )
!= $true )
& ( $true
= ( in @ sK86 @ sK83 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK83 ) )
| ( $true
= ( sK85 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK84 ) ) )
| ( $true
!= ( in @ X4 @ sK84 ) ) )
& ( setukpairinjL2 = $true )
& ( upairset2IR = $true )
& ( brelnall1 = $true )
& ( setadjoinIR = $true )
& ( ap2apEq2 = $true )
& ( powersetsubset = $true )
& ( setadjoinAx = $true )
& ( iffalseProp1 = $true )
& ( binintersectEL = $true )
& ( cartprodpairmemER = $true )
& ( kfstpairEq = $true )
& ( complementImpComplementIntersect = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrER = $true )
& ( notdexE = $true )
& ( ex1I2 = $true )
& ( nonemptyImpWitness = $true )
& ( subsetTI = $true )
& ( eqinunit = $true )
& ( demorgan2a2 = $true )
& ( app = $true )
& ( subsetemptysetimpeq = $true )
& ( demorgan2b2 = $true )
& ( setunionsingleton2 = $true )
& ( contrasubsetT = $true )
& ( setbeta = $true )
& ( setminusLsub = $true )
& ( funcGraphProp3 = $true )
& ( dpsetconstrEL1 = $true )
& ( setminusI = $true )
& ( woz13rule2 = $true )
& ( ksndsingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( woz1_5 = $true )
& ( nonemptyI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( binunionIR = $true )
& ( singletonsuniq = $true )
& ( exuEu = $true )
& ( woz13rule1 = $true )
& ( dpsetconstrER = $true )
& ( binintersectI = $true )
& ( setunionAx = $true )
& ( beta2 = $true )
& ( notdallE = $true )
& ( exuI2 = $true )
& ( setminusER = $true )
& ( iftrueorfalse = $true )
& ( quantDeMorgan2 = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( doubleComplementSub1 = $true )
& ( ex1E1 = $true )
& ( setukpairinjR2 = $true )
& ( lam2lamEq = $true )
& ( secondinupair = $true )
& ( eqimpsubset2 = $true )
& ( cartprodfstin = $true )
& ( cartprodsndpairEq = $true )
& ( exu__Cong = $true )
& ( notequalI2 = $true )
& ( setminusIRneg = $true )
& ( symdiffE = $true )
& ( setunionI = $true )
& ( nonemptyI = $true )
& ( setukpairinjL = $true )
& ( demorgan1 = $true )
& ( setminusILneg = $true )
& ( setunionE2 = $true )
& ( setadjoinSub = $true )
& ( emptyE1 = $true )
& ( woz13rule4 = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementE1 = $true )
& ( complementTcontraSubset = $true )
& ( dpsetconstrEL2 = $true )
& ( demorgan2 = $true )
& ( setminusERneg = $true )
& ( theeq = $true )
& ( emptyset__Cong = $true )
& ( setminusSubset1 = $true )
& ( contrasubsetT1 = $true )
& ( beta1 = $true )
& ( powersetI1 = $true )
& ( lam2p = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( omegaIndAx = $true )
& ( setoftrueEq = $true )
& ( prop2setI = $true )
& ( cartprodpairmemEL = $true )
& ( eta1 = $true )
& ( inPowerset = $true )
& ( complementTI1 = $true )
& ( exuI3 = $true )
& ( subset2powerset = $true )
& ( notinemptyset = $true )
& ( singletonprop = $true )
& ( upairequniteq = $true )
& ( upairsetIR = $true )
& ( replAx = $true )
& ( subsetE2 = $true )
& ( upairsubunion = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectRsub = $true )
& ( symdiffI2 = $true )
& ( binintersectT_lem = $true )
& ( noeltsimpempty = $true )
& ( iffalseProp2 = $true )
& ( ex1E2 = $true )
& ( quantDeMorgan3 = $true )
& ( ifSingleton = $true )
& ( doubleComplementSub2 = $true )
& ( ubforcartprodlem2 = $true )
& ( theprop = $true )
& ( complementSubsetComplementIntersect = $true )
& ( funcinfuncset = $true )
& ( nonemptyE1 = $true )
& ( woz13rule0 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( kpairsurjEq = $true )
& ( upairinpowunion = $true )
& ( contrasubsetT3 = $true )
& ( demorgan2b = $true )
& ( subPowSU = $true )
& ( binunionTE = $true )
& ( demorgan1b = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( emptysetAx = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( symdiffIneg1 = $true )
& ( complementT_lem = $true )
& ( subsetRefl = $true )
& ( funcext = $true )
& ( exuE3e = $true )
& ( singletoninpowerset = $true )
& ( ifp = $true )
& ( notsubsetI = $true )
& ( setadjoinE = $true )
& ( funcGraphProp1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( bs114d = $true )
& ( binintersectSubset3 = $true )
& ( eqimpsubset1 = $true )
& ( dpsetconstrSub = $true )
& ( woz1_4 = $true )
& ( binintersectTERcontra = $true )
& ( binunionTIRcontra = $true )
& ( binunionT_lem = $true )
& ( binintersectSubset5 = $true )
& ( lamp = $true )
& ( binintersectSubset2 = $true )
& ( binunionIL = $true )
& ( setukpairinjR12 = $true )
& ( setextsub = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectER = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton = $true )
& ( emptyInPowerset = $true )
& ( notinsingleton = $true )
& ( emptysetimpfalse = $true )
& ( funcextLem = $true )
& ( notequalI1 = $true )
& ( emptysetsubset = $true )
& ( setadjoinSub2 = $true )
& ( kfstsingleton = $true )
& ( ex1I = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( powersetT_lem = $true )
& ( symdiffIneg2 = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( binunionTILcontra = $true )
& ( in__Cong = $true )
& ( kpairiskpair = $true )
& ( setadjoinOr = $true )
& ( woz1_3 = $true )
& ( singletonsswitch = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR1 = $true )
& ( ap2apEq1 = $true )
& ( binunionEcases = $true )
& ( woz13rule3 = $true )
& ( ksndpairEq = $true )
& ( setunionE = $true )
& ( doubleComplementEq = $true )
& ( powersetTI1 = $true )
& ( ubforcartprodlem3 = $true )
& ( sepInPowerset = $true )
& ( omegaSAx = $true )
& ( subsetE = $true )
& ( powersetAx = $true )
& ( quantDeMorgan4 = $true )
& ( sepSubset = $true )
& ( binintersectSubset4 = $true )
& ( woz1_1 = $true )
& ( inCongP = $true )
& ( iftrue = $true )
& ( funcGraphProp4 = $true )
& ( binintersectTELcontra = $true )
& ( demorgan2a1 = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( emptyI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83,sK84,sK85,sK86])],[f1410,f1413,f1412,f1411]) ).
thf(f1411,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
!= ( X2 @ X3 ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ X1 ) ) )
| ( $true
!= ( in @ X4 @ X1 ) ) ) ) )
=> ( ( $true
= ( breln1 @ sK84 @ sK83 ) )
& ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
!= ( X2 @ X3 ) )
& ( $true
= ( in @ X3 @ sK83 ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK83 ) )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK84 ) ) )
| ( $true
!= ( in @ X4 @ sK84 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1412,plain,
( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
!= ( X2 @ X3 ) )
& ( $true
= ( in @ X3 @ sK83 ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK83 ) )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK84 ) ) )
| ( $true
!= ( in @ X4 @ sK84 ) ) ) )
=> ( ? [X3: $i] :
( ( $true
!= ( sK85 @ X3 ) )
& ( $true
= ( in @ X3 @ sK83 ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK83 ) )
| ( $true
= ( sK85 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK84 ) ) )
| ( $true
!= ( in @ X4 @ sK84 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1413,plain,
( ? [X3: $i] :
( ( $true
!= ( sK85 @ X3 ) )
& ( $true
= ( in @ X3 @ sK83 ) ) )
=> ( ( ( sK85 @ sK86 )
!= $true )
& ( $true
= ( in @ sK86 @ sK83 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1410,plain,
( ( setminusELneg = $true )
& ( lamProp = $true )
& ( kpairp = $true )
& ( setextT = $true )
& ( setminusEL = $true )
& ( cartprodsndin = $true )
& ( setukpairinjR11 = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrI = $true )
& ( emptyinPowerset = $true )
& ( singletoninpowunion = $true )
& ( setminusSubset2 = $true )
& ( contrasubsetT2 = $true )
& ( doubleComplementI1 = $true )
& ( binunionLsub = $true )
& ( cartprodpairin = $true )
& ( setminusT_lem = $true )
& ( setadjoinIL = $true )
& ( dsetconstrEL = $true )
& ( funcImageSingleton = $true )
& ( prop2setE = $true )
& ( powersetE1 = $true )
& ( complementTE1 = $true )
& ( demorgan2a = $true )
& ( symdiffI1 = $true )
& ( exuI1 = $true )
& ( prop2set2propI = $true )
& ( binunionTEcontra = $true )
& ( binunionRsub = $true )
& ( setextAx = $true )
& ( eta2 = $true )
& ( contraSubsetComplement = $true )
& ( setext = $true )
& ( iftrueProp1 = $true )
& ( cartprodpairsurjEq = $true )
& ( descrp = $true )
& ( singletonsubset = $true )
& ( cartprodmempair1 = $true )
& ( subsetI2 = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( woz1_2 = $true )
& ( vacuousDall = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subbreln = $true )
& ( omega__Cong = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjR = $true )
& ( demorgan1a = $true )
& ( setunionsingleton1 = $true )
& ( apProp = $true )
& ( binintersectLsub = $true )
& ( cartprodmempair = $true )
& ( setukpairIR = $true )
& ( subsetI1 = $true )
& ( uniqinunit = $true )
& ( upairsetIL = $true )
& ( brelnall2 = $true )
& ( dpsetconstrERa = $true )
& ( binintersectSubset1 = $true )
& ( binunionE = $true )
& ( iffalse = $true )
& ( funcGraphProp2 = $true )
& ( iftrueProp2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( infuncsetfunc = $true )
& ( eqbreln = $true )
& ( powersetI = $true )
& ( upairsetE = $true )
& ( setukpairIL = $true )
& ( subsetTrans = $true )
& ( ap2p = $true )
& ( powersetTE1 = $true )
& ( powerset__Cong = $true )
& ( funcext2 = $true )
& ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
!= ( X2 @ X3 ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ X1 ) ) )
| ( $true
!= ( in @ X4 @ X1 ) ) ) ) )
& ( setukpairinjL2 = $true )
& ( upairset2IR = $true )
& ( brelnall1 = $true )
& ( setadjoinIR = $true )
& ( ap2apEq2 = $true )
& ( powersetsubset = $true )
& ( setadjoinAx = $true )
& ( iffalseProp1 = $true )
& ( binintersectEL = $true )
& ( cartprodpairmemER = $true )
& ( kfstpairEq = $true )
& ( complementImpComplementIntersect = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrER = $true )
& ( notdexE = $true )
& ( ex1I2 = $true )
& ( nonemptyImpWitness = $true )
& ( subsetTI = $true )
& ( eqinunit = $true )
& ( demorgan2a2 = $true )
& ( app = $true )
& ( subsetemptysetimpeq = $true )
& ( demorgan2b2 = $true )
& ( setunionsingleton2 = $true )
& ( contrasubsetT = $true )
& ( setbeta = $true )
& ( setminusLsub = $true )
& ( funcGraphProp3 = $true )
& ( dpsetconstrEL1 = $true )
& ( setminusI = $true )
& ( woz13rule2 = $true )
& ( ksndsingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( woz1_5 = $true )
& ( nonemptyI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( binunionIR = $true )
& ( singletonsuniq = $true )
& ( exuEu = $true )
& ( woz13rule1 = $true )
& ( dpsetconstrER = $true )
& ( binintersectI = $true )
& ( setunionAx = $true )
& ( beta2 = $true )
& ( notdallE = $true )
& ( exuI2 = $true )
& ( setminusER = $true )
& ( iftrueorfalse = $true )
& ( quantDeMorgan2 = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( doubleComplementSub1 = $true )
& ( ex1E1 = $true )
& ( setukpairinjR2 = $true )
& ( lam2lamEq = $true )
& ( secondinupair = $true )
& ( eqimpsubset2 = $true )
& ( cartprodfstin = $true )
& ( cartprodsndpairEq = $true )
& ( exu__Cong = $true )
& ( notequalI2 = $true )
& ( setminusIRneg = $true )
& ( symdiffE = $true )
& ( setunionI = $true )
& ( nonemptyI = $true )
& ( setukpairinjL = $true )
& ( demorgan1 = $true )
& ( setminusILneg = $true )
& ( setunionE2 = $true )
& ( setadjoinSub = $true )
& ( emptyE1 = $true )
& ( woz13rule4 = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementE1 = $true )
& ( complementTcontraSubset = $true )
& ( dpsetconstrEL2 = $true )
& ( demorgan2 = $true )
& ( setminusERneg = $true )
& ( theeq = $true )
& ( emptyset__Cong = $true )
& ( setminusSubset1 = $true )
& ( contrasubsetT1 = $true )
& ( beta1 = $true )
& ( powersetI1 = $true )
& ( lam2p = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( omegaIndAx = $true )
& ( setoftrueEq = $true )
& ( prop2setI = $true )
& ( cartprodpairmemEL = $true )
& ( eta1 = $true )
& ( inPowerset = $true )
& ( complementTI1 = $true )
& ( exuI3 = $true )
& ( subset2powerset = $true )
& ( notinemptyset = $true )
& ( singletonprop = $true )
& ( upairequniteq = $true )
& ( upairsetIR = $true )
& ( replAx = $true )
& ( subsetE2 = $true )
& ( upairsubunion = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectRsub = $true )
& ( symdiffI2 = $true )
& ( binintersectT_lem = $true )
& ( noeltsimpempty = $true )
& ( iffalseProp2 = $true )
& ( ex1E2 = $true )
& ( quantDeMorgan3 = $true )
& ( ifSingleton = $true )
& ( doubleComplementSub2 = $true )
& ( ubforcartprodlem2 = $true )
& ( theprop = $true )
& ( complementSubsetComplementIntersect = $true )
& ( funcinfuncset = $true )
& ( nonemptyE1 = $true )
& ( woz13rule0 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( kpairsurjEq = $true )
& ( upairinpowunion = $true )
& ( contrasubsetT3 = $true )
& ( demorgan2b = $true )
& ( subPowSU = $true )
& ( binunionTE = $true )
& ( demorgan1b = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( emptysetAx = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( symdiffIneg1 = $true )
& ( complementT_lem = $true )
& ( subsetRefl = $true )
& ( funcext = $true )
& ( exuE3e = $true )
& ( singletoninpowerset = $true )
& ( ifp = $true )
& ( notsubsetI = $true )
& ( setadjoinE = $true )
& ( funcGraphProp1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( bs114d = $true )
& ( binintersectSubset3 = $true )
& ( eqimpsubset1 = $true )
& ( dpsetconstrSub = $true )
& ( woz1_4 = $true )
& ( binintersectTERcontra = $true )
& ( binunionTIRcontra = $true )
& ( binunionT_lem = $true )
& ( binintersectSubset5 = $true )
& ( lamp = $true )
& ( binintersectSubset2 = $true )
& ( binunionIL = $true )
& ( setukpairinjR12 = $true )
& ( setextsub = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectER = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton = $true )
& ( emptyInPowerset = $true )
& ( notinsingleton = $true )
& ( emptysetimpfalse = $true )
& ( funcextLem = $true )
& ( notequalI1 = $true )
& ( emptysetsubset = $true )
& ( setadjoinSub2 = $true )
& ( kfstsingleton = $true )
& ( ex1I = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( powersetT_lem = $true )
& ( symdiffIneg2 = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( binunionTILcontra = $true )
& ( in__Cong = $true )
& ( kpairiskpair = $true )
& ( setadjoinOr = $true )
& ( woz1_3 = $true )
& ( singletonsswitch = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR1 = $true )
& ( ap2apEq1 = $true )
& ( binunionEcases = $true )
& ( woz13rule3 = $true )
& ( ksndpairEq = $true )
& ( setunionE = $true )
& ( doubleComplementEq = $true )
& ( powersetTI1 = $true )
& ( ubforcartprodlem3 = $true )
& ( sepInPowerset = $true )
& ( omegaSAx = $true )
& ( subsetE = $true )
& ( powersetAx = $true )
& ( quantDeMorgan4 = $true )
& ( sepSubset = $true )
& ( binintersectSubset4 = $true )
& ( woz1_1 = $true )
& ( inCongP = $true )
& ( iftrue = $true )
& ( funcGraphProp4 = $true )
& ( binintersectTELcontra = $true )
& ( demorgan2a1 = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( emptyI = $true ) ),
inference(rectify,[status(thm)],[f1251]) ).
thf(f1251,plain,
( ( setminusELneg = $true )
& ( lamProp = $true )
& ( kpairp = $true )
& ( setextT = $true )
& ( setminusEL = $true )
& ( cartprodsndin = $true )
& ( setukpairinjR11 = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrI = $true )
& ( emptyinPowerset = $true )
& ( singletoninpowunion = $true )
& ( setminusSubset2 = $true )
& ( contrasubsetT2 = $true )
& ( doubleComplementI1 = $true )
& ( binunionLsub = $true )
& ( cartprodpairin = $true )
& ( setminusT_lem = $true )
& ( setadjoinIL = $true )
& ( dsetconstrEL = $true )
& ( funcImageSingleton = $true )
& ( prop2setE = $true )
& ( powersetE1 = $true )
& ( complementTE1 = $true )
& ( demorgan2a = $true )
& ( symdiffI1 = $true )
& ( exuI1 = $true )
& ( prop2set2propI = $true )
& ( binunionTEcontra = $true )
& ( binunionRsub = $true )
& ( setextAx = $true )
& ( eta2 = $true )
& ( contraSubsetComplement = $true )
& ( setext = $true )
& ( iftrueProp1 = $true )
& ( cartprodpairsurjEq = $true )
& ( descrp = $true )
& ( singletonsubset = $true )
& ( cartprodmempair1 = $true )
& ( subsetI2 = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( woz1_2 = $true )
& ( vacuousDall = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subbreln = $true )
& ( omega__Cong = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjR = $true )
& ( demorgan1a = $true )
& ( setunionsingleton1 = $true )
& ( apProp = $true )
& ( binintersectLsub = $true )
& ( cartprodmempair = $true )
& ( setukpairIR = $true )
& ( subsetI1 = $true )
& ( uniqinunit = $true )
& ( upairsetIL = $true )
& ( brelnall2 = $true )
& ( dpsetconstrERa = $true )
& ( binintersectSubset1 = $true )
& ( binunionE = $true )
& ( iffalse = $true )
& ( funcGraphProp2 = $true )
& ( iftrueProp2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( infuncsetfunc = $true )
& ( eqbreln = $true )
& ( powersetI = $true )
& ( upairsetE = $true )
& ( setukpairIL = $true )
& ( subsetTrans = $true )
& ( ap2p = $true )
& ( powersetTE1 = $true )
& ( powerset__Cong = $true )
& ( funcext2 = $true )
& ? [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
& ? [X2: $i > $o] :
( ? [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( in @ X5 @ X0 )
= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) )
| ( $true
!= ( in @ X4 @ X1 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) ) )
& ( setukpairinjL2 = $true )
& ( upairset2IR = $true )
& ( brelnall1 = $true )
& ( setadjoinIR = $true )
& ( ap2apEq2 = $true )
& ( powersetsubset = $true )
& ( setadjoinAx = $true )
& ( iffalseProp1 = $true )
& ( binintersectEL = $true )
& ( cartprodpairmemER = $true )
& ( kfstpairEq = $true )
& ( complementImpComplementIntersect = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrER = $true )
& ( notdexE = $true )
& ( ex1I2 = $true )
& ( nonemptyImpWitness = $true )
& ( subsetTI = $true )
& ( eqinunit = $true )
& ( demorgan2a2 = $true )
& ( app = $true )
& ( subsetemptysetimpeq = $true )
& ( demorgan2b2 = $true )
& ( setunionsingleton2 = $true )
& ( contrasubsetT = $true )
& ( setbeta = $true )
& ( setminusLsub = $true )
& ( funcGraphProp3 = $true )
& ( dpsetconstrEL1 = $true )
& ( setminusI = $true )
& ( woz13rule2 = $true )
& ( ksndsingleton = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( woz1_5 = $true )
& ( nonemptyI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( binunionIR = $true )
& ( singletonsuniq = $true )
& ( exuEu = $true )
& ( woz13rule1 = $true )
& ( dpsetconstrER = $true )
& ( binintersectI = $true )
& ( setunionAx = $true )
& ( beta2 = $true )
& ( notdallE = $true )
& ( exuI2 = $true )
& ( setminusER = $true )
& ( iftrueorfalse = $true )
& ( quantDeMorgan2 = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( doubleComplementSub1 = $true )
& ( ex1E1 = $true )
& ( setukpairinjR2 = $true )
& ( lam2lamEq = $true )
& ( secondinupair = $true )
& ( eqimpsubset2 = $true )
& ( cartprodfstin = $true )
& ( cartprodsndpairEq = $true )
& ( exu__Cong = $true )
& ( notequalI2 = $true )
& ( setminusIRneg = $true )
& ( symdiffE = $true )
& ( setunionI = $true )
& ( nonemptyI = $true )
& ( setukpairinjL = $true )
& ( demorgan1 = $true )
& ( setminusILneg = $true )
& ( setunionE2 = $true )
& ( setadjoinSub = $true )
& ( emptyE1 = $true )
& ( woz13rule4 = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementE1 = $true )
& ( complementTcontraSubset = $true )
& ( dpsetconstrEL2 = $true )
& ( demorgan2 = $true )
& ( setminusERneg = $true )
& ( theeq = $true )
& ( emptyset__Cong = $true )
& ( setminusSubset1 = $true )
& ( contrasubsetT1 = $true )
& ( beta1 = $true )
& ( powersetI1 = $true )
& ( lam2p = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( omegaIndAx = $true )
& ( setoftrueEq = $true )
& ( prop2setI = $true )
& ( cartprodpairmemEL = $true )
& ( eta1 = $true )
& ( inPowerset = $true )
& ( complementTI1 = $true )
& ( exuI3 = $true )
& ( subset2powerset = $true )
& ( notinemptyset = $true )
& ( singletonprop = $true )
& ( upairequniteq = $true )
& ( upairsetIR = $true )
& ( replAx = $true )
& ( subsetE2 = $true )
& ( upairsubunion = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectRsub = $true )
& ( symdiffI2 = $true )
& ( binintersectT_lem = $true )
& ( noeltsimpempty = $true )
& ( iffalseProp2 = $true )
& ( ex1E2 = $true )
& ( quantDeMorgan3 = $true )
& ( ifSingleton = $true )
& ( doubleComplementSub2 = $true )
& ( ubforcartprodlem2 = $true )
& ( theprop = $true )
& ( complementSubsetComplementIntersect = $true )
& ( funcinfuncset = $true )
& ( nonemptyE1 = $true )
& ( woz13rule0 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( kpairsurjEq = $true )
& ( upairinpowunion = $true )
& ( contrasubsetT3 = $true )
& ( demorgan2b = $true )
& ( subPowSU = $true )
& ( binunionTE = $true )
& ( demorgan1b = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( emptysetAx = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( symdiffIneg1 = $true )
& ( complementT_lem = $true )
& ( subsetRefl = $true )
& ( funcext = $true )
& ( exuE3e = $true )
& ( singletoninpowerset = $true )
& ( ifp = $true )
& ( notsubsetI = $true )
& ( setadjoinE = $true )
& ( funcGraphProp1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( bs114d = $true )
& ( binintersectSubset3 = $true )
& ( eqimpsubset1 = $true )
& ( dpsetconstrSub = $true )
& ( woz1_4 = $true )
& ( binintersectTERcontra = $true )
& ( binunionTIRcontra = $true )
& ( binunionT_lem = $true )
& ( binintersectSubset5 = $true )
& ( lamp = $true )
& ( binintersectSubset2 = $true )
& ( binunionIL = $true )
& ( setukpairinjR12 = $true )
& ( setextsub = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectER = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton = $true )
& ( emptyInPowerset = $true )
& ( notinsingleton = $true )
& ( emptysetimpfalse = $true )
& ( funcextLem = $true )
& ( notequalI1 = $true )
& ( emptysetsubset = $true )
& ( setadjoinSub2 = $true )
& ( kfstsingleton = $true )
& ( ex1I = $true )
& ( exuE2 = $true )
& ( emptysetE = $true )
& ( powersetT_lem = $true )
& ( symdiffIneg2 = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( binunionTILcontra = $true )
& ( in__Cong = $true )
& ( kpairiskpair = $true )
& ( setadjoinOr = $true )
& ( woz1_3 = $true )
& ( singletonsswitch = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR1 = $true )
& ( ap2apEq1 = $true )
& ( binunionEcases = $true )
& ( woz13rule3 = $true )
& ( ksndpairEq = $true )
& ( setunionE = $true )
& ( doubleComplementEq = $true )
& ( powersetTI1 = $true )
& ( ubforcartprodlem3 = $true )
& ( sepInPowerset = $true )
& ( omegaSAx = $true )
& ( subsetE = $true )
& ( powersetAx = $true )
& ( quantDeMorgan4 = $true )
& ( sepSubset = $true )
& ( binintersectSubset4 = $true )
& ( woz1_1 = $true )
& ( inCongP = $true )
& ( iftrue = $true )
& ( funcGraphProp4 = $true )
& ( binintersectTELcontra = $true )
& ( demorgan2a1 = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( emptyI = $true ) ),
inference(flattening,[status(thm)],[f1250]) ).
thf(f1250,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( in @ X5 @ X0 )
= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true
!= ( in @ X4 @ X1 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $true )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f539]) ).
thf(f539,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
=> ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X0 )
= $true )
=> ( $true
= ( X2 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f538]) ).
thf(f538,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( X2 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f291]) ).
thf(f291,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ! [X13: $i,X3: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X13 )
=> ( X0 @ ( kpair @ X1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X13 )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f290]) ).
thf(f290,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ! [X13: $i,X3: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X13 )
=> ( X0 @ ( kpair @ X1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X13 )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',breln1all2) ).
thf(f7075,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK83 )
!= $true )
| ( ( in @ X0 @ ( cartprod @ sK84 @ sK84 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f7071]) ).
thf(f7071,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( cartprod @ sK84 @ sK84 ) )
= $true )
| ( ( in @ X0 @ sK83 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f5637,f6017]) ).
thf(f6017,plain,
( $true
= ( subset @ sK83 @ ( cartprod @ sK84 @ sK84 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4456]) ).
thf(f4456,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK84
@ sK83 ) ),
inference(definition_unfolding,[status(thm)],[f3079,f4420]) ).
thf(f4420,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[status(thm)],[f3812,f4394]) ).
thf(f4394,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f799]) ).
thf(f799,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f798]) ).
thf(f798,plain,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f185]) ).
thf(f185,axiom,
( breln
= ( ^ [X3: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',breln) ).
thf(f3812,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f801]) ).
thf(f801,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f800]) ).
thf(f800,plain,
( ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) )
= breln1 ),
inference(rectify,[status(thm)],[f289]) ).
thf(f289,axiom,
( ( ^ [X3: $i,X13: $i] : ( breln @ X3 @ X3 @ X13 ) )
= breln1 ),
file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',breln1) ).
thf(f3079,plain,
( $true
= ( breln1 @ sK84 @ sK83 ) ),
inference(cnf_transformation,[status(thm)],[f1414]) ).
thf(f5637,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5128]) ).
thf(f5128,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f3996,f2937]) ).
thf(f2937,plain,
notsubsetI = $true,
inference(cnf_transformation,[status(thm)],[f1414]) ).
thf(f3996,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( notsubsetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f2343]) ).
thf(f2343,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ( ( $true
= ( subset @ sK675 @ sK674 ) )
& ( ( in @ sK673 @ sK675 )
= $true )
& ( ( in @ sK673 @ sK674 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK673,sK674,sK675])],[f2341,f2342]) ).
thf(f2342,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X4 )
= $true )
& ( $true
= ( in @ X3 @ X5 ) )
& ( ( in @ X3 @ X4 )
!= $true ) )
=> ( ( $true
= ( subset @ sK675 @ sK674 ) )
& ( ( in @ sK673 @ sK675 )
= $true )
& ( ( in @ sK673 @ sK674 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2341,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X4 )
= $true )
& ( $true
= ( in @ X3 @ X5 ) )
& ( ( in @ X3 @ X4 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f2340]) ).
thf(f2340,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1203]) ).
thf(f1203,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) )
<=> ( notsubsetI = $true ) ),
inference(flattening,[status(thm)],[f1202]) ).
thf(f1202,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f874]) ).
thf(f874,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( subset @ X2 @ X1 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f381]) ).
thf(f381,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( subset @ X2 @ X1 )
!= $true ) ) )
<=> ( notsubsetI = $true ) ),
inference(fool_elimination,[status(thm)],[f380]) ).
thf(f380,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ~ ( subset @ X2 @ X1 ) ) )
= notsubsetI ),
inference(rectify,[status(thm)],[f85]) ).
thf(f85,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( subset @ X3 @ X4 ) ) )
= notsubsetI ),
file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',notsubsetI) ).
thf(f5620,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) )
| ( $true
= ( in @ ( kfst @ X4 ) @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5238]) ).
thf(f5238,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) )
| ( $true
= ( in @ ( kfst @ X4 ) @ X5 ) ) ),
inference(definition_unfolding,[status(thm)],[f4126,f3018]) ).
thf(f3018,plain,
cartprodfstin = $true,
inference(cnf_transformation,[status(thm)],[f1414]) ).
thf(f4126,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kfst @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) )
| ( cartprodfstin != $true ) ),
inference(cnf_transformation,[status(thm)],[f2489]) ).
thf(f2489,plain,
( ( ( cartprodfstin = $true )
| ( ( $true
!= ( in @ ( kfst @ sK761 ) @ sK762 ) )
& ( ( in @ sK761 @ ( cartprod @ sK762 @ sK760 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kfst @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) ) )
| ( cartprodfstin != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK760,sK761,sK762])],[f2487,f2488]) ).
thf(f2488,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( kfst @ X1 ) @ X2 ) )
& ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true ) )
=> ( ( $true
!= ( in @ ( kfst @ sK761 ) @ sK762 ) )
& ( ( in @ sK761 @ ( cartprod @ sK762 @ sK760 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2487,plain,
( ( ( cartprodfstin = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( kfst @ X1 ) @ X2 ) )
& ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kfst @ X4 ) @ X5 ) )
| ( $true
!= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) ) )
| ( cartprodfstin != $true ) ) ),
inference(rectify,[status(thm)],[f2486]) ).
thf(f2486,plain,
( ( ( cartprodfstin = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( kfst @ X1 ) @ X2 ) )
& ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( kfst @ X1 ) @ X2 ) )
| ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
!= $true ) )
| ( cartprodfstin != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1160]) ).
thf(f1160,plain,
( ( cartprodfstin = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( kfst @ X1 ) @ X2 ) )
| ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f429]) ).
thf(f429,plain,
( ( cartprodfstin = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true )
=> ( $true
= ( in @ ( kfst @ X1 ) @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f428]) ).
thf(f428,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
=> ( in @ ( kfst @ X1 ) @ X2 ) )
= cartprodfstin ),
inference(rectify,[status(thm)],[f166]) ).
thf(f166,axiom,
! [X4: $i,X10: $i,X3: $i] :
( ( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( kfst @ X10 ) @ X3 ) )
= cartprodfstin ),
file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',cartprodfstin) ).
thf(f25327,plain,
( ( in @ ( kfst @ sK86 ) @ sK84 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f25326,f3078]) ).
thf(f3078,plain,
( ( sK85 @ sK86 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1414]) ).
thf(f25326,plain,
( ( ( sK85 @ sK86 )
= $true )
| ( ( in @ ( kfst @ sK86 ) @ sK84 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f25325,f24436]) ).
thf(f24436,plain,
( $true
= ( in @ ( ksnd @ sK86 ) @ sK84 ) ),
inference(trivial_inequality_removal,[status(thm)],[f24381]) ).
thf(f24381,plain,
( ( $true != $true )
| ( $true
= ( in @ ( ksnd @ sK86 ) @ sK84 ) ) ),
inference(superposition,[status(thm)],[f6148,f24365]) ).
thf(f6148,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
!= $true )
| ( $true
= ( in @ ( ksnd @ X2 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f4873]) ).
thf(f4873,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( ksnd @ X2 ) @ X1 ) )
| ( $true != $true )
| ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f3644,f3150]) ).
thf(f3150,plain,
cartprodsndin = $true,
inference(cnf_transformation,[status(thm)],[f1414]) ).
thf(f3644,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( ksnd @ X2 ) @ X1 ) )
| ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
!= $true )
| ( cartprodsndin != $true ) ),
inference(cnf_transformation,[status(thm)],[f1961]) ).
thf(f1961,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( ksnd @ X2 ) @ X1 ) )
| ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
!= $true ) )
| ( cartprodsndin != $true ) )
& ( ( cartprodsndin = $true )
| ( ( ( in @ ( ksnd @ sK433 ) @ sK432 )
!= $true )
& ( $true
= ( in @ sK433 @ ( cartprod @ sK431 @ sK432 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK431,sK432,sK433])],[f1959,f1960]) ).
thf(f1960,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( ksnd @ X5 ) @ X4 )
!= $true )
& ( ( in @ X5 @ ( cartprod @ X3 @ X4 ) )
= $true ) )
=> ( ( ( in @ ( ksnd @ sK433 ) @ sK432 )
!= $true )
& ( $true
= ( in @ sK433 @ ( cartprod @ sK431 @ sK432 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1959,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( ksnd @ X2 ) @ X1 ) )
| ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
!= $true ) )
| ( cartprodsndin != $true ) )
& ( ( cartprodsndin = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( ksnd @ X5 ) @ X4 )
!= $true )
& ( ( in @ X5 @ ( cartprod @ X3 @ X4 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1958]) ).
thf(f1958,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( ksnd @ X2 ) @ X1 ) )
| ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
!= $true ) )
| ( cartprodsndin != $true ) )
& ( ( cartprodsndin = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( ksnd @ X2 ) @ X1 ) )
& ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1179]) ).
thf(f1179,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( ksnd @ X2 ) @ X1 ) )
| ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
!= $true ) )
<=> ( cartprodsndin = $true ) ),
inference(ennf_transformation,[status(thm)],[f553]) ).
thf(f553,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
= $true )
=> ( $true
= ( in @ ( ksnd @ X2 ) @ X1 ) ) )
<=> ( cartprodsndin = $true ) ),
inference(fool_elimination,[status(thm)],[f552]) ).
thf(f552,plain,
( cartprodsndin
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X0 @ X1 ) )
=> ( in @ ( ksnd @ X2 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f178]) ).
thf(f178,axiom,
( cartprodsndin
= ( ! [X3: $i,X4: $i,X10: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( ksnd @ X10 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',cartprodsndin) ).
thf(f25325,plain,
( ( $true
!= ( in @ ( ksnd @ sK86 ) @ sK84 ) )
| ( ( sK85 @ sK86 )
= $true )
| ( ( in @ ( kfst @ sK86 ) @ sK84 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f25306,f3077]) ).
thf(f25306,plain,
( ( $true
!= ( in @ sK86 @ sK83 ) )
| ( ( sK85 @ sK86 )
= $true )
| ( ( in @ ( kfst @ sK86 ) @ sK84 )
!= $true )
| ( $true
!= ( in @ ( ksnd @ sK86 ) @ sK84 ) ) ),
inference(superposition,[status(thm)],[f3076,f24458]) ).
thf(f24458,plain,
( ( kpair @ ( kfst @ sK86 ) @ ( ksnd @ sK86 ) )
= sK86 ),
inference(trivial_inequality_removal,[status(thm)],[f24380]) ).
thf(f24380,plain,
( ( $true != $true )
| ( ( kpair @ ( kfst @ sK86 ) @ ( ksnd @ sK86 ) )
= sK86 ) ),
inference(superposition,[status(thm)],[f5624,f24365]) ).
thf(f5624,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true )
| ( ( kpair @ ( kfst @ X5 ) @ ( ksnd @ X5 ) )
= X5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f5034]) ).
thf(f5034,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true )
| ( ( kpair @ ( kfst @ X5 ) @ ( ksnd @ X5 ) )
= X5 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3847,f3121]) ).
thf(f3121,plain,
cartprodpairsurjEq = $true,
inference(cnf_transformation,[status(thm)],[f1414]) ).
thf(f3847,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true )
| ( ( kpair @ ( kfst @ X5 ) @ ( ksnd @ X5 ) )
= X5 )
| ( cartprodpairsurjEq != $true ) ),
inference(cnf_transformation,[status(thm)],[f2174]) ).
thf(f2174,plain,
( ( ( cartprodpairsurjEq = $true )
| ( ( $true
= ( in @ sK575 @ ( cartprod @ sK574 @ sK573 ) ) )
& ( ( kpair @ ( kfst @ sK575 ) @ ( ksnd @ sK575 ) )
!= sK575 ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true )
| ( ( kpair @ ( kfst @ X5 ) @ ( ksnd @ X5 ) )
= X5 ) )
| ( cartprodpairsurjEq != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK573,sK574,sK575])],[f2172,f2173]) ).
thf(f2173,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $true )
& ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
!= X2 ) )
=> ( ( $true
= ( in @ sK575 @ ( cartprod @ sK574 @ sK573 ) ) )
& ( ( kpair @ ( kfst @ sK575 ) @ ( ksnd @ sK575 ) )
!= sK575 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2172,plain,
( ( ( cartprodpairsurjEq = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $true )
& ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
!= X2 ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X4 @ X3 ) )
!= $true )
| ( ( kpair @ ( kfst @ X5 ) @ ( ksnd @ X5 ) )
= X5 ) )
| ( cartprodpairsurjEq != $true ) ) ),
inference(rectify,[status(thm)],[f2171]) ).
thf(f2171,plain,
( ( ( cartprodpairsurjEq = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $true )
& ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
!= X2 ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
!= $true )
| ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 ) )
| ( cartprodpairsurjEq != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1224]) ).
thf(f1224,plain,
( ( cartprodpairsurjEq = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
!= $true )
| ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f395]) ).
thf(f395,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $true )
=> ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 ) )
<=> ( cartprodpairsurjEq = $true ) ),
inference(fool_elimination,[status(thm)],[f394]) ).
thf(f394,plain,
( cartprodpairsurjEq
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
=> ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
= X2 ) ) ) ),
inference(rectify,[status(thm)],[f184]) ).
thf(f184,axiom,
( cartprodpairsurjEq
= ( ! [X4: $i,X3: $i,X10: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( ( kpair @ ( kfst @ X10 ) @ ( ksnd @ X10 ) )
= X10 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',cartprodpairsurjEq) ).
thf(f3076,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK83 ) )
| ( $true
!= ( in @ X4 @ sK84 ) )
| ( $true
= ( sK85 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK84 ) ) ),
inference(cnf_transformation,[status(thm)],[f1414]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU768^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n014.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:33:27 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU768^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Binary Relations on a Set
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : (! A:i.! R:i.breln1 A R -> (! phi:i>o.(! x:i.in x A ->
% 0.31/0.47 % (! y:i.in y A -> in (kpair x y) R -> phi (kpair x y))) ->
% 0.31/0.47 % (! x:i.in x R -> phi x)))
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC270g [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 613 ( 289 unt; 323 typ; 289 def)
% 0.31/0.47 % Number of atoms : 1729 ( 418 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 289 ( 5 avg)
% 0.31/0.47 % Number of connectives : 3701 ( 73 ~; 12 |; 44 &;2682 @)
% 0.31/0.47 % ( 14 <=>; 876 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 299 ( 2 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 135 ( 135 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 326 ( 323 usr; 288 con; 0-4 aty)
% 0.31/0.47 % Number of variables : 991 ( 76 ^; 880 !; 35 ?; 991 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=378
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu_type,type,
% 0.31/0.47 exu: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu,definition,
% 0.31/0.47 ( exu
% 0.31/0.47 = ( ^ [Xphi: $i > $o] :
% 0.31/0.47 ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx_type,type,
% 0.31/0.47 setextAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx,definition,
% 0.31/0.47 ( setextAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xx @ B ) )
% 0.31/0.47 => ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset_type,type,
% 0.31/0.47 emptyset: $i ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx_type,type,
% 0.31/0.47 emptysetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx,definition,
% 0.31/0.47 ( emptysetAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin_type,type,
% 0.31/0.47 setadjoin: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx_type,type,
% 0.31/0.47 setadjoinAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx,definition,
% 0.31/0.47 ( setadjoinAx
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 <=> ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset_type,type,
% 0.31/0.47 powerset: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx_type,type,
% 0.31/0.47 powersetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx,definition,
% 0.31/0.47 ( powersetAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 <=> ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion_type,type,
% 0.31/0.47 setunion: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx_type,type,
% 0.31/0.47 setunionAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx,definition,
% 0.31/0.47 ( setunionAx
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 <=> ? [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega_type,type,
% 0.31/0.47 omega: $i ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax_type,type,
% 0.31/0.47 omega0Ax: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax,definition,
% 0.31/0.47 ( omega0Ax
% 0.31/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx_type,type,
% 0.31/0.47 omegaSAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx,definition,
% 0.31/0.47 ( omegaSAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx_type,type,
% 0.31/0.47 omegaIndAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx,definition,
% 0.31/0.47 ( omegaIndAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( ( in @ emptyset @ A )
% 0.31/0.47 & ! [Xx: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ omega )
% 0.31/0.47 & ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(replAx_type,type,
% 0.31/0.47 replAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(replAx,definition,
% 0.31/0.47 ( replAx
% 0.31/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 <=> ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx_type,type,
% 0.31/0.47 foundationAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx,definition,
% 0.31/0.47 ( foundationAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ( ( in @ B @ A )
% 0.31/0.47 & ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx_type,type,
% 0.31/0.47 wellorderingAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx,definition,
% 0.31/0.47 ( wellorderingAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ? [B: $i] :
% 0.31/0.47 ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) ) )
% 0.31/0.47 & ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ A )
% 0.31/0.47 & ( in @ Xy @ A ) )
% 0.31/0.47 => ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ( ( in @ Xx @ C )
% 0.31/0.47 <=> ( in @ Xy @ C ) ) )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 & ! [C: $i,D: $i] :
% 0.31/0.47 ( ( ( in @ C @ B )
% 0.31/0.47 & ( in @ D @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ D ) )
% 0.31/0.47 | ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ D )
% 0.31/0.47 => ( in @ Xx @ C ) ) ) )
% 0.31/0.47 & ! [C: $i] :
% 0.31/0.47 ( ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/0.47 => ? [D: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ D @ B )
% 0.31/0.47 & ( in @ Xx @ C )
% 0.31/0.47 & ~ ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ D )
% 0.31/0.47 & ( in @ Xy @ C ) )
% 0.31/0.47 & ! [E: $i] :
% 0.31/0.47 ( ( in @ E @ B )
% 0.31/0.47 => ( ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ E )
% 0.31/0.47 => ( in @ Xy @ D ) )
% 0.31/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr_type,type,
% 0.31/0.47 descr: ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(descrp_type,type,
% 0.31/0.47 descrp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descrp,definition,
% 0.31/0.47 ( descrp
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 @ ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr_type,type,
% 0.31/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI_type,type,
% 0.31/0.47 dsetconstrI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI,definition,
% 0.31/0.47 ( dsetconstrI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL_type,type,
% 0.31/0.47 dsetconstrEL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL,definition,
% 0.31/0.47 ( dsetconstrEL
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER_type,type,
% 0.31/0.47 dsetconstrER: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER,definition,
% 0.31/0.47 ( dsetconstrER
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1_type,type,
% 0.31/0.47 exuE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1,definition,
% 0.31/0.47 ( exuE1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set_type,type,
% 0.31/0.47 prop2set: $o > $i ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE_type,type,
% 0.31/0.47 prop2setE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE,definition,
% 0.31/0.47 ( prop2setE
% 0.31/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE_type,type,
% 0.31/0.47 emptysetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE,definition,
% 0.31/0.47 ( emptysetE
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse_type,type,
% 0.31/0.47 emptysetimpfalse: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse,definition,
% 0.31/0.47 ( emptysetimpfalse
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => $false ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset_type,type,
% 0.31/0.47 notinemptyset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset,definition,
% 0.31/0.47 ( notinemptyset
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e_type,type,
% 0.31/0.47 exuE3e: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e,definition,
% 0.31/0.47 ( exuE3e
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setext_type,type,
% 0.31/0.47 setext: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setext,definition,
% 0.31/0.47 ( setext
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( A = B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI_type,type,
% 0.31/0.47 emptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI,definition,
% 0.31/0.47 ( emptyI
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty_type,type,
% 0.31/0.47 noeltsimpempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty,definition,
% 0.31/0.47 ( noeltsimpempty
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta_type,type,
% 0.31/0.47 setbeta: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta,definition,
% 0.31/0.47 ( setbeta
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty_type,type,
% 0.31/0.47 nonempty: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty,definition,
% 0.31/0.47 ( nonempty
% 0.31/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1_type,type,
% 0.31/0.47 nonemptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1,definition,
% 0.31/0.47 ( nonemptyE1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI_type,type,
% 0.31/0.47 nonemptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI,definition,
% 0.31/0.47 ( nonemptyI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( nonempty
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1_type,type,
% 0.31/0.47 nonemptyI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1,definition,
% 0.31/0.47 ( nonemptyI1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL_type,type,
% 0.31/0.47 setadjoinIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL,definition,
% 0.31/0.47 ( setadjoinIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty_type,type,
% 0.31/0.47 emptyinunitempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty,definition,
% 0.31/0.47 ( emptyinunitempty
% 0.31/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR_type,type,
% 0.31/0.47 setadjoinIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR,definition,
% 0.31/0.47 ( setadjoinIR
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE_type,type,
% 0.31/0.47 setadjoinE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE,definition,
% 0.31/0.47 ( setadjoinE
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ( ( Xy = Xx )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xy @ A )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr_type,type,
% 0.31/0.47 setadjoinOr: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr,definition,
% 0.31/0.47 ( setadjoinOr
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq_type,type,
% 0.31/0.47 setoftrueEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq,definition,
% 0.31/0.47 ( setoftrueEq
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : $true )
% 0.31/0.47 = A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI_type,type,
% 0.31/0.47 powersetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI,definition,
% 0.31/0.47 ( powersetI
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset_type,type,
% 0.31/0.47 emptyinPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset,definition,
% 0.31/0.47 ( emptyinPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset_type,type,
% 0.31/0.47 emptyInPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset,definition,
% 0.31/0.47 ( emptyInPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE_type,type,
% 0.31/0.47 powersetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE,definition,
% 0.31/0.47 ( powersetE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 => ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunionI_type,type,
% 0.31/0.47 setunionI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionI,definition,
% 0.31/0.47 ( setunionI
% 0.31/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( ( in @ B @ A )
% 0.31/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunionE_type,type,
% 0.31/0.47 setunionE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionE,definition,
% 0.31/0.47 ( setunionE
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ! [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( ( in @ B @ A )
% 0.31/0.47 => Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subPowSU_type,type,
% 0.31/0.47 subPowSU: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subPowSU,definition,
% 0.31/0.47 ( subPowSU
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE2_type,type,
% 0.31/0.47 exuE2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE2,definition,
% 0.31/0.47 ( exuE2
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyImpWitness_type,type,
% 0.31/0.47 nonemptyImpWitness: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyImpWitness,definition,
% 0.31/0.47 ( nonemptyImpWitness
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & $true ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(uniqinunit_type,type,
% 0.31/0.47 uniqinunit: $o ).
% 0.31/0.47
% 0.31/0.47 thf(uniqinunit,definition,
% 0.31/0.47 ( uniqinunit
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinsingleton_type,type,
% 0.31/0.47 notinsingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinsingleton,definition,
% 0.31/0.47 ( notinsingleton
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx != Xy )
% 0.31/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqinunit_type,type,
% 0.31/0.47 eqinunit: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqinunit,definition,
% 0.31/0.47 ( eqinunit
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(singletonsswitch_type,type,
% 0.31/0.47 singletonsswitch: $o ).
% 0.31/0.47
% 0.31/0.47 thf(singletonsswitch,definition,
% 0.31/0.47 ( singletonsswitch
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetE_type,type,
% 0.31/0.47 upairsetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetE,definition,
% 0.31/0.47 ( upairsetE
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.31/0.47 => ( ( Xz = Xx )
% 0.31/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIL_type,type,
% 0.31/0.47 upairsetIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIL,definition,
% 0.31/0.47 ( upairsetIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIR_type,type,
% 0.31/0.47 upairsetIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIR,definition,
% 0.31/0.47 ( upairsetIR
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyE1_type,type,
% 0.31/0.47 emptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyE1,definition,
% 0.31/0.47 ( emptyE1
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ( ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = emptyset )
% 0.31/0.47 => $false ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(vacuousDall_type,type,
% 0.31/0.47 vacuousDall: $o ).
% 0.31/0.47
% 0.31/0.47 thf(vacuousDall,definition,
% 0.31/0.47 ( vacuousDall
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan1_type,type,
% 0.31/0.47 quantDeMorgan1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan1,definition,
% 0.31/0.47 ( quantDeMorgan1
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan2_type,type,
% 0.31/0.47 quantDeMorgan2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan2,definition,
% 0.31/0.47 ( quantDeMorgan2
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) )
% 0.31/0.47 => ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan3_type,type,
% 0.31/0.47 quantDeMorgan3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan3,definition,
% 0.31/0.47 ( quantDeMorgan3
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan4_type,type,
% 0.31/0.47 quantDeMorgan4: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan4,definition,
% 0.31/0.47 ( quantDeMorgan4
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) )
% 0.31/0.47 => ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setI_type,type,
% 0.31/0.47 prop2setI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setI,definition,
% 0.31/0.47 ( prop2setI
% 0.31/0.47 = ( ! [Xphi: $o] :
% 0.31/0.47 ( Xphi
% 0.31/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(set2prop_type,type,
% 0.31/0.47 set2prop: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set2propI_type,type,
% 0.31/0.47 prop2set2propI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set2propI,definition,
% 0.31/0.47 ( prop2set2propI
% 0.31/0.47 = ( ! [Xphi: $o] :
% 0.31/0.47 ( Xphi
% 0.31/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notdexE_type,type,
% 0.31/0.47 notdexE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notdexE,definition,
% 0.31/0.47 ( notdexE
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notdallE_type,type,
% 0.31/0.47 notdallE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notdallE,definition,
% 0.31/0.47 ( notdallE
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI1_type,type,
% 0.31/0.47 exuI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI1,definition,
% 0.31/0.47 ( exuI1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI3_type,type,
% 0.31/0.47 exuI3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI3,definition,
% 0.31/0.47 ( exuI3
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.31/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI2_type,type,
% 0.31/0.47 exuI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI2,definition,
% 0.31/0.47 ( exuI2
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 <=> ( Xy = Xx ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inCongP_type,type,
% 0.31/0.47 inCongP: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inCongP,definition,
% 0.31/0.47 ( inCongP
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong_type,type,
% 0.31/0.47 in__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong,definition,
% 0.31/0.47 ( in__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3u_type,type,
% 0.31/0.47 exuE3u: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3u,definition,
% 0.31/0.47 ( exuE3u
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exu__Cong_type,type,
% 0.31/0.47 exu__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu__Cong,definition,
% 0.31/0.47 ( exu__Cong
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 <=> ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset__Cong_type,type,
% 0.31/0.47 emptyset__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset__Cong,definition,
% 0.31/0.47 ( emptyset__Cong
% 0.31/0.47 = ( emptyset = emptyset ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin__Cong_type,type,
% 0.31/0.47 setadjoin__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin__Cong,definition,
% 0.31/0.47 ( setadjoin__Cong
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ! [Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( Xz = Xu )
% 0.31/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.31/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset__Cong_type,type,
% 0.31/0.47 powerset__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powerset__Cong,definition,
% 0.31/0.47 ( powerset__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( powerset @ A )
% 0.31/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion__Cong_type,type,
% 0.31/0.47 setunion__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunion__Cong,definition,
% 0.31/0.47 ( setunion__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( setunion @ A )
% 0.31/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega__Cong_type,type,
% 0.31/0.47 omega__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega__Cong,definition,
% 0.31/0.47 ( omega__Cong
% 0.31/0.47 = ( omega = omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuEu_type,type,
% 0.31/0.47 exuEu: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuEu,definition,
% 0.31/0.47 ( exuEu
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr__Cong_type,type,
% 0.31/0.47 descr__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descr__Cong,definition,
% 0.31/0.47 ( descr__Cong
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.31/0.47 => ( ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr__Cong_type,type,
% 0.31/0.47 dsetconstr__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr__Cong,definition,
% 0.31/0.47 ( dsetconstr__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.31/0.47 => ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = ( dsetconstr @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subset_type,type,
% 0.31/0.47 subset: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(disjoint_type,type,
% 0.31/0.47 disjoint: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(setsmeet_type,type,
% 0.31/0.47 setsmeet: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI1_type,type,
% 0.31/0.47 subsetI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI1,definition,
% 0.31/0.47 ( subsetI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset2_type,type,
% 0.31/0.47 eqimpsubset2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset2,definition,
% 0.31/0.47 ( eqimpsubset2
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset1_type,type,
% 0.31/0.47 eqimpsubset1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset1,definition,
% 0.31/0.47 ( eqimpsubset1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI2_type,type,
% 0.31/0.47 subsetI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI2,definition,
% 0.31/0.47 ( subsetI2
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetsubset_type,type,
% 0.31/0.47 emptysetsubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetsubset,definition,
% 0.31/0.47 ( emptysetsubset
% 0.31/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE_type,type,
% 0.31/0.47 subsetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE,definition,
% 0.31/0.47 ( subsetE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE2_type,type,
% 0.31/0.47 subsetE2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE2,definition,
% 0.31/0.47 ( subsetE2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notsubsetI_type,type,
% 0.31/0.47 notsubsetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notsubsetI,definition,
% 0.31/0.47 ( notsubsetI
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ B )
% 0.31/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(notequalI1_type,type,
% 0.31/0.48 notequalI1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(notequalI1,definition,
% 0.31/0.48 ( notequalI1
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ~ ( subset @ A @ B )
% 0.31/0.48 => ( A != B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(notequalI2_type,type,
% 0.31/0.48 notequalI2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(notequalI2,definition,
% 0.31/0.48 ( notequalI2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ B )
% 0.31/0.48 => ( A != B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subsetRefl_type,type,
% 0.31/0.48 subsetRefl: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subsetRefl,definition,
% 0.31/0.48 ( subsetRefl
% 0.31/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subsetTrans_type,type,
% 0.31/0.48 subsetTrans: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subsetTrans,definition,
% 0.31/0.48 ( subsetTrans
% 0.31/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/0.48 ( ( subset @ A @ B )
% 0.31/0.48 => ( ( subset @ B @ C )
% 0.31/0.48 => ( subset @ A @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setadjoinSub_type,type,
% 0.31/0.48 setadjoinSub: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setadjoinSub,definition,
% 0.31/0.48 ( setadjoinSub
% 0.31/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setadjoinSub2_type,type,
% 0.31/0.48 setadjoinSub2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setadjoinSub2,definition,
% 0.31/0.48 ( setadjoinSub2
% 0.31/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/0.48 ( ( subset @ A @ B )
% 0.31/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subset2powerset_type,type,
% 0.31/0.48 subset2powerset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subset2powerset,definition,
% 0.31/0.48 ( subset2powerset
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( subset @ A @ B )
% 0.31/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setextsub_type,type,
% 0.31/0.48 setextsub: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setextsub,definition,
% 0.31/0.48 ( setextsub
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( subset @ A @ B )
% 0.31/0.48 => ( ( subset @ B @ A )
% 0.31/0.48 => ( A = B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subsetemptysetimpeq_type,type,
% 0.31/0.48 subsetemptysetimpeq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subsetemptysetimpeq,definition,
% 0.31/0.48 ( subsetemptysetimpeq
% 0.31/0.48 = ( ! [A: $i] :
% 0.31/0.48 ( ( subset @ A @ emptyset )
% 0.31/0.48 => ( A = emptyset ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(powersetI1_type,type,
% 0.31/0.48 powersetI1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(powersetI1,definition,
% 0.31/0.48 ( powersetI1
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( subset @ B @ A )
% 0.31/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(powersetE1_type,type,
% 0.31/0.48 powersetE1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(powersetE1,definition,
% 0.31/0.48 ( powersetE1
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(inPowerset_type,type,
% 0.31/0.48 inPowerset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(inPowerset,definition,
% 0.31/0.48 ( inPowerset
% 0.31/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(powersetsubset_type,type,
% 0.31/0.48 powersetsubset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(powersetsubset,definition,
% 0.31/0.48 ( powersetsubset
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( subset @ A @ B )
% 0.31/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sepInPowerset_type,type,
% 0.31/0.48 sepInPowerset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(sepInPowerset,definition,
% 0.31/0.48 ( sepInPowerset
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.48 ( in
% 0.31/0.48 @ ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.48 @ ( powerset @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sepSubset_type,type,
% 0.31/0.48 sepSubset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(sepSubset,definition,
% 0.31/0.48 ( sepSubset
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.48 ( subset
% 0.31/0.48 @ ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.48 @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunion_type,type,
% 0.31/0.48 binunion: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(binunionIL_type,type,
% 0.31/0.48 binunionIL: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionIL,definition,
% 0.31/0.48 ( binunionIL
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(upairset2IR_type,type,
% 0.31/0.48 upairset2IR: $o ).
% 0.31/0.48
% 0.31/0.48 thf(upairset2IR,definition,
% 0.31/0.48 ( upairset2IR
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionIR_type,type,
% 0.31/0.48 binunionIR: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionIR,definition,
% 0.31/0.48 ( binunionIR
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ B )
% 0.31/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionEcases_type,type,
% 0.31/0.48 binunionEcases: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionEcases,definition,
% 0.31/0.48 ( binunionEcases
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.31/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.31/0.48 => ( ( ( in @ Xx @ A )
% 0.31/0.48 => Xphi )
% 0.31/0.48 => ( ( ( in @ Xx @ B )
% 0.31/0.48 => Xphi )
% 0.31/0.48 => Xphi ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionE_type,type,
% 0.31/0.48 binunionE: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionE,definition,
% 0.31/0.48 ( binunionE
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.31/0.48 => ( ( in @ Xx @ A )
% 0.31/0.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionLsub_type,type,
% 0.31/0.48 binunionLsub: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionLsub,definition,
% 0.31/0.48 ( binunionLsub
% 0.31/0.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionRsub_type,type,
% 0.31/0.48 binunionRsub: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionRsub,definition,
% 0.31/0.48 ( binunionRsub
% 0.31/0.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersect_type,type,
% 0.31/0.48 binintersect: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectI_type,type,
% 0.31/0.48 binintersectI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectI,definition,
% 0.31/0.48 ( binintersectI
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ B )
% 0.31/0.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset5_type,type,
% 0.31/0.48 binintersectSubset5: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset5,definition,
% 0.31/0.48 ( binintersectSubset5
% 0.31/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/0.48 ( ( subset @ C @ A )
% 0.31/0.48 => ( ( subset @ C @ B )
% 0.31/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectEL_type,type,
% 0.31/0.48 binintersectEL: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectEL,definition,
% 0.31/0.48 ( binintersectEL
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.31/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectLsub_type,type,
% 0.31/0.48 binintersectLsub: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectLsub,definition,
% 0.31/0.48 ( binintersectLsub
% 0.31/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset2_type,type,
% 0.31/0.48 binintersectSubset2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset2,definition,
% 0.31/0.48 ( binintersectSubset2
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( subset @ A @ B )
% 0.31/0.48 => ( ( binintersect @ A @ B )
% 0.31/0.48 = A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset3_type,type,
% 0.31/0.48 binintersectSubset3: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset3,definition,
% 0.31/0.48 ( binintersectSubset3
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( ( binintersect @ A @ B )
% 0.31/0.48 = B )
% 0.31/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectER_type,type,
% 0.31/0.48 binintersectER: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectER,definition,
% 0.31/0.48 ( binintersectER
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.31/0.48 => ( in @ Xx @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(disjointsetsI1_type,type,
% 0.31/0.48 disjointsetsI1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(disjointsetsI1,definition,
% 0.31/0.48 ( disjointsetsI1
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ~ ? [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 & ( in @ Xx @ B ) )
% 0.31/0.48 => ( ( binintersect @ A @ B )
% 0.31/0.48 = emptyset ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectRsub_type,type,
% 0.31/0.48 binintersectRsub: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectRsub,definition,
% 0.31/0.48 ( binintersectRsub
% 0.31/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset4_type,type,
% 0.31/0.48 binintersectSubset4: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset4,definition,
% 0.31/0.48 ( binintersectSubset4
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( subset @ B @ A )
% 0.31/0.48 => ( ( binintersect @ A @ B )
% 0.31/0.48 = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset1_type,type,
% 0.31/0.48 binintersectSubset1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectSubset1,definition,
% 0.31/0.48 ( binintersectSubset1
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( ( binintersect @ A @ B )
% 0.31/0.48 = A )
% 0.31/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(bs114d_type,type,
% 0.31/0.48 bs114d: $o ).
% 0.31/0.48
% 0.31/0.48 thf(bs114d,definition,
% 0.31/0.48 ( bs114d
% 0.31/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/0.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.31/0.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(regular_type,type,
% 0.31/0.48 regular: $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminus_type,type,
% 0.31/0.48 setminus: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(setminusI_type,type,
% 0.31/0.48 setminusI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusI,definition,
% 0.31/0.48 ( setminusI
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ B )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusEL_type,type,
% 0.31/0.48 setminusEL: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusEL,definition,
% 0.31/0.48 ( setminusEL
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusER_type,type,
% 0.31/0.48 setminusER: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusER,definition,
% 0.31/0.48 ( setminusER
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/0.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusSubset2_type,type,
% 0.31/0.48 setminusSubset2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusSubset2,definition,
% 0.31/0.48 ( setminusSubset2
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( subset @ A @ B )
% 0.31/0.48 => ( ( setminus @ A @ B )
% 0.31/0.48 = emptyset ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusERneg_type,type,
% 0.31/0.48 setminusERneg: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusERneg,definition,
% 0.31/0.48 ( setminusERneg
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/0.48 => ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusELneg_type,type,
% 0.31/0.48 setminusELneg: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusELneg,definition,
% 0.31/0.48 ( setminusELneg
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/0.48 => ( ~ ( in @ Xx @ B )
% 0.31/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusILneg_type,type,
% 0.31/0.48 setminusILneg: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusILneg,definition,
% 0.31/0.48 ( setminusILneg
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ~ ( in @ Xx @ A )
% 0.31/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusIRneg_type,type,
% 0.31/0.48 setminusIRneg: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusIRneg,definition,
% 0.31/0.48 ( setminusIRneg
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ B )
% 0.31/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusLsub_type,type,
% 0.31/0.48 setminusLsub: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusLsub,definition,
% 0.31/0.48 ( setminusLsub
% 0.31/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusSubset1_type,type,
% 0.31/0.48 setminusSubset1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusSubset1,definition,
% 0.31/0.48 ( setminusSubset1
% 0.31/0.48 = ( ! [A: $i,B: $i] :
% 0.31/0.48 ( ( ( setminus @ A @ B )
% 0.31/0.48 = emptyset )
% 0.31/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(symdiff_type,type,
% 0.31/0.48 symdiff: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffE_type,type,
% 0.31/0.48 symdiffE: $o ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffE,definition,
% 0.31/0.48 ( symdiffE
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.31/0.48 => ! [Xphi: $o] :
% 0.31/0.48 ( ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ B )
% 0.31/0.48 => Xphi ) )
% 0.31/0.48 => ( ( ~ ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ B )
% 0.31/0.48 => Xphi ) )
% 0.31/0.48 => Xphi ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffI1_type,type,
% 0.31/0.48 symdiffI1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffI1,definition,
% 0.31/0.48 ( symdiffI1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ B )
% 0.31/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffI2_type,type,
% 0.31/0.48 symdiffI2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffI2,definition,
% 0.31/0.48 ( symdiffI2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ~ ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ B )
% 0.31/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffIneg1_type,type,
% 0.31/0.48 symdiffIneg1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffIneg1,definition,
% 0.31/0.48 ( symdiffIneg1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ B )
% 0.31/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffIneg2_type,type,
% 0.31/0.48 symdiffIneg2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(symdiffIneg2,definition,
% 0.31/0.48 ( symdiffIneg2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ~ ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ B )
% 0.31/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(iskpair_type,type,
% 0.31/0.48 iskpair: $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(secondinupair_type,type,
% 0.31/0.48 secondinupair: $o ).
% 0.31/0.48
% 0.31/0.48 thf(secondinupair,definition,
% 0.31/0.48 ( secondinupair
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairIL_type,type,
% 0.31/0.48 setukpairIL: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairIL,definition,
% 0.31/0.48 ( setukpairIL
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairIR_type,type,
% 0.31/0.48 setukpairIR: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairIR,definition,
% 0.31/0.48 ( setukpairIR
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(kpairiskpair_type,type,
% 0.31/0.48 kpairiskpair: $o ).
% 0.31/0.48
% 0.31/0.48 thf(kpairiskpair,definition,
% 0.31/0.48 ( kpairiskpair
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(kpair_type,type,
% 0.31/0.48 kpair: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(kpairp_type,type,
% 0.31/0.48 kpairp: $o ).
% 0.31/0.48
% 0.31/0.48 thf(kpairp,definition,
% 0.31/0.48 ( kpairp
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprod_type,type,
% 0.31/0.48 cartprod: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(singletonsubset_type,type,
% 0.31/0.48 singletonsubset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(singletonsubset,definition,
% 0.31/0.48 ( singletonsubset
% 0.31/0.48 = ( ! [A: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(singletoninpowerset_type,type,
% 0.31/0.48 singletoninpowerset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(singletoninpowerset,definition,
% 0.31/0.48 ( singletoninpowerset
% 0.31/0.48 = ( ! [A: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(singletoninpowunion_type,type,
% 0.31/0.48 singletoninpowunion: $o ).
% 0.31/0.48
% 0.31/0.48 thf(singletoninpowunion,definition,
% 0.31/0.48 ( singletoninpowunion
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(upairset2E_type,type,
% 0.31/0.48 upairset2E: $o ).
% 0.31/0.48
% 0.31/0.48 thf(upairset2E,definition,
% 0.31/0.48 ( upairset2E
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.31/0.48 => ( ( Xz = Xx )
% 0.31/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(upairsubunion_type,type,
% 0.31/0.48 upairsubunion: $o ).
% 0.31/0.48
% 0.31/0.48 thf(upairsubunion,definition,
% 0.31/0.48 ( upairsubunion
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(upairinpowunion_type,type,
% 0.31/0.48 upairinpowunion: $o ).
% 0.31/0.48
% 0.31/0.48 thf(upairinpowunion,definition,
% 0.31/0.48 ( upairinpowunion
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ubforcartprodlem1_type,type,
% 0.31/0.48 ubforcartprodlem1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ubforcartprodlem1,definition,
% 0.31/0.48 ( ubforcartprodlem1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ubforcartprodlem2_type,type,
% 0.31/0.48 ubforcartprodlem2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ubforcartprodlem2,definition,
% 0.31/0.48 ( ubforcartprodlem2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ubforcartprodlem3_type,type,
% 0.31/0.48 ubforcartprodlem3: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ubforcartprodlem3,definition,
% 0.31/0.48 ( ubforcartprodlem3
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodpairin_type,type,
% 0.31/0.48 cartprodpairin: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodpairin,definition,
% 0.31/0.48 ( cartprodpairin
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodmempair1_type,type,
% 0.31/0.48 cartprodmempair1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodmempair1,definition,
% 0.31/0.48 ( cartprodmempair1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.31/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.31/0.48 => ? [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 & ? [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 & ( Xu
% 0.31/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodmempair_type,type,
% 0.31/0.48 cartprodmempair: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodmempair,definition,
% 0.31/0.48 ( cartprodmempair
% 0.31/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.31/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.31/0.48 => ( iskpair @ Xu ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setunionE2_type,type,
% 0.31/0.48 setunionE2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setunionE2,definition,
% 0.31/0.48 ( setunionE2
% 0.31/0.48 = ( ! [A: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.48 => ? [X: $i] :
% 0.31/0.48 ( ( in @ X @ A )
% 0.31/0.48 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setunionsingleton1_type,type,
% 0.31/0.48 setunionsingleton1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setunionsingleton1,definition,
% 0.31/0.48 ( setunionsingleton1
% 0.31/0.48 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setunionsingleton2_type,type,
% 0.31/0.48 setunionsingleton2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setunionsingleton2,definition,
% 0.31/0.48 ( setunionsingleton2
% 0.31/0.48 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setunionsingleton_type,type,
% 0.31/0.48 setunionsingleton: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setunionsingleton,definition,
% 0.31/0.48 ( setunionsingleton
% 0.31/0.48 = ( ! [Xx: $i] :
% 0.31/0.48 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.31/0.48 = Xx ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(singleton_type,type,
% 0.31/0.48 singleton: $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(singletonprop_type,type,
% 0.31/0.48 singletonprop: $o ).
% 0.31/0.48
% 0.31/0.48 thf(singletonprop,definition,
% 0.31/0.48 ( singletonprop
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( Xphi @ Xx )
% 0.31/0.48 => ( ( Xphi @ Xy )
% 0.31/0.48 => ( Xx = Xy ) ) ) ) )
% 0.31/0.48 => ( ? [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 & ( Xphi @ Xx ) )
% 0.31/0.48 => ( singleton
% 0.31/0.48 @ ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ex1_type,type,
% 0.31/0.48 ex1: $i > ( $i > $o ) > $o ).
% 0.31/0.48
% 0.31/0.48 thf(ex1,definition,
% 0.31/0.48 ( ex1
% 0.31/0.48 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.31/0.48 ( singleton
% 0.31/0.48 @ ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ex1E1_type,type,
% 0.31/0.48 ex1E1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ex1E1,definition,
% 0.31/0.48 ( ex1E1
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.48 ( ( ex1 @ A
% 0.31/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.48 => ? [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ex1I_type,type,
% 0.31/0.48 ex1I: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ex1I,definition,
% 0.31/0.48 ( ex1I
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( Xphi @ Xx )
% 0.31/0.48 => ( ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( Xphi @ Xy )
% 0.31/0.48 => ( Xy = Xx ) ) )
% 0.31/0.48 => ( ex1 @ A
% 0.31/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ex1I2_type,type,
% 0.31/0.48 ex1I2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ex1I2,definition,
% 0.31/0.48 ( ex1I2
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( Xphi @ Xx )
% 0.31/0.48 => ( ( Xphi @ Xy )
% 0.31/0.48 => ( Xx = Xy ) ) ) ) )
% 0.31/0.48 => ( ? [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 & ( Xphi @ Xx ) )
% 0.31/0.48 => ( ex1 @ A
% 0.31/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(singletonsuniq_type,type,
% 0.31/0.48 singletonsuniq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(singletonsuniq,definition,
% 0.31/0.48 ( singletonsuniq
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( ( setadjoin @ Xx @ emptyset )
% 0.31/0.48 = ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(atmost1p_type,type,
% 0.31/0.48 atmost1p: $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(atleast2p_type,type,
% 0.31/0.48 atleast2p: $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(atmost2p_type,type,
% 0.31/0.48 atmost2p: $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(upairsetp_type,type,
% 0.31/0.48 upairsetp: $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjL1_type,type,
% 0.31/0.48 setukpairinjL1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjL1,definition,
% 0.31/0.48 ( setukpairinjL1
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.48 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.31/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(kfstsingleton_type,type,
% 0.31/0.48 kfstsingleton: $o ).
% 0.31/0.48
% 0.31/0.48 thf(kfstsingleton,definition,
% 0.31/0.48 ( kfstsingleton
% 0.31/0.48 = ( ! [Xu: $i] :
% 0.31/0.48 ( ( iskpair @ Xu )
% 0.31/0.48 => ( singleton
% 0.31/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.31/0.48 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(theprop_type,type,
% 0.31/0.48 theprop: $o ).
% 0.31/0.48
% 0.31/0.48 thf(theprop,definition,
% 0.31/0.48 ( theprop
% 0.31/0.48 = ( ! [X: $i] :
% 0.31/0.48 ( ( singleton @ X )
% 0.31/0.48 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(kfst_type,type,
% 0.31/0.48 kfst: $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(kfstpairEq_type,type,
% 0.31/0.48 kfstpairEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(kfstpairEq,definition,
% 0.31/0.48 ( kfstpairEq
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.31/0.48 = Xx ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodfstin_type,type,
% 0.31/0.48 cartprodfstin: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodfstin,definition,
% 0.31/0.48 ( cartprodfstin
% 0.31/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.31/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.31/0.48 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjL2_type,type,
% 0.31/0.48 setukpairinjL2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjL2,definition,
% 0.31/0.48 ( setukpairinjL2
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.31/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.31/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjL_type,type,
% 0.31/0.48 setukpairinjL: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjL,definition,
% 0.31/0.48 ( setukpairinjL
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.31/0.48 = ( kpair @ Xz @ Xu ) )
% 0.31/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR11_type,type,
% 0.31/0.48 setukpairinjR11: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR11,definition,
% 0.31/0.48 ( setukpairinjR11
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( Xx = Xy )
% 0.31/0.48 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR12_type,type,
% 0.31/0.48 setukpairinjR12: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR12,definition,
% 0.31/0.48 ( setukpairinjR12
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( Xx = Xy )
% 0.31/0.48 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.31/0.48 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR1_type,type,
% 0.31/0.48 setukpairinjR1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR1,definition,
% 0.31/0.48 ( setukpairinjR1
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.31/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.31/0.48 => ( ( Xz = Xu )
% 0.31/0.48 => ( Xy = Xu ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(upairequniteq_type,type,
% 0.31/0.48 upairequniteq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(upairequniteq,definition,
% 0.31/0.48 ( upairequniteq
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.48 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.48 = ( setadjoin @ Xz @ emptyset ) )
% 0.31/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR2_type,type,
% 0.31/0.48 setukpairinjR2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR2,definition,
% 0.31/0.48 ( setukpairinjR2
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.31/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.31/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR_type,type,
% 0.31/0.48 setukpairinjR: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setukpairinjR,definition,
% 0.31/0.48 ( setukpairinjR
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.31/0.48 = ( kpair @ Xz @ Xu ) )
% 0.31/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ksndsingleton_type,type,
% 0.31/0.48 ksndsingleton: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ksndsingleton,definition,
% 0.31/0.48 ( ksndsingleton
% 0.31/0.48 = ( ! [Xu: $i] :
% 0.31/0.48 ( ( iskpair @ Xu )
% 0.31/0.48 => ( singleton
% 0.31/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.31/0.48 @ ^ [Xx: $i] :
% 0.31/0.48 ( Xu
% 0.31/0.48 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ksnd_type,type,
% 0.31/0.48 ksnd: $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(ksndpairEq_type,type,
% 0.31/0.48 ksndpairEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ksndpairEq,definition,
% 0.31/0.48 ( ksndpairEq
% 0.31/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.31/0.48 = Xy ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(kpairsurjEq_type,type,
% 0.31/0.48 kpairsurjEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(kpairsurjEq,definition,
% 0.31/0.48 ( kpairsurjEq
% 0.31/0.48 = ( ! [Xu: $i] :
% 0.31/0.48 ( ( iskpair @ Xu )
% 0.31/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.31/0.48 = Xu ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodsndin_type,type,
% 0.31/0.48 cartprodsndin: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodsndin,definition,
% 0.31/0.48 ( cartprodsndin
% 0.31/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.31/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.31/0.48 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodpairmemEL_type,type,
% 0.31/0.48 cartprodpairmemEL: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodpairmemEL,definition,
% 0.31/0.48 ( cartprodpairmemEL
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.31/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodpairmemER_type,type,
% 0.31/0.48 cartprodpairmemER: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodpairmemER,definition,
% 0.31/0.48 ( cartprodpairmemER
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.31/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodmempaircEq_type,type,
% 0.31/0.48 cartprodmempaircEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodmempaircEq,definition,
% 0.31/0.48 ( cartprodmempaircEq
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( kpair @ Xx @ Xy )
% 0.31/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodfstpairEq_type,type,
% 0.31/0.48 cartprodfstpairEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodfstpairEq,definition,
% 0.31/0.48 ( cartprodfstpairEq
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.31/0.48 = Xx ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodsndpairEq_type,type,
% 0.31/0.48 cartprodsndpairEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodsndpairEq,definition,
% 0.31/0.48 ( cartprodsndpairEq
% 0.31/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.31/0.48 = Xy ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodpairsurjEq_type,type,
% 0.31/0.48 cartprodpairsurjEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(cartprodpairsurjEq,definition,
% 0.31/0.48 ( cartprodpairsurjEq
% 0.31/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.31/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.31/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.31/0.48 = Xu ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln_type,type,
% 0.31/0.48 breln: $i > $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln,definition,
% 0.31/0.48 ( breln
% 0.31/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstr_type,type,
% 0.31/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrI_type,type,
% 0.31/0.48 dpsetconstrI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrI,definition,
% 0.31/0.48 ( dpsetconstrI
% 0.31/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( Xphi @ Xx @ Xy )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.48 @ ( dpsetconstr @ A @ B
% 0.31/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrSub_type,type,
% 0.31/0.48 dpsetconstrSub: $o ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrSub,definition,
% 0.31/0.48 ( dpsetconstrSub
% 0.31/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.31/0.48 ( subset
% 0.31/0.48 @ ( dpsetconstr @ A @ B
% 0.31/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.31/0.48 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setOfPairsIsBReln_type,type,
% 0.31/0.48 setOfPairsIsBReln: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setOfPairsIsBReln,definition,
% 0.31/0.48 ( setOfPairsIsBReln
% 0.31/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.31/0.48 ( breln @ A @ B
% 0.31/0.48 @ ( dpsetconstr @ A @ B
% 0.31/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrERa_type,type,
% 0.31/0.48 dpsetconstrERa: $o ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrERa,definition,
% 0.31/0.48 ( dpsetconstrERa
% 0.31/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.48 @ ( dpsetconstr @ A @ B
% 0.31/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.31/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrEL1_type,type,
% 0.31/0.48 dpsetconstrEL1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrEL1,definition,
% 0.31/0.48 ( dpsetconstrEL1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.48 @ ( dpsetconstr @ A @ B
% 0.31/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.31/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrEL2_type,type,
% 0.31/0.48 dpsetconstrEL2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrEL2,definition,
% 0.31/0.48 ( dpsetconstrEL2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.48 @ ( dpsetconstr @ A @ B
% 0.31/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.31/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrER_type,type,
% 0.31/0.48 dpsetconstrER: $o ).
% 0.31/0.48
% 0.31/0.48 thf(dpsetconstrER,definition,
% 0.31/0.48 ( dpsetconstrER
% 0.31/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.48 @ ( dpsetconstr @ A @ B
% 0.31/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.31/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(func_type,type,
% 0.31/0.48 func: $i > $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcSet_type,type,
% 0.31/0.48 funcSet: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(funcImageSingleton_type,type,
% 0.31/0.48 funcImageSingleton: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcImageSingleton,definition,
% 0.31/0.48 ( funcImageSingleton
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( singleton
% 0.31/0.48 @ ( dsetconstr @ B
% 0.31/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(apProp_type,type,
% 0.31/0.48 apProp: $o ).
% 0.31/0.48
% 0.31/0.48 thf(apProp,definition,
% 0.31/0.48 ( apProp
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in
% 0.31/0.48 @ ( setunion
% 0.31/0.48 @ ( dsetconstr @ B
% 0.31/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.31/0.48 @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ap_type,type,
% 0.31/0.48 ap: $i > $i > $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(app_type,type,
% 0.31/0.48 app: $o ).
% 0.31/0.48
% 0.31/0.48 thf(app,definition,
% 0.31/0.48 ( app
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(infuncsetfunc_type,type,
% 0.31/0.48 infuncsetfunc: $o ).
% 0.31/0.48
% 0.31/0.48 thf(infuncsetfunc,definition,
% 0.31/0.48 ( infuncsetfunc
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.48 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ap2p_type,type,
% 0.31/0.48 ap2p: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ap2p,definition,
% 0.31/0.48 ( ap2p
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(funcinfuncset_type,type,
% 0.31/0.48 funcinfuncset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcinfuncset,definition,
% 0.31/0.48 ( funcinfuncset
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(lamProp_type,type,
% 0.31/0.48 lamProp: $o ).
% 0.31/0.48
% 0.31/0.48 thf(lamProp,definition,
% 0.31/0.48 ( lamProp
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.48 => ( func @ A @ B
% 0.31/0.48 @ ( dpsetconstr @ A @ B
% 0.31/0.48 @ ^ [Xx: $i,Xy: $i] :
% 0.31/0.48 ( ( Xf @ Xx )
% 0.31/0.48 = Xy ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(lam_type,type,
% 0.31/0.48 lam: $i > $i > ( $i > $i ) > $i ).
% 0.31/0.48
% 0.31/0.48 thf(lamp_type,type,
% 0.31/0.48 lamp: $o ).
% 0.31/0.48
% 0.31/0.48 thf(lamp,definition,
% 0.31/0.48 ( lamp
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.48 => ( func @ A @ B
% 0.31/0.48 @ ( lam @ A @ B
% 0.31/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(lam2p_type,type,
% 0.31/0.48 lam2p: $o ).
% 0.31/0.48
% 0.31/0.48 thf(lam2p,definition,
% 0.31/0.48 ( lam2p
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.48 => ( in
% 0.31/0.48 @ ( lam @ A @ B
% 0.31/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.31/0.48 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(brelnall1_type,type,
% 0.31/0.48 brelnall1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(brelnall1,definition,
% 0.31/0.48 ( brelnall1
% 0.31/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.48 ( ( breln @ A @ B @ R )
% 0.31/0.48 => ! [Xphi: $i > $o] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ R )
% 0.31/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(brelnall2_type,type,
% 0.31/0.48 brelnall2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(brelnall2,definition,
% 0.31/0.48 ( brelnall2
% 0.31/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.48 ( ( breln @ A @ B @ R )
% 0.31/0.48 => ! [Xphi: $i > $o] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ R )
% 0.31/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ex1E2_type,type,
% 0.31/0.48 ex1E2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ex1E2,definition,
% 0.31/0.48 ( ex1E2
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.48 ( ( ex1 @ A
% 0.31/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( Xphi @ Xx )
% 0.31/0.48 => ( ( Xphi @ Xy )
% 0.31/0.48 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(funcGraphProp1_type,type,
% 0.31/0.48 funcGraphProp1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcGraphProp1,definition,
% 0.31/0.48 ( funcGraphProp1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(funcGraphProp3_type,type,
% 0.31/0.48 funcGraphProp3: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcGraphProp3,definition,
% 0.31/0.48 ( funcGraphProp3
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(funcGraphProp2_type,type,
% 0.31/0.48 funcGraphProp2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcGraphProp2,definition,
% 0.31/0.48 ( funcGraphProp2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.31/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.48 = Xy ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(funcextLem_type,type,
% 0.31/0.48 funcextLem: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcextLem,definition,
% 0.31/0.48 ( funcextLem
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ! [Xg: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xg )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(funcGraphProp4_type,type,
% 0.31/0.48 funcGraphProp4: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcGraphProp4,definition,
% 0.31/0.48 ( funcGraphProp4
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.31/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.48 = Xy ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subbreln_type,type,
% 0.31/0.48 subbreln: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subbreln,definition,
% 0.31/0.48 ( subbreln
% 0.31/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.48 ( ( breln @ A @ B @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln @ A @ B @ S )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.31/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(eqbreln_type,type,
% 0.31/0.48 eqbreln: $o ).
% 0.31/0.48
% 0.31/0.48 thf(eqbreln,definition,
% 0.31/0.48 ( eqbreln
% 0.31/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.48 ( ( breln @ A @ B @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln @ A @ B @ S )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.31/0.48 => ( R = S ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(funcext_type,type,
% 0.31/0.48 funcext: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcext,definition,
% 0.31/0.48 ( funcext
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ! [Xg: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xg )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.31/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(funcext2_type,type,
% 0.31/0.48 funcext2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(funcext2,definition,
% 0.31/0.48 ( funcext2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.48 => ! [Xg: $i] :
% 0.31/0.48 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.31/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ap2apEq1_type,type,
% 0.31/0.48 ap2apEq1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ap2apEq1,definition,
% 0.31/0.48 ( ap2apEq1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.48 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ap2apEq2_type,type,
% 0.31/0.48 ap2apEq2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ap2apEq2,definition,
% 0.31/0.48 ( ap2apEq2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.48 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(beta1_type,type,
% 0.31/0.48 beta1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(beta1,definition,
% 0.31/0.48 ( beta1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( ap @ A @ B
% 0.31/0.48 @ ( lam @ A @ B
% 0.31/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.31/0.48 @ Xx )
% 0.31/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(eta1_type,type,
% 0.31/0.48 eta1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(eta1,definition,
% 0.31/0.48 ( eta1
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( func @ A @ B @ Xf )
% 0.31/0.48 => ( ( lam @ A @ B
% 0.31/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.31/0.48 = Xf ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(lam2lamEq_type,type,
% 0.31/0.48 lam2lamEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(lam2lamEq,definition,
% 0.31/0.48 ( lam2lamEq
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.48 => ( ( lam @ A @ B
% 0.31/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.31/0.48 = ( lam @ A @ B
% 0.31/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(beta2_type,type,
% 0.31/0.48 beta2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(beta2,definition,
% 0.31/0.48 ( beta2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( ap @ A @ B
% 0.31/0.48 @ ( lam @ A @ B
% 0.31/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.31/0.48 @ Xx )
% 0.31/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(eta2_type,type,
% 0.31/0.48 eta2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(eta2,definition,
% 0.31/0.48 ( eta2
% 0.31/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.48 => ( ( lam @ A @ B
% 0.31/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.31/0.48 = Xf ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(iffalseProp1_type,type,
% 0.31/0.48 iffalseProp1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(iffalseProp1,definition,
% 0.31/0.48 ( iffalseProp1
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ~ Xphi
% 0.31/0.48 => ( in @ Xy
% 0.31/0.48 @ ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xz: $i] :
% 0.31/0.48 ( ( Xphi
% 0.31/0.48 & ( Xz = Xx ) )
% 0.31/0.48 | ( ~ Xphi
% 0.31/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(iffalseProp2_type,type,
% 0.31/0.48 iffalseProp2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(iffalseProp2,definition,
% 0.31/0.48 ( iffalseProp2
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ~ Xphi
% 0.31/0.48 => ( ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xz: $i] :
% 0.31/0.48 ( ( Xphi
% 0.31/0.48 & ( Xz = Xx ) )
% 0.31/0.48 | ( ~ Xphi
% 0.31/0.48 & ( Xz = Xy ) ) ) )
% 0.31/0.48 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(iftrueProp1_type,type,
% 0.31/0.48 iftrueProp1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(iftrueProp1,definition,
% 0.31/0.48 ( iftrueProp1
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( Xphi
% 0.31/0.48 => ( in @ Xx
% 0.31/0.48 @ ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xz: $i] :
% 0.31/0.48 ( ( Xphi
% 0.31/0.48 & ( Xz = Xx ) )
% 0.31/0.48 | ( ~ Xphi
% 0.31/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(iftrueProp2_type,type,
% 0.31/0.48 iftrueProp2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(iftrueProp2,definition,
% 0.31/0.48 ( iftrueProp2
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( Xphi
% 0.31/0.48 => ( ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xz: $i] :
% 0.31/0.48 ( ( Xphi
% 0.31/0.48 & ( Xz = Xx ) )
% 0.31/0.48 | ( ~ Xphi
% 0.31/0.48 & ( Xz = Xy ) ) ) )
% 0.31/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ifSingleton_type,type,
% 0.31/0.48 ifSingleton: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ifSingleton,definition,
% 0.31/0.48 ( ifSingleton
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( singleton
% 0.31/0.48 @ ( dsetconstr @ A
% 0.31/0.48 @ ^ [Xz: $i] :
% 0.31/0.48 ( ( Xphi
% 0.31/0.48 & ( Xz = Xx ) )
% 0.31/0.48 | ( ~ Xphi
% 0.31/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(if_type,type,
% 0.31/0.48 if: $i > $o > $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(ifp_type,type,
% 0.31/0.48 ifp: $o ).
% 0.31/0.48
% 0.31/0.48 thf(ifp,definition,
% 0.31/0.48 ( ifp
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(theeq_type,type,
% 0.31/0.48 theeq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(theeq,definition,
% 0.31/0.48 ( theeq
% 0.31/0.48 = ( ! [X: $i] :
% 0.31/0.48 ( ( singleton @ X )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ X )
% 0.31/0.48 => ( ( setunion @ X )
% 0.31/0.48 = Xx ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(iftrue_type,type,
% 0.31/0.48 iftrue: $o ).
% 0.31/0.48
% 0.31/0.48 thf(iftrue,definition,
% 0.31/0.48 ( iftrue
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( Xphi
% 0.31/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.31/0.48 = Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(iffalse_type,type,
% 0.31/0.48 iffalse: $o ).
% 0.31/0.48
% 0.31/0.48 thf(iffalse,definition,
% 0.31/0.48 ( iffalse
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ~ Xphi
% 0.31/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.31/0.48 = Xy ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(iftrueorfalse_type,type,
% 0.31/0.48 iftrueorfalse: $o ).
% 0.31/0.48
% 0.31/0.48 thf(iftrueorfalse,definition,
% 0.31/0.48 ( iftrueorfalse
% 0.31/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectT_lem_type,type,
% 0.31/0.48 binintersectT_lem: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectT_lem,definition,
% 0.31/0.48 ( binintersectT_lem
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionT_lem_type,type,
% 0.31/0.48 binunionT_lem: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionT_lem,definition,
% 0.31/0.48 ( binunionT_lem
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(powersetT_lem_type,type,
% 0.31/0.48 powersetT_lem: $o ).
% 0.31/0.48
% 0.31/0.48 thf(powersetT_lem,definition,
% 0.31/0.48 ( powersetT_lem
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setminusT_lem_type,type,
% 0.31/0.48 setminusT_lem: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setminusT_lem,definition,
% 0.31/0.48 ( setminusT_lem
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementT_lem_type,type,
% 0.31/0.48 complementT_lem: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementT_lem,definition,
% 0.31/0.48 ( complementT_lem
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setextT_type,type,
% 0.31/0.48 setextT: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setextT,definition,
% 0.31/0.48 ( setextT
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ X )
% 0.31/0.48 => ( in @ Xx @ Y ) ) )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ Y )
% 0.31/0.48 => ( in @ Xx @ X ) ) )
% 0.31/0.48 => ( X = Y ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subsetTI_type,type,
% 0.31/0.48 subsetTI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subsetTI,definition,
% 0.31/0.48 ( subsetTI
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ X )
% 0.31/0.48 => ( in @ Xx @ Y ) ) )
% 0.31/0.48 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(powersetTI1_type,type,
% 0.31/0.48 powersetTI1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(powersetTI1,definition,
% 0.31/0.48 ( powersetTI1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ X )
% 0.31/0.48 => ( in @ Xx @ Y ) ) )
% 0.31/0.48 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(powersetTE1_type,type,
% 0.31/0.48 powersetTE1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(powersetTE1,definition,
% 0.31/0.48 ( powersetTE1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ X @ ( powerset @ Y ) )
% 0.31/0.48 => ( ( in @ Xx @ X )
% 0.31/0.48 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementTI1_type,type,
% 0.31/0.48 complementTI1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementTI1,definition,
% 0.31/0.48 ( complementTI1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ X )
% 0.31/0.48 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementTE1_type,type,
% 0.31/0.48 complementTE1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementTE1,definition,
% 0.31/0.48 ( complementTE1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectTELcontra_type,type,
% 0.31/0.48 binintersectTELcontra: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectTELcontra,definition,
% 0.31/0.48 ( binintersectTELcontra
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ X )
% 0.31/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectTERcontra_type,type,
% 0.31/0.48 binintersectTERcontra: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binintersectTERcontra,definition,
% 0.31/0.48 ( binintersectTERcontra
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ Y )
% 0.31/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(contrasubsetT_type,type,
% 0.31/0.48 contrasubsetT: $o ).
% 0.31/0.48
% 0.31/0.48 thf(contrasubsetT,definition,
% 0.31/0.48 ( contrasubsetT
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.48 => ( ( in @ Xx @ Y )
% 0.31/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(contrasubsetT1_type,type,
% 0.31/0.48 contrasubsetT1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(contrasubsetT1,definition,
% 0.31/0.48 ( contrasubsetT1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( subset @ X @ Y )
% 0.31/0.48 => ( ~ ( in @ Xx @ Y )
% 0.31/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(contrasubsetT2_type,type,
% 0.31/0.48 contrasubsetT2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(contrasubsetT2,definition,
% 0.31/0.48 ( contrasubsetT2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ Y )
% 0.31/0.48 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(contrasubsetT3_type,type,
% 0.31/0.48 contrasubsetT3: $o ).
% 0.31/0.48
% 0.31/0.48 thf(contrasubsetT3,definition,
% 0.31/0.48 ( contrasubsetT3
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.31/0.48 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementI1_type,type,
% 0.31/0.48 doubleComplementI1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementI1,definition,
% 0.31/0.48 ( doubleComplementI1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ X )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementE1_type,type,
% 0.31/0.48 doubleComplementE1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementE1,definition,
% 0.31/0.48 ( doubleComplementE1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.31/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementSub1_type,type,
% 0.31/0.48 doubleComplementSub1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementSub1,definition,
% 0.31/0.48 ( doubleComplementSub1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementSub2_type,type,
% 0.31/0.48 doubleComplementSub2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementSub2,definition,
% 0.31/0.48 ( doubleComplementSub2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementEq_type,type,
% 0.31/0.48 doubleComplementEq: $o ).
% 0.31/0.48
% 0.31/0.48 thf(doubleComplementEq,definition,
% 0.31/0.48 ( doubleComplementEq
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ( X
% 0.31/0.48 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementTnotintersectT_type,type,
% 0.31/0.48 complementTnotintersectT: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementTnotintersectT,definition,
% 0.31/0.48 ( complementTnotintersectT
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementImpComplementIntersect_type,type,
% 0.31/0.48 complementImpComplementIntersect: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementImpComplementIntersect,definition,
% 0.31/0.48 ( complementImpComplementIntersect
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementSubsetComplementIntersect_type,type,
% 0.31/0.48 complementSubsetComplementIntersect: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementSubsetComplementIntersect,definition,
% 0.31/0.48 ( complementSubsetComplementIntersect
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementInPowersetComplementIntersect_type,type,
% 0.31/0.48 complementInPowersetComplementIntersect: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementInPowersetComplementIntersect,definition,
% 0.31/0.48 ( complementInPowersetComplementIntersect
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(contraSubsetComplement_type,type,
% 0.31/0.48 contraSubsetComplement: $o ).
% 0.31/0.48
% 0.31/0.48 thf(contraSubsetComplement,definition,
% 0.31/0.48 ( contraSubsetComplement
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ Y )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementTcontraSubset_type,type,
% 0.31/0.48 complementTcontraSubset: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementTcontraSubset,definition,
% 0.31/0.48 ( complementTcontraSubset
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.48 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionTILcontra_type,type,
% 0.31/0.48 binunionTILcontra: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionTILcontra,definition,
% 0.31/0.48 ( binunionTILcontra
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.31/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionTIRcontra_type,type,
% 0.31/0.48 binunionTIRcontra: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionTIRcontra,definition,
% 0.31/0.48 ( binunionTIRcontra
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.31/0.48 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(inIntersectImpInUnion_type,type,
% 0.31/0.48 inIntersectImpInUnion: $o ).
% 0.31/0.48
% 0.31/0.48 thf(inIntersectImpInUnion,definition,
% 0.31/0.48 ( inIntersectImpInUnion
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.31/0.48 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(inIntersectImpInUnion2_type,type,
% 0.31/0.48 inIntersectImpInUnion2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(inIntersectImpInUnion2,definition,
% 0.31/0.48 ( inIntersectImpInUnion2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.31/0.48 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(inIntersectImpInIntersectUnions_type,type,
% 0.31/0.48 inIntersectImpInIntersectUnions: $o ).
% 0.31/0.48
% 0.31/0.48 thf(inIntersectImpInIntersectUnions,definition,
% 0.31/0.48 ( inIntersectImpInIntersectUnions
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.31/0.48 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(intersectInPowersetIntersectUnions_type,type,
% 0.31/0.48 intersectInPowersetIntersectUnions: $o ).
% 0.31/0.48
% 0.31/0.48 thf(intersectInPowersetIntersectUnions,definition,
% 0.31/0.48 ( intersectInPowersetIntersectUnions
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(inComplementUnionImpNotIn1_type,type,
% 0.31/0.48 inComplementUnionImpNotIn1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(inComplementUnionImpNotIn1,definition,
% 0.31/0.48 ( inComplementUnionImpNotIn1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(inComplementUnionImpInComplement1_type,type,
% 0.31/0.48 inComplementUnionImpInComplement1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(inComplementUnionImpInComplement1,definition,
% 0.31/0.48 ( inComplementUnionImpInComplement1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionTE_type,type,
% 0.31/0.48 binunionTE: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionTE,definition,
% 0.31/0.48 ( binunionTE
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xphi: $o,Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.31/0.48 => ( ( ( in @ Xx @ X )
% 0.31/0.48 => Xphi )
% 0.31/0.48 => ( ( ( in @ Xx @ Y )
% 0.31/0.48 => Xphi )
% 0.31/0.48 => Xphi ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(binunionTEcontra_type,type,
% 0.31/0.48 binunionTEcontra: $o ).
% 0.31/0.48
% 0.31/0.48 thf(binunionTEcontra,definition,
% 0.31/0.48 ( binunionTEcontra
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ~ ( in @ Xx @ X )
% 0.31/0.48 => ( ~ ( in @ Xx @ Y )
% 0.31/0.48 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2a1_type,type,
% 0.31/0.48 demorgan2a1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2a1,definition,
% 0.31/0.48 ( demorgan2a1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(complementUnionInPowersetComplement_type,type,
% 0.31/0.48 complementUnionInPowersetComplement: $o ).
% 0.31/0.48
% 0.31/0.48 thf(complementUnionInPowersetComplement,definition,
% 0.31/0.48 ( complementUnionInPowersetComplement
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2a2_type,type,
% 0.31/0.48 demorgan2a2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2a2,definition,
% 0.31/0.48 ( demorgan2a2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan1a_type,type,
% 0.31/0.48 demorgan1a: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan1a,definition,
% 0.31/0.48 ( demorgan1a
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.31/0.48 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan1b_type,type,
% 0.31/0.48 demorgan1b: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan1b,definition,
% 0.31/0.48 ( demorgan1b
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan1_type,type,
% 0.31/0.48 demorgan1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan1,definition,
% 0.31/0.48 ( demorgan1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.31/0.48 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2a_type,type,
% 0.31/0.48 demorgan2a: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2a,definition,
% 0.31/0.48 ( demorgan2a
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.48 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2b2_type,type,
% 0.31/0.48 demorgan2b2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2b2,definition,
% 0.31/0.48 ( demorgan2b2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/0.48 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2b_type,type,
% 0.31/0.48 demorgan2b: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2b,definition,
% 0.31/0.48 ( demorgan2b
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.31/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2_type,type,
% 0.31/0.48 demorgan2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(demorgan2,definition,
% 0.31/0.48 ( demorgan2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.31/0.48 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule0_type,type,
% 0.31/0.48 woz13rule0: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule0,definition,
% 0.31/0.48 ( woz13rule0
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.31/0.48 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule1_type,type,
% 0.31/0.48 woz13rule1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule1,definition,
% 0.31/0.48 ( woz13rule1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ Z )
% 0.31/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule2_type,type,
% 0.31/0.48 woz13rule2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule2,definition,
% 0.31/0.48 ( woz13rule2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ Y @ Z )
% 0.31/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule3_type,type,
% 0.31/0.48 woz13rule3: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule3,definition,
% 0.31/0.48 ( woz13rule3
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ Y )
% 0.31/0.48 => ( ( subset @ X @ Z )
% 0.31/0.48 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule4_type,type,
% 0.31/0.48 woz13rule4: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz13rule4,definition,
% 0.31/0.48 ( woz13rule4
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ! [W: $i] :
% 0.31/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ Z )
% 0.31/0.48 => ( ( subset @ Y @ W )
% 0.31/0.48 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_1_type,type,
% 0.31/0.48 woz1_1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_1,definition,
% 0.31/0.48 ( woz1_1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_2_type,type,
% 0.31/0.48 woz1_2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_2,definition,
% 0.31/0.48 ( woz1_2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ! [W: $i] :
% 0.31/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.31/0.48 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.31/0.48 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_3_type,type,
% 0.31/0.48 woz1_3: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_3,definition,
% 0.31/0.48 ( woz1_3
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_4_type,type,
% 0.31/0.48 woz1_4: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_4,definition,
% 0.31/0.48 ( woz1_4
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.48 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_5_type,type,
% 0.31/0.48 woz1_5: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_5,definition,
% 0.31/0.48 ( woz1_5
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1_type,type,
% 0.31/0.48 breln1: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1,definition,
% 0.31/0.48 ( breln1
% 0.31/0.48 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1all2,conjecture,
% 0.31/0.48 ( setextAx
% 0.31/0.48 => ( emptysetAx
% 0.31/0.48 => ( setadjoinAx
% 0.31/0.48 => ( powersetAx
% 0.31/0.48 => ( setunionAx
% 0.31/0.48 => ( omega0Ax
% 0.31/0.48 => ( omegaSAx
% 0.31/0.48 => ( omegaIndAx
% 0.31/0.48 => ( replAx
% 0.31/0.48 => ( foundationAx
% 0.31/0.48 => ( wellorderingAx
% 0.31/0.48 => ( descrp
% 0.31/0.48 => ( dsetconstrI
% 0.31/0.48 => ( dsetconstrEL
% 0.31/0.48 => ( dsetconstrER
% 0.31/0.48 => ( exuE1
% 0.31/0.48 => ( prop2setE
% 0.31/0.48 => ( emptysetE
% 0.31/0.48 => ( emptysetimpfalse
% 0.31/0.48 => ( notinemptyset
% 0.31/0.48 => ( exuE3e
% 0.31/0.48 => ( setext
% 0.31/0.48 => ( emptyI
% 0.31/0.48 => ( noeltsimpempty
% 0.31/0.48 => ( setbeta
% 0.31/0.48 => ( nonemptyE1
% 0.31/0.48 => ( nonemptyI
% 0.31/0.48 => ( nonemptyI1
% 0.31/0.48 => ( setadjoinIL
% 0.31/0.48 => ( emptyinunitempty
% 0.31/0.48 => ( setadjoinIR
% 0.31/0.48 => ( setadjoinE
% 0.31/0.48 => ( setadjoinOr
% 0.31/0.48 => ( setoftrueEq
% 0.31/0.48 => ( powersetI
% 0.31/0.48 => ( emptyinPowerset
% 0.31/0.48 => ( emptyInPowerset
% 0.31/0.48 => ( powersetE
% 0.31/0.48 => ( setunionI
% 0.31/0.48 => ( setunionE
% 0.31/0.48 => ( subPowSU
% 0.31/0.48 => ( exuE2
% 0.31/0.48 => ( nonemptyImpWitness
% 0.31/0.48 => ( uniqinunit
% 0.31/0.48 => ( notinsingleton
% 0.31/0.48 => ( eqinunit
% 0.31/0.48 => ( singletonsswitch
% 0.31/0.48 => ( upairsetE
% 0.31/0.48 => ( upairsetIL
% 0.31/0.48 => ( upairsetIR
% 0.31/0.48 => ( emptyE1
% 0.31/0.49 => ( vacuousDall
% 0.31/0.49 => ( quantDeMorgan1
% 0.31/0.49 => ( quantDeMorgan2
% 0.31/0.49 => ( quantDeMorgan3
% 0.31/0.49 => ( quantDeMorgan4
% 0.31/0.49 => ( prop2setI
% 0.31/0.49 => ( prop2set2propI
% 0.31/0.49 => ( notdexE
% 0.31/0.49 => ( notdallE
% 0.31/0.49 => ( exuI1
% 0.31/0.49 => ( exuI3
% 0.31/0.49 => ( exuI2
% 0.31/0.49 => ( inCongP
% 0.31/0.49 => ( in__Cong
% 0.31/0.49 => ( exuE3u
% 0.31/0.49 => ( exu__Cong
% 0.31/0.49 => ( emptyset__Cong
% 0.31/0.49 => ( setadjoin__Cong
% 0.31/0.49 => ( powerset__Cong
% 0.31/0.49 => ( setunion__Cong
% 0.31/0.49 => ( omega__Cong
% 0.31/0.49 => ( exuEu
% 0.31/0.49 => ( descr__Cong
% 0.31/0.49 => ( dsetconstr__Cong
% 0.31/0.49 => ( subsetI1
% 0.31/0.49 => ( eqimpsubset2
% 0.31/0.49 => ( eqimpsubset1
% 0.31/0.49 => ( subsetI2
% 0.31/0.49 => ( emptysetsubset
% 0.31/0.49 => ( subsetE
% 0.31/0.49 => ( subsetE2
% 0.31/0.49 => ( notsubsetI
% 0.31/0.49 => ( notequalI1
% 0.31/0.49 => ( notequalI2
% 0.31/0.49 => ( subsetRefl
% 0.31/0.49 => ( subsetTrans
% 0.31/0.49 => ( setadjoinSub
% 0.31/0.49 => ( setadjoinSub2
% 0.31/0.49 => ( subset2powerset
% 0.31/0.49 => ( setextsub
% 0.31/0.49 => ( subsetemptysetimpeq
% 0.31/0.49 => ( powersetI1
% 0.31/0.49 => ( powersetE1
% 0.31/0.49 => ( inPowerset
% 0.31/0.49 => ( powersetsubset
% 0.31/0.49 => ( sepInPowerset
% 0.31/0.49 => ( sepSubset
% 0.31/0.49 => ( binunionIL
% 0.31/0.49 => ( upairset2IR
% 0.31/0.49 => ( binunionIR
% 0.31/0.49 => ( binunionEcases
% 0.31/0.49 => ( binunionE
% 0.31/0.49 => ( binunionLsub
% 0.31/0.49 => ( binunionRsub
% 0.31/0.49 => ( binintersectI
% 0.31/0.49 => ( binintersectSubset5
% 0.31/0.49 => ( binintersectEL
% 0.31/0.49 => ( binintersectLsub
% 0.31/0.49 => ( binintersectSubset2
% 0.31/0.49 => ( binintersectSubset3
% 0.31/0.49 => ( binintersectER
% 0.31/0.49 => ( disjointsetsI1
% 0.31/0.49 => ( binintersectRsub
% 0.31/0.49 => ( binintersectSubset4
% 0.31/0.49 => ( binintersectSubset1
% 0.31/0.49 => ( bs114d
% 0.31/0.49 => ( setminusI
% 0.31/0.49 => ( setminusEL
% 0.31/0.49 => ( setminusER
% 0.31/0.49 => ( setminusSubset2
% 0.31/0.49 => ( setminusERneg
% 0.31/0.49 => ( setminusELneg
% 0.31/0.49 => ( setminusILneg
% 0.31/0.49 => ( setminusIRneg
% 0.31/0.49 => ( setminusLsub
% 0.31/0.49 => ( setminusSubset1
% 0.31/0.49 => ( symdiffE
% 0.31/0.49 => ( symdiffI1
% 0.31/0.49 => ( symdiffI2
% 0.31/0.49 => ( symdiffIneg1
% 0.31/0.49 => ( symdiffIneg2
% 0.31/0.49 => ( secondinupair
% 0.31/0.49 => ( setukpairIL
% 0.31/0.49 => ( setukpairIR
% 0.31/0.49 => ( kpairiskpair
% 0.31/0.49 => ( kpairp
% 0.31/0.49 => ( singletonsubset
% 0.31/0.49 => ( singletoninpowerset
% 0.31/0.49 => ( singletoninpowunion
% 0.31/0.49 => ( upairset2E
% 0.31/0.49 => ( upairsubunion
% 0.31/0.49 => ( upairinpowunion
% 0.31/0.49 => ( ubforcartprodlem1
% 0.31/0.49 => ( ubforcartprodlem2
% 0.31/0.49 => ( ubforcartprodlem3
% 0.31/0.49 => ( cartprodpairin
% 0.31/0.49 => ( cartprodmempair1
% 0.31/0.49 => ( cartprodmempair
% 0.31/0.49 => ( setunionE2
% 0.31/0.49 => ( setunionsingleton1
% 0.31/0.49 => ( setunionsingleton2
% 0.31/0.49 => ( setunionsingleton
% 0.31/0.49 => ( singletonprop
% 0.31/0.49 => ( ex1E1
% 0.31/0.49 => ( ex1I
% 0.31/0.49 => ( ex1I2
% 0.31/0.49 => ( singletonsuniq
% 0.31/0.49 => ( setukpairinjL1
% 0.31/0.49 => ( kfstsingleton
% 0.31/0.49 => ( theprop
% 0.31/0.49 => ( kfstpairEq
% 0.31/0.49 => ( cartprodfstin
% 0.31/0.49 => ( setukpairinjL2
% 0.31/0.49 => ( setukpairinjL
% 0.31/0.49 => ( setukpairinjR11
% 0.31/0.49 => ( setukpairinjR12
% 0.31/0.49 => ( setukpairinjR1
% 0.31/0.49 => ( upairequniteq
% 0.31/0.49 => ( setukpairinjR2
% 0.31/0.49 => ( setukpairinjR
% 0.31/0.49 => ( ksndsingleton
% 0.31/0.49 => ( ksndpairEq
% 0.31/0.49 => ( kpairsurjEq
% 0.31/0.49 => ( cartprodsndin
% 0.31/0.49 => ( cartprodpairmemEL
% 0.31/0.49 => ( cartprodpairmemER
% 0.31/0.49 => ( cartprodmempaircEq
% 0.31/0.49 => ( cartprodfstpairEq
% 0.31/0.49 => ( cartprodsndpairEq
% 0.31/0.49 => ( cartprodpairsurjEq
% 0.31/0.49 => ( dpsetconstrI
% 0.31/0.49 => ( dpsetconstrSub
% 0.31/0.49 => ( setOfPairsIsBReln
% 0.31/0.49 => ( dpsetconstrERa
% 0.31/0.49 => ( dpsetconstrEL1
% 0.31/0.49 => ( dpsetconstrEL2
% 0.31/0.49 => ( dpsetconstrER
% 0.31/0.49 => ( funcImageSingleton
% 0.31/0.49 => ( apProp
% 0.31/0.49 => ( app
% 0.31/0.49 => ( infuncsetfunc
% 0.31/0.49 => ( ap2p
% 0.31/0.49 => ( funcinfuncset
% 0.31/0.49 => ( lamProp
% 0.31/0.49 => ( lamp
% 0.31/0.49 => ( lam2p
% 0.31/0.49 => ( brelnall1
% 0.31/0.49 => ( brelnall2
% 0.31/0.49 => ( ex1E2
% 0.31/0.49 => ( funcGraphProp1
% 0.31/0.49 => ( funcGraphProp3
% 0.31/0.49 => ( funcGraphProp2
% 0.31/0.49 => ( funcextLem
% 0.31/0.49 => ( funcGraphProp4
% 0.31/0.49 => ( subbreln
% 0.31/0.49 => ( eqbreln
% 0.31/0.49 => ( funcext
% 0.31/0.49 => ( funcext2
% 0.31/0.49 => ( ap2apEq1
% 0.31/0.49 => ( ap2apEq2
% 0.31/0.49 => ( beta1
% 0.31/0.49 => ( eta1
% 0.31/0.49 => ( lam2lamEq
% 0.31/0.49 => ( beta2
% 0.31/0.49 => ( eta2
% 0.31/0.49 => ( iffalseProp1
% 0.31/0.49 => ( iffalseProp2
% 0.31/0.49 => ( iftrueProp1
% 0.31/0.49 => ( iftrueProp2
% 0.31/0.49 => ( ifSingleton
% 0.31/0.49 => ( ifp
% 0.31/0.49 => ( theeq
% 0.31/0.49 => ( iftrue
% 0.31/0.49 => ( iffalse
% 0.31/0.49 => ( iftrueorfalse
% 0.31/0.49 => ( binintersectT_lem
% 0.31/0.49 => ( binunionT_lem
% 0.31/0.49 => ( powersetT_lem
% 0.31/0.49 => ( setminusT_lem
% 0.31/0.49 => ( complementT_lem
% 0.31/0.49 => ( setextT
% 0.31/0.49 => ( subsetTI
% 0.31/0.49 => ( powersetTI1
% 0.31/0.49 => ( powersetTE1
% 0.31/0.49 => ( complementTI1
% 0.31/0.49 => ( complementTE1
% 0.31/0.49 => ( binintersectTELcontra
% 0.31/0.49 => ( binintersectTERcontra
% 0.31/0.49 => ( contrasubsetT
% 0.31/0.49 => ( contrasubsetT1
% 0.31/0.49 => ( contrasubsetT2
% 0.31/0.49 => ( contrasubsetT3
% 0.31/0.49 => ( doubleComplementI1
% 0.31/0.49 => ( doubleComplementE1
% 0.31/0.49 => ( doubleComplementSub1
% 0.31/0.49 => ( doubleComplementSub2
% 0.31/0.49 => ( doubleComplementEq
% 0.31/0.49 => ( complementTnotintersectT
% 0.31/0.49 => ( complementImpComplementIntersect
% 0.31/0.49 => ( complementSubsetComplementIntersect
% 0.31/0.49 => ( complementInPowersetComplementIntersect
% 0.31/0.49 => ( contraSubsetComplement
% 0.31/0.49 => ( complementTcontraSubset
% 0.31/0.49 => ( binunionTILcontra
% 0.31/0.49 => ( binunionTIRcontra
% 0.31/0.49 => ( inIntersectImpInUnion
% 0.31/0.49 => ( inIntersectImpInUnion2
% 0.31/0.49 => ( inIntersectImpInIntersectUnions
% 0.31/0.49 => ( intersectInPowersetIntersectUnions
% 0.31/0.49 => ( inComplementUnionImpNotIn1
% 0.31/0.49 => ( inComplementUnionImpInComplement1
% 0.31/0.49 => ( binunionTE
% 0.31/0.49 => ( binunionTEcontra
% 0.31/0.49 => ( demorgan2a1
% 0.31/0.49 => ( complementUnionInPowersetComplement
% 0.31/0.49 => ( demorgan2a2
% 0.31/0.49 => ( demorgan1a
% 0.31/0.49 => ( demorgan1b
% 0.31/0.49 => ( demorgan1
% 0.31/0.49 => ( demorgan2a
% 0.31/0.49 => ( demorgan2b2
% 0.31/0.49 => ( demorgan2b
% 0.31/0.49 => ( demorgan2
% 0.31/0.49 => ( woz13rule0
% 0.31/0.49 => ( woz13rule1
% 0.31/0.49 => ( woz13rule2
% 0.31/0.49 => ( woz13rule3
% 0.31/0.49 => ( woz13rule4
% 0.31/0.49 => ( woz1_1
% 0.31/0.49 => ( woz1_2
% 0.31/0.49 => ( woz1_3
% 0.31/0.49 => ( woz1_4
% 0.31/0.49 => ( woz1_5
% 0.31/0.49 => ! [A: $i,R: $i] :
% 0.31/0.49 ( ( breln1 @ A @ R )
% 0.31/0.49 => ! [Xphi: $i > $o] :
% 0.31/0.49 ( ! [Xx: $i] :
% 0.31/0.49 ( ( in @ Xx @ A )
% 0.31/0.49 => ! [Xy: $i] :
% 0.31/0.49 ( ( in @ Xy @ A )
% 0.31/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.49 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.49 => ! [Xx: $i] :
% 0.31/0.49 ( ( in @ Xx @ R )
% 0.31/0.49 => ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 ------------------------
% 2.83/1.57 ---- Embedded in THF ---
% 2.83/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.83/1.57 %%% Generated on Tue Feb 24 12:33:28 EST 2026
% 2.83/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.83/1.57 %%% Logic specification used:
% 2.83/1.57 %%% thf(spec, logic, $$dhol).
% 2.83/1.57
% 2.83/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2DTF9951.p
% See solution above
% 2.83/1.57 ------------------------
% 2.99/1.60 ---- Cleaned THF ---
% 2.99/1.60 thf(in_type,type,
% 2.99/1.60 in: $i > $i > $o ).
% 2.99/1.60
% 2.99/1.60 thf(exu_type,type,
% 2.99/1.60 exu: ( $i > $o ) > $o ).
% 2.99/1.60
% 2.99/1.60 thf(exu,definition,
% 2.99/1.60 ( exu
% 2.99/1.60 = ( ^ [Xphi: $i > $o] :
% 2.99/1.60 ? [Xx: $i] :
% 2.99/1.60 ( ( Xphi @ Xx )
% 2.99/1.60 & ! [Xy: $i] :
% 2.99/1.60 ( ( Xphi @ Xy )
% 2.99/1.60 => ( Xx = Xy ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setextAx_type,type,
% 2.99/1.60 setextAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setextAx,definition,
% 2.99/1.60 ( setextAx
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 <=> ( in @ Xx @ B ) )
% 2.99/1.60 => ( A = B ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptyset_type,type,
% 2.99/1.60 emptyset: $i ).
% 2.99/1.60
% 2.99/1.60 thf(emptysetAx_type,type,
% 2.99/1.60 emptysetAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptysetAx,definition,
% 2.99/1.60 ( emptysetAx
% 2.99/1.60 = ( ! [Xx: $i] :
% 2.99/1.60 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoin_type,type,
% 2.99/1.60 setadjoin: $i > $i > $i ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinAx_type,type,
% 2.99/1.60 setadjoinAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinAx,definition,
% 2.99/1.60 ( setadjoinAx
% 2.99/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.60 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.60 <=> ( ( Xy = Xx )
% 2.99/1.60 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(powerset_type,type,
% 2.99/1.60 powerset: $i > $i ).
% 2.99/1.60
% 2.99/1.60 thf(powersetAx_type,type,
% 2.99/1.60 powersetAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(powersetAx,definition,
% 2.99/1.60 ( powersetAx
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.60 <=> ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ B )
% 2.99/1.60 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setunion_type,type,
% 2.99/1.60 setunion: $i > $i ).
% 2.99/1.60
% 2.99/1.60 thf(setunionAx_type,type,
% 2.99/1.60 setunionAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setunionAx,definition,
% 2.99/1.60 ( setunionAx
% 2.99/1.60 = ( ! [A: $i,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.60 <=> ? [B: $i] :
% 2.99/1.60 ( ( in @ Xx @ B )
% 2.99/1.60 & ( in @ B @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(omega_type,type,
% 2.99/1.60 omega: $i ).
% 2.99/1.60
% 2.99/1.60 thf(omega0Ax_type,type,
% 2.99/1.60 omega0Ax: $o ).
% 2.99/1.60
% 2.99/1.60 thf(omega0Ax,definition,
% 2.99/1.60 ( omega0Ax
% 2.99/1.60 = ( in @ emptyset @ omega ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(omegaSAx_type,type,
% 2.99/1.60 omegaSAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(omegaSAx,definition,
% 2.99/1.60 ( omegaSAx
% 2.99/1.60 = ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ omega )
% 2.99/1.60 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(omegaIndAx_type,type,
% 2.99/1.60 omegaIndAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(omegaIndAx,definition,
% 2.99/1.60 ( omegaIndAx
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ( ( ( in @ emptyset @ A )
% 2.99/1.60 & ! [Xx: $i] :
% 2.99/1.60 ( ( ( in @ Xx @ omega )
% 2.99/1.60 & ( in @ Xx @ A ) )
% 2.99/1.60 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.99/1.60 => ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ omega )
% 2.99/1.60 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(replAx_type,type,
% 2.99/1.60 replAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(replAx,definition,
% 2.99/1.60 ( replAx
% 2.99/1.60 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( exu
% 2.99/1.60 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.99/1.60 => ? [B: $i] :
% 2.99/1.60 ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ B )
% 2.99/1.60 <=> ? [Xy: $i] :
% 2.99/1.60 ( ( in @ Xy @ A )
% 2.99/1.60 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(foundationAx_type,type,
% 2.99/1.60 foundationAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(foundationAx,definition,
% 2.99/1.60 ( foundationAx
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.99/1.60 => ? [B: $i] :
% 2.99/1.60 ( ( in @ B @ A )
% 2.99/1.60 & ~ ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ B )
% 2.99/1.60 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(wellorderingAx_type,type,
% 2.99/1.60 wellorderingAx: $o ).
% 2.99/1.60
% 2.99/1.60 thf(wellorderingAx,definition,
% 2.99/1.60 ( wellorderingAx
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ? [B: $i] :
% 2.99/1.60 ( ! [C: $i] :
% 2.99/1.60 ( ( in @ C @ B )
% 2.99/1.60 => ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ C )
% 2.99/1.60 => ( in @ Xx @ A ) ) )
% 2.99/1.60 & ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( ( in @ Xx @ A )
% 2.99/1.60 & ( in @ Xy @ A ) )
% 2.99/1.60 => ( ! [C: $i] :
% 2.99/1.60 ( ( in @ C @ B )
% 2.99/1.60 => ( ( in @ Xx @ C )
% 2.99/1.60 <=> ( in @ Xy @ C ) ) )
% 2.99/1.60 => ( Xx = Xy ) ) )
% 2.99/1.60 & ! [C: $i,D: $i] :
% 2.99/1.60 ( ( ( in @ C @ B )
% 2.99/1.60 & ( in @ D @ B ) )
% 2.99/1.60 => ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ C )
% 2.99/1.60 => ( in @ Xx @ D ) )
% 2.99/1.60 | ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ D )
% 2.99/1.60 => ( in @ Xx @ C ) ) ) )
% 2.99/1.60 & ! [C: $i] :
% 2.99/1.60 ( ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ C )
% 2.99/1.60 => ( in @ Xx @ A ) )
% 2.99/1.60 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.99/1.60 => ? [D: $i,Xx: $i] :
% 2.99/1.60 ( ( in @ D @ B )
% 2.99/1.60 & ( in @ Xx @ C )
% 2.99/1.60 & ~ ? [Xy: $i] :
% 2.99/1.60 ( ( in @ Xy @ D )
% 2.99/1.60 & ( in @ Xy @ C ) )
% 2.99/1.60 & ! [E: $i] :
% 2.99/1.60 ( ( in @ E @ B )
% 2.99/1.60 => ( ! [Xy: $i] :
% 2.99/1.60 ( ( in @ Xy @ E )
% 2.99/1.60 => ( in @ Xy @ D ) )
% 2.99/1.60 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(descr_type,type,
% 2.99/1.60 descr: ( $i > $o ) > $i ).
% 2.99/1.60
% 2.99/1.60 thf(descrp_type,type,
% 2.99/1.60 descrp: $o ).
% 2.99/1.60
% 2.99/1.60 thf(descrp,definition,
% 2.99/1.60 ( descrp
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 => ( Xphi
% 2.99/1.60 @ ( descr
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstr_type,type,
% 2.99/1.60 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstrI_type,type,
% 2.99/1.60 dsetconstrI: $o ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstrI,definition,
% 2.99/1.60 ( dsetconstrI
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( ( Xphi @ Xx )
% 2.99/1.60 => ( in @ Xx
% 2.99/1.60 @ ( dsetconstr @ A
% 2.99/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstrEL_type,type,
% 2.99/1.60 dsetconstrEL: $o ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstrEL,definition,
% 2.99/1.60 ( dsetconstrEL
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx
% 2.99/1.60 @ ( dsetconstr @ A
% 2.99/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.60 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstrER_type,type,
% 2.99/1.60 dsetconstrER: $o ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstrER,definition,
% 2.99/1.60 ( dsetconstrER
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx
% 2.99/1.60 @ ( dsetconstr @ A
% 2.99/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.60 => ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exuE1_type,type,
% 2.99/1.60 exuE1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exuE1,definition,
% 2.99/1.60 ( exuE1
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 => ? [Xx: $i] :
% 2.99/1.60 ( ( Xphi @ Xx )
% 2.99/1.60 & ! [Xy: $i] :
% 2.99/1.60 ( ( Xphi @ Xy )
% 2.99/1.60 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(prop2set_type,type,
% 2.99/1.60 prop2set: $o > $i ).
% 2.99/1.60
% 2.99/1.60 thf(prop2setE_type,type,
% 2.99/1.60 prop2setE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(prop2setE,definition,
% 2.99/1.60 ( prop2setE
% 2.99/1.60 = ( ! [Xphi: $o,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.99/1.60 => Xphi ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptysetE_type,type,
% 2.99/1.60 emptysetE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptysetE,definition,
% 2.99/1.60 ( emptysetE
% 2.99/1.60 = ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ emptyset )
% 2.99/1.60 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptysetimpfalse_type,type,
% 2.99/1.60 emptysetimpfalse: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptysetimpfalse,definition,
% 2.99/1.60 ( emptysetimpfalse
% 2.99/1.60 = ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ emptyset )
% 2.99/1.60 => $false ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(notinemptyset_type,type,
% 2.99/1.60 notinemptyset: $o ).
% 2.99/1.60
% 2.99/1.60 thf(notinemptyset,definition,
% 2.99/1.60 ( notinemptyset
% 2.99/1.60 = ( ! [Xx: $i] :
% 2.99/1.60 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exuE3e_type,type,
% 2.99/1.60 exuE3e: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exuE3e,definition,
% 2.99/1.60 ( exuE3e
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setext_type,type,
% 2.99/1.60 setext: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setext,definition,
% 2.99/1.60 ( setext
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( in @ Xx @ B ) )
% 2.99/1.60 => ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ B )
% 2.99/1.60 => ( in @ Xx @ A ) )
% 2.99/1.60 => ( A = B ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptyI_type,type,
% 2.99/1.60 emptyI: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptyI,definition,
% 2.99/1.60 ( emptyI
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ~ ( in @ Xx @ A )
% 2.99/1.60 => ( A = emptyset ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(noeltsimpempty_type,type,
% 2.99/1.60 noeltsimpempty: $o ).
% 2.99/1.60
% 2.99/1.60 thf(noeltsimpempty,definition,
% 2.99/1.60 ( noeltsimpempty
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ~ ( in @ Xx @ A )
% 2.99/1.60 => ( A = emptyset ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setbeta_type,type,
% 2.99/1.60 setbeta: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setbeta,definition,
% 2.99/1.60 ( setbeta
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( ( in @ Xx
% 2.99/1.60 @ ( dsetconstr @ A
% 2.99/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.60 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(nonempty_type,type,
% 2.99/1.60 nonempty: $i > $o ).
% 2.99/1.60
% 2.99/1.60 thf(nonempty,definition,
% 2.99/1.60 ( nonempty
% 2.99/1.60 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(nonemptyE1_type,type,
% 2.99/1.60 nonemptyE1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(nonemptyE1,definition,
% 2.99/1.60 ( nonemptyE1
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ( ( nonempty @ A )
% 2.99/1.60 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(nonemptyI_type,type,
% 2.99/1.60 nonemptyI: $o ).
% 2.99/1.60
% 2.99/1.60 thf(nonemptyI,definition,
% 2.99/1.60 ( nonemptyI
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( ( Xphi @ Xx )
% 2.99/1.60 => ( nonempty
% 2.99/1.60 @ ( dsetconstr @ A
% 2.99/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(nonemptyI1_type,type,
% 2.99/1.60 nonemptyI1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(nonemptyI1,definition,
% 2.99/1.60 ( nonemptyI1
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.99/1.60 => ( nonempty @ A ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinIL_type,type,
% 2.99/1.60 setadjoinIL: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinIL,definition,
% 2.99/1.60 ( setadjoinIL
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptyinunitempty_type,type,
% 2.99/1.60 emptyinunitempty: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptyinunitempty,definition,
% 2.99/1.60 ( emptyinunitempty
% 2.99/1.60 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinIR_type,type,
% 2.99/1.60 setadjoinIR: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinIR,definition,
% 2.99/1.60 ( setadjoinIR
% 2.99/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.60 ( ( in @ Xy @ A )
% 2.99/1.60 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinE_type,type,
% 2.99/1.60 setadjoinE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinE,definition,
% 2.99/1.60 ( setadjoinE
% 2.99/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.60 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.60 => ! [Xphi: $o] :
% 2.99/1.60 ( ( ( Xy = Xx )
% 2.99/1.60 => Xphi )
% 2.99/1.60 => ( ( ( in @ Xy @ A )
% 2.99/1.60 => Xphi )
% 2.99/1.60 => Xphi ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinOr_type,type,
% 2.99/1.60 setadjoinOr: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoinOr,definition,
% 2.99/1.60 ( setadjoinOr
% 2.99/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.60 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.60 => ( ( Xy = Xx )
% 2.99/1.60 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setoftrueEq_type,type,
% 2.99/1.60 setoftrueEq: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setoftrueEq,definition,
% 2.99/1.60 ( setoftrueEq
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ( ( dsetconstr @ A
% 2.99/1.60 @ ^ [Xx: $i] : $true )
% 2.99/1.60 = A ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(powersetI_type,type,
% 2.99/1.60 powersetI: $o ).
% 2.99/1.60
% 2.99/1.60 thf(powersetI,definition,
% 2.99/1.60 ( powersetI
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ B )
% 2.99/1.60 => ( in @ Xx @ A ) )
% 2.99/1.60 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptyinPowerset_type,type,
% 2.99/1.60 emptyinPowerset: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptyinPowerset,definition,
% 2.99/1.60 ( emptyinPowerset
% 2.99/1.60 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptyInPowerset_type,type,
% 2.99/1.60 emptyInPowerset: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptyInPowerset,definition,
% 2.99/1.60 ( emptyInPowerset
% 2.99/1.60 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(powersetE_type,type,
% 2.99/1.60 powersetE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(powersetE,definition,
% 2.99/1.60 ( powersetE
% 2.99/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.60 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.60 => ( ( in @ Xx @ B )
% 2.99/1.60 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setunionI_type,type,
% 2.99/1.60 setunionI: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setunionI,definition,
% 2.99/1.60 ( setunionI
% 2.99/1.60 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.99/1.60 ( ( in @ Xx @ B )
% 2.99/1.60 => ( ( in @ B @ A )
% 2.99/1.60 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setunionE_type,type,
% 2.99/1.60 setunionE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setunionE,definition,
% 2.99/1.60 ( setunionE
% 2.99/1.60 = ( ! [A: $i,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.60 => ! [Xphi: $o] :
% 2.99/1.60 ( ! [B: $i] :
% 2.99/1.60 ( ( in @ Xx @ B )
% 2.99/1.60 => ( ( in @ B @ A )
% 2.99/1.60 => Xphi ) )
% 2.99/1.60 => Xphi ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(subPowSU_type,type,
% 2.99/1.60 subPowSU: $o ).
% 2.99/1.60
% 2.99/1.60 thf(subPowSU,definition,
% 2.99/1.60 ( subPowSU
% 2.99/1.60 = ( ! [A: $i,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exuE2_type,type,
% 2.99/1.60 exuE2: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exuE2,definition,
% 2.99/1.60 ( exuE2
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 => ? [Xx: $i] :
% 2.99/1.60 ! [Xy: $i] :
% 2.99/1.60 ( ( Xphi @ Xy )
% 2.99/1.60 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(nonemptyImpWitness_type,type,
% 2.99/1.60 nonemptyImpWitness: $o ).
% 2.99/1.60
% 2.99/1.60 thf(nonemptyImpWitness,definition,
% 2.99/1.60 ( nonemptyImpWitness
% 2.99/1.60 = ( ! [A: $i] :
% 2.99/1.60 ( ( nonempty @ A )
% 2.99/1.60 => ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 & $true ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(uniqinunit_type,type,
% 2.99/1.60 uniqinunit: $o ).
% 2.99/1.60
% 2.99/1.60 thf(uniqinunit,definition,
% 2.99/1.60 ( uniqinunit
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.60 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(notinsingleton_type,type,
% 2.99/1.60 notinsingleton: $o ).
% 2.99/1.60
% 2.99/1.60 thf(notinsingleton,definition,
% 2.99/1.60 ( notinsingleton
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xx != Xy )
% 2.99/1.60 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(eqinunit_type,type,
% 2.99/1.60 eqinunit: $o ).
% 2.99/1.60
% 2.99/1.60 thf(eqinunit,definition,
% 2.99/1.60 ( eqinunit
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xx = Xy )
% 2.99/1.60 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(singletonsswitch_type,type,
% 2.99/1.60 singletonsswitch: $o ).
% 2.99/1.60
% 2.99/1.60 thf(singletonsswitch,definition,
% 2.99/1.60 ( singletonsswitch
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.60 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(upairsetE_type,type,
% 2.99/1.60 upairsetE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(upairsetE,definition,
% 2.99/1.60 ( upairsetE
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.60 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.99/1.60 => ( ( Xz = Xx )
% 2.99/1.60 | ( Xz = Xy ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(upairsetIL_type,type,
% 2.99/1.60 upairsetIL: $o ).
% 2.99/1.60
% 2.99/1.60 thf(upairsetIL,definition,
% 2.99/1.60 ( upairsetIL
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(upairsetIR_type,type,
% 2.99/1.60 upairsetIR: $o ).
% 2.99/1.60
% 2.99/1.60 thf(upairsetIR,definition,
% 2.99/1.60 ( upairsetIR
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptyE1_type,type,
% 2.99/1.60 emptyE1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptyE1,definition,
% 2.99/1.60 ( emptyE1
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.60 ( ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 & ( Xphi @ Xx ) )
% 2.99/1.60 => ( ( ( dsetconstr @ A
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 = emptyset )
% 2.99/1.60 => $false ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(vacuousDall_type,type,
% 2.99/1.60 vacuousDall: $o ).
% 2.99/1.60
% 2.99/1.60 thf(vacuousDall,definition,
% 2.99/1.60 ( vacuousDall
% 2.99/1.60 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ emptyset )
% 2.99/1.60 => ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(quantDeMorgan1_type,type,
% 2.99/1.60 quantDeMorgan1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(quantDeMorgan1,definition,
% 2.99/1.60 ( quantDeMorgan1
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.60 ( ~ ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( Xphi @ Xx ) )
% 2.99/1.60 => ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(quantDeMorgan2_type,type,
% 2.99/1.60 quantDeMorgan2: $o ).
% 2.99/1.60
% 2.99/1.60 thf(quantDeMorgan2,definition,
% 2.99/1.60 ( quantDeMorgan2
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ~ ( Xphi @ Xx ) )
% 2.99/1.60 => ~ ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(quantDeMorgan3_type,type,
% 2.99/1.60 quantDeMorgan3: $o ).
% 2.99/1.60
% 2.99/1.60 thf(quantDeMorgan3,definition,
% 2.99/1.60 ( quantDeMorgan3
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.60 ( ~ ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 & ( Xphi @ Xx ) )
% 2.99/1.60 => ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(quantDeMorgan4_type,type,
% 2.99/1.60 quantDeMorgan4: $o ).
% 2.99/1.60
% 2.99/1.60 thf(quantDeMorgan4,definition,
% 2.99/1.60 ( quantDeMorgan4
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.60 ( ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 & ~ ( Xphi @ Xx ) )
% 2.99/1.60 => ~ ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(prop2setI_type,type,
% 2.99/1.60 prop2setI: $o ).
% 2.99/1.60
% 2.99/1.60 thf(prop2setI,definition,
% 2.99/1.60 ( prop2setI
% 2.99/1.60 = ( ! [Xphi: $o] :
% 2.99/1.60 ( Xphi
% 2.99/1.60 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(set2prop_type,type,
% 2.99/1.60 set2prop: $i > $o ).
% 2.99/1.60
% 2.99/1.60 thf(prop2set2propI_type,type,
% 2.99/1.60 prop2set2propI: $o ).
% 2.99/1.60
% 2.99/1.60 thf(prop2set2propI,definition,
% 2.99/1.60 ( prop2set2propI
% 2.99/1.60 = ( ! [Xphi: $o] :
% 2.99/1.60 ( Xphi
% 2.99/1.60 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(notdexE_type,type,
% 2.99/1.60 notdexE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(notdexE,definition,
% 2.99/1.60 ( notdexE
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.60 ( ~ ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 & ( Xphi @ Xx ) )
% 2.99/1.60 => ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(notdallE_type,type,
% 2.99/1.60 notdallE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(notdallE,definition,
% 2.99/1.60 ( notdallE
% 2.99/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.60 ( ~ ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( Xphi @ Xx ) )
% 2.99/1.60 => ? [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exuI1_type,type,
% 2.99/1.60 exuI1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exuI1,definition,
% 2.99/1.60 ( exuI1
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ? [Xx: $i] :
% 2.99/1.60 ( ( Xphi @ Xx )
% 2.99/1.60 & ! [Xy: $i] :
% 2.99/1.60 ( ( Xphi @ Xy )
% 2.99/1.60 => ( Xx = Xy ) ) )
% 2.99/1.60 => ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exuI3_type,type,
% 2.99/1.60 exuI3: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exuI3,definition,
% 2.99/1.60 ( exuI3
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.99/1.60 => ( ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xphi @ Xx )
% 2.99/1.60 => ( ( Xphi @ Xy )
% 2.99/1.60 => ( Xx = Xy ) ) )
% 2.99/1.60 => ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exuI2_type,type,
% 2.99/1.60 exuI2: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exuI2,definition,
% 2.99/1.60 ( exuI2
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ? [Xx: $i] :
% 2.99/1.60 ! [Xy: $i] :
% 2.99/1.60 ( ( Xphi @ Xy )
% 2.99/1.60 <=> ( Xy = Xx ) )
% 2.99/1.60 => ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(inCongP_type,type,
% 2.99/1.60 inCongP: $o ).
% 2.99/1.60
% 2.99/1.60 thf(inCongP,definition,
% 2.99/1.60 ( inCongP
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ( A = B )
% 2.99/1.60 => ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xx = Xy )
% 2.99/1.60 => ( ( in @ Xx @ A )
% 2.99/1.60 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(in__Cong_type,type,
% 2.99/1.60 in__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(in__Cong,definition,
% 2.99/1.60 ( in__Cong
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ( A = B )
% 2.99/1.60 => ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xx = Xy )
% 2.99/1.60 => ( ( in @ Xx @ A )
% 2.99/1.60 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exuE3u_type,type,
% 2.99/1.60 exuE3u: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exuE3u,definition,
% 2.99/1.60 ( exuE3u
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 => ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xphi @ Xx )
% 2.99/1.60 => ( ( Xphi @ Xy )
% 2.99/1.60 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exu__Cong_type,type,
% 2.99/1.60 exu__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exu__Cong,definition,
% 2.99/1.60 ( exu__Cong
% 2.99/1.60 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.60 ( ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xx = Xy )
% 2.99/1.60 => ( ( Xphi @ Xx )
% 2.99/1.60 <=> ( Xpsi @ Xy ) ) )
% 2.99/1.60 => ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 <=> ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptyset__Cong_type,type,
% 2.99/1.60 emptyset__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptyset__Cong,definition,
% 2.99/1.60 ( emptyset__Cong
% 2.99/1.60 = ( emptyset = emptyset ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoin__Cong_type,type,
% 2.99/1.60 setadjoin__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setadjoin__Cong,definition,
% 2.99/1.60 ( setadjoin__Cong
% 2.99/1.60 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xx = Xy )
% 2.99/1.60 => ! [Xz: $i,Xu: $i] :
% 2.99/1.60 ( ( Xz = Xu )
% 2.99/1.60 => ( ( setadjoin @ Xx @ Xz )
% 2.99/1.60 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(powerset__Cong_type,type,
% 2.99/1.60 powerset__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(powerset__Cong,definition,
% 2.99/1.60 ( powerset__Cong
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ( A = B )
% 2.99/1.60 => ( ( powerset @ A )
% 2.99/1.60 = ( powerset @ B ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(setunion__Cong_type,type,
% 2.99/1.60 setunion__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(setunion__Cong,definition,
% 2.99/1.60 ( setunion__Cong
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ( A = B )
% 2.99/1.60 => ( ( setunion @ A )
% 2.99/1.60 = ( setunion @ B ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(omega__Cong_type,type,
% 2.99/1.60 omega__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(omega__Cong,definition,
% 2.99/1.60 ( omega__Cong
% 2.99/1.60 = ( omega = omega ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(exuEu_type,type,
% 2.99/1.60 exuEu: $o ).
% 2.99/1.60
% 2.99/1.60 thf(exuEu,definition,
% 2.99/1.60 ( exuEu
% 2.99/1.60 = ( ! [Xphi: $i > $o] :
% 2.99/1.60 ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 => ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xphi @ Xx )
% 2.99/1.60 => ( ( Xphi @ Xy )
% 2.99/1.60 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(descr__Cong_type,type,
% 2.99/1.60 descr__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(descr__Cong,definition,
% 2.99/1.60 ( descr__Cong
% 2.99/1.60 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.60 ( ! [Xx: $i,Xy: $i] :
% 2.99/1.60 ( ( Xx = Xy )
% 2.99/1.60 => ( ( Xphi @ Xx )
% 2.99/1.60 <=> ( Xpsi @ Xy ) ) )
% 2.99/1.60 => ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 => ( ( exu
% 2.99/1.60 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.99/1.60 => ( ( descr
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 = ( descr
% 2.99/1.60 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstr__Cong_type,type,
% 2.99/1.60 dsetconstr__Cong: $o ).
% 2.99/1.60
% 2.99/1.60 thf(dsetconstr__Cong,definition,
% 2.99/1.60 ( dsetconstr__Cong
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ( A = B )
% 2.99/1.60 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ! [Xy: $i] :
% 2.99/1.60 ( ( in @ Xy @ B )
% 2.99/1.60 => ( ( Xx = Xy )
% 2.99/1.60 => ( ( Xphi @ Xx )
% 2.99/1.60 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.99/1.60 => ( ( dsetconstr @ A
% 2.99/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.60 = ( dsetconstr @ B
% 2.99/1.60 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(subset_type,type,
% 2.99/1.60 subset: $i > $i > $o ).
% 2.99/1.60
% 2.99/1.60 thf(disjoint_type,type,
% 2.99/1.60 disjoint: $i > $i > $o ).
% 2.99/1.60
% 2.99/1.60 thf(setsmeet_type,type,
% 2.99/1.60 setsmeet: $i > $i > $o ).
% 2.99/1.60
% 2.99/1.60 thf(subsetI1_type,type,
% 2.99/1.60 subsetI1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(subsetI1,definition,
% 2.99/1.60 ( subsetI1
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( in @ Xx @ B ) )
% 2.99/1.60 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(eqimpsubset2_type,type,
% 2.99/1.60 eqimpsubset2: $o ).
% 2.99/1.60
% 2.99/1.60 thf(eqimpsubset2,definition,
% 2.99/1.60 ( eqimpsubset2
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ( A = B )
% 2.99/1.60 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(eqimpsubset1_type,type,
% 2.99/1.60 eqimpsubset1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(eqimpsubset1,definition,
% 2.99/1.60 ( eqimpsubset1
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ( A = B )
% 2.99/1.60 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(subsetI2_type,type,
% 2.99/1.60 subsetI2: $o ).
% 2.99/1.60
% 2.99/1.60 thf(subsetI2,definition,
% 2.99/1.60 ( subsetI2
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ! [Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( in @ Xx @ B ) )
% 2.99/1.60 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(emptysetsubset_type,type,
% 2.99/1.60 emptysetsubset: $o ).
% 2.99/1.60
% 2.99/1.60 thf(emptysetsubset,definition,
% 2.99/1.60 ( emptysetsubset
% 2.99/1.60 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(subsetE_type,type,
% 2.99/1.60 subsetE: $o ).
% 2.99/1.60
% 2.99/1.60 thf(subsetE,definition,
% 2.99/1.60 ( subsetE
% 2.99/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.60 ( ( subset @ A @ B )
% 2.99/1.60 => ( ( in @ Xx @ A )
% 2.99/1.60 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(subsetE2_type,type,
% 2.99/1.60 subsetE2: $o ).
% 2.99/1.60
% 2.99/1.60 thf(subsetE2,definition,
% 2.99/1.60 ( subsetE2
% 2.99/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.60 ( ( subset @ A @ B )
% 2.99/1.60 => ( ~ ( in @ Xx @ B )
% 2.99/1.60 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(notsubsetI_type,type,
% 2.99/1.60 notsubsetI: $o ).
% 2.99/1.60
% 2.99/1.60 thf(notsubsetI,definition,
% 2.99/1.60 ( notsubsetI
% 2.99/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( ~ ( in @ Xx @ B )
% 2.99/1.60 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(notequalI1_type,type,
% 2.99/1.60 notequalI1: $o ).
% 2.99/1.60
% 2.99/1.60 thf(notequalI1,definition,
% 2.99/1.60 ( notequalI1
% 2.99/1.60 = ( ! [A: $i,B: $i] :
% 2.99/1.60 ( ~ ( subset @ A @ B )
% 2.99/1.60 => ( A != B ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(notequalI2_type,type,
% 2.99/1.60 notequalI2: $o ).
% 2.99/1.60
% 2.99/1.60 thf(notequalI2,definition,
% 2.99/1.60 ( notequalI2
% 2.99/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.60 ( ( in @ Xx @ A )
% 2.99/1.60 => ( ~ ( in @ Xx @ B )
% 2.99/1.60 => ( A != B ) ) ) ) ) ).
% 2.99/1.60
% 2.99/1.60 thf(subsetRefl_type,type,
% 2.99/1.60 subsetRefl: $o ).
% 2.99/1.60
% 2.99/1.60 thf(subsetRefl,definition,
% 2.99/1.60 ( subsetRefl
% 2.99/1.60 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(subsetTrans_type,type,
% 2.99/1.61 subsetTrans: $o ).
% 2.99/1.61
% 2.99/1.61 thf(subsetTrans,definition,
% 2.99/1.61 ( subsetTrans
% 2.99/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.61 ( ( subset @ A @ B )
% 2.99/1.61 => ( ( subset @ B @ C )
% 2.99/1.61 => ( subset @ A @ C ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setadjoinSub_type,type,
% 2.99/1.61 setadjoinSub: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setadjoinSub,definition,
% 2.99/1.61 ( setadjoinSub
% 2.99/1.61 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setadjoinSub2_type,type,
% 2.99/1.61 setadjoinSub2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setadjoinSub2,definition,
% 2.99/1.61 ( setadjoinSub2
% 2.99/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.99/1.61 ( ( subset @ A @ B )
% 2.99/1.61 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(subset2powerset_type,type,
% 2.99/1.61 subset2powerset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(subset2powerset,definition,
% 2.99/1.61 ( subset2powerset
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( subset @ A @ B )
% 2.99/1.61 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setextsub_type,type,
% 2.99/1.61 setextsub: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setextsub,definition,
% 2.99/1.61 ( setextsub
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( subset @ A @ B )
% 2.99/1.61 => ( ( subset @ B @ A )
% 2.99/1.61 => ( A = B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(subsetemptysetimpeq_type,type,
% 2.99/1.61 subsetemptysetimpeq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(subsetemptysetimpeq,definition,
% 2.99/1.61 ( subsetemptysetimpeq
% 2.99/1.61 = ( ! [A: $i] :
% 2.99/1.61 ( ( subset @ A @ emptyset )
% 2.99/1.61 => ( A = emptyset ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(powersetI1_type,type,
% 2.99/1.61 powersetI1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(powersetI1,definition,
% 2.99/1.61 ( powersetI1
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( subset @ B @ A )
% 2.99/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(powersetE1_type,type,
% 2.99/1.61 powersetE1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(powersetE1,definition,
% 2.99/1.61 ( powersetE1
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.61 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(inPowerset_type,type,
% 2.99/1.61 inPowerset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(inPowerset,definition,
% 2.99/1.61 ( inPowerset
% 2.99/1.61 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(powersetsubset_type,type,
% 2.99/1.61 powersetsubset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(powersetsubset,definition,
% 2.99/1.61 ( powersetsubset
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( subset @ A @ B )
% 2.99/1.61 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(sepInPowerset_type,type,
% 2.99/1.61 sepInPowerset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(sepInPowerset,definition,
% 2.99/1.61 ( sepInPowerset
% 2.99/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.61 ( in
% 2.99/1.61 @ ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.61 @ ( powerset @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(sepSubset_type,type,
% 2.99/1.61 sepSubset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(sepSubset,definition,
% 2.99/1.61 ( sepSubset
% 2.99/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.61 ( subset
% 2.99/1.61 @ ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.61 @ A ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunion_type,type,
% 2.99/1.61 binunion: $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(binunionIL_type,type,
% 2.99/1.61 binunionIL: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionIL,definition,
% 2.99/1.61 ( binunionIL
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(upairset2IR_type,type,
% 2.99/1.61 upairset2IR: $o ).
% 2.99/1.61
% 2.99/1.61 thf(upairset2IR,definition,
% 2.99/1.61 ( upairset2IR
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionIR_type,type,
% 2.99/1.61 binunionIR: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionIR,definition,
% 2.99/1.61 ( binunionIR
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ B )
% 2.99/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionEcases_type,type,
% 2.99/1.61 binunionEcases: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionEcases,definition,
% 2.99/1.61 ( binunionEcases
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.99/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.99/1.61 => ( ( ( in @ Xx @ A )
% 2.99/1.61 => Xphi )
% 2.99/1.61 => ( ( ( in @ Xx @ B )
% 2.99/1.61 => Xphi )
% 2.99/1.61 => Xphi ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionE_type,type,
% 2.99/1.61 binunionE: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionE,definition,
% 2.99/1.61 ( binunionE
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.99/1.61 => ( ( in @ Xx @ A )
% 2.99/1.61 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionLsub_type,type,
% 2.99/1.61 binunionLsub: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionLsub,definition,
% 2.99/1.61 ( binunionLsub
% 2.99/1.61 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionRsub_type,type,
% 2.99/1.61 binunionRsub: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionRsub,definition,
% 2.99/1.61 ( binunionRsub
% 2.99/1.61 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersect_type,type,
% 2.99/1.61 binintersect: $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectI_type,type,
% 2.99/1.61 binintersectI: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectI,definition,
% 2.99/1.61 ( binintersectI
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ B )
% 2.99/1.61 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset5_type,type,
% 2.99/1.61 binintersectSubset5: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset5,definition,
% 2.99/1.61 ( binintersectSubset5
% 2.99/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.61 ( ( subset @ C @ A )
% 2.99/1.61 => ( ( subset @ C @ B )
% 2.99/1.61 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectEL_type,type,
% 2.99/1.61 binintersectEL: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectEL,definition,
% 2.99/1.61 ( binintersectEL
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.99/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectLsub_type,type,
% 2.99/1.61 binintersectLsub: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectLsub,definition,
% 2.99/1.61 ( binintersectLsub
% 2.99/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset2_type,type,
% 2.99/1.61 binintersectSubset2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset2,definition,
% 2.99/1.61 ( binintersectSubset2
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( subset @ A @ B )
% 2.99/1.61 => ( ( binintersect @ A @ B )
% 2.99/1.61 = A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset3_type,type,
% 2.99/1.61 binintersectSubset3: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset3,definition,
% 2.99/1.61 ( binintersectSubset3
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( ( binintersect @ A @ B )
% 2.99/1.61 = B )
% 2.99/1.61 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectER_type,type,
% 2.99/1.61 binintersectER: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectER,definition,
% 2.99/1.61 ( binintersectER
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.99/1.61 => ( in @ Xx @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(disjointsetsI1_type,type,
% 2.99/1.61 disjointsetsI1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(disjointsetsI1,definition,
% 2.99/1.61 ( disjointsetsI1
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ~ ? [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 & ( in @ Xx @ B ) )
% 2.99/1.61 => ( ( binintersect @ A @ B )
% 2.99/1.61 = emptyset ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectRsub_type,type,
% 2.99/1.61 binintersectRsub: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectRsub,definition,
% 2.99/1.61 ( binintersectRsub
% 2.99/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset4_type,type,
% 2.99/1.61 binintersectSubset4: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset4,definition,
% 2.99/1.61 ( binintersectSubset4
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( subset @ B @ A )
% 2.99/1.61 => ( ( binintersect @ A @ B )
% 2.99/1.61 = B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset1_type,type,
% 2.99/1.61 binintersectSubset1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectSubset1,definition,
% 2.99/1.61 ( binintersectSubset1
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( ( binintersect @ A @ B )
% 2.99/1.61 = A )
% 2.99/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(bs114d_type,type,
% 2.99/1.61 bs114d: $o ).
% 2.99/1.61
% 2.99/1.61 thf(bs114d,definition,
% 2.99/1.61 ( bs114d
% 2.99/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.61 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.99/1.61 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(regular_type,type,
% 2.99/1.61 regular: $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminus_type,type,
% 2.99/1.61 setminus: $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(setminusI_type,type,
% 2.99/1.61 setminusI: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusI,definition,
% 2.99/1.61 ( setminusI
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ B )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusEL_type,type,
% 2.99/1.61 setminusEL: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusEL,definition,
% 2.99/1.61 ( setminusEL
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusER_type,type,
% 2.99/1.61 setminusER: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusER,definition,
% 2.99/1.61 ( setminusER
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.61 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusSubset2_type,type,
% 2.99/1.61 setminusSubset2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusSubset2,definition,
% 2.99/1.61 ( setminusSubset2
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( subset @ A @ B )
% 2.99/1.61 => ( ( setminus @ A @ B )
% 2.99/1.61 = emptyset ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusERneg_type,type,
% 2.99/1.61 setminusERneg: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusERneg,definition,
% 2.99/1.61 ( setminusERneg
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.61 => ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusELneg_type,type,
% 2.99/1.61 setminusELneg: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusELneg,definition,
% 2.99/1.61 ( setminusELneg
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.61 => ( ~ ( in @ Xx @ B )
% 2.99/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusILneg_type,type,
% 2.99/1.61 setminusILneg: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusILneg,definition,
% 2.99/1.61 ( setminusILneg
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ~ ( in @ Xx @ A )
% 2.99/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusIRneg_type,type,
% 2.99/1.61 setminusIRneg: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusIRneg,definition,
% 2.99/1.61 ( setminusIRneg
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ B )
% 2.99/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusLsub_type,type,
% 2.99/1.61 setminusLsub: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusLsub,definition,
% 2.99/1.61 ( setminusLsub
% 2.99/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusSubset1_type,type,
% 2.99/1.61 setminusSubset1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusSubset1,definition,
% 2.99/1.61 ( setminusSubset1
% 2.99/1.61 = ( ! [A: $i,B: $i] :
% 2.99/1.61 ( ( ( setminus @ A @ B )
% 2.99/1.61 = emptyset )
% 2.99/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(symdiff_type,type,
% 2.99/1.61 symdiff: $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffE_type,type,
% 2.99/1.61 symdiffE: $o ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffE,definition,
% 2.99/1.61 ( symdiffE
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.99/1.61 => ! [Xphi: $o] :
% 2.99/1.61 ( ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ B )
% 2.99/1.61 => Xphi ) )
% 2.99/1.61 => ( ( ~ ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ B )
% 2.99/1.61 => Xphi ) )
% 2.99/1.61 => Xphi ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffI1_type,type,
% 2.99/1.61 symdiffI1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffI1,definition,
% 2.99/1.61 ( symdiffI1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ B )
% 2.99/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffI2_type,type,
% 2.99/1.61 symdiffI2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffI2,definition,
% 2.99/1.61 ( symdiffI2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ~ ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ B )
% 2.99/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffIneg1_type,type,
% 2.99/1.61 symdiffIneg1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffIneg1,definition,
% 2.99/1.61 ( symdiffIneg1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ B )
% 2.99/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffIneg2_type,type,
% 2.99/1.61 symdiffIneg2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(symdiffIneg2,definition,
% 2.99/1.61 ( symdiffIneg2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ~ ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ B )
% 2.99/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(iskpair_type,type,
% 2.99/1.61 iskpair: $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(secondinupair_type,type,
% 2.99/1.61 secondinupair: $o ).
% 2.99/1.61
% 2.99/1.61 thf(secondinupair,definition,
% 2.99/1.61 ( secondinupair
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairIL_type,type,
% 2.99/1.61 setukpairIL: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairIL,definition,
% 2.99/1.61 ( setukpairIL
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairIR_type,type,
% 2.99/1.61 setukpairIR: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairIR,definition,
% 2.99/1.61 ( setukpairIR
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(kpairiskpair_type,type,
% 2.99/1.61 kpairiskpair: $o ).
% 2.99/1.61
% 2.99/1.61 thf(kpairiskpair,definition,
% 2.99/1.61 ( kpairiskpair
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(kpair_type,type,
% 2.99/1.61 kpair: $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(kpairp_type,type,
% 2.99/1.61 kpairp: $o ).
% 2.99/1.61
% 2.99/1.61 thf(kpairp,definition,
% 2.99/1.61 ( kpairp
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprod_type,type,
% 2.99/1.61 cartprod: $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(singletonsubset_type,type,
% 2.99/1.61 singletonsubset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(singletonsubset,definition,
% 2.99/1.61 ( singletonsubset
% 2.99/1.61 = ( ! [A: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(singletoninpowerset_type,type,
% 2.99/1.61 singletoninpowerset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(singletoninpowerset,definition,
% 2.99/1.61 ( singletoninpowerset
% 2.99/1.61 = ( ! [A: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(singletoninpowunion_type,type,
% 2.99/1.61 singletoninpowunion: $o ).
% 2.99/1.61
% 2.99/1.61 thf(singletoninpowunion,definition,
% 2.99/1.61 ( singletoninpowunion
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(upairset2E_type,type,
% 2.99/1.61 upairset2E: $o ).
% 2.99/1.61
% 2.99/1.61 thf(upairset2E,definition,
% 2.99/1.61 ( upairset2E
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.99/1.61 => ( ( Xz = Xx )
% 2.99/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(upairsubunion_type,type,
% 2.99/1.61 upairsubunion: $o ).
% 2.99/1.61
% 2.99/1.61 thf(upairsubunion,definition,
% 2.99/1.61 ( upairsubunion
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(upairinpowunion_type,type,
% 2.99/1.61 upairinpowunion: $o ).
% 2.99/1.61
% 2.99/1.61 thf(upairinpowunion,definition,
% 2.99/1.61 ( upairinpowunion
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ubforcartprodlem1_type,type,
% 2.99/1.61 ubforcartprodlem1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ubforcartprodlem1,definition,
% 2.99/1.61 ( ubforcartprodlem1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ubforcartprodlem2_type,type,
% 2.99/1.61 ubforcartprodlem2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ubforcartprodlem2,definition,
% 2.99/1.61 ( ubforcartprodlem2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ubforcartprodlem3_type,type,
% 2.99/1.61 ubforcartprodlem3: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ubforcartprodlem3,definition,
% 2.99/1.61 ( ubforcartprodlem3
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodpairin_type,type,
% 2.99/1.61 cartprodpairin: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodpairin,definition,
% 2.99/1.61 ( cartprodpairin
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodmempair1_type,type,
% 2.99/1.61 cartprodmempair1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodmempair1,definition,
% 2.99/1.61 ( cartprodmempair1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.61 => ? [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 & ? [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 & ( Xu
% 2.99/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodmempair_type,type,
% 2.99/1.61 cartprodmempair: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodmempair,definition,
% 2.99/1.61 ( cartprodmempair
% 2.99/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.61 => ( iskpair @ Xu ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setunionE2_type,type,
% 2.99/1.61 setunionE2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setunionE2,definition,
% 2.99/1.61 ( setunionE2
% 2.99/1.61 = ( ! [A: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.61 => ? [X: $i] :
% 2.99/1.61 ( ( in @ X @ A )
% 2.99/1.61 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setunionsingleton1_type,type,
% 2.99/1.61 setunionsingleton1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setunionsingleton1,definition,
% 2.99/1.61 ( setunionsingleton1
% 2.99/1.61 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setunionsingleton2_type,type,
% 2.99/1.61 setunionsingleton2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setunionsingleton2,definition,
% 2.99/1.61 ( setunionsingleton2
% 2.99/1.61 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setunionsingleton_type,type,
% 2.99/1.61 setunionsingleton: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setunionsingleton,definition,
% 2.99/1.61 ( setunionsingleton
% 2.99/1.61 = ( ! [Xx: $i] :
% 2.99/1.61 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.99/1.61 = Xx ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(singleton_type,type,
% 2.99/1.61 singleton: $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(singletonprop_type,type,
% 2.99/1.61 singletonprop: $o ).
% 2.99/1.61
% 2.99/1.61 thf(singletonprop,definition,
% 2.99/1.61 ( singletonprop
% 2.99/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( ( Xphi @ Xx )
% 2.99/1.61 => ( ( Xphi @ Xy )
% 2.99/1.61 => ( Xx = Xy ) ) ) ) )
% 2.99/1.61 => ( ? [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 & ( Xphi @ Xx ) )
% 2.99/1.61 => ( singleton
% 2.99/1.61 @ ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ex1_type,type,
% 2.99/1.61 ex1: $i > ( $i > $o ) > $o ).
% 2.99/1.61
% 2.99/1.61 thf(ex1,definition,
% 2.99/1.61 ( ex1
% 2.99/1.61 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.99/1.61 ( singleton
% 2.99/1.61 @ ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ex1E1_type,type,
% 2.99/1.61 ex1E1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ex1E1,definition,
% 2.99/1.61 ( ex1E1
% 2.99/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.61 ( ( ex1 @ A
% 2.99/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.61 => ? [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ex1I_type,type,
% 2.99/1.61 ex1I: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ex1I,definition,
% 2.99/1.61 ( ex1I
% 2.99/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( Xphi @ Xx )
% 2.99/1.61 => ( ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( ( Xphi @ Xy )
% 2.99/1.61 => ( Xy = Xx ) ) )
% 2.99/1.61 => ( ex1 @ A
% 2.99/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ex1I2_type,type,
% 2.99/1.61 ex1I2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ex1I2,definition,
% 2.99/1.61 ( ex1I2
% 2.99/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( ( Xphi @ Xx )
% 2.99/1.61 => ( ( Xphi @ Xy )
% 2.99/1.61 => ( Xx = Xy ) ) ) ) )
% 2.99/1.61 => ( ? [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 & ( Xphi @ Xx ) )
% 2.99/1.61 => ( ex1 @ A
% 2.99/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(singletonsuniq_type,type,
% 2.99/1.61 singletonsuniq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(singletonsuniq,definition,
% 2.99/1.61 ( singletonsuniq
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( ( setadjoin @ Xx @ emptyset )
% 2.99/1.61 = ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.61 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(atmost1p_type,type,
% 2.99/1.61 atmost1p: $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(atleast2p_type,type,
% 2.99/1.61 atleast2p: $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(atmost2p_type,type,
% 2.99/1.61 atmost2p: $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(upairsetp_type,type,
% 2.99/1.61 upairsetp: $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjL1_type,type,
% 2.99/1.61 setukpairinjL1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjL1,definition,
% 2.99/1.61 ( setukpairinjL1
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.61 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(kfstsingleton_type,type,
% 2.99/1.61 kfstsingleton: $o ).
% 2.99/1.61
% 2.99/1.61 thf(kfstsingleton,definition,
% 2.99/1.61 ( kfstsingleton
% 2.99/1.61 = ( ! [Xu: $i] :
% 2.99/1.61 ( ( iskpair @ Xu )
% 2.99/1.61 => ( singleton
% 2.99/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 2.99/1.61 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(theprop_type,type,
% 2.99/1.61 theprop: $o ).
% 2.99/1.61
% 2.99/1.61 thf(theprop,definition,
% 2.99/1.61 ( theprop
% 2.99/1.61 = ( ! [X: $i] :
% 2.99/1.61 ( ( singleton @ X )
% 2.99/1.61 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(kfst_type,type,
% 2.99/1.61 kfst: $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(kfstpairEq_type,type,
% 2.99/1.61 kfstpairEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(kfstpairEq,definition,
% 2.99/1.61 ( kfstpairEq
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.99/1.61 = Xx ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodfstin_type,type,
% 2.99/1.61 cartprodfstin: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodfstin,definition,
% 2.99/1.61 ( cartprodfstin
% 2.99/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.61 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjL2_type,type,
% 2.99/1.61 setukpairinjL2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjL2,definition,
% 2.99/1.61 ( setukpairinjL2
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjL_type,type,
% 2.99/1.61 setukpairinjL: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjL,definition,
% 2.99/1.61 ( setukpairinjL
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.61 ( ( ( kpair @ Xx @ Xy )
% 2.99/1.61 = ( kpair @ Xz @ Xu ) )
% 2.99/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR11_type,type,
% 2.99/1.61 setukpairinjR11: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR11,definition,
% 2.99/1.61 ( setukpairinjR11
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( Xx = Xy )
% 2.99/1.61 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR12_type,type,
% 2.99/1.61 setukpairinjR12: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR12,definition,
% 2.99/1.61 ( setukpairinjR12
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( Xx = Xy )
% 2.99/1.61 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.61 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR1_type,type,
% 2.99/1.61 setukpairinjR1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR1,definition,
% 2.99/1.61 ( setukpairinjR1
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.61 => ( ( Xz = Xu )
% 2.99/1.61 => ( Xy = Xu ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(upairequniteq_type,type,
% 2.99/1.61 upairequniteq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(upairequniteq,definition,
% 2.99/1.61 ( upairequniteq
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.61 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.61 = ( setadjoin @ Xz @ emptyset ) )
% 2.99/1.61 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR2_type,type,
% 2.99/1.61 setukpairinjR2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR2,definition,
% 2.99/1.61 ( setukpairinjR2
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.61 => ( Xy = Xu ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR_type,type,
% 2.99/1.61 setukpairinjR: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setukpairinjR,definition,
% 2.99/1.61 ( setukpairinjR
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.61 ( ( ( kpair @ Xx @ Xy )
% 2.99/1.61 = ( kpair @ Xz @ Xu ) )
% 2.99/1.61 => ( Xy = Xu ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ksndsingleton_type,type,
% 2.99/1.61 ksndsingleton: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ksndsingleton,definition,
% 2.99/1.61 ( ksndsingleton
% 2.99/1.61 = ( ! [Xu: $i] :
% 2.99/1.61 ( ( iskpair @ Xu )
% 2.99/1.61 => ( singleton
% 2.99/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 2.99/1.61 @ ^ [Xx: $i] :
% 2.99/1.61 ( Xu
% 2.99/1.61 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ksnd_type,type,
% 2.99/1.61 ksnd: $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(ksndpairEq_type,type,
% 2.99/1.61 ksndpairEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ksndpairEq,definition,
% 2.99/1.61 ( ksndpairEq
% 2.99/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.99/1.61 = Xy ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(kpairsurjEq_type,type,
% 2.99/1.61 kpairsurjEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(kpairsurjEq,definition,
% 2.99/1.61 ( kpairsurjEq
% 2.99/1.61 = ( ! [Xu: $i] :
% 2.99/1.61 ( ( iskpair @ Xu )
% 2.99/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.99/1.61 = Xu ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodsndin_type,type,
% 2.99/1.61 cartprodsndin: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodsndin,definition,
% 2.99/1.61 ( cartprodsndin
% 2.99/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.61 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodpairmemEL_type,type,
% 2.99/1.61 cartprodpairmemEL: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodpairmemEL,definition,
% 2.99/1.61 ( cartprodpairmemEL
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.99/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodpairmemER_type,type,
% 2.99/1.61 cartprodpairmemER: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodpairmemER,definition,
% 2.99/1.61 ( cartprodpairmemER
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.99/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodmempaircEq_type,type,
% 2.99/1.61 cartprodmempaircEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodmempaircEq,definition,
% 2.99/1.61 ( cartprodmempaircEq
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( kpair @ Xx @ Xy )
% 2.99/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodfstpairEq_type,type,
% 2.99/1.61 cartprodfstpairEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodfstpairEq,definition,
% 2.99/1.61 ( cartprodfstpairEq
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.99/1.61 = Xx ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodsndpairEq_type,type,
% 2.99/1.61 cartprodsndpairEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodsndpairEq,definition,
% 2.99/1.61 ( cartprodsndpairEq
% 2.99/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.99/1.61 = Xy ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodpairsurjEq_type,type,
% 2.99/1.61 cartprodpairsurjEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(cartprodpairsurjEq,definition,
% 2.99/1.61 ( cartprodpairsurjEq
% 2.99/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.99/1.61 = Xu ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(breln_type,type,
% 2.99/1.61 breln: $i > $i > $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(breln,definition,
% 2.99/1.61 ( breln
% 2.99/1.61 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstr_type,type,
% 2.99/1.61 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrI_type,type,
% 2.99/1.61 dpsetconstrI: $o ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrI,definition,
% 2.99/1.61 ( dpsetconstrI
% 2.99/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( Xphi @ Xx @ Xy )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.61 @ ( dpsetconstr @ A @ B
% 2.99/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrSub_type,type,
% 2.99/1.61 dpsetconstrSub: $o ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrSub,definition,
% 2.99/1.61 ( dpsetconstrSub
% 2.99/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.99/1.61 ( subset
% 2.99/1.61 @ ( dpsetconstr @ A @ B
% 2.99/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.99/1.61 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setOfPairsIsBReln_type,type,
% 2.99/1.61 setOfPairsIsBReln: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setOfPairsIsBReln,definition,
% 2.99/1.61 ( setOfPairsIsBReln
% 2.99/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.99/1.61 ( breln @ A @ B
% 2.99/1.61 @ ( dpsetconstr @ A @ B
% 2.99/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrERa_type,type,
% 2.99/1.61 dpsetconstrERa: $o ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrERa,definition,
% 2.99/1.61 ( dpsetconstrERa
% 2.99/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.61 @ ( dpsetconstr @ A @ B
% 2.99/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrEL1_type,type,
% 2.99/1.61 dpsetconstrEL1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrEL1,definition,
% 2.99/1.61 ( dpsetconstrEL1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.61 @ ( dpsetconstr @ A @ B
% 2.99/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrEL2_type,type,
% 2.99/1.61 dpsetconstrEL2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrEL2,definition,
% 2.99/1.61 ( dpsetconstrEL2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.61 @ ( dpsetconstr @ A @ B
% 2.99/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrER_type,type,
% 2.99/1.61 dpsetconstrER: $o ).
% 2.99/1.61
% 2.99/1.61 thf(dpsetconstrER,definition,
% 2.99/1.61 ( dpsetconstrER
% 2.99/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.61 @ ( dpsetconstr @ A @ B
% 2.99/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(func_type,type,
% 2.99/1.61 func: $i > $i > $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcSet_type,type,
% 2.99/1.61 funcSet: $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(funcImageSingleton_type,type,
% 2.99/1.61 funcImageSingleton: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcImageSingleton,definition,
% 2.99/1.61 ( funcImageSingleton
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( singleton
% 2.99/1.61 @ ( dsetconstr @ B
% 2.99/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(apProp_type,type,
% 2.99/1.61 apProp: $o ).
% 2.99/1.61
% 2.99/1.61 thf(apProp,definition,
% 2.99/1.61 ( apProp
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in
% 2.99/1.61 @ ( setunion
% 2.99/1.61 @ ( dsetconstr @ B
% 2.99/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.99/1.61 @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ap_type,type,
% 2.99/1.61 ap: $i > $i > $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(app_type,type,
% 2.99/1.61 app: $o ).
% 2.99/1.61
% 2.99/1.61 thf(app,definition,
% 2.99/1.61 ( app
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(infuncsetfunc_type,type,
% 2.99/1.61 infuncsetfunc: $o ).
% 2.99/1.61
% 2.99/1.61 thf(infuncsetfunc,definition,
% 2.99/1.61 ( infuncsetfunc
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.61 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ap2p_type,type,
% 2.99/1.61 ap2p: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ap2p,definition,
% 2.99/1.61 ( ap2p
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(funcinfuncset_type,type,
% 2.99/1.61 funcinfuncset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcinfuncset,definition,
% 2.99/1.61 ( funcinfuncset
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(lamProp_type,type,
% 2.99/1.61 lamProp: $o ).
% 2.99/1.61
% 2.99/1.61 thf(lamProp,definition,
% 2.99/1.61 ( lamProp
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.61 => ( func @ A @ B
% 2.99/1.61 @ ( dpsetconstr @ A @ B
% 2.99/1.61 @ ^ [Xx: $i,Xy: $i] :
% 2.99/1.61 ( ( Xf @ Xx )
% 2.99/1.61 = Xy ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(lam_type,type,
% 2.99/1.61 lam: $i > $i > ( $i > $i ) > $i ).
% 2.99/1.61
% 2.99/1.61 thf(lamp_type,type,
% 2.99/1.61 lamp: $o ).
% 2.99/1.61
% 2.99/1.61 thf(lamp,definition,
% 2.99/1.61 ( lamp
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.61 => ( func @ A @ B
% 2.99/1.61 @ ( lam @ A @ B
% 2.99/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(lam2p_type,type,
% 2.99/1.61 lam2p: $o ).
% 2.99/1.61
% 2.99/1.61 thf(lam2p,definition,
% 2.99/1.61 ( lam2p
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.61 => ( in
% 2.99/1.61 @ ( lam @ A @ B
% 2.99/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.99/1.61 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(brelnall1_type,type,
% 2.99/1.61 brelnall1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(brelnall1,definition,
% 2.99/1.61 ( brelnall1
% 2.99/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.61 ( ( breln @ A @ B @ R )
% 2.99/1.61 => ! [Xphi: $i > $o] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ R )
% 2.99/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(brelnall2_type,type,
% 2.99/1.61 brelnall2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(brelnall2,definition,
% 2.99/1.61 ( brelnall2
% 2.99/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.61 ( ( breln @ A @ B @ R )
% 2.99/1.61 => ! [Xphi: $i > $o] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ R )
% 2.99/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ex1E2_type,type,
% 2.99/1.61 ex1E2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ex1E2,definition,
% 2.99/1.61 ( ex1E2
% 2.99/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.61 ( ( ex1 @ A
% 2.99/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( ( Xphi @ Xx )
% 2.99/1.61 => ( ( Xphi @ Xy )
% 2.99/1.61 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(funcGraphProp1_type,type,
% 2.99/1.61 funcGraphProp1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcGraphProp1,definition,
% 2.99/1.61 ( funcGraphProp1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(funcGraphProp3_type,type,
% 2.99/1.61 funcGraphProp3: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcGraphProp3,definition,
% 2.99/1.61 ( funcGraphProp3
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(funcGraphProp2_type,type,
% 2.99/1.61 funcGraphProp2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcGraphProp2,definition,
% 2.99/1.61 ( funcGraphProp2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.99/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.61 = Xy ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(funcextLem_type,type,
% 2.99/1.61 funcextLem: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcextLem,definition,
% 2.99/1.61 ( funcextLem
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ! [Xg: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xg )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(funcGraphProp4_type,type,
% 2.99/1.61 funcGraphProp4: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcGraphProp4,definition,
% 2.99/1.61 ( funcGraphProp4
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.99/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.61 = Xy ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(subbreln_type,type,
% 2.99/1.61 subbreln: $o ).
% 2.99/1.61
% 2.99/1.61 thf(subbreln,definition,
% 2.99/1.61 ( subbreln
% 2.99/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.61 ( ( breln @ A @ B @ R )
% 2.99/1.61 => ! [S: $i] :
% 2.99/1.61 ( ( breln @ A @ B @ S )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.61 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(eqbreln_type,type,
% 2.99/1.61 eqbreln: $o ).
% 2.99/1.61
% 2.99/1.61 thf(eqbreln,definition,
% 2.99/1.61 ( eqbreln
% 2.99/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.61 ( ( breln @ A @ B @ R )
% 2.99/1.61 => ! [S: $i] :
% 2.99/1.61 ( ( breln @ A @ B @ S )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ B )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.99/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.99/1.61 => ( R = S ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(funcext_type,type,
% 2.99/1.61 funcext: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcext,definition,
% 2.99/1.61 ( funcext
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ! [Xg: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xg )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.61 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(funcext2_type,type,
% 2.99/1.61 funcext2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(funcext2,definition,
% 2.99/1.61 ( funcext2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.61 => ! [Xg: $i] :
% 2.99/1.61 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.61 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ap2apEq1_type,type,
% 2.99/1.61 ap2apEq1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ap2apEq1,definition,
% 2.99/1.61 ( ap2apEq1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.61 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ap2apEq2_type,type,
% 2.99/1.61 ap2apEq2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ap2apEq2,definition,
% 2.99/1.61 ( ap2apEq2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.61 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(beta1_type,type,
% 2.99/1.61 beta1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(beta1,definition,
% 2.99/1.61 ( beta1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( ap @ A @ B
% 2.99/1.61 @ ( lam @ A @ B
% 2.99/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.99/1.61 @ Xx )
% 2.99/1.61 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(eta1_type,type,
% 2.99/1.61 eta1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(eta1,definition,
% 2.99/1.61 ( eta1
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( func @ A @ B @ Xf )
% 2.99/1.61 => ( ( lam @ A @ B
% 2.99/1.61 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.99/1.61 = Xf ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(lam2lamEq_type,type,
% 2.99/1.61 lam2lamEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(lam2lamEq,definition,
% 2.99/1.61 ( lam2lamEq
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.61 => ( ( lam @ A @ B
% 2.99/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.99/1.61 = ( lam @ A @ B
% 2.99/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(beta2_type,type,
% 2.99/1.61 beta2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(beta2,definition,
% 2.99/1.61 ( beta2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( ap @ A @ B
% 2.99/1.61 @ ( lam @ A @ B
% 2.99/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.99/1.61 @ Xx )
% 2.99/1.61 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(eta2_type,type,
% 2.99/1.61 eta2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(eta2,definition,
% 2.99/1.61 ( eta2
% 2.99/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.61 => ( ( lam @ A @ B
% 2.99/1.61 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.99/1.61 = Xf ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(iffalseProp1_type,type,
% 2.99/1.61 iffalseProp1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(iffalseProp1,definition,
% 2.99/1.61 ( iffalseProp1
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( ~ Xphi
% 2.99/1.61 => ( in @ Xy
% 2.99/1.61 @ ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xz: $i] :
% 2.99/1.61 ( ( Xphi
% 2.99/1.61 & ( Xz = Xx ) )
% 2.99/1.61 | ( ~ Xphi
% 2.99/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(iffalseProp2_type,type,
% 2.99/1.61 iffalseProp2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(iffalseProp2,definition,
% 2.99/1.61 ( iffalseProp2
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( ~ Xphi
% 2.99/1.61 => ( ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xz: $i] :
% 2.99/1.61 ( ( Xphi
% 2.99/1.61 & ( Xz = Xx ) )
% 2.99/1.61 | ( ~ Xphi
% 2.99/1.61 & ( Xz = Xy ) ) ) )
% 2.99/1.61 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(iftrueProp1_type,type,
% 2.99/1.61 iftrueProp1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(iftrueProp1,definition,
% 2.99/1.61 ( iftrueProp1
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( Xphi
% 2.99/1.61 => ( in @ Xx
% 2.99/1.61 @ ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xz: $i] :
% 2.99/1.61 ( ( Xphi
% 2.99/1.61 & ( Xz = Xx ) )
% 2.99/1.61 | ( ~ Xphi
% 2.99/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(iftrueProp2_type,type,
% 2.99/1.61 iftrueProp2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(iftrueProp2,definition,
% 2.99/1.61 ( iftrueProp2
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( Xphi
% 2.99/1.61 => ( ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xz: $i] :
% 2.99/1.61 ( ( Xphi
% 2.99/1.61 & ( Xz = Xx ) )
% 2.99/1.61 | ( ~ Xphi
% 2.99/1.61 & ( Xz = Xy ) ) ) )
% 2.99/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(ifSingleton_type,type,
% 2.99/1.61 ifSingleton: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ifSingleton,definition,
% 2.99/1.61 ( ifSingleton
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( singleton
% 2.99/1.61 @ ( dsetconstr @ A
% 2.99/1.61 @ ^ [Xz: $i] :
% 2.99/1.61 ( ( Xphi
% 2.99/1.61 & ( Xz = Xx ) )
% 2.99/1.61 | ( ~ Xphi
% 2.99/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(if_type,type,
% 2.99/1.61 if: $i > $o > $i > $i > $i ).
% 2.99/1.61
% 2.99/1.61 thf(ifp_type,type,
% 2.99/1.61 ifp: $o ).
% 2.99/1.61
% 2.99/1.61 thf(ifp,definition,
% 2.99/1.61 ( ifp
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(theeq_type,type,
% 2.99/1.61 theeq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(theeq,definition,
% 2.99/1.61 ( theeq
% 2.99/1.61 = ( ! [X: $i] :
% 2.99/1.61 ( ( singleton @ X )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ X )
% 2.99/1.61 => ( ( setunion @ X )
% 2.99/1.61 = Xx ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(iftrue_type,type,
% 2.99/1.61 iftrue: $o ).
% 2.99/1.61
% 2.99/1.61 thf(iftrue,definition,
% 2.99/1.61 ( iftrue
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( Xphi
% 2.99/1.61 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.99/1.61 = Xx ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(iffalse_type,type,
% 2.99/1.61 iffalse: $o ).
% 2.99/1.61
% 2.99/1.61 thf(iffalse,definition,
% 2.99/1.61 ( iffalse
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( ~ Xphi
% 2.99/1.61 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.99/1.61 = Xy ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(iftrueorfalse_type,type,
% 2.99/1.61 iftrueorfalse: $o ).
% 2.99/1.61
% 2.99/1.61 thf(iftrueorfalse,definition,
% 2.99/1.61 ( iftrueorfalse
% 2.99/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectT_lem_type,type,
% 2.99/1.61 binintersectT_lem: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectT_lem,definition,
% 2.99/1.61 ( binintersectT_lem
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionT_lem_type,type,
% 2.99/1.61 binunionT_lem: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionT_lem,definition,
% 2.99/1.61 ( binunionT_lem
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(powersetT_lem_type,type,
% 2.99/1.61 powersetT_lem: $o ).
% 2.99/1.61
% 2.99/1.61 thf(powersetT_lem,definition,
% 2.99/1.61 ( powersetT_lem
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setminusT_lem_type,type,
% 2.99/1.61 setminusT_lem: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setminusT_lem,definition,
% 2.99/1.61 ( setminusT_lem
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementT_lem_type,type,
% 2.99/1.61 complementT_lem: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementT_lem,definition,
% 2.99/1.61 ( complementT_lem
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(setextT_type,type,
% 2.99/1.61 setextT: $o ).
% 2.99/1.61
% 2.99/1.61 thf(setextT,definition,
% 2.99/1.61 ( setextT
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ X )
% 2.99/1.61 => ( in @ Xx @ Y ) ) )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ Y )
% 2.99/1.61 => ( in @ Xx @ X ) ) )
% 2.99/1.61 => ( X = Y ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(subsetTI_type,type,
% 2.99/1.61 subsetTI: $o ).
% 2.99/1.61
% 2.99/1.61 thf(subsetTI,definition,
% 2.99/1.61 ( subsetTI
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ X )
% 2.99/1.61 => ( in @ Xx @ Y ) ) )
% 2.99/1.61 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(powersetTI1_type,type,
% 2.99/1.61 powersetTI1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(powersetTI1,definition,
% 2.99/1.61 ( powersetTI1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ X )
% 2.99/1.61 => ( in @ Xx @ Y ) ) )
% 2.99/1.61 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(powersetTE1_type,type,
% 2.99/1.61 powersetTE1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(powersetTE1,definition,
% 2.99/1.61 ( powersetTE1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ X @ ( powerset @ Y ) )
% 2.99/1.61 => ( ( in @ Xx @ X )
% 2.99/1.61 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementTI1_type,type,
% 2.99/1.61 complementTI1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementTI1,definition,
% 2.99/1.61 ( complementTI1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ X )
% 2.99/1.61 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementTE1_type,type,
% 2.99/1.61 complementTE1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementTE1,definition,
% 2.99/1.61 ( complementTE1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.61 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectTELcontra_type,type,
% 2.99/1.61 binintersectTELcontra: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectTELcontra,definition,
% 2.99/1.61 ( binintersectTELcontra
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ X )
% 2.99/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectTERcontra_type,type,
% 2.99/1.61 binintersectTERcontra: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binintersectTERcontra,definition,
% 2.99/1.61 ( binintersectTERcontra
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ Y )
% 2.99/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(contrasubsetT_type,type,
% 2.99/1.61 contrasubsetT: $o ).
% 2.99/1.61
% 2.99/1.61 thf(contrasubsetT,definition,
% 2.99/1.61 ( contrasubsetT
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.61 => ( ( in @ Xx @ Y )
% 2.99/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(contrasubsetT1_type,type,
% 2.99/1.61 contrasubsetT1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(contrasubsetT1,definition,
% 2.99/1.61 ( contrasubsetT1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( subset @ X @ Y )
% 2.99/1.61 => ( ~ ( in @ Xx @ Y )
% 2.99/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(contrasubsetT2_type,type,
% 2.99/1.61 contrasubsetT2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(contrasubsetT2,definition,
% 2.99/1.61 ( contrasubsetT2
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ X @ Y )
% 2.99/1.61 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(contrasubsetT3_type,type,
% 2.99/1.61 contrasubsetT3: $o ).
% 2.99/1.61
% 2.99/1.61 thf(contrasubsetT3,definition,
% 2.99/1.61 ( contrasubsetT3
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.99/1.61 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementI1_type,type,
% 2.99/1.61 doubleComplementI1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementI1,definition,
% 2.99/1.61 ( doubleComplementI1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ X )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementE1_type,type,
% 2.99/1.61 doubleComplementE1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementE1,definition,
% 2.99/1.61 ( doubleComplementE1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.99/1.61 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementSub1_type,type,
% 2.99/1.61 doubleComplementSub1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementSub1,definition,
% 2.99/1.61 ( doubleComplementSub1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementSub2_type,type,
% 2.99/1.61 doubleComplementSub2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementSub2,definition,
% 2.99/1.61 ( doubleComplementSub2
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementEq_type,type,
% 2.99/1.61 doubleComplementEq: $o ).
% 2.99/1.61
% 2.99/1.61 thf(doubleComplementEq,definition,
% 2.99/1.61 ( doubleComplementEq
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ( X
% 2.99/1.61 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementTnotintersectT_type,type,
% 2.99/1.61 complementTnotintersectT: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementTnotintersectT,definition,
% 2.99/1.61 ( complementTnotintersectT
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementImpComplementIntersect_type,type,
% 2.99/1.61 complementImpComplementIntersect: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementImpComplementIntersect,definition,
% 2.99/1.61 ( complementImpComplementIntersect
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementSubsetComplementIntersect_type,type,
% 2.99/1.61 complementSubsetComplementIntersect: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementSubsetComplementIntersect,definition,
% 2.99/1.61 ( complementSubsetComplementIntersect
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementInPowersetComplementIntersect_type,type,
% 2.99/1.61 complementInPowersetComplementIntersect: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementInPowersetComplementIntersect,definition,
% 2.99/1.61 ( complementInPowersetComplementIntersect
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(contraSubsetComplement_type,type,
% 2.99/1.61 contraSubsetComplement: $o ).
% 2.99/1.61
% 2.99/1.61 thf(contraSubsetComplement,definition,
% 2.99/1.61 ( contraSubsetComplement
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ Y )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementTcontraSubset_type,type,
% 2.99/1.61 complementTcontraSubset: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementTcontraSubset,definition,
% 2.99/1.61 ( complementTcontraSubset
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.61 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionTILcontra_type,type,
% 2.99/1.61 binunionTILcontra: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionTILcontra,definition,
% 2.99/1.61 ( binunionTILcontra
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionTIRcontra_type,type,
% 2.99/1.61 binunionTIRcontra: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionTIRcontra,definition,
% 2.99/1.61 ( binunionTIRcontra
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.61 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(inIntersectImpInUnion_type,type,
% 2.99/1.61 inIntersectImpInUnion: $o ).
% 2.99/1.61
% 2.99/1.61 thf(inIntersectImpInUnion,definition,
% 2.99/1.61 ( inIntersectImpInUnion
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.61 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(inIntersectImpInUnion2_type,type,
% 2.99/1.61 inIntersectImpInUnion2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(inIntersectImpInUnion2,definition,
% 2.99/1.61 ( inIntersectImpInUnion2
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.61 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(inIntersectImpInIntersectUnions_type,type,
% 2.99/1.61 inIntersectImpInIntersectUnions: $o ).
% 2.99/1.61
% 2.99/1.61 thf(inIntersectImpInIntersectUnions,definition,
% 2.99/1.61 ( inIntersectImpInIntersectUnions
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.61 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(intersectInPowersetIntersectUnions_type,type,
% 2.99/1.61 intersectInPowersetIntersectUnions: $o ).
% 2.99/1.61
% 2.99/1.61 thf(intersectInPowersetIntersectUnions,definition,
% 2.99/1.61 ( intersectInPowersetIntersectUnions
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(inComplementUnionImpNotIn1_type,type,
% 2.99/1.61 inComplementUnionImpNotIn1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(inComplementUnionImpNotIn1,definition,
% 2.99/1.61 ( inComplementUnionImpNotIn1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(inComplementUnionImpInComplement1_type,type,
% 2.99/1.61 inComplementUnionImpInComplement1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(inComplementUnionImpInComplement1,definition,
% 2.99/1.61 ( inComplementUnionImpInComplement1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionTE_type,type,
% 2.99/1.61 binunionTE: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionTE,definition,
% 2.99/1.61 ( binunionTE
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xphi: $o,Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.61 => ( ( ( in @ Xx @ X )
% 2.99/1.61 => Xphi )
% 2.99/1.61 => ( ( ( in @ Xx @ Y )
% 2.99/1.61 => Xphi )
% 2.99/1.61 => Xphi ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(binunionTEcontra_type,type,
% 2.99/1.61 binunionTEcontra: $o ).
% 2.99/1.61
% 2.99/1.61 thf(binunionTEcontra,definition,
% 2.99/1.61 ( binunionTEcontra
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ~ ( in @ Xx @ X )
% 2.99/1.61 => ( ~ ( in @ Xx @ Y )
% 2.99/1.61 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2a1_type,type,
% 2.99/1.61 demorgan2a1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2a1,definition,
% 2.99/1.61 ( demorgan2a1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(complementUnionInPowersetComplement_type,type,
% 2.99/1.61 complementUnionInPowersetComplement: $o ).
% 2.99/1.61
% 2.99/1.61 thf(complementUnionInPowersetComplement,definition,
% 2.99/1.61 ( complementUnionInPowersetComplement
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2a2_type,type,
% 2.99/1.61 demorgan2a2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2a2,definition,
% 2.99/1.61 ( demorgan2a2
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan1a_type,type,
% 2.99/1.61 demorgan1a: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan1a,definition,
% 2.99/1.61 ( demorgan1a
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 2.99/1.61 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan1b_type,type,
% 2.99/1.61 demorgan1b: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan1b,definition,
% 2.99/1.61 ( demorgan1b
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan1_type,type,
% 2.99/1.61 demorgan1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan1,definition,
% 2.99/1.61 ( demorgan1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 2.99/1.61 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2a_type,type,
% 2.99/1.61 demorgan2a: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2a,definition,
% 2.99/1.61 ( demorgan2a
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.61 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2b2_type,type,
% 2.99/1.61 demorgan2b2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2b2,definition,
% 2.99/1.61 ( demorgan2b2
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.61 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2b_type,type,
% 2.99/1.61 demorgan2b: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2b,definition,
% 2.99/1.61 ( demorgan2b
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.99/1.61 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2_type,type,
% 2.99/1.61 demorgan2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(demorgan2,definition,
% 2.99/1.61 ( demorgan2
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 2.99/1.61 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule0_type,type,
% 2.99/1.61 woz13rule0: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule0,definition,
% 2.99/1.61 ( woz13rule0
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.61 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule1_type,type,
% 2.99/1.61 woz13rule1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule1,definition,
% 2.99/1.61 ( woz13rule1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ X @ Z )
% 2.99/1.61 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule2_type,type,
% 2.99/1.61 woz13rule2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule2,definition,
% 2.99/1.61 ( woz13rule2
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ Y @ Z )
% 2.99/1.61 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule3_type,type,
% 2.99/1.61 woz13rule3: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule3,definition,
% 2.99/1.61 ( woz13rule3
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ X @ Y )
% 2.99/1.61 => ( ( subset @ X @ Z )
% 2.99/1.61 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule4_type,type,
% 2.99/1.61 woz13rule4: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz13rule4,definition,
% 2.99/1.61 ( woz13rule4
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ! [W: $i] :
% 2.99/1.61 ( ( in @ W @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ X @ Z )
% 2.99/1.61 => ( ( subset @ Y @ W )
% 2.99/1.61 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_1_type,type,
% 2.99/1.61 woz1_1: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_1,definition,
% 2.99/1.61 ( woz1_1
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_2_type,type,
% 2.99/1.61 woz1_2: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_2,definition,
% 2.99/1.61 ( woz1_2
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ! [W: $i] :
% 2.99/1.61 ( ( in @ W @ ( powerset @ A ) )
% 2.99/1.61 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 2.99/1.61 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_3_type,type,
% 2.99/1.61 woz1_3: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_3,definition,
% 2.99/1.61 ( woz1_3
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ! [Z: $i] :
% 2.99/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_4_type,type,
% 2.99/1.61 woz1_4: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_4,definition,
% 2.99/1.61 ( woz1_4
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.61 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_5_type,type,
% 2.99/1.61 woz1_5: $o ).
% 2.99/1.61
% 2.99/1.61 thf(woz1_5,definition,
% 2.99/1.61 ( woz1_5
% 2.99/1.61 = ( ! [A: $i,X: $i] :
% 2.99/1.61 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.61 => ! [Y: $i] :
% 2.99/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.61 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(breln1_type,type,
% 2.99/1.61 breln1: $i > $i > $o ).
% 2.99/1.61
% 2.99/1.61 thf(breln1,definition,
% 2.99/1.61 ( breln1
% 2.99/1.61 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 2.99/1.61
% 2.99/1.61 thf(breln1all2,conjecture,
% 2.99/1.61 ( setextAx
% 2.99/1.61 => ( emptysetAx
% 2.99/1.61 => ( setadjoinAx
% 2.99/1.61 => ( powersetAx
% 2.99/1.61 => ( setunionAx
% 2.99/1.61 => ( omega0Ax
% 2.99/1.61 => ( omegaSAx
% 2.99/1.61 => ( omegaIndAx
% 2.99/1.61 => ( replAx
% 2.99/1.61 => ( foundationAx
% 2.99/1.61 => ( wellorderingAx
% 2.99/1.61 => ( descrp
% 2.99/1.61 => ( dsetconstrI
% 2.99/1.61 => ( dsetconstrEL
% 2.99/1.61 => ( dsetconstrER
% 2.99/1.61 => ( exuE1
% 2.99/1.61 => ( prop2setE
% 2.99/1.61 => ( emptysetE
% 2.99/1.61 => ( emptysetimpfalse
% 2.99/1.61 => ( notinemptyset
% 2.99/1.61 => ( exuE3e
% 2.99/1.61 => ( setext
% 2.99/1.61 => ( emptyI
% 2.99/1.61 => ( noeltsimpempty
% 2.99/1.61 => ( setbeta
% 2.99/1.61 => ( nonemptyE1
% 2.99/1.61 => ( nonemptyI
% 2.99/1.61 => ( nonemptyI1
% 2.99/1.61 => ( setadjoinIL
% 2.99/1.61 => ( emptyinunitempty
% 2.99/1.61 => ( setadjoinIR
% 2.99/1.61 => ( setadjoinE
% 2.99/1.61 => ( setadjoinOr
% 2.99/1.61 => ( setoftrueEq
% 2.99/1.61 => ( powersetI
% 2.99/1.61 => ( emptyinPowerset
% 2.99/1.61 => ( emptyInPowerset
% 2.99/1.61 => ( powersetE
% 2.99/1.61 => ( setunionI
% 2.99/1.61 => ( setunionE
% 2.99/1.61 => ( subPowSU
% 2.99/1.61 => ( exuE2
% 2.99/1.61 => ( nonemptyImpWitness
% 2.99/1.61 => ( uniqinunit
% 2.99/1.61 => ( notinsingleton
% 2.99/1.61 => ( eqinunit
% 2.99/1.61 => ( singletonsswitch
% 2.99/1.61 => ( upairsetE
% 2.99/1.61 => ( upairsetIL
% 2.99/1.61 => ( upairsetIR
% 2.99/1.61 => ( emptyE1
% 2.99/1.61 => ( vacuousDall
% 2.99/1.61 => ( quantDeMorgan1
% 2.99/1.61 => ( quantDeMorgan2
% 2.99/1.61 => ( quantDeMorgan3
% 2.99/1.61 => ( quantDeMorgan4
% 2.99/1.61 => ( prop2setI
% 2.99/1.61 => ( prop2set2propI
% 2.99/1.61 => ( notdexE
% 2.99/1.61 => ( notdallE
% 2.99/1.61 => ( exuI1
% 2.99/1.61 => ( exuI3
% 2.99/1.61 => ( exuI2
% 2.99/1.61 => ( inCongP
% 2.99/1.61 => ( in__Cong
% 2.99/1.61 => ( exuE3u
% 2.99/1.61 => ( exu__Cong
% 2.99/1.61 => ( emptyset__Cong
% 2.99/1.61 => ( setadjoin__Cong
% 2.99/1.61 => ( powerset__Cong
% 2.99/1.61 => ( setunion__Cong
% 2.99/1.61 => ( omega__Cong
% 2.99/1.61 => ( exuEu
% 2.99/1.61 => ( descr__Cong
% 2.99/1.61 => ( dsetconstr__Cong
% 2.99/1.61 => ( subsetI1
% 2.99/1.61 => ( eqimpsubset2
% 2.99/1.61 => ( eqimpsubset1
% 2.99/1.61 => ( subsetI2
% 2.99/1.61 => ( emptysetsubset
% 2.99/1.61 => ( subsetE
% 2.99/1.61 => ( subsetE2
% 2.99/1.61 => ( notsubsetI
% 2.99/1.61 => ( notequalI1
% 2.99/1.61 => ( notequalI2
% 2.99/1.61 => ( subsetRefl
% 2.99/1.61 => ( subsetTrans
% 2.99/1.61 => ( setadjoinSub
% 2.99/1.61 => ( setadjoinSub2
% 2.99/1.61 => ( subset2powerset
% 2.99/1.61 => ( setextsub
% 2.99/1.61 => ( subsetemptysetimpeq
% 2.99/1.61 => ( powersetI1
% 2.99/1.61 => ( powersetE1
% 2.99/1.61 => ( inPowerset
% 2.99/1.61 => ( powersetsubset
% 2.99/1.61 => ( sepInPowerset
% 2.99/1.61 => ( sepSubset
% 2.99/1.61 => ( binunionIL
% 2.99/1.61 => ( upairset2IR
% 2.99/1.61 => ( binunionIR
% 2.99/1.61 => ( binunionEcases
% 2.99/1.61 => ( binunionE
% 2.99/1.61 => ( binunionLsub
% 2.99/1.61 => ( binunionRsub
% 2.99/1.61 => ( binintersectI
% 2.99/1.61 => ( binintersectSubset5
% 2.99/1.61 => ( binintersectEL
% 2.99/1.61 => ( binintersectLsub
% 2.99/1.61 => ( binintersectSubset2
% 2.99/1.61 => ( binintersectSubset3
% 2.99/1.61 => ( binintersectER
% 2.99/1.61 => ( disjointsetsI1
% 2.99/1.61 => ( binintersectRsub
% 2.99/1.61 => ( binintersectSubset4
% 2.99/1.61 => ( binintersectSubset1
% 2.99/1.61 => ( bs114d
% 2.99/1.61 => ( setminusI
% 2.99/1.61 => ( setminusEL
% 2.99/1.61 => ( setminusER
% 2.99/1.61 => ( setminusSubset2
% 2.99/1.61 => ( setminusERneg
% 2.99/1.61 => ( setminusELneg
% 2.99/1.61 => ( setminusILneg
% 2.99/1.61 => ( setminusIRneg
% 2.99/1.61 => ( setminusLsub
% 2.99/1.61 => ( setminusSubset1
% 2.99/1.61 => ( symdiffE
% 2.99/1.61 => ( symdiffI1
% 2.99/1.61 => ( symdiffI2
% 2.99/1.61 => ( symdiffIneg1
% 2.99/1.61 => ( symdiffIneg2
% 2.99/1.61 => ( secondinupair
% 2.99/1.61 => ( setukpairIL
% 2.99/1.61 => ( setukpairIR
% 2.99/1.61 => ( kpairiskpair
% 2.99/1.61 => ( kpairp
% 2.99/1.61 => ( singletonsubset
% 2.99/1.61 => ( singletoninpowerset
% 2.99/1.61 => ( singletoninpowunion
% 2.99/1.61 => ( upairset2E
% 2.99/1.61 => ( upairsubunion
% 2.99/1.61 => ( upairinpowunion
% 2.99/1.61 => ( ubforcartprodlem1
% 2.99/1.61 => ( ubforcartprodlem2
% 2.99/1.61 => ( ubforcartprodlem3
% 2.99/1.61 => ( cartprodpairin
% 2.99/1.61 => ( cartprodmempair1
% 2.99/1.61 => ( cartprodmempair
% 2.99/1.61 => ( setunionE2
% 2.99/1.61 => ( setunionsingleton1
% 2.99/1.61 => ( setunionsingleton2
% 2.99/1.61 => ( setunionsingleton
% 2.99/1.61 => ( singletonprop
% 2.99/1.61 => ( ex1E1
% 2.99/1.61 => ( ex1I
% 2.99/1.61 => ( ex1I2
% 2.99/1.61 => ( singletonsuniq
% 2.99/1.61 => ( setukpairinjL1
% 2.99/1.61 => ( kfstsingleton
% 2.99/1.61 => ( theprop
% 2.99/1.61 => ( kfstpairEq
% 2.99/1.61 => ( cartprodfstin
% 2.99/1.61 => ( setukpairinjL2
% 2.99/1.61 => ( setukpairinjL
% 2.99/1.61 => ( setukpairinjR11
% 2.99/1.61 => ( setukpairinjR12
% 2.99/1.61 => ( setukpairinjR1
% 2.99/1.61 => ( upairequniteq
% 2.99/1.61 => ( setukpairinjR2
% 2.99/1.61 => ( setukpairinjR
% 2.99/1.61 => ( ksndsingleton
% 2.99/1.61 => ( ksndpairEq
% 2.99/1.61 => ( kpairsurjEq
% 2.99/1.61 => ( cartprodsndin
% 2.99/1.61 => ( cartprodpairmemEL
% 2.99/1.61 => ( cartprodpairmemER
% 2.99/1.61 => ( cartprodmempaircEq
% 2.99/1.61 => ( cartprodfstpairEq
% 2.99/1.61 => ( cartprodsndpairEq
% 2.99/1.61 => ( cartprodpairsurjEq
% 2.99/1.61 => ( dpsetconstrI
% 2.99/1.61 => ( dpsetconstrSub
% 2.99/1.61 => ( setOfPairsIsBReln
% 2.99/1.61 => ( dpsetconstrERa
% 2.99/1.61 => ( dpsetconstrEL1
% 2.99/1.61 => ( dpsetconstrEL2
% 2.99/1.61 => ( dpsetconstrER
% 2.99/1.61 => ( funcImageSingleton
% 2.99/1.61 => ( apProp
% 2.99/1.61 => ( app
% 2.99/1.61 => ( infuncsetfunc
% 2.99/1.61 => ( ap2p
% 2.99/1.61 => ( funcinfuncset
% 2.99/1.61 => ( lamProp
% 2.99/1.61 => ( lamp
% 2.99/1.61 => ( lam2p
% 2.99/1.61 => ( brelnall1
% 2.99/1.61 => ( brelnall2
% 2.99/1.61 => ( ex1E2
% 2.99/1.61 => ( funcGraphProp1
% 2.99/1.61 => ( funcGraphProp3
% 2.99/1.61 => ( funcGraphProp2
% 2.99/1.61 => ( funcextLem
% 2.99/1.61 => ( funcGraphProp4
% 2.99/1.61 => ( subbreln
% 2.99/1.61 => ( eqbreln
% 2.99/1.61 => ( funcext
% 2.99/1.61 => ( funcext2
% 2.99/1.61 => ( ap2apEq1
% 2.99/1.61 => ( ap2apEq2
% 2.99/1.61 => ( beta1
% 2.99/1.61 => ( eta1
% 2.99/1.61 => ( lam2lamEq
% 2.99/1.61 => ( beta2
% 2.99/1.61 => ( eta2
% 2.99/1.61 => ( iffalseProp1
% 2.99/1.61 => ( iffalseProp2
% 2.99/1.61 => ( iftrueProp1
% 2.99/1.61 => ( iftrueProp2
% 2.99/1.61 => ( ifSingleton
% 2.99/1.61 => ( ifp
% 2.99/1.61 => ( theeq
% 2.99/1.61 => ( iftrue
% 2.99/1.61 => ( iffalse
% 2.99/1.61 => ( iftrueorfalse
% 2.99/1.61 => ( binintersectT_lem
% 2.99/1.61 => ( binunionT_lem
% 2.99/1.61 => ( powersetT_lem
% 2.99/1.61 => ( setminusT_lem
% 2.99/1.61 => ( complementT_lem
% 2.99/1.61 => ( setextT
% 2.99/1.61 => ( subsetTI
% 2.99/1.61 => ( powersetTI1
% 2.99/1.61 => ( powersetTE1
% 2.99/1.61 => ( complementTI1
% 2.99/1.61 => ( complementTE1
% 2.99/1.61 => ( binintersectTELcontra
% 2.99/1.61 => ( binintersectTERcontra
% 2.99/1.61 => ( contrasubsetT
% 2.99/1.61 => ( contrasubsetT1
% 2.99/1.61 => ( contrasubsetT2
% 2.99/1.61 => ( contrasubsetT3
% 2.99/1.61 => ( doubleComplementI1
% 2.99/1.61 => ( doubleComplementE1
% 2.99/1.61 => ( doubleComplementSub1
% 2.99/1.61 => ( doubleComplementSub2
% 2.99/1.61 => ( doubleComplementEq
% 2.99/1.61 => ( complementTnotintersectT
% 2.99/1.61 => ( complementImpComplementIntersect
% 2.99/1.61 => ( complementSubsetComplementIntersect
% 2.99/1.61 => ( complementInPowersetComplementIntersect
% 2.99/1.61 => ( contraSubsetComplement
% 2.99/1.61 => ( complementTcontraSubset
% 2.99/1.61 => ( binunionTILcontra
% 2.99/1.61 => ( binunionTIRcontra
% 2.99/1.61 => ( inIntersectImpInUnion
% 2.99/1.61 => ( inIntersectImpInUnion2
% 2.99/1.61 => ( inIntersectImpInIntersectUnions
% 2.99/1.61 => ( intersectInPowersetIntersectUnions
% 2.99/1.61 => ( inComplementUnionImpNotIn1
% 2.99/1.61 => ( inComplementUnionImpInComplement1
% 2.99/1.61 => ( binunionTE
% 2.99/1.61 => ( binunionTEcontra
% 2.99/1.61 => ( demorgan2a1
% 2.99/1.61 => ( complementUnionInPowersetComplement
% 2.99/1.61 => ( demorgan2a2
% 2.99/1.61 => ( demorgan1a
% 2.99/1.61 => ( demorgan1b
% 2.99/1.61 => ( demorgan1
% 2.99/1.61 => ( demorgan2a
% 2.99/1.61 => ( demorgan2b2
% 2.99/1.61 => ( demorgan2b
% 2.99/1.61 => ( demorgan2
% 2.99/1.61 => ( woz13rule0
% 2.99/1.61 => ( woz13rule1
% 2.99/1.61 => ( woz13rule2
% 2.99/1.61 => ( woz13rule3
% 2.99/1.61 => ( woz13rule4
% 2.99/1.61 => ( woz1_1
% 2.99/1.61 => ( woz1_2
% 2.99/1.61 => ( woz1_3
% 2.99/1.61 => ( woz1_4
% 2.99/1.61 => ( woz1_5
% 2.99/1.61 => ! [A: $i,R: $i] :
% 2.99/1.61 ( ( breln1 @ A @ R )
% 2.99/1.61 => ! [Xphi: $i > $o] :
% 2.99/1.61 ( ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ A )
% 2.99/1.61 => ! [Xy: $i] :
% 2.99/1.61 ( ( in @ Xy @ A )
% 2.99/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.61 => ! [Xx: $i] :
% 2.99/1.61 ( ( in @ Xx @ R )
% 2.99/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.61 ------------------------
% 2.99/1.65 % (10219)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/4Mi)
% 2.99/1.65 % (10218)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/183Mi)
% 2.99/1.65 % (10220)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/27Mi)
% 2.99/1.65 % (10219)Instruction limit reached!
% 2.99/1.65 % (10219)------------------------------
% 2.99/1.65 % (10219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.65 % (10219)Termination reason: Unknown
% 2.99/1.65 % (10219)Termination phase: shuffling
% 2.99/1.65
% 2.99/1.65 % (10219)Memory used [KB]: 1535
% 2.99/1.65 % (10219)Time elapsed: 0.003 s
% 2.99/1.65 % (10219)Instructions burned: 4 (million)
% 2.99/1.65 % (10219)------------------------------
% 2.99/1.65 % (10219)------------------------------
% 2.99/1.66 % (10221)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/2Mi)
% 2.99/1.66 % (10224)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/275Mi)
% 2.99/1.66 % (10223)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/2Mi)
% 2.99/1.66 % (10225)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/18Mi)
% 2.99/1.66 % (10220)Instruction limit reached!
% 2.99/1.66 % (10220)------------------------------
% 2.99/1.66 % (10220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.66 % (10220)Termination reason: Unknown
% 2.99/1.66 % (10220)Termination phase: shuffling
% 2.99/1.66
% 2.99/1.66 % (10220)Memory used [KB]: 2046
% 2.99/1.66 % (10220)Time elapsed: 0.010 s
% 2.99/1.66 % (10220)Instructions burned: 29 (million)
% 2.99/1.66 % (10220)------------------------------
% 2.99/1.66 % (10220)------------------------------
% 2.99/1.66 % (10221)Instruction limit reached!
% 2.99/1.66 % (10221)------------------------------
% 2.99/1.66 % (10221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.66 % (10221)Termination reason: Unknown
% 2.99/1.66 % (10221)Termination phase: shuffling
% 2.99/1.66
% 2.99/1.66 % (10221)Memory used [KB]: 1535
% 2.99/1.66 % (10221)Time elapsed: 0.003 s
% 2.99/1.66 % (10221)Instructions burned: 2 (million)
% 2.99/1.66 % (10221)------------------------------
% 2.99/1.66 % (10221)------------------------------
% 2.99/1.66 % (10223)Instruction limit reached!
% 2.99/1.66 % (10223)------------------------------
% 2.99/1.66 % (10223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.66 % (10223)Termination reason: Unknown
% 2.99/1.66 % (10223)Termination phase: shuffling
% 2.99/1.66
% 2.99/1.66 % (10223)Memory used [KB]: 1535
% 2.99/1.66 % (10223)Time elapsed: 0.003 s
% 2.99/1.66 % (10223)Instructions burned: 2 (million)
% 2.99/1.66 % (10223)------------------------------
% 2.99/1.66 % (10223)------------------------------
% 2.99/1.66 % (10227)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/3Mi)
% 2.99/1.67 % (10227)Instruction limit reached!
% 2.99/1.67 % (10227)------------------------------
% 2.99/1.67 % (10227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.67 % (10227)Termination reason: Unknown
% 2.99/1.67 % (10227)Termination phase: shuffling
% 2.99/1.67
% 2.99/1.67 % (10227)Memory used [KB]: 1535
% 2.99/1.67 % (10227)Time elapsed: 0.003 s
% 2.99/1.67 % (10227)Instructions burned: 6 (million)
% 2.99/1.67 % (10227)------------------------------
% 2.99/1.67 % (10227)------------------------------
% 2.99/1.67 % (10229)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/37Mi)
% 2.99/1.67 % (10225)Instruction limit reached!
% 2.99/1.67 % (10225)------------------------------
% 2.99/1.67 % (10225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.67 % (10225)Termination reason: Unknown
% 2.99/1.67 % (10225)Termination phase: shuffling
% 2.99/1.67
% 2.99/1.67 % (10225)Memory used [KB]: 1791
% 2.99/1.67 % (10225)Time elapsed: 0.013 s
% 2.99/1.67 % (10225)Instructions burned: 19 (million)
% 2.99/1.67 % (10225)------------------------------
% 2.99/1.67 % (10225)------------------------------
% 2.99/1.68 % (10236)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/1041Mi)
% 2.99/1.68 % (10230)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/15Mi)
% 2.99/1.68 % (10231)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/3Mi)
% 2.99/1.68 % (10231)Instruction limit reached!
% 2.99/1.68 % (10231)------------------------------
% 2.99/1.68 % (10231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.68 % (10231)Termination reason: Unknown
% 2.99/1.68 % (10231)Termination phase: shuffling
% 2.99/1.68
% 2.99/1.68 % (10231)Memory used [KB]: 1535
% 2.99/1.68 % (10231)Time elapsed: 0.004 s
% 2.99/1.68 % (10231)Instructions burned: 3 (million)
% 2.99/1.68 % (10231)------------------------------
% 2.99/1.68 % (10231)------------------------------
% 2.99/1.68 % (10229)Instruction limit reached!
% 2.99/1.68 % (10229)------------------------------
% 2.99/1.68 % (10229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.68 % (10229)Termination reason: Unknown
% 2.99/1.68 % (10229)Termination phase: shuffling
% 2.99/1.68
% 2.99/1.68 % (10229)Memory used [KB]: 2302
% 2.99/1.68 % (10229)Time elapsed: 0.012 s
% 2.99/1.68 % (10229)Instructions burned: 39 (million)
% 2.99/1.68 % (10229)------------------------------
% 2.99/1.68 % (10229)------------------------------
% 2.99/1.69 % (10243)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/7Mi)
% 2.99/1.69 % (10230)Instruction limit reached!
% 2.99/1.69 % (10230)------------------------------
% 2.99/1.69 % (10230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.69 % (10230)Termination reason: Unknown
% 2.99/1.69 % (10230)Termination phase: shuffling
% 2.99/1.69
% 2.99/1.69 % (10230)Memory used [KB]: 1791
% 2.99/1.69 % (10230)Time elapsed: 0.012 s
% 2.99/1.69 % (10230)Instructions burned: 16 (million)
% 2.99/1.69 % (10230)------------------------------
% 2.99/1.69 % (10230)------------------------------
% 2.99/1.69 % (10243)Instruction limit reached!
% 2.99/1.69 % (10243)------------------------------
% 2.99/1.69 % (10243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.69 % (10243)Termination reason: Unknown
% 2.99/1.69 % (10243)Termination phase: shuffling
% 2.99/1.69
% 2.99/1.69 % (10243)Memory used [KB]: 1663
% 2.99/1.69 % (10243)Time elapsed: 0.004 s
% 2.99/1.69 % (10243)Instructions burned: 8 (million)
% 2.99/1.69 % (10243)------------------------------
% 2.99/1.69 % (10243)------------------------------
% 2.99/1.69 % (10249)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/3Mi)
% 2.99/1.70 % (10249)Instruction limit reached!
% 2.99/1.70 % (10249)------------------------------
% 2.99/1.70 % (10249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.70 % (10249)Termination reason: Unknown
% 2.99/1.70 % (10249)Termination phase: shuffling
% 2.99/1.70
% 2.99/1.70 % (10249)Memory used [KB]: 1535
% 2.99/1.70 % (10249)Time elapsed: 0.002 s
% 2.99/1.70 % (10249)Instructions burned: 4 (million)
% 2.99/1.70 % (10249)------------------------------
% 2.99/1.70 % (10249)------------------------------
% 3.02/1.70 % (10248)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/16Mi)
% 3.02/1.70 % (10218)Instruction limit reached!
% 3.02/1.70 % (10218)------------------------------
% 3.02/1.70 % (10218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.70 % (10218)Termination reason: Unknown
% 3.02/1.70 % (10218)Termination phase: Saturation
% 3.02/1.70
% 3.02/1.70 % (10218)Memory used [KB]: 7419
% 3.02/1.70 % (10218)Time elapsed: 0.048 s
% 3.02/1.70 % (10218)Instructions burned: 185 (million)
% 3.02/1.70 % (10218)------------------------------
% 3.02/1.70 % (10218)------------------------------
% 3.02/1.70 % (10253)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/7Mi)
% 3.02/1.71 % (10248)Instruction limit reached!
% 3.02/1.71 % (10248)------------------------------
% 3.02/1.71 % (10248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (10248)Termination reason: Unknown
% 3.02/1.71 % (10248)Termination phase: shuffling
% 3.02/1.71
% 3.02/1.71 % (10248)Memory used [KB]: 1918
% 3.02/1.71 % (10248)Time elapsed: 0.008 s
% 3.02/1.71 % (10248)Instructions burned: 17 (million)
% 3.02/1.71 % (10248)------------------------------
% 3.02/1.71 % (10248)------------------------------
% 3.02/1.71 % (10253)Instruction limit reached!
% 3.02/1.71 % (10253)------------------------------
% 3.02/1.71 % (10253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (10253)Termination reason: Unknown
% 3.02/1.71 % (10253)Termination phase: shuffling
% 3.02/1.71
% 3.02/1.71 % (10253)Memory used [KB]: 1535
% 3.02/1.71 % (10253)Time elapsed: 0.003 s
% 3.02/1.71 % (10253)Instructions burned: 7 (million)
% 3.02/1.71 % (10253)------------------------------
% 3.02/1.71 % (10253)------------------------------
% 3.02/1.71 % (10255)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/3Mi)
% 3.02/1.71 % (10255)Instruction limit reached!
% 3.02/1.71 % (10255)------------------------------
% 3.02/1.71 % (10255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (10255)Termination reason: Unknown
% 3.02/1.71 % (10255)Termination phase: shuffling
% 3.02/1.71
% 3.02/1.71 % (10255)Memory used [KB]: 1535
% 3.02/1.71 % (10255)Time elapsed: 0.002 s
% 3.02/1.71 % (10255)Instructions burned: 4 (million)
% 3.02/1.71 % (10255)------------------------------
% 3.02/1.71 % (10255)------------------------------
% 3.02/1.71 % (10251)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/3Mi)
% 3.02/1.71 % (10259)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/4Mi)
% 3.02/1.71 % (10251)Instruction limit reached!
% 3.02/1.71 % (10251)------------------------------
% 3.02/1.71 % (10251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (10251)Termination reason: Unknown
% 3.02/1.71 % (10251)Termination phase: shuffling
% 3.02/1.71
% 3.02/1.71 % (10251)Memory used [KB]: 1535
% 3.02/1.71 % (10251)Time elapsed: 0.004 s
% 3.02/1.71 % (10251)Instructions burned: 4 (million)
% 3.02/1.71 % (10251)------------------------------
% 3.02/1.71 % (10251)------------------------------
% 3.02/1.71 % (10259)Instruction limit reached!
% 3.02/1.71 % (10259)------------------------------
% 3.02/1.71 % (10259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71 % (10259)Termination reason: Unknown
% 3.02/1.71 % (10259)Termination phase: shuffling
% 3.02/1.71
% 3.02/1.71 % (10259)Memory used [KB]: 1535
% 3.02/1.71 % (10259)Time elapsed: 0.003 s
% 3.02/1.71 % (10259)Instructions burned: 6 (million)
% 3.02/1.71 % (10259)------------------------------
% 3.02/1.71 % (10259)------------------------------
% 3.02/1.72 % (10262)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/18Mi)
% 3.02/1.72 % (10263)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/710Mi)
% 3.02/1.72 % (10265)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/6Mi)
% 3.02/1.72 % (10265)Instruction limit reached!
% 3.02/1.72 % (10265)------------------------------
% 3.02/1.72 % (10265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.72 % (10265)Termination reason: Unknown
% 3.02/1.72 % (10265)Termination phase: shuffling
% 3.02/1.72
% 3.02/1.72 % (10265)Memory used [KB]: 1535
% 3.02/1.72 % (10265)Time elapsed: 0.003 s
% 3.02/1.72 % (10265)Instructions burned: 7 (million)
% 3.02/1.72 % (10265)------------------------------
% 3.02/1.72 % (10265)------------------------------
% 3.02/1.72 % (10262)Instruction limit reached!
% 3.02/1.72 % (10262)------------------------------
% 3.02/1.72 % (10262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.72 % (10262)Termination reason: Unknown
% 3.02/1.72 % (10262)Termination phase: shuffling
% 3.02/1.72
% 3.02/1.72 % (10262)Memory used [KB]: 1791
% 3.02/1.72 % (10262)Time elapsed: 0.006 s
% 3.02/1.72 % (10262)Instructions burned: 18 (million)
% 3.02/1.72 % (10262)------------------------------
% 3.02/1.72 % (10262)------------------------------
% 3.02/1.72 % (10270)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/21Mi)
% 3.02/1.73 % (10270)Instruction limit reached!
% 3.02/1.73 % (10270)------------------------------
% 3.02/1.73 % (10270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.73 % (10270)Termination reason: Unknown
% 3.02/1.73 % (10270)Termination phase: shuffling
% 3.02/1.73
% 3.02/1.73 % (10270)Memory used [KB]: 1918
% 3.02/1.73 % (10270)Time elapsed: 0.007 s
% 3.02/1.73 % (10270)Instructions burned: 22 (million)
% 3.02/1.73 % (10270)------------------------------
% 3.02/1.73 % (10270)------------------------------
% 3.02/1.73 % (10269)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/902Mi)
% 3.02/1.73 % (10274)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/5Mi)
% 3.02/1.73 % (10275)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_9951 for (2999ds/6Mi)
% 3.02/1.73 % (10274)Instruction limit reached!
% 3.02/1.73 % (10274)------------------------------
% 3.02/1.73 % (10274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.73 % (10274)Termination reason: Unknown
% 3.02/1.73 % (10274)Termination phase: shuffling
% 3.02/1.73
% 3.02/1.73 % (10274)Memory used [KB]: 1663
% 3.02/1.73 % (10274)Time elapsed: 0.003 s
% 3.02/1.73 % (10274)Instructions burned: 8 (million)
% 3.02/1.73 % (10274)------------------------------
% 3.02/1.73 % (10274)------------------------------
% 3.02/1.73 % (10275)Instruction limit reached!
% 3.02/1.73 % (10275)------------------------------
% 3.02/1.73 % (10275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.73 % (10275)Termination reason: Unknown
% 3.02/1.73 % (10275)Termination phase: shuffling
% 3.02/1.73
% 3.02/1.73 % (10275)Memory used [KB]: 1535
% 3.02/1.73 % (10275)Time elapsed: 0.003 s
% 3.02/1.73 % (10275)Instructions burned: 6 (million)
% 3.02/1.73 % (10275)------------------------------
% 3.02/1.73 % (10275)------------------------------
% 3.02/1.74 % (10277)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_9951 for (2998ds/377Mi)
% 3.02/1.74 % (10280)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_9951 for (2998ds/779Mi)
% 3.02/1.74 % (10281)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_9951 for (2998ds/19Mi)
% 3.02/1.75 % (10281)Instruction limit reached!
% 3.02/1.75 % (10281)------------------------------
% 3.02/1.75 % (10281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.75 % (10281)Termination reason: Unknown
% 3.02/1.75 % (10281)Termination phase: shuffling
% 3.02/1.75
% 3.02/1.75 % (10281)Memory used [KB]: 1918
% 3.02/1.75 % (10281)Time elapsed: 0.007 s
% 3.02/1.75 % (10281)Instructions burned: 20 (million)
% 3.02/1.75 % (10281)------------------------------
% 3.02/1.75 % (10281)------------------------------
% 3.02/1.76 % (10287)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_9951 for (2998ds/879Mi)
% 3.02/1.79 % (10224)Instruction limit reached!
% 3.02/1.79 % (10224)------------------------------
% 3.02/1.79 % (10224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.79 % (10224)Termination reason: Unknown
% 3.02/1.79 % (10224)Termination phase: Saturation
% 3.02/1.79
% 3.02/1.79 % (10224)Memory used [KB]: 10106
% 3.02/1.79 % (10224)Time elapsed: 0.128 s
% 3.02/1.79 % (10224)Instructions burned: 276 (million)
% 3.02/1.79 % (10224)------------------------------
% 3.02/1.79 % (10224)------------------------------
% 3.02/1.80 % (10304)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_9951 for (2998ds/17Mi)
% 3.02/1.81 % (10304)Instruction limit reached!
% 3.02/1.81 % (10304)------------------------------
% 3.02/1.81 % (10304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.81 % (10304)Termination reason: Unknown
% 3.02/1.81 % (10304)Termination phase: shuffling
% 3.02/1.81
% 3.02/1.81 % (10304)Memory used [KB]: 1791
% 3.02/1.81 % (10304)Time elapsed: 0.007 s
% 3.02/1.81 % (10304)Instructions burned: 19 (million)
% 3.02/1.81 % (10304)------------------------------
% 3.02/1.81 % (10304)------------------------------
% 3.02/1.82 % (10310)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9951 for (2998ds/3Mi)
% 3.02/1.82 % (10310)Instruction limit reached!
% 3.02/1.82 % (10310)------------------------------
% 3.02/1.82 % (10310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.82 % (10310)Termination reason: Unknown
% 3.02/1.82 % (10310)Termination phase: shuffling
% 3.02/1.82
% 3.02/1.82 % (10310)Memory used [KB]: 1535
% 3.02/1.82 % (10310)Time elapsed: 0.002 s
% 3.02/1.82 % (10310)Instructions burned: 3 (million)
% 3.02/1.82 % (10310)------------------------------
% 3.02/1.82 % (10310)------------------------------
% 3.02/1.83 % (10314)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_9951 for (2998ds/30Mi)
% 3.02/1.84 % (10314)Instruction limit reached!
% 3.02/1.84 % (10314)------------------------------
% 3.02/1.84 % (10314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.84 % (10314)Termination reason: Unknown
% 3.02/1.84 % (10314)Termination phase: shuffling
% 3.02/1.84
% 3.02/1.84 % (10314)Memory used [KB]: 2046
% 3.02/1.84 % (10314)Time elapsed: 0.010 s
% 3.02/1.84 % (10314)Instructions burned: 31 (million)
% 3.02/1.84 % (10314)------------------------------
% 3.02/1.84 % (10314)------------------------------
% 3.02/1.84 % (10277)Instruction limit reached!
% 3.02/1.84 % (10277)------------------------------
% 3.02/1.84 % (10277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.84 % (10277)Termination reason: Unknown
% 3.02/1.84 % (10277)Termination phase: Saturation
% 3.02/1.84
% 3.02/1.84 % (10277)Memory used [KB]: 9466
% 3.02/1.84 % (10277)Time elapsed: 0.102 s
% 3.02/1.84 % (10277)Instructions burned: 378 (million)
% 3.02/1.84 % (10277)------------------------------
% 3.02/1.84 % (10277)------------------------------
% 3.02/1.85 % (10318)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_9951 for (2997ds/127Mi)
% 3.02/1.85 % (10320)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_9951 for (2997ds/100Mi)
% 3.02/1.87 % (10320)Instruction limit reached!
% 3.02/1.87 % (10320)------------------------------
% 3.02/1.87 % (10320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.87 % (10320)Termination reason: Unknown
% 3.02/1.87 % (10320)Termination phase: Property scanning
% 3.02/1.87
% 3.02/1.87 % (10320)Memory used [KB]: 2686
% 3.02/1.87 % (10320)Time elapsed: 0.027 s
% 3.02/1.87 % (10320)Instructions burned: 102 (million)
% 3.02/1.87 % (10320)------------------------------
% 3.02/1.87 % (10320)------------------------------
% 3.02/1.88 % (10318)Instruction limit reached!
% 3.02/1.88 % (10318)------------------------------
% 3.02/1.88 % (10318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.88 % (10318)Termination reason: Unknown
% 3.02/1.88 % (10318)Termination phase: Property scanning
% 3.02/1.88
% 3.02/1.88 % (10318)Memory used [KB]: 2686
% 3.02/1.88 % (10318)Time elapsed: 0.036 s
% 3.02/1.88 % (10318)Instructions burned: 127 (million)
% 3.02/1.88 % (10318)------------------------------
% 3.02/1.88 % (10318)------------------------------
% 3.02/1.88 % (10334)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_9951 for (2997ds/3Mi)
% 3.02/1.89 % (10334)Instruction limit reached!
% 3.02/1.89 % (10334)------------------------------
% 3.02/1.89 % (10334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.89 % (10334)Termination reason: Unknown
% 3.02/1.89 % (10334)Termination phase: shuffling
% 3.02/1.89
% 3.02/1.89 % (10334)Memory used [KB]: 1535
% 3.02/1.89 % (10334)Time elapsed: 0.003 s
% 3.02/1.89 % (10334)Instructions burned: 6 (million)
% 3.02/1.89 % (10334)------------------------------
% 3.02/1.89 % (10334)------------------------------
% 3.02/1.89 % (10336)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_9951 for (2997ds/20Mi)
% 3.02/1.89 % (10339)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_9951 for (2997ds/86Mi)
% 3.02/1.90 % (10336)Instruction limit reached!
% 3.02/1.90 % (10336)------------------------------
% 3.02/1.90 % (10336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.90 % (10336)Termination reason: Unknown
% 3.02/1.90 % (10336)Termination phase: shuffling
% 3.02/1.90
% 3.02/1.90 % (10336)Memory used [KB]: 1918
% 3.02/1.90 % (10336)Time elapsed: 0.008 s
% 3.02/1.90 % (10336)Instructions burned: 20 (million)
% 3.02/1.90 % (10336)------------------------------
% 3.02/1.90 % (10336)------------------------------
% 3.02/1.91 % (10341)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_9951 for (2997ds/107Mi)
% 3.02/1.92 % (10339)Instruction limit reached!
% 3.02/1.92 % (10339)------------------------------
% 3.02/1.92 % (10339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.92 % (10339)Termination reason: Unknown
% 3.02/1.92 % (10339)Termination phase: Preprocessing 2
% 3.02/1.92
% 3.02/1.92 % (10339)Memory used [KB]: 2558
% 3.02/1.92 % (10339)Time elapsed: 0.024 s
% 3.02/1.92 % (10339)Instructions burned: 87 (million)
% 3.02/1.92 % (10339)------------------------------
% 3.02/1.92 % (10339)------------------------------
% 3.02/1.93 % (10354)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_9951 for (2997ds/39Mi)
% 3.02/1.94 % (10280)Instruction limit reached!
% 3.02/1.94 % (10280)------------------------------
% 3.02/1.94 % (10280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.94 % (10280)Termination reason: Unknown
% 3.02/1.94 % (10280)Termination phase: Saturation
% 3.02/1.94
% 3.02/1.94 % (10280)Memory used [KB]: 7675
% 3.02/1.94 % (10280)Time elapsed: 0.195 s
% 3.02/1.94 % (10280)Instructions burned: 780 (million)
% 3.02/1.94 % (10280)------------------------------
% 3.02/1.94 % (10280)------------------------------
% 3.02/1.94 % (10354)Instruction limit reached!
% 3.02/1.94 % (10354)------------------------------
% 3.02/1.94 % (10354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.94 % (10354)Termination reason: Unknown
% 3.02/1.94 % (10354)Termination phase: shuffling
% 3.02/1.94
% 3.02/1.94 % (10354)Memory used [KB]: 2302
% 3.02/1.94 % (10354)Time elapsed: 0.012 s
% 3.02/1.94 % (10354)Instructions burned: 40 (million)
% 3.02/1.94 % (10354)------------------------------
% 3.02/1.94 % (10354)------------------------------
% 3.02/1.94 % (10341)Instruction limit reached!
% 3.02/1.94 % (10341)------------------------------
% 3.02/1.94 % (10341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.94 % (10341)Termination reason: Unknown
% 3.02/1.94 % (10341)Termination phase: SInE selection
% 3.02/1.94
% 3.02/1.94 % (10341)Memory used [KB]: 2558
% 3.02/1.94 % (10341)Time elapsed: 0.031 s
% 3.02/1.94 % (10341)Instructions burned: 109 (million)
% 3.02/1.94 % (10341)------------------------------
% 3.02/1.94 % (10341)------------------------------
% 3.02/1.94 % (10236)Instruction limit reached!
% 3.02/1.94 % (10236)------------------------------
% 3.02/1.94 % (10236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.94 % (10236)Termination reason: Unknown
% 3.02/1.94 % (10236)Termination phase: Saturation
% 3.02/1.94
% 3.02/1.94 % (10236)Memory used [KB]: 16119
% 3.02/1.94 % (10236)Time elapsed: 0.270 s
% 3.02/1.94 % (10236)Instructions burned: 1043 (million)
% 3.02/1.94 % (10236)------------------------------
% 3.02/1.94 % (10236)------------------------------
% 3.02/1.95 % (10364)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/448Mi)
% 3.02/1.95 % (10367)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/46Mi)
% 3.02/1.95 % (10369)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/98Mi)
% 3.02/1.95 % (10263)Instruction limit reached!
% 3.02/1.95 % (10263)------------------------------
% 3.02/1.95 % (10263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.95 % (10263)Termination reason: Unknown
% 3.02/1.95 % (10263)Termination phase: Saturation
% 3.02/1.95
% 3.02/1.95 % (10263)Memory used [KB]: 11001
% 3.02/1.95 % (10263)Time elapsed: 0.236 s
% 3.02/1.95 % (10263)Instructions burned: 712 (million)
% 3.02/1.95 % (10263)------------------------------
% 3.02/1.95 % (10263)------------------------------
% 3.02/1.96 % (10374)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/507Mi)
% 3.02/1.96 % (10367)Instruction limit reached!
% 3.02/1.96 % (10367)------------------------------
% 3.02/1.96 % (10367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.96 % (10367)Termination reason: Unknown
% 3.02/1.96 % (10367)Termination phase: shuffling
% 3.02/1.96
% 3.02/1.96 % (10367)Memory used [KB]: 2430
% 3.02/1.96 % (10367)Time elapsed: 0.014 s
% 3.02/1.96 % (10367)Instructions burned: 47 (million)
% 3.02/1.96 % (10367)------------------------------
% 3.02/1.96 % (10367)------------------------------
% 3.02/1.96 % (10378)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/149Mi)
% 3.02/1.97 % (10383)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/39Mi)
% 3.02/1.98 % (10369)Instruction limit reached!
% 3.02/1.98 % (10369)------------------------------
% 3.02/1.98 % (10369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.98 % (10369)Termination reason: Unknown
% 3.02/1.98 % (10369)Termination phase: Property scanning
% 3.02/1.98
% 3.02/1.98 % (10369)Memory used [KB]: 2558
% 3.02/1.98 % (10369)Time elapsed: 0.028 s
% 3.02/1.98 % (10369)Instructions burned: 98 (million)
% 3.02/1.98 % (10369)------------------------------
% 3.02/1.98 % (10369)------------------------------
% 3.02/1.98 % (10383)Instruction limit reached!
% 3.02/1.98 % (10383)------------------------------
% 3.02/1.98 % (10383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.98 % (10383)Termination reason: Unknown
% 3.02/1.98 % (10383)Termination phase: shuffling
% 3.02/1.98
% 3.02/1.98 % (10383)Memory used [KB]: 2302
% 3.02/1.98 % (10383)Time elapsed: 0.012 s
% 3.02/1.98 % (10383)Instructions burned: 40 (million)
% 3.02/1.98 % (10383)------------------------------
% 3.02/1.98 % (10383)------------------------------
% 3.02/1.99 % (10388)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/6Mi)
% 3.02/1.99 % (10388)Instruction limit reached!
% 3.02/1.99 % (10388)------------------------------
% 3.02/1.99 % (10388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.99 % (10388)Termination reason: Unknown
% 3.02/1.99 % (10388)Termination phase: shuffling
% 3.02/1.99
% 3.02/1.99 % (10388)Memory used [KB]: 1535
% 3.02/1.99 % (10388)Time elapsed: 0.003 s
% 3.02/1.99 % (10388)Instructions burned: 7 (million)
% 3.02/1.99 % (10388)------------------------------
% 3.02/1.99 % (10388)------------------------------
% 3.02/1.99 % (10390)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/1087Mi)
% 3.02/2.00 % (10391)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/47Mi)
% 3.02/2.00 % (10378)Instruction limit reached!
% 3.02/2.00 % (10378)------------------------------
% 3.02/2.00 % (10378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/2.00 % (10378)Termination reason: Unknown
% 3.02/2.00 % (10378)Termination phase: Twee Goal Transformation
% 3.02/2.00
% 3.02/2.00 % (10378)Memory used [KB]: 3070
% 3.02/2.00 % (10378)Time elapsed: 0.043 s
% 3.02/2.00 % (10378)Instructions burned: 151 (million)
% 3.02/2.00 % (10378)------------------------------
% 3.02/2.00 % (10378)------------------------------
% 5.55/2.01 % (10391)Instruction limit reached!
% 5.55/2.01 % (10391)------------------------------
% 5.55/2.01 % (10391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.01 % (10391)Termination reason: Unknown
% 5.55/2.01 % (10391)Termination phase: shuffling
% 5.55/2.01
% 5.55/2.01 % (10391)Memory used [KB]: 2430
% 5.55/2.01 % (10391)Time elapsed: 0.016 s
% 5.55/2.01 % (10391)Instructions burned: 49 (million)
% 5.55/2.01 % (10391)------------------------------
% 5.55/2.01 % (10391)------------------------------
% 5.55/2.01 % (10392)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/44Mi)
% 5.55/2.02 % (10287)Instruction limit reached!
% 5.55/2.02 % (10287)------------------------------
% 5.55/2.02 % (10287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.02 % (10287)Termination reason: Unknown
% 5.55/2.02 % (10287)Termination phase: Saturation
% 5.55/2.02
% 5.55/2.02 % (10287)Memory used [KB]: 10106
% 5.55/2.02 % (10287)Time elapsed: 0.262 s
% 5.55/2.02 % (10287)Instructions burned: 879 (million)
% 5.55/2.02 % (10287)------------------------------
% 5.55/2.02 % (10287)------------------------------
% 5.55/2.02 % (10393)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_9951 for (2996ds/432Mi)
% 5.55/2.03 % (10392)Instruction limit reached!
% 5.55/2.03 % (10392)------------------------------
% 5.55/2.03 % (10392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.03 % (10392)Termination reason: Unknown
% 5.55/2.03 % (10392)Termination phase: shuffling
% 5.55/2.03
% 5.55/2.03 % (10392)Memory used [KB]: 2430
% 5.55/2.03 % (10392)Time elapsed: 0.014 s
% 5.55/2.03 % (10392)Instructions burned: 46 (million)
% 5.55/2.03 % (10392)------------------------------
% 5.55/2.03 % (10392)------------------------------
% 5.55/2.03 % (10394)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/62Mi)
% 5.55/2.04 % (10395)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/31Mi)
% 5.55/2.04 % (10394)Instruction limit reached!
% 5.55/2.04 % (10394)------------------------------
% 5.55/2.04 % (10394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.04 % (10394)Termination reason: Unknown
% 5.55/2.04 % (10394)Termination phase: Property scanning
% 5.55/2.04
% 5.55/2.04 % (10394)Memory used [KB]: 2558
% 5.55/2.04 % (10394)Time elapsed: 0.018 s
% 5.55/2.04 % (10394)Instructions burned: 65 (million)
% 5.55/2.04 % (10394)------------------------------
% 5.55/2.04 % (10394)------------------------------
% 5.55/2.05 % (10395)Instruction limit reached!
% 5.55/2.05 % (10395)------------------------------
% 5.55/2.05 % (10395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.05 % (10395)Termination reason: Unknown
% 5.55/2.05 % (10395)Termination phase: shuffling
% 5.55/2.05
% 5.55/2.05 % (10395)Memory used [KB]: 2174
% 5.55/2.05 % (10395)Time elapsed: 0.011 s
% 5.55/2.05 % (10395)Instructions burned: 33 (million)
% 5.55/2.05 % (10395)------------------------------
% 5.55/2.05 % (10395)------------------------------
% 5.55/2.05 % (10396)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/96Mi)
% 5.55/2.05 % (10364)Instruction limit reached!
% 5.55/2.05 % (10364)------------------------------
% 5.55/2.05 % (10364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.05 % (10364)Termination reason: Unknown
% 5.55/2.05 % (10364)Termination phase: Saturation
% 5.55/2.05
% 5.55/2.05 % (10364)Memory used [KB]: 7547
% 5.55/2.05 % (10364)Time elapsed: 0.111 s
% 5.55/2.05 % (10364)Instructions burned: 449 (million)
% 5.55/2.05 % (10364)------------------------------
% 5.55/2.05 % (10364)------------------------------
% 5.55/2.06 % (10397)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/453Mi)
% 5.55/2.06 % (10398)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/71Mi)
% 5.55/2.08 % (10269)Instruction limit reached!
% 5.55/2.08 % (10269)------------------------------
% 5.55/2.08 % (10269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.08 % (10269)Termination reason: Unknown
% 5.55/2.08 % (10269)Termination phase: Saturation
% 5.55/2.08
% 5.55/2.08 % (10269)Memory used [KB]: 11641
% 5.55/2.08 % (10269)Time elapsed: 0.350 s
% 5.55/2.08 % (10269)Instructions burned: 902 (million)
% 5.55/2.08 % (10269)------------------------------
% 5.55/2.08 % (10269)------------------------------
% 5.55/2.08 % (10396)Instruction limit reached!
% 5.55/2.08 % (10396)------------------------------
% 5.55/2.08 % (10396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.08 % (10396)Termination reason: Unknown
% 5.55/2.08 % (10396)Termination phase: Property scanning
% 5.55/2.08
% 5.55/2.08 % (10396)Memory used [KB]: 2686
% 5.55/2.08 % (10396)Time elapsed: 0.028 s
% 5.55/2.08 % (10396)Instructions burned: 100 (million)
% 5.55/2.08 % (10396)------------------------------
% 5.55/2.08 % (10396)------------------------------
% 5.55/2.08 % (10398)Instruction limit reached!
% 5.55/2.08 % (10398)------------------------------
% 5.55/2.08 % (10398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.08 % (10398)Termination reason: Unknown
% 5.55/2.08 % (10398)Termination phase: Property scanning
% 5.55/2.08
% 5.55/2.08 % (10398)Memory used [KB]: 2558
% 5.55/2.08 % (10398)Time elapsed: 0.021 s
% 5.55/2.08 % (10398)Instructions burned: 72 (million)
% 5.55/2.08 % (10398)------------------------------
% 5.55/2.08 % (10398)------------------------------
% 5.55/2.09 % (10400)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/11Mi)
% 5.55/2.09 % (10401)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/41Mi)
% 5.55/2.09 % (10400)Instruction limit reached!
% 5.55/2.09 % (10400)------------------------------
% 5.55/2.09 % (10400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.09 % (10400)Termination reason: Unknown
% 5.55/2.09 % (10400)Termination phase: shuffling
% 5.55/2.09
% 5.55/2.09 % (10400)Memory used [KB]: 1791
% 5.55/2.09 % (10400)Time elapsed: 0.005 s
% 5.55/2.09 % (10400)Instructions burned: 14 (million)
% 5.55/2.09 % (10400)------------------------------
% 5.55/2.09 % (10400)------------------------------
% 5.55/2.10 % (10399)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/83Mi)
% 5.55/2.10 % (10374)Instruction limit reached!
% 5.55/2.10 % (10374)------------------------------
% 5.55/2.10 % (10374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.10 % (10374)Termination reason: Unknown
% 5.55/2.10 % (10374)Termination phase: Saturation
% 5.55/2.10
% 5.55/2.10 % (10374)Memory used [KB]: 8187
% 5.55/2.10 % (10374)Time elapsed: 0.169 s
% 5.55/2.10 % (10374)Instructions burned: 509 (million)
% 5.55/2.10 % (10374)------------------------------
% 5.55/2.10 % (10374)------------------------------
% 5.55/2.10 % (10402)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/6Mi)
% 5.55/2.10 % (10401)Instruction limit reached!
% 5.55/2.10 % (10401)------------------------------
% 5.55/2.10 % (10401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.10 % (10401)Termination reason: Unknown
% 5.55/2.10 % (10401)Termination phase: shuffling
% 5.55/2.10
% 5.55/2.10 % (10401)Memory used [KB]: 2302
% 5.55/2.10 % (10401)Time elapsed: 0.012 s
% 5.55/2.10 % (10401)Instructions burned: 42 (million)
% 5.55/2.10 % (10401)------------------------------
% 5.55/2.10 % (10401)------------------------------
% 5.55/2.11 % (10402)Instruction limit reached!
% 5.55/2.11 % (10402)------------------------------
% 5.55/2.11 % (10402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.11 % (10402)Termination reason: Unknown
% 5.55/2.11 % (10402)Termination phase: shuffling
% 5.55/2.11
% 5.55/2.11 % (10402)Memory used [KB]: 1535
% 5.55/2.11 % (10402)Time elapsed: 0.003 s
% 5.55/2.11 % (10402)Instructions burned: 7 (million)
% 5.55/2.11 % (10402)------------------------------
% 5.55/2.11 % (10402)------------------------------
% 5.55/2.11 % (10403)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/150Mi)
% 6.07/2.11 % (10404)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/343Mi)
% 6.07/2.12 % (10405)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_9951 for (2995ds/109Mi)
% 6.07/2.12 % (10399)Instruction limit reached!
% 6.07/2.12 % (10399)------------------------------
% 6.07/2.12 % (10399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.12 % (10399)Termination reason: Unknown
% 6.07/2.12 % (10399)Termination phase: Property scanning
% 6.07/2.12
% 6.07/2.12 % (10399)Memory used [KB]: 2558
% 6.07/2.12 % (10399)Time elapsed: 0.030 s
% 6.07/2.12 % (10399)Instructions burned: 83 (million)
% 6.07/2.12 % (10399)------------------------------
% 6.07/2.12 % (10399)------------------------------
% 6.07/2.13 % (10406)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/253Mi)
% 6.07/2.14 % (10393)Instruction limit reached!
% 6.07/2.14 % (10393)------------------------------
% 6.07/2.14 % (10393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.14 % (10393)Termination reason: Unknown
% 6.07/2.14 % (10393)Termination phase: Saturation
% 6.07/2.14
% 6.07/2.14 % (10393)Memory used [KB]: 3070
% 6.07/2.14 % (10393)Time elapsed: 0.116 s
% 6.07/2.14 % (10393)Instructions burned: 433 (million)
% 6.07/2.14 % (10393)------------------------------
% 6.07/2.14 % (10393)------------------------------
% 6.07/2.14 % (10405)Instruction limit reached!
% 6.07/2.14 % (10405)------------------------------
% 6.07/2.14 % (10405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.14 % (10405)Termination reason: Unknown
% 6.07/2.14 % (10405)Termination phase: SInE selection
% 6.07/2.14
% 6.07/2.14 % (10405)Memory used [KB]: 2558
% 6.07/2.14 % (10405)Time elapsed: 0.029 s
% 6.07/2.14 % (10405)Instructions burned: 110 (million)
% 6.07/2.14 % (10405)------------------------------
% 6.07/2.14 % (10405)------------------------------
% 6.07/2.15 % (10407)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/140Mi)
% 6.07/2.15 % (10408)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/614Mi)
% 6.07/2.15 % (10403)Instruction limit reached!
% 6.07/2.15 % (10403)------------------------------
% 6.07/2.15 % (10403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.15 % (10403)Termination reason: Unknown
% 6.07/2.15 % (10403)Termination phase: Property scanning
% 6.07/2.15
% 6.07/2.15 % (10403)Memory used [KB]: 4989
% 6.07/2.15 % (10403)Time elapsed: 0.045 s
% 6.07/2.15 % (10403)Instructions burned: 154 (million)
% 6.07/2.15 % (10403)------------------------------
% 6.07/2.15 % (10403)------------------------------
% 6.07/2.16 % (10409)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/202Mi)
% 6.07/2.17 % (10397)Instruction limit reached!
% 6.07/2.17 % (10397)------------------------------
% 6.07/2.17 % (10397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.17 % (10397)Termination reason: Unknown
% 6.07/2.17 % (10397)Termination phase: Saturation
% 6.07/2.17
% 6.07/2.17 % (10397)Memory used [KB]: 7547
% 6.07/2.17 % (10397)Time elapsed: 0.115 s
% 6.07/2.17 % (10397)Instructions burned: 455 (million)
% 6.07/2.17 % (10397)------------------------------
% 6.07/2.17 % (10397)------------------------------
% 6.07/2.18 % (10410)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/339Mi)
% 6.07/2.18 % (10407)Instruction limit reached!
% 6.07/2.18 % (10407)------------------------------
% 6.07/2.18 % (10407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.18 % (10407)Termination reason: Unknown
% 6.07/2.18 % (10407)Termination phase: Function definition elimination
% 6.07/2.18
% 6.07/2.18 % (10407)Memory used [KB]: 2814
% 6.07/2.18 % (10407)Time elapsed: 0.037 s
% 6.07/2.18 % (10407)Instructions burned: 140 (million)
% 6.07/2.18 % (10407)------------------------------
% 6.07/2.18 % (10407)------------------------------
% 6.07/2.20 % (10411)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/283Mi)
% 6.59/2.20 % (10404)Instruction limit reached!
% 6.59/2.20 % (10404)------------------------------
% 6.59/2.20 % (10404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.20 % (10404)Termination reason: Unknown
% 6.59/2.20 % (10404)Termination phase: Saturation
% 6.59/2.20
% 6.59/2.20 % (10404)Memory used [KB]: 8443
% 6.59/2.20 % (10404)Time elapsed: 0.091 s
% 6.59/2.20 % (10404)Instructions burned: 345 (million)
% 6.59/2.20 % (10404)------------------------------
% 6.59/2.20 % (10404)------------------------------
% 6.59/2.21 % (10406)Instruction limit reached!
% 6.59/2.21 % (10406)------------------------------
% 6.59/2.21 % (10406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.21 % (10406)Termination reason: Unknown
% 6.59/2.21 % (10406)Termination phase: Saturation
% 6.59/2.21
% 6.59/2.21 % (10406)Memory used [KB]: 10106
% 6.59/2.21 % (10406)Time elapsed: 0.077 s
% 6.59/2.21 % (10406)Instructions burned: 255 (million)
% 6.59/2.21 % (10406)------------------------------
% 6.59/2.21 % (10406)------------------------------
% 6.59/2.21 % (10412)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/134Mi)
% 6.59/2.22 % (10409)Instruction limit reached!
% 6.59/2.22 % (10409)------------------------------
% 6.59/2.22 % (10409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.22 % (10409)Termination reason: Unknown
% 6.59/2.22 % (10409)Termination phase: Property scanning
% 6.59/2.22
% 6.59/2.22 % (10409)Memory used [KB]: 5117
% 6.59/2.22 % (10409)Time elapsed: 0.059 s
% 6.59/2.22 % (10409)Instructions burned: 203 (million)
% 6.59/2.22 % (10409)------------------------------
% 6.59/2.22 % (10409)------------------------------
% 6.59/2.22 % (10413)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/298Mi)
% 6.59/2.23 % (10414)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_9951 for (2994ds/192Mi)
% 6.59/2.25 % (10412)Instruction limit reached!
% 6.59/2.25 % (10412)------------------------------
% 6.59/2.25 % (10412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.25 % (10412)Termination reason: Unknown
% 6.59/2.25 % (10412)Termination phase: Property scanning
% 6.59/2.25
% 6.59/2.25 % (10412)Memory used [KB]: 2814
% 6.59/2.25 % (10412)Time elapsed: 0.036 s
% 6.59/2.25 % (10412)Instructions burned: 136 (million)
% 6.59/2.25 % (10412)------------------------------
% 6.59/2.25 % (10412)------------------------------
% 6.59/2.26 % (10415)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/258Mi)
% 6.59/2.27 % (10411)Instruction limit reached!
% 6.59/2.27 % (10411)------------------------------
% 6.59/2.27 % (10411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.27 % (10411)Termination reason: Unknown
% 6.59/2.27 % (10411)Termination phase: Saturation
% 6.59/2.27
% 6.59/2.27 % (10411)Memory used [KB]: 7547
% 6.59/2.27 % (10411)Time elapsed: 0.073 s
% 6.59/2.27 % (10411)Instructions burned: 285 (million)
% 6.59/2.27 % (10411)------------------------------
% 6.59/2.27 % (10411)------------------------------
% 6.59/2.27 % (10410)Instruction limit reached!
% 6.59/2.27 % (10410)------------------------------
% 6.59/2.27 % (10410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.27 % (10410)Termination reason: Unknown
% 6.59/2.27 % (10410)Termination phase: Saturation
% 6.59/2.27
% 6.59/2.27 % (10410)Memory used [KB]: 7803
% 6.59/2.27 % (10410)Time elapsed: 0.095 s
% 6.59/2.27 % (10410)Instructions burned: 341 (million)
% 6.59/2.27 % (10410)------------------------------
% 6.59/2.27 % (10410)------------------------------
% 6.59/2.28 % (10416)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/90Mi)
% 6.59/2.28 % (10414)Instruction limit reached!
% 6.59/2.28 % (10414)------------------------------
% 6.59/2.28 % (10414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.28 % (10414)Termination reason: Unknown
% 6.59/2.28 % (10414)Termination phase: Saturation
% 6.59/2.28
% 6.59/2.28 % (10414)Memory used [KB]: 7547
% 6.59/2.28 % (10414)Time elapsed: 0.051 s
% 6.59/2.28 % (10414)Instructions burned: 195 (million)
% 6.59/2.28 % (10414)------------------------------
% 6.59/2.28 % (10414)------------------------------
% 6.59/2.28 % (10417)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/231Mi)
% 6.59/2.29 % (10418)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/458Mi)
% 7.24/2.30 % (10416)Instruction limit reached!
% 7.24/2.30 % (10416)------------------------------
% 7.24/2.30 % (10416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.30 % (10416)Termination reason: Unknown
% 7.24/2.30 % (10416)Termination phase: Property scanning
% 7.24/2.30
% 7.24/2.30 % (10416)Memory used [KB]: 2686
% 7.24/2.30 % (10416)Time elapsed: 0.025 s
% 7.24/2.30 % (10416)Instructions burned: 91 (million)
% 7.24/2.30 % (10416)------------------------------
% 7.24/2.30 % (10416)------------------------------
% 7.24/2.30 % (10413)Instruction limit reached!
% 7.24/2.30 % (10413)------------------------------
% 7.24/2.30 % (10413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.30 % (10413)Termination reason: Unknown
% 7.24/2.30 % (10413)Termination phase: Saturation
% 7.24/2.30
% 7.24/2.30 % (10413)Memory used [KB]: 7547
% 7.24/2.30 % (10413)Time elapsed: 0.081 s
% 7.24/2.30 % (10413)Instructions burned: 301 (million)
% 7.24/2.30 % (10413)------------------------------
% 7.24/2.30 % (10413)------------------------------
% 7.24/2.31 % (10419)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/31Mi)
% 7.24/2.31 % (10420)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/297Mi)
% 7.24/2.32 % (10419)Instruction limit reached!
% 7.24/2.32 % (10419)------------------------------
% 7.24/2.32 % (10419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.32 % (10419)Termination reason: Unknown
% 7.24/2.32 % (10419)Termination phase: shuffling
% 7.24/2.32
% 7.24/2.32 % (10419)Memory used [KB]: 2174
% 7.24/2.32 % (10419)Time elapsed: 0.010 s
% 7.24/2.32 % (10419)Instructions burned: 33 (million)
% 7.24/2.32 % (10419)------------------------------
% 7.24/2.32 % (10419)------------------------------
% 7.24/2.33 % (10415)Instruction limit reached!
% 7.24/2.33 % (10415)------------------------------
% 7.24/2.33 % (10415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.33 % (10415)Termination reason: Unknown
% 7.24/2.33 % (10415)Termination phase: Saturation
% 7.24/2.33
% 7.24/2.33 % (10415)Memory used [KB]: 7931
% 7.24/2.33 % (10415)Time elapsed: 0.068 s
% 7.24/2.33 % (10415)Instructions burned: 259 (million)
% 7.24/2.33 % (10415)------------------------------
% 7.24/2.33 % (10415)------------------------------
% 7.24/2.33 % (10421)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/987Mi)
% 7.24/2.33 % (10408)Instruction limit reached!
% 7.24/2.33 % (10408)------------------------------
% 7.24/2.33 % (10408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.33 % (10408)Termination reason: Unknown
% 7.24/2.33 % (10408)Termination phase: Saturation
% 7.24/2.33
% 7.24/2.33 % (10408)Memory used [KB]: 9978
% 7.24/2.33 % (10408)Time elapsed: 0.179 s
% 7.24/2.33 % (10408)Instructions burned: 615 (million)
% 7.24/2.33 % (10408)------------------------------
% 7.24/2.33 % (10408)------------------------------
% 7.24/2.33 % (10390)Instruction limit reached!
% 7.24/2.33 % (10390)------------------------------
% 7.24/2.33 % (10390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.33 % (10390)Termination reason: Unknown
% 7.24/2.33 % (10390)Termination phase: Saturation
% 7.24/2.33
% 7.24/2.33 % (10390)Memory used [KB]: 12537
% 7.24/2.33 % (10390)Time elapsed: 0.367 s
% 7.24/2.33 % (10390)Instructions burned: 1087 (million)
% 7.24/2.33 % (10390)------------------------------
% 7.24/2.33 % (10390)------------------------------
% 7.24/2.34 % (10422)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/182Mi)
% 7.24/2.34 % (10423)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_9951 for (2993ds/182Mi)
% 7.24/2.34 % (10424)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/154Mi)
% 7.24/2.34 % (10417)Instruction limit reached!
% 7.24/2.34 % (10417)------------------------------
% 7.24/2.34 % (10417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.34 % (10417)Termination reason: Unknown
% 7.24/2.34 % (10417)Termination phase: Saturation
% 7.24/2.34
% 7.24/2.34 % (10417)Memory used [KB]: 8443
% 7.24/2.34 % (10417)Time elapsed: 0.060 s
% 7.24/2.34 % (10417)Instructions burned: 232 (million)
% 7.24/2.34 % (10417)------------------------------
% 7.24/2.34 % (10417)------------------------------
% 7.24/2.35 % (10425)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/79Mi)
% 7.24/2.37 % (10425)Instruction limit reached!
% 7.24/2.37 % (10425)------------------------------
% 7.24/2.37 % (10425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.37 % (10425)Termination reason: Unknown
% 7.24/2.37 % (10425)Termination phase: Property scanning
% 7.24/2.37
% 7.24/2.37 % (10425)Memory used [KB]: 2558
% 7.24/2.37 % (10425)Time elapsed: 0.022 s
% 7.24/2.37 % (10425)Instructions burned: 80 (million)
% 7.24/2.37 % (10425)------------------------------
% 7.24/2.37 % (10425)------------------------------
% 7.24/2.38 % (10424)Instruction limit reached!
% 7.24/2.38 % (10424)------------------------------
% 7.24/2.38 % (10424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.38 % (10424)Termination reason: Unknown
% 7.24/2.38 % (10424)Termination phase: Property scanning
% 7.24/2.38
% 7.24/2.38 % (10424)Memory used [KB]: 2686
% 7.24/2.38 % (10424)Time elapsed: 0.040 s
% 7.24/2.38 % (10424)Instructions burned: 157 (million)
% 7.24/2.38 % (10424)------------------------------
% 7.24/2.38 % (10424)------------------------------
% 7.24/2.38 % (10422)Instruction limit reached!
% 7.24/2.38 % (10422)------------------------------
% 7.24/2.38 % (10422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.38 % (10422)Termination reason: Unknown
% 7.24/2.38 % (10422)Termination phase: Saturation
% 7.24/2.38
% 7.24/2.38 % (10422)Memory used [KB]: 7419
% 7.24/2.38 % (10422)Time elapsed: 0.048 s
% 7.24/2.38 % (10422)Instructions burned: 184 (million)
% 7.24/2.38 % (10422)------------------------------
% 7.24/2.38 % (10422)------------------------------
% 7.24/2.38 % (10426)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/216Mi)
% 7.24/2.39 % (10427)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/114Mi)
% 7.24/2.39 % (10420)Instruction limit reached!
% 7.24/2.39 % (10420)------------------------------
% 7.24/2.39 % (10420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.39 % (10420)Termination reason: Unknown
% 7.24/2.39 % (10420)Termination phase: Saturation
% 7.24/2.39
% 7.24/2.39 % (10420)Memory used [KB]: 7547
% 7.24/2.39 % (10420)Time elapsed: 0.080 s
% 7.24/2.39 % (10420)Instructions burned: 300 (million)
% 7.24/2.39 % (10420)------------------------------
% 7.24/2.39 % (10420)------------------------------
% 7.24/2.39 % (10428)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/922Mi)
% 7.24/2.39 % (10423)Instruction limit reached!
% 7.24/2.39 % (10423)------------------------------
% 7.24/2.39 % (10423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.39 % (10423)Termination reason: Unknown
% 7.24/2.39 % (10423)Termination phase: Equality resolution with deletion
% 7.24/2.39
% 7.24/2.39 % (10423)Memory used [KB]: 5117
% 7.24/2.39 % (10423)Time elapsed: 0.053 s
% 7.24/2.39 % (10423)Instructions burned: 184 (million)
% 7.24/2.39 % (10423)------------------------------
% 7.24/2.39 % (10423)------------------------------
% 8.05/2.40 % (10429)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/182Mi)
% 8.05/2.40 % (10430)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/164Mi)
% 8.05/2.41 % (10418)Instruction limit reached!
% 8.05/2.41 % (10418)------------------------------
% 8.05/2.41 % (10418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.41 % (10418)Termination reason: Unknown
% 8.05/2.41 % (10418)Termination phase: Saturation
% 8.05/2.41
% 8.05/2.41 % (10418)Memory used [KB]: 9594
% 8.05/2.41 % (10418)Time elapsed: 0.124 s
% 8.05/2.41 % (10418)Instructions burned: 459 (million)
% 8.05/2.41 % (10418)------------------------------
% 8.05/2.41 % (10418)------------------------------
% 8.05/2.42 % (10427)Instruction limit reached!
% 8.05/2.42 % (10427)------------------------------
% 8.05/2.42 % (10427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.42 % (10427)Termination reason: Unknown
% 8.05/2.42 % (10427)Termination phase: Property scanning
% 8.05/2.42
% 8.05/2.42 % (10427)Memory used [KB]: 2686
% 8.05/2.42 % (10427)Time elapsed: 0.031 s
% 8.05/2.42 % (10427)Instructions burned: 116 (million)
% 8.05/2.42 % (10427)------------------------------
% 8.05/2.42 % (10427)------------------------------
% 8.05/2.42 % (10431)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/50Mi)
% 8.05/2.43 % (10432)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_9951 for (2992ds/368Mi)
% 8.05/2.44 % (10426)Instruction limit reached!
% 8.05/2.44 % (10426)------------------------------
% 8.05/2.44 % (10426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.44 % (10426)Termination reason: Unknown
% 8.05/2.44 % (10426)Termination phase: Saturation
% 8.05/2.44
% 8.05/2.44 % (10426)Memory used [KB]: 7291
% 8.05/2.44 % (10426)Time elapsed: 0.054 s
% 8.05/2.44 % (10426)Instructions burned: 217 (million)
% 8.05/2.44 % (10426)------------------------------
% 8.05/2.44 % (10426)------------------------------
% 8.05/2.44 % (10431)Instruction limit reached!
% 8.05/2.44 % (10431)------------------------------
% 8.05/2.44 % (10431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.44 % (10431)Termination reason: Unknown
% 8.05/2.44 % (10431)Termination phase: shuffling
% 8.05/2.44
% 8.05/2.44 % (10431)Memory used [KB]: 2430
% 8.05/2.44 % (10431)Time elapsed: 0.015 s
% 8.05/2.44 % (10431)Instructions burned: 52 (million)
% 8.05/2.44 % (10431)------------------------------
% 8.05/2.44 % (10431)------------------------------
% 8.05/2.44 % (10430)Instruction limit reached!
% 8.05/2.44 % (10430)------------------------------
% 8.05/2.44 % (10430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.44 % (10430)Termination reason: Unknown
% 8.05/2.44 % (10430)Termination phase: Property scanning
% 8.05/2.44
% 8.05/2.44 % (10430)Memory used [KB]: 2814
% 8.05/2.44 % (10430)Time elapsed: 0.043 s
% 8.05/2.44 % (10430)Instructions burned: 167 (million)
% 8.05/2.44 % (10430)------------------------------
% 8.05/2.44 % (10430)------------------------------
% 8.05/2.45 % (10433)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_9951 for (2991ds/1021Mi)
% 8.05/2.45 % (10434)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_9951 for (2991ds/267Mi)
% 8.05/2.45 % (10429)Instruction limit reached!
% 8.05/2.45 % (10429)------------------------------
% 8.05/2.45 % (10429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.45 % (10429)Termination reason: Unknown
% 8.05/2.45 % (10429)Termination phase: Saturation
% 8.05/2.45
% 8.05/2.45 % (10429)Memory used [KB]: 7547
% 8.05/2.45 % (10429)Time elapsed: 0.049 s
% 8.05/2.45 % (10429)Instructions burned: 183 (million)
% 8.05/2.45 % (10429)------------------------------
% 8.05/2.45 % (10429)------------------------------
% 8.05/2.45 % (10435)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_9951 for (2991ds/204Mi)
% 8.05/2.46 % (10436)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_9951 for (2991ds/26Mi)
% 8.05/2.47 % (10436)Instruction limit reached!
% 8.05/2.47 % (10436)------------------------------
% 8.05/2.47 % (10436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.47 % (10436)Termination reason: Unknown
% 8.05/2.47 % (10436)Termination phase: shuffling
% 8.05/2.47
% 8.05/2.47 % (10436)Memory used [KB]: 2046
% 8.05/2.47 % (10436)Time elapsed: 0.009 s
% 8.05/2.47 % (10436)Instructions burned: 28 (million)
% 8.05/2.47 % (10436)------------------------------
% 8.05/2.47 % (10436)------------------------------
% 8.05/2.48 % (10437)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_9951 for (2991ds/53Mi)
% 8.05/2.49 % (10437)Instruction limit reached!
% 8.05/2.49 % (10437)------------------------------
% 8.05/2.49 % (10437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.49 % (10437)Termination reason: Unknown
% 8.05/2.49 % (10437)Termination phase: shuffling
% 8.05/2.49
% 8.05/2.49 % (10437)Memory used [KB]: 2558
% 8.05/2.49 % (10437)Time elapsed: 0.015 s
% 8.05/2.49 % (10437)Instructions burned: 53 (million)
% 8.05/2.49 % (10437)------------------------------
% 8.05/2.49 % (10437)------------------------------
% 8.46/2.50 % (10438)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_9951 for (2991ds/4436Mi)
% 8.46/2.50 % (10435)Instruction limit reached!
% 8.46/2.50 % (10435)------------------------------
% 8.46/2.50 % (10435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.50 % (10435)Termination reason: Unknown
% 8.46/2.50 % (10435)Termination phase: Property scanning
% 8.46/2.50
% 8.46/2.50 % (10435)Memory used [KB]: 2814
% 8.46/2.50 % (10435)Time elapsed: 0.052 s
% 8.46/2.50 % (10435)Instructions burned: 204 (million)
% 8.46/2.50 % (10435)------------------------------
% 8.46/2.50 % (10435)------------------------------
% 8.46/2.51 % (10434)Instruction limit reached!
% 8.46/2.51 % (10434)------------------------------
% 8.46/2.51 % (10434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.51 % (10434)Termination reason: Unknown
% 8.46/2.51 % (10434)Termination phase: Saturation
% 8.46/2.51
% 8.46/2.51 % (10434)Memory used [KB]: 7547
% 8.46/2.51 % (10434)Time elapsed: 0.068 s
% 8.46/2.51 % (10434)Instructions burned: 270 (million)
% 8.46/2.51 % (10434)------------------------------
% 8.46/2.51 % (10434)------------------------------
% 8.46/2.51 % (10439)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_9951 for (2991ds/1539Mi)
% 8.46/2.52 % (10440)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_9951 for (2991ds/408Mi)
% 8.46/2.53 % (10432)Instruction limit reached!
% 8.46/2.53 % (10432)------------------------------
% 8.46/2.53 % (10432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.53 % (10432)Termination reason: Unknown
% 8.46/2.53 % (10432)Termination phase: Saturation
% 8.46/2.53
% 8.46/2.53 % (10432)Memory used [KB]: 9466
% 8.46/2.53 % (10432)Time elapsed: 0.100 s
% 8.46/2.53 % (10432)Instructions burned: 370 (million)
% 8.46/2.53 % (10432)------------------------------
% 8.46/2.53 % (10432)------------------------------
% 8.46/2.54 % (10441)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_9951 for (2990ds/5205Mi)
% 8.46/2.58 % (10421)Instruction limit reached!
% 8.46/2.58 % (10421)------------------------------
% 8.46/2.58 % (10421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.58 % (10421)Termination reason: Unknown
% 8.46/2.58 % (10421)Termination phase: Saturation
% 8.46/2.58
% 8.46/2.58 % (10421)Memory used [KB]: 16247
% 8.46/2.58 % (10421)Time elapsed: 0.252 s
% 8.46/2.58 % (10421)Instructions burned: 988 (million)
% 8.46/2.58 % (10421)------------------------------
% 8.46/2.58 % (10421)------------------------------
% 8.46/2.59 % (10442)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_9951 for (2990ds/1913Mi)
% 8.98/2.65 % (10440)Instruction limit reached!
% 8.98/2.65 % (10440)------------------------------
% 8.98/2.65 % (10440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.98/2.65 % (10440)Termination reason: Unknown
% 8.98/2.65 % (10440)Termination phase: Saturation
% 8.98/2.65
% 8.98/2.65 % (10440)Memory used [KB]: 11257
% 8.98/2.65 % (10440)Time elapsed: 0.126 s
% 8.98/2.65 % (10440)Instructions burned: 408 (million)
% 8.98/2.65 % (10440)------------------------------
% 8.98/2.65 % (10440)------------------------------
% 8.98/2.66 % (10443)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_9951 for (2989ds/4350Mi)
% 8.98/2.68 % (10428)Instruction limit reached!
% 8.98/2.68 % (10428)------------------------------
% 8.98/2.68 % (10428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.98/2.68 % (10428)Termination reason: Unknown
% 8.98/2.68 % (10428)Termination phase: Saturation
% 8.98/2.68
% 8.98/2.68 % (10428)Memory used [KB]: 12153
% 8.98/2.68 % (10428)Time elapsed: 0.292 s
% 8.98/2.68 % (10428)Instructions burned: 924 (million)
% 8.98/2.68 % (10428)------------------------------
% 8.98/2.68 % (10428)------------------------------
% 8.98/2.69 % (10444)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_9951 for (2989ds/68Mi)
% 9.41/2.71 % (10444)Instruction limit reached!
% 9.41/2.71 % (10444)------------------------------
% 9.41/2.71 % (10444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.71 % (10444)Termination reason: Unknown
% 9.41/2.71 % (10444)Termination phase: Property scanning
% 9.41/2.71
% 9.41/2.71 % (10444)Memory used [KB]: 2558
% 9.41/2.71 % (10444)Time elapsed: 0.020 s
% 9.41/2.71 % (10444)Instructions burned: 71 (million)
% 9.41/2.71 % (10444)------------------------------
% 9.41/2.71 % (10444)------------------------------
% 9.41/2.72 % (10445)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_9951 for (2989ds/358Mi)
% 9.41/2.77 % (10433)Instruction limit reached!
% 9.41/2.77 % (10433)------------------------------
% 9.41/2.77 % (10433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.77 % (10433)Termination reason: Unknown
% 9.41/2.77 % (10433)Termination phase: Saturation
% 9.41/2.77
% 9.41/2.77 % (10433)Memory used [KB]: 12665
% 9.41/2.77 % (10433)Time elapsed: 0.346 s
% 9.41/2.77 % (10433)Instructions burned: 1022 (million)
% 9.41/2.77 % (10433)------------------------------
% 9.41/2.77 % (10433)------------------------------
% 9.41/2.78 % (10446)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_9951 for (2988ds/31Mi)
% 9.41/2.79 % (10446)Instruction limit reached!
% 9.41/2.79 % (10446)------------------------------
% 9.41/2.79 % (10446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.79 % (10446)Termination reason: Unknown
% 9.41/2.79 % (10446)Termination phase: shuffling
% 9.41/2.79
% 9.41/2.79 % (10446)Memory used [KB]: 2046
% 9.41/2.79 % (10446)Time elapsed: 0.011 s
% 9.41/2.79 % (10446)Instructions burned: 33 (million)
% 9.41/2.79 % (10446)------------------------------
% 9.41/2.79 % (10446)------------------------------
% 9.79/2.80 % (10447)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_9951 for (2988ds/279Mi)
% 9.79/2.81 % (10445)Instruction limit reached!
% 9.79/2.81 % (10445)------------------------------
% 9.79/2.81 % (10445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.79/2.81 % (10445)Termination reason: Unknown
% 9.79/2.81 % (10445)Termination phase: Saturation
% 9.79/2.81
% 9.79/2.81 % (10445)Memory used [KB]: 8571
% 9.79/2.81 % (10445)Time elapsed: 0.093 s
% 9.79/2.81 % (10445)Instructions burned: 359 (million)
% 9.79/2.81 % (10445)------------------------------
% 9.79/2.81 % (10445)------------------------------
% 9.79/2.82 % (10448)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_9951 for (2988ds/258Mi)
% 9.79/2.87 % (10447)Instruction limit reached!
% 9.79/2.87 % (10447)------------------------------
% 9.79/2.87 % (10447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.79/2.87 % (10447)Termination reason: Unknown
% 9.79/2.87 % (10447)Termination phase: Saturation
% 9.79/2.87
% 9.79/2.87 % (10447)Memory used [KB]: 7547
% 9.79/2.87 % (10447)Time elapsed: 0.070 s
% 9.79/2.87 % (10447)Instructions burned: 281 (million)
% 9.79/2.87 % (10447)------------------------------
% 9.79/2.87 % (10447)------------------------------
% 9.79/2.88 % (10449)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_9951 for (2987ds/26Mi)
% 9.79/2.89 % (10449)Instruction limit reached!
% 9.79/2.89 % (10449)------------------------------
% 9.79/2.89 % (10449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.79/2.89 % (10449)Termination reason: Unknown
% 9.79/2.89 % (10449)Termination phase: shuffling
% 9.79/2.89
% 9.79/2.89 % (10449)Memory used [KB]: 2046
% 9.79/2.89 % (10449)Time elapsed: 0.009 s
% 9.79/2.89 % (10449)Instructions burned: 27 (million)
% 9.79/2.89 % (10449)------------------------------
% 9.79/2.89 % (10449)------------------------------
% 9.79/2.89 % (10448)Instruction limit reached!
% 9.79/2.89 % (10448)------------------------------
% 9.79/2.89 % (10448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.79/2.89 % (10448)Termination reason: Unknown
% 9.79/2.89 % (10448)Termination phase: Saturation
% 9.79/2.89
% 9.79/2.89 % (10448)Memory used [KB]: 8315
% 9.79/2.89 % (10448)Time elapsed: 0.069 s
% 9.79/2.89 % (10448)Instructions burned: 261 (million)
% 9.79/2.89 % (10448)------------------------------
% 9.79/2.89 % (10448)------------------------------
% 9.79/2.90 % (10450)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_9951 for (2987ds/995Mi)
% 10.07/2.90 % (10451)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_9951 for (2987ds/373Mi)
% 10.07/3.00 % (10439)Instruction limit reached!
% 10.07/3.00 % (10439)------------------------------
% 10.07/3.00 % (10439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.07/3.00 % (10439)Termination reason: Unknown
% 10.07/3.00 % (10439)Termination phase: Saturation
% 10.07/3.00
% 10.07/3.00 % (10439)Memory used [KB]: 10618
% 10.07/3.00 % (10439)Time elapsed: 0.487 s
% 10.07/3.00 % (10439)Instructions burned: 1539 (million)
% 10.07/3.00 % (10439)------------------------------
% 10.07/3.00 % (10439)------------------------------
% 10.07/3.00 % (10451)Instruction limit reached!
% 10.07/3.00 % (10451)------------------------------
% 10.07/3.00 % (10451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.07/3.00 % (10451)Termination reason: Unknown
% 10.07/3.00 % (10451)Termination phase: Saturation
% 10.07/3.00
% 10.07/3.00 % (10451)Memory used [KB]: 9466
% 10.07/3.00 % (10451)Time elapsed: 0.105 s
% 10.07/3.00 % (10451)Instructions burned: 375 (million)
% 10.07/3.00 % (10451)------------------------------
% 10.07/3.00 % (10451)------------------------------
% 10.07/3.01 % (10452)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_9951 for (2986ds/253Mi)
% 10.07/3.01 % (10453)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_9951 for (2986ds/832Mi)
% 12.62/3.07 % (10452)Instruction limit reached!
% 12.62/3.07 % (10452)------------------------------
% 12.62/3.07 % (10452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.62/3.07 % (10452)Termination reason: Unknown
% 12.62/3.07 % (10452)Termination phase: Saturation
% 12.62/3.07
% 12.62/3.07 % (10452)Memory used [KB]: 7547
% 12.62/3.07 % (10452)Time elapsed: 0.065 s
% 12.62/3.07 % (10452)Instructions burned: 256 (million)
% 12.62/3.07 % (10452)------------------------------
% 12.62/3.07 % (10452)------------------------------
% 12.62/3.08 % (10454)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_9951 for (2985ds/668Mi)
% 13.20/3.15 % (10450)Instruction limit reached!
% 13.20/3.15 % (10450)------------------------------
% 13.20/3.15 % (10450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.20/3.15 % (10450)Termination reason: Unknown
% 13.20/3.15 % (10450)Termination phase: Saturation
% 13.20/3.15
% 13.20/3.15 % (10450)Memory used [KB]: 15863
% 13.20/3.15 % (10450)Time elapsed: 0.255 s
% 13.20/3.15 % (10450)Instructions burned: 998 (million)
% 13.20/3.15 % (10450)------------------------------
% 13.20/3.15 % (10450)------------------------------
% 13.20/3.16 % (10455)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_9951 for (2984ds/40Mi)
% 13.20/3.17 % (10455)Instruction limit reached!
% 13.20/3.17 % (10455)------------------------------
% 13.20/3.17 % (10455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.20/3.17 % (10455)Termination reason: Unknown
% 13.20/3.17 % (10455)Termination phase: shuffling
% 13.20/3.17
% 13.20/3.17 % (10455)Memory used [KB]: 2302
% 13.20/3.17 % (10455)Time elapsed: 0.013 s
% 13.20/3.17 % (10455)Instructions burned: 43 (million)
% 13.20/3.17 % (10455)------------------------------
% 13.20/3.17 % (10455)------------------------------
% 13.20/3.18 % (10442)Instruction limit reached!
% 13.20/3.18 % (10442)------------------------------
% 13.20/3.18 % (10442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.20/3.18 % (10442)Termination reason: Unknown
% 13.20/3.18 % (10442)Termination phase: Saturation
% 13.20/3.18
% 13.20/3.18 % (10442)Memory used [KB]: 6268
% 13.20/3.18 % (10442)Time elapsed: 0.588 s
% 13.20/3.18 % (10442)Instructions burned: 1914 (million)
% 13.20/3.18 % (10442)------------------------------
% 13.20/3.18 % (10442)------------------------------
% 13.20/3.18 % (10456)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_9951 for (2984ds/294Mi)
% 13.20/3.19 % (10457)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_9951 for (2984ds/187Mi)
% 13.55/3.24 % (10457)Instruction limit reached!
% 13.55/3.24 % (10457)------------------------------
% 13.55/3.24 % (10457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.55/3.24 % (10457)Termination reason: Unknown
% 13.55/3.24 % (10457)Termination phase: Saturation
% 13.55/3.24
% 13.55/3.24 % (10457)Memory used [KB]: 7419
% 13.55/3.24 % (10457)Time elapsed: 0.051 s
% 13.55/3.24 % (10457)Instructions burned: 188 (million)
% 13.55/3.24 % (10457)------------------------------
% 13.55/3.24 % (10457)------------------------------
% 13.55/3.25 % (10458)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_9951 for (2983ds/371Mi)
% 13.55/3.25 % (10454)Instruction limit reached!
% 13.55/3.25 % (10454)------------------------------
% 13.55/3.25 % (10454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.55/3.25 % (10454)Termination reason: Unknown
% 13.55/3.25 % (10454)Termination phase: Saturation
% 13.55/3.25
% 13.55/3.25 % (10454)Memory used [KB]: 16119
% 13.55/3.25 % (10454)Time elapsed: 0.171 s
% 13.55/3.25 % (10454)Instructions burned: 668 (million)
% 13.55/3.25 % (10454)------------------------------
% 13.55/3.25 % (10454)------------------------------
% 13.55/3.26 % (10456)Instruction limit reached!
% 13.55/3.26 % (10456)------------------------------
% 13.55/3.26 % (10456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.55/3.26 % (10456)Termination reason: Unknown
% 13.55/3.26 % (10456)Termination phase: Saturation
% 13.55/3.26
% 13.55/3.26 % (10456)Memory used [KB]: 7547
% 13.55/3.26 % (10456)Time elapsed: 0.076 s
% 13.55/3.26 % (10456)Instructions burned: 295 (million)
% 13.55/3.26 % (10456)------------------------------
% 13.55/3.26 % (10456)------------------------------
% 13.55/3.26 % (10453)Instruction limit reached!
% 13.55/3.26 % (10453)------------------------------
% 13.55/3.26 % (10453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.55/3.26 % (10453)Termination reason: Unknown
% 13.55/3.26 % (10453)Termination phase: Saturation
% 13.55/3.26
% 13.55/3.26 % (10453)Memory used [KB]: 11513
% 13.55/3.26 % (10453)Time elapsed: 0.249 s
% 13.55/3.26 % (10453)Instructions burned: 832 (million)
% 13.55/3.26 % (10453)------------------------------
% 13.55/3.26 % (10453)------------------------------
% 13.55/3.26 % (10459)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_9951 for (2983ds/1827Mi)
% 13.55/3.27 % (10460)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_9951 for (2983ds/70Mi)
% 13.55/3.27 % (10461)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_9951 for (2983ds/316Mi)
% 13.55/3.28 % (10460)Instruction limit reached!
% 13.55/3.28 % (10460)------------------------------
% 13.55/3.28 % (10460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.55/3.28 % (10460)Termination reason: Unknown
% 13.55/3.28 % (10460)Termination phase: Property scanning
% 13.55/3.28
% 13.55/3.28 % (10460)Memory used [KB]: 2558
% 13.55/3.28 % (10460)Time elapsed: 0.019 s
% 13.55/3.28 % (10460)Instructions burned: 70 (million)
% 13.55/3.28 % (10460)------------------------------
% 13.55/3.28 % (10460)------------------------------
% 13.55/3.29 % (10462)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_9951 for (2983ds/932Mi)
% 14.46/3.34 % (10458)Instruction limit reached!
% 14.46/3.34 % (10458)------------------------------
% 14.46/3.34 % (10458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.34 % (10458)Termination reason: Unknown
% 14.46/3.34 % (10458)Termination phase: Saturation
% 14.46/3.34
% 14.46/3.34 % (10458)Memory used [KB]: 9338
% 14.46/3.34 % (10458)Time elapsed: 0.098 s
% 14.46/3.34 % (10458)Instructions burned: 373 (million)
% 14.46/3.34 % (10458)------------------------------
% 14.46/3.34 % (10458)------------------------------
% 14.46/3.35 % (10461)Instruction limit reached!
% 14.46/3.35 % (10461)------------------------------
% 14.46/3.35 % (10461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.35 % (10461)Termination reason: Unknown
% 14.46/3.35 % (10461)Termination phase: Saturation
% 14.46/3.35
% 14.46/3.35 % (10461)Memory used [KB]: 7547
% 14.46/3.35 % (10461)Time elapsed: 0.079 s
% 14.46/3.35 % (10461)Instructions burned: 316 (million)
% 14.46/3.35 % (10461)------------------------------
% 14.46/3.35 % (10461)------------------------------
% 14.46/3.35 % (10463)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_9951 for (2982ds/4714Mi)
% 14.46/3.36 % (10464)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_9951 for (2982ds/8250Mi)
% 15.26/3.53 % (10462)Instruction limit reached!
% 15.26/3.53 % (10462)------------------------------
% 15.26/3.53 % (10462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/3.53 % (10462)Termination reason: Unknown
% 15.26/3.53 % (10462)Termination phase: Saturation
% 15.26/3.53
% 15.26/3.53 % (10462)Memory used [KB]: 16119
% 15.26/3.53 % (10462)Time elapsed: 0.235 s
% 15.26/3.53 % (10462)Instructions burned: 934 (million)
% 15.26/3.53 % (10462)------------------------------
% 15.26/3.53 % (10462)------------------------------
% 15.26/3.54 % (10465)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_9951 for (2980ds/770Mi)
% 16.10/3.74 % (10465)Instruction limit reached!
% 16.10/3.74 % (10465)------------------------------
% 16.10/3.74 % (10465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.10/3.74 % (10465)Termination reason: Unknown
% 16.10/3.74 % (10465)Termination phase: Saturation
% 16.10/3.74
% 16.10/3.74 % (10465)Memory used [KB]: 7675
% 16.10/3.74 % (10465)Time elapsed: 0.208 s
% 16.10/3.74 % (10465)Instructions burned: 770 (million)
% 16.10/3.74 % (10465)------------------------------
% 16.10/3.74 % (10465)------------------------------
% 16.10/3.75 % (10466)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_9951 for (2978ds/794Mi)
% 16.10/3.78 % (10459)Instruction limit reached!
% 16.10/3.78 % (10459)------------------------------
% 16.10/3.78 % (10459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.10/3.78 % (10459)Termination reason: Unknown
% 16.10/3.78 % (10459)Termination phase: Saturation
% 16.10/3.78
% 16.10/3.78 % (10459)Memory used [KB]: 20980
% 16.10/3.78 % (10459)Time elapsed: 0.522 s
% 16.10/3.78 % (10459)Instructions burned: 1829 (million)
% 16.10/3.78 % (10459)------------------------------
% 16.10/3.78 % (10459)------------------------------
% 16.10/3.80 % (10467)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_9951 for (2978ds/464Mi)
% 17.16/3.84 % (10441)Instruction limit reached!
% 17.16/3.84 % (10441)------------------------------
% 17.16/3.84 % (10441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.16/3.84 % (10441)Termination reason: Unknown
% 17.16/3.84 % (10441)Termination phase: Saturation
% 17.16/3.84
% 17.16/3.84 % (10441)Memory used [KB]: 16886
% 17.16/3.84 % (10441)Time elapsed: 1.298 s
% 17.16/3.84 % (10441)Instructions burned: 5208 (million)
% 17.16/3.84 % (10441)------------------------------
% 17.16/3.84 % (10441)------------------------------
% 17.16/3.85 % (10468)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_9951 for (2977ds/1376Mi)
% 17.41/3.91 % (10438)Instruction limit reached!
% 17.41/3.91 % (10438)------------------------------
% 17.41/3.91 % (10438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.41/3.91 % (10438)Termination reason: Unknown
% 17.41/3.91 % (10438)Termination phase: Saturation
% 17.41/3.91
% 17.41/3.91 % (10438)Memory used [KB]: 15095
% 17.41/3.91 % (10438)Time elapsed: 1.411 s
% 17.41/3.91 % (10438)Instructions burned: 4438 (million)
% 17.41/3.91 % (10438)------------------------------
% 17.41/3.91 % (10438)------------------------------
% 17.41/3.92 % (10469)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_9951 for (2977ds/906Mi)
% 17.41/3.92 % (10467)Instruction limit reached!
% 17.41/3.92 % (10467)------------------------------
% 17.41/3.92 % (10467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.41/3.92 % (10467)Termination reason: Unknown
% 17.41/3.92 % (10467)Termination phase: Saturation
% 17.41/3.92
% 17.41/3.92 % (10467)Memory used [KB]: 9722
% 17.41/3.92 % (10467)Time elapsed: 0.127 s
% 17.41/3.92 % (10467)Instructions burned: 465 (million)
% 17.41/3.92 % (10467)------------------------------
% 17.41/3.92 % (10467)------------------------------
% 17.41/3.93 % (10470)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_9951 for (2976ds/434Mi)
% 17.41/3.99 % (10466)Instruction limit reached!
% 17.41/3.99 % (10466)------------------------------
% 17.41/3.99 % (10466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.41/3.99 % (10466)Termination reason: Unknown
% 17.41/3.99 % (10466)Termination phase: Saturation
% 17.41/3.99
% 17.41/3.99 % (10466)Memory used [KB]: 6012
% 17.41/3.99 % (10466)Time elapsed: 0.238 s
% 17.41/3.99 % (10466)Instructions burned: 795 (million)
% 17.41/3.99 % (10466)------------------------------
% 17.41/3.99 % (10466)------------------------------
% 17.41/3.99 % (10443)Instruction limit reached!
% 17.41/3.99 % (10443)------------------------------
% 17.41/3.99 % (10443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.41/3.99 % (10443)Termination reason: Unknown
% 17.41/3.99 % (10443)Termination phase: Saturation
% 17.41/3.99
% 17.41/3.99 % (10443)Memory used [KB]: 13688
% 17.41/3.99 % (10443)Time elapsed: 1.335 s
% 17.41/3.99 % (10443)Instructions burned: 4352 (million)
% 17.41/3.99 % (10443)------------------------------
% 17.41/3.99 % (10443)------------------------------
% 17.41/4.00 % (10471)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_9951 for (2976ds/865Mi)
% 17.41/4.00 % (10472)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_9951 for (2976ds/593Mi)
% 19.65/4.06 % (10470)Instruction limit reached!
% 19.65/4.06 % (10470)------------------------------
% 19.65/4.06 % (10470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.65/4.06 % (10470)Termination reason: Unknown
% 19.65/4.06 % (10470)Termination phase: Saturation
% 19.65/4.06
% 19.65/4.06 % (10470)Memory used [KB]: 11129
% 19.65/4.06 % (10470)Time elapsed: 0.130 s
% 19.65/4.06 % (10470)Instructions burned: 434 (million)
% 19.65/4.06 % (10470)------------------------------
% 19.65/4.06 % (10470)------------------------------
% 19.65/4.07 % (10473)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_9951 for (2975ds/443Mi)
% 20.32/4.15 % (10472)Instruction limit reached!
% 20.32/4.15 % (10472)------------------------------
% 20.32/4.15 % (10472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.15 % (10472)Termination reason: Unknown
% 20.32/4.15 % (10472)Termination phase: Saturation
% 20.32/4.15
% 20.32/4.15 % (10472)Memory used [KB]: 7675
% 20.32/4.15 % (10472)Time elapsed: 0.150 s
% 20.32/4.15 % (10472)Instructions burned: 593 (million)
% 20.32/4.15 % (10472)------------------------------
% 20.32/4.15 % (10472)------------------------------
% 20.32/4.16 % (10474)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_9951 for (2974ds/594Mi)
% 20.32/4.19 % (10473)Instruction limit reached!
% 20.32/4.19 % (10473)------------------------------
% 20.32/4.19 % (10473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.32/4.19 % (10473)Termination reason: Unknown
% 20.32/4.19 % (10473)Termination phase: Saturation
% 20.32/4.19
% 20.32/4.19 % (10473)Memory used [KB]: 9594
% 20.32/4.19 % (10473)Time elapsed: 0.147 s
% 20.32/4.19 % (10473)Instructions burned: 444 (million)
% 20.32/4.19 % (10473)------------------------------
% 20.32/4.19 % (10473)------------------------------
% 20.86/4.20 % (10468)Instruction limit reached!
% 20.86/4.20 % (10468)------------------------------
% 20.86/4.20 % (10468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.20 % (10468)Termination reason: Unknown
% 20.86/4.20 % (10468)Termination phase: Saturation
% 20.86/4.20
% 20.86/4.20 % (10468)Memory used [KB]: 9338
% 20.86/4.20 % (10468)Time elapsed: 0.353 s
% 20.86/4.20 % (10468)Instructions burned: 1376 (million)
% 20.86/4.20 % (10468)------------------------------
% 20.86/4.20 % (10468)------------------------------
% 20.86/4.20 % (10469)Instruction limit reached!
% 20.86/4.20 % (10469)------------------------------
% 20.86/4.20 % (10469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.20 % (10469)Termination reason: Unknown
% 20.86/4.20 % (10469)Termination phase: Saturation
% 20.86/4.20
% 20.86/4.20 % (10469)Memory used [KB]: 11257
% 20.86/4.20 % (10469)Time elapsed: 0.279 s
% 20.86/4.20 % (10469)Instructions burned: 908 (million)
% 20.86/4.20 % (10469)------------------------------
% 20.86/4.20 % (10469)------------------------------
% 20.86/4.20 % (10475)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_9951 for (2974ds/327Mi)
% 20.86/4.21 % (10476)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_9951 for (2974ds/5411Mi)
% 20.86/4.21 % (10477)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_9951 for (2974ds/1762Mi)
% 20.86/4.24 % (10471)Instruction limit reached!
% 20.86/4.24 % (10471)------------------------------
% 20.86/4.24 % (10471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.24 % (10471)Termination reason: Unknown
% 20.86/4.24 % (10471)Termination phase: Saturation
% 20.86/4.24
% 20.86/4.24 % (10471)Memory used [KB]: 9594
% 20.86/4.24 % (10471)Time elapsed: 0.240 s
% 20.86/4.24 % (10471)Instructions burned: 866 (million)
% 20.86/4.24 % (10471)------------------------------
% 20.86/4.24 % (10471)------------------------------
% 20.86/4.25 % (10478)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_9951 for (2973ds/96Mi)
% 20.86/4.28 % (10478)Instruction limit reached!
% 20.86/4.28 % (10478)------------------------------
% 20.86/4.28 % (10478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.28 % (10478)Termination reason: Unknown
% 20.86/4.28 % (10478)Termination phase: Property scanning
% 20.86/4.28
% 20.86/4.28 % (10478)Memory used [KB]: 2558
% 20.86/4.28 % (10478)Time elapsed: 0.027 s
% 20.86/4.28 % (10478)Instructions burned: 96 (million)
% 20.86/4.28 % (10478)------------------------------
% 20.86/4.28 % (10478)------------------------------
% 20.86/4.29 % (10479)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_9951 for (2973ds/503Mi)
% 21.18/4.30 % (10475)Instruction limit reached!
% 21.18/4.30 % (10475)------------------------------
% 21.18/4.30 % (10475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.30 % (10475)Termination reason: Unknown
% 21.18/4.30 % (10475)Termination phase: Saturation
% 21.18/4.30
% 21.18/4.30 % (10475)Memory used [KB]: 11257
% 21.18/4.30 % (10475)Time elapsed: 0.098 s
% 21.18/4.30 % (10475)Instructions burned: 327 (million)
% 21.18/4.30 % (10475)------------------------------
% 21.18/4.30 % (10475)------------------------------
% 21.18/4.31 % (10480)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_9951 for (2973ds/90Mi)
% 21.18/4.33 % (10474)Instruction limit reached!
% 21.18/4.33 % (10474)------------------------------
% 21.18/4.33 % (10474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.33 % (10474)Termination reason: Unknown
% 21.18/4.33 % (10474)Termination phase: Saturation
% 21.18/4.33
% 21.18/4.33 % (10474)Memory used [KB]: 9722
% 21.18/4.33 % (10474)Time elapsed: 0.192 s
% 21.18/4.33 % (10474)Instructions burned: 596 (million)
% 21.18/4.33 % (10474)------------------------------
% 21.18/4.33 % (10474)------------------------------
% 21.18/4.34 % (10480)Instruction limit reached!
% 21.18/4.34 % (10480)------------------------------
% 21.18/4.34 % (10480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.34 % (10480)Termination reason: Unknown
% 21.18/4.34 % (10480)Termination phase: Property scanning
% 21.18/4.34
% 21.18/4.34 % (10480)Memory used [KB]: 2686
% 21.18/4.34 % (10480)Time elapsed: 0.025 s
% 21.18/4.34 % (10480)Instructions burned: 90 (million)
% 21.18/4.34 % (10480)------------------------------
% 21.18/4.34 % (10480)------------------------------
% 21.18/4.34 % (10481)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_9951 for (2972ds/593Mi)
% 21.18/4.34 % (10482)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_9951 for (2972ds/1512Mi)
% 21.70/4.42 % (10479)Instruction limit reached!
% 21.70/4.42 % (10479)------------------------------
% 21.70/4.42 % (10479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.70/4.42 % (10479)Termination reason: Unknown
% 21.70/4.42 % (10479)Termination phase: Saturation
% 21.70/4.42
% 21.70/4.42 % (10479)Memory used [KB]: 9850
% 21.70/4.42 % (10479)Time elapsed: 0.140 s
% 21.70/4.42 % (10479)Instructions burned: 506 (million)
% 21.70/4.42 % (10479)------------------------------
% 21.70/4.42 % (10479)------------------------------
% 21.70/4.43 % (10483)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_9951 for (2971ds/569Mi)
% 22.03/4.51 % (10481)Instruction limit reached!
% 22.03/4.51 % (10481)------------------------------
% 22.03/4.51 % (10481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.03/4.51 % (10481)Termination reason: Unknown
% 22.03/4.51 % (10481)Termination phase: Saturation
% 22.03/4.51
% 22.03/4.51 % (10481)Memory used [KB]: 10106
% 22.03/4.51 % (10481)Time elapsed: 0.168 s
% 22.03/4.51 % (10481)Instructions burned: 595 (million)
% 22.03/4.51 % (10481)------------------------------
% 22.03/4.51 % (10481)------------------------------
% 22.03/4.52 % (10484)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_9951 for (2971ds/501Mi)
% 22.03/4.53 % (10463)Instruction limit reached!
% 22.03/4.53 % (10463)------------------------------
% 22.03/4.53 % (10463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.03/4.53 % (10463)Termination reason: Unknown
% 22.03/4.53 % (10463)Termination phase: Saturation
% 22.03/4.53
% 22.03/4.53 % (10463)Memory used [KB]: 7675
% 22.03/4.53 % (10463)Time elapsed: 1.179 s
% 22.03/4.53 % (10463)Instructions burned: 4715 (million)
% 22.03/4.53 % (10463)------------------------------
% 22.03/4.53 % (10463)------------------------------
% 22.03/4.54 % (10485)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_9951 for (2970ds/562Mi)
% 22.03/4.58 % (10483)Instruction limit reached!
% 22.03/4.58 % (10483)------------------------------
% 22.03/4.58 % (10483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.03/4.58 % (10483)Termination reason: Unknown
% 22.03/4.58 % (10483)Termination phase: Saturation
% 22.03/4.58
% 22.03/4.58 % (10483)Memory used [KB]: 7675
% 22.03/4.58 % (10483)Time elapsed: 0.144 s
% 22.03/4.58 % (10483)Instructions burned: 572 (million)
% 22.03/4.58 % (10483)------------------------------
% 22.03/4.58 % (10483)------------------------------
% 22.03/4.59 % (10486)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_9951 for (2970ds/406Mi)
% 22.52/4.64 % (10477)Instruction limit reached!
% 22.52/4.64 % (10477)------------------------------
% 22.52/4.64 % (10477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.52/4.64 % (10477)Termination reason: Unknown
% 22.52/4.64 % (10477)Termination phase: Saturation
% 22.52/4.64
% 22.52/4.64 % (10477)Memory used [KB]: 23155
% 22.52/4.64 % (10477)Time elapsed: 0.433 s
% 22.52/4.64 % (10477)Instructions burned: 1764 (million)
% 22.52/4.64 % (10477)------------------------------
% 22.52/4.64 % (10477)------------------------------
% 22.52/4.65 % (10487)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_9951 for (2969ds/582Mi)
% 22.52/4.67 % (10484)Instruction limit reached!
% 22.52/4.67 % (10484)------------------------------
% 22.52/4.67 % (10484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.52/4.67 % (10484)Termination reason: Unknown
% 22.52/4.67 % (10484)Termination phase: Saturation
% 22.52/4.67
% 22.52/4.67 % (10484)Memory used [KB]: 10490
% 22.52/4.67 % (10484)Time elapsed: 0.154 s
% 22.52/4.67 % (10484)Instructions burned: 503 (million)
% 22.52/4.67 % (10484)------------------------------
% 22.52/4.67 % (10484)------------------------------
% 22.52/4.68 % (10488)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_9951 for (2969ds/456Mi)
% 23.23/4.70 % (10486)Instruction limit reached!
% 23.23/4.70 % (10486)------------------------------
% 23.23/4.70 % (10486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.23/4.70 % (10486)Termination reason: Unknown
% 23.23/4.70 % (10486)Termination phase: Saturation
% 23.23/4.70
% 23.23/4.70 % (10486)Memory used [KB]: 7803
% 23.23/4.70 % (10486)Time elapsed: 0.114 s
% 23.23/4.70 % (10486)Instructions burned: 407 (million)
% 23.23/4.70 % (10486)------------------------------
% 23.23/4.70 % (10486)------------------------------
% 23.23/4.71 % (10485)Instruction limit reached!
% 23.23/4.71 % (10485)------------------------------
% 23.23/4.71 % (10485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.23/4.71 % (10485)Termination reason: Unknown
% 23.23/4.71 % (10485)Termination phase: Saturation
% 23.23/4.71
% 23.23/4.71 % (10485)Memory used [KB]: 9210
% 23.23/4.71 % (10485)Time elapsed: 0.165 s
% 23.23/4.71 % (10485)Instructions burned: 563 (million)
% 23.23/4.71 % (10485)------------------------------
% 23.23/4.71 % (10485)------------------------------
% 23.23/4.71 % (10489)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_9951 for (2969ds/393Mi)
% 23.23/4.72 % (10491)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_9951 for (2969ds/1335Mi)
% 23.63/4.80 % (10488)Instruction limit reached!
% 23.63/4.80 % (10488)------------------------------
% 23.63/4.80 % (10488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.80 % (10488)Termination reason: Unknown
% 23.63/4.80 % (10488)Termination phase: Saturation
% 23.63/4.80
% 23.63/4.80 % (10488)Memory used [KB]: 9722
% 23.63/4.80 % (10488)Time elapsed: 0.124 s
% 23.63/4.80 % (10488)Instructions burned: 457 (million)
% 23.63/4.80 % (10488)------------------------------
% 23.63/4.80 % (10488)------------------------------
% 23.63/4.81 % (10482)Instruction limit reached!
% 23.63/4.81 % (10482)------------------------------
% 23.63/4.81 % (10482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.81 % (10482)Termination reason: Unknown
% 23.63/4.81 % (10482)Termination phase: Saturation
% 23.63/4.81
% 23.63/4.81 % (10482)Memory used [KB]: 12537
% 23.63/4.81 % (10482)Time elapsed: 0.468 s
% 23.63/4.81 % (10482)Instructions burned: 1513 (million)
% 23.63/4.81 % (10482)------------------------------
% 23.63/4.81 % (10482)------------------------------
% 23.63/4.81 % (10492)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_9951 for (2968ds/3373Mi)
% 23.63/4.82 % (10489)Instruction limit reached!
% 23.63/4.82 % (10489)------------------------------
% 23.63/4.82 % (10489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.82 % (10489)Termination reason: Unknown
% 23.63/4.82 % (10489)Termination phase: Saturation
% 23.63/4.82
% 23.63/4.82 % (10489)Memory used [KB]: 9978
% 23.63/4.82 % (10489)Time elapsed: 0.108 s
% 23.63/4.82 % (10489)Instructions burned: 393 (million)
% 23.63/4.82 % (10489)------------------------------
% 23.63/4.82 % (10489)------------------------------
% 23.63/4.82 % (10493)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_9951 for (2968ds/474Mi)
% 23.63/4.83 % (10494)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_9951 for (2968ds/157Mi)
% 23.63/4.83 % (10487)Instruction limit reached!
% 23.63/4.83 % (10487)------------------------------
% 23.63/4.83 % (10487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.83 % (10487)Termination reason: Unknown
% 23.63/4.83 % (10487)Termination phase: Saturation
% 23.63/4.83
% 23.63/4.83 % (10487)Memory used [KB]: 10874
% 23.63/4.83 % (10487)Time elapsed: 0.176 s
% 23.63/4.83 % (10487)Instructions burned: 582 (million)
% 23.63/4.83 % (10487)------------------------------
% 23.63/4.83 % (10487)------------------------------
% 23.63/4.84 % (10495)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_9951 for (2967ds/590Mi)
% 23.63/4.87 % (10494)Instruction limit reached!
% 23.63/4.87 % (10494)------------------------------
% 23.63/4.87 % (10494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.87 % (10494)Termination reason: Unknown
% 23.63/4.87 % (10494)Termination phase: Property scanning
% 23.63/4.87
% 23.63/4.87 % (10494)Memory used [KB]: 2686
% 23.63/4.87 % (10494)Time elapsed: 0.041 s
% 23.63/4.87 % (10494)Instructions burned: 157 (million)
% 23.63/4.87 % (10494)------------------------------
% 23.63/4.87 % (10494)------------------------------
% 23.63/4.88 % (10496)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_9951 for (2967ds/104Mi)
% 24.69/4.90 % (10496)Instruction limit reached!
% 24.69/4.90 % (10496)------------------------------
% 24.69/4.90 % (10496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/4.90 % (10496)Termination reason: Unknown
% 24.69/4.90 % (10496)Termination phase: Property scanning
% 24.69/4.90
% 24.69/4.90 % (10496)Memory used [KB]: 2686
% 24.69/4.90 % (10496)Time elapsed: 0.030 s
% 24.69/4.90 % (10496)Instructions burned: 107 (million)
% 24.69/4.90 % (10496)------------------------------
% 24.69/4.90 % (10496)------------------------------
% 24.69/4.91 % (10497)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_9951 for (2967ds/414Mi)
% 24.69/4.94 % (10493)Instruction limit reached!
% 24.69/4.94 % (10493)------------------------------
% 24.69/4.94 % (10493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/4.94 % (10493)Termination reason: Unknown
% 24.69/4.94 % (10493)Termination phase: Saturation
% 24.69/4.94
% 24.69/4.94 % (10493)Memory used [KB]: 7547
% 24.69/4.94 % (10493)Time elapsed: 0.121 s
% 24.69/4.94 % (10493)Instructions burned: 474 (million)
% 24.69/4.94 % (10493)------------------------------
% 24.69/4.94 % (10493)------------------------------
% 24.69/4.95 % (10498)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_9951 for (2966ds/715Mi)
% 24.69/5.01 % (10495)Instruction limit reached!
% 24.69/5.01 % (10495)------------------------------
% 24.69/5.01 % (10495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/5.01 % (10495)Termination reason: Unknown
% 24.69/5.01 % (10495)Termination phase: Saturation
% 24.69/5.01
% 24.69/5.01 % (10495)Memory used [KB]: 9210
% 24.69/5.01 % (10495)Time elapsed: 0.172 s
% 24.69/5.01 % (10495)Instructions burned: 592 (million)
% 24.69/5.01 % (10495)------------------------------
% 24.69/5.01 % (10495)------------------------------
% 24.69/5.02 % (10499)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_9951 for (2966ds/961Mi)
% 24.69/5.02 % (10497)Instruction limit reached!
% 24.69/5.02 % (10497)------------------------------
% 24.69/5.02 % (10497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/5.02 % (10497)Termination reason: Unknown
% 24.69/5.02 % (10497)Termination phase: Saturation
% 24.69/5.02
% 24.69/5.02 % (10497)Memory used [KB]: 7547
% 24.69/5.02 % (10497)Time elapsed: 0.105 s
% 24.69/5.02 % (10497)Instructions burned: 417 (million)
% 24.69/5.02 % (10497)------------------------------
% 24.69/5.02 % (10497)------------------------------
% 26.68/5.03 % (10500)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_9951 for (2966ds/1213Mi)
% 26.68/5.11 % (10491)Instruction limit reached!
% 26.68/5.11 % (10491)------------------------------
% 26.68/5.11 % (10491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.68/5.11 % (10491)Termination reason: Unknown
% 26.68/5.11 % (10491)Termination phase: Saturation
% 26.68/5.11
% 26.68/5.11 % (10491)Memory used [KB]: 10362
% 26.68/5.11 % (10491)Time elapsed: 0.401 s
% 26.68/5.11 % (10491)Instructions burned: 1338 (million)
% 26.68/5.12 % (10491)------------------------------
% 26.68/5.12 % (10491)------------------------------
% 27.18/5.13 % (10501)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_9951 for (2965ds/1979Mi)
% 27.18/5.17 % (10498)Instruction limit reached!
% 27.18/5.17 % (10498)------------------------------
% 27.18/5.17 % (10498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.18/5.17 % (10498)Termination reason: Unknown
% 27.18/5.17 % (10498)Termination phase: Saturation
% 27.18/5.17
% 27.18/5.17 % (10498)Memory used [KB]: 5500
% 27.18/5.17 % (10498)Time elapsed: 0.215 s
% 27.18/5.17 % (10498)Instructions burned: 717 (million)
% 27.18/5.17 % (10498)------------------------------
% 27.18/5.17 % (10498)------------------------------
% 27.18/5.18 % (10502)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_9951 for (2964ds/481Mi)
% 27.46/5.29 % (10502)Instruction limit reached!
% 27.46/5.29 % (10502)------------------------------
% 27.46/5.29 % (10502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.46/5.29 % (10502)Termination reason: Unknown
% 27.46/5.29 % (10502)Termination phase: Saturation
% 27.46/5.29
% 27.46/5.29 % (10502)Memory used [KB]: 7547
% 27.46/5.29 % (10502)Time elapsed: 0.120 s
% 27.46/5.29 % (10502)Instructions burned: 481 (million)
% 27.46/5.29 % (10502)------------------------------
% 27.46/5.29 % (10502)------------------------------
% 27.89/5.30 % (10503)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_9951 for (2963ds/783Mi)
% 27.89/5.31 % (10499)Instruction limit reached!
% 27.89/5.31 % (10499)------------------------------
% 27.89/5.31 % (10499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.89/5.31 % (10499)Termination reason: Unknown
% 27.89/5.31 % (10499)Termination phase: Saturation
% 27.89/5.31
% 27.89/5.31 % (10499)Memory used [KB]: 10106
% 27.89/5.31 % (10499)Time elapsed: 0.310 s
% 27.89/5.31 % (10499)Instructions burned: 962 (million)
% 27.89/5.31 % (10499)------------------------------
% 27.89/5.31 % (10499)------------------------------
% 27.89/5.32 % (10504)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_9951 for (2963ds/432Mi)
% 28.48/5.41 % (10500)Instruction limit reached!
% 28.48/5.41 % (10500)------------------------------
% 28.48/5.41 % (10500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.48/5.41 % (10500)Termination reason: Unknown
% 28.48/5.41 % (10500)Termination phase: Saturation
% 28.48/5.41
% 28.48/5.41 % (10500)Memory used [KB]: 15223
% 28.48/5.41 % (10500)Time elapsed: 0.404 s
% 28.48/5.41 % (10500)Instructions burned: 1214 (million)
% 28.48/5.41 % (10500)------------------------------
% 28.48/5.41 % (10500)------------------------------
% 28.48/5.42 % (10505)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_9951 for (2962ds/1670Mi)
% 28.48/5.43 % (10504)Instruction limit reached!
% 28.48/5.43 % (10504)------------------------------
% 28.48/5.43 % (10504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.48/5.43 % (10504)Termination reason: Unknown
% 28.48/5.43 % (10504)Termination phase: Saturation
% 28.48/5.43
% 28.48/5.43 % (10504)Memory used [KB]: 9594
% 28.48/5.43 % (10504)Time elapsed: 0.119 s
% 28.48/5.43 % (10504)Instructions burned: 433 (million)
% 28.48/5.43 % (10504)------------------------------
% 28.48/5.43 % (10504)------------------------------
% 28.48/5.44 % (10506)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_9951 for (2961ds/90Mi)
% 28.48/5.47 % (10506)Instruction limit reached!
% 28.48/5.47 % (10506)------------------------------
% 28.48/5.47 % (10506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.48/5.47 % (10506)Termination reason: Unknown
% 28.48/5.47 % (10506)Termination phase: Property scanning
% 28.48/5.47
% 28.48/5.47 % (10506)Memory used [KB]: 2686
% 28.48/5.47 % (10506)Time elapsed: 0.025 s
% 28.48/5.47 % (10506)Instructions burned: 92 (million)
% 28.48/5.47 % (10506)------------------------------
% 28.48/5.47 % (10506)------------------------------
% 28.48/5.48 % (10507)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_9951 for (2961ds/346Mi)
% 29.35/5.55 % (10503)Instruction limit reached!
% 29.35/5.55 % (10503)------------------------------
% 29.35/5.55 % (10503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.35/5.55 % (10503)Termination reason: Unknown
% 29.35/5.55 % (10503)Termination phase: Saturation
% 29.35/5.55
% 29.35/5.55 % (10503)Memory used [KB]: 11769
% 29.35/5.55 % (10503)Time elapsed: 0.246 s
% 29.35/5.55 % (10503)Instructions burned: 784 (million)
% 29.35/5.55 % (10503)------------------------------
% 29.35/5.55 % (10503)------------------------------
% 29.35/5.56 % (10508)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_9951 for (2960ds/401Mi)
% 29.35/5.57 % (10507)Instruction limit reached!
% 29.35/5.57 % (10507)------------------------------
% 29.35/5.57 % (10507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.35/5.57 % (10507)Termination reason: Unknown
% 29.35/5.57 % (10507)Termination phase: Saturation
% 29.35/5.57
% 29.35/5.57 % (10507)Memory used [KB]: 7547
% 29.35/5.57 % (10507)Time elapsed: 0.090 s
% 29.35/5.57 % (10507)Instructions burned: 348 (million)
% 29.35/5.57 % (10507)------------------------------
% 29.35/5.57 % (10507)------------------------------
% 29.35/5.58 % (10509)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_9951 for (2960ds/6454Mi)
% 30.00/5.66 % (10508)Instruction limit reached!
% 30.00/5.66 % (10508)------------------------------
% 30.00/5.66 % (10508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.00/5.66 % (10508)Termination reason: Unknown
% 30.00/5.66 % (10508)Termination phase: Saturation
% 30.00/5.66
% 30.00/5.66 % (10508)Memory used [KB]: 7547
% 30.00/5.66 % (10508)Time elapsed: 0.100 s
% 30.00/5.66 % (10508)Instructions burned: 401 (million)
% 30.00/5.66 % (10508)------------------------------
% 30.00/5.66 % (10508)------------------------------
% 30.00/5.67 % (10510)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_9951 for (2959ds/283Mi)
% 30.41/5.72 % (10501)Instruction limit reached!
% 30.41/5.72 % (10501)------------------------------
% 30.41/5.72 % (10501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.41/5.72 % (10501)Termination reason: Unknown
% 30.41/5.72 % (10501)Termination phase: Saturation
% 30.41/5.72
% 30.41/5.72 % (10501)Memory used [KB]: 10362
% 30.41/5.72 % (10501)Time elapsed: 0.592 s
% 30.41/5.72 % (10501)Instructions burned: 1979 (million)
% 30.41/5.72 % (10501)------------------------------
% 30.41/5.72 % (10501)------------------------------
% 30.41/5.73 % (10511)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_9951 for (2959ds/865Mi)
% 30.41/5.74 % (10510)Instruction limit reached!
% 30.41/5.74 % (10510)------------------------------
% 30.41/5.74 % (10510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.41/5.74 % (10510)Termination reason: Unknown
% 30.41/5.74 % (10510)Termination phase: Saturation
% 30.41/5.74
% 30.41/5.74 % (10510)Memory used [KB]: 8315
% 30.41/5.74 % (10510)Time elapsed: 0.077 s
% 30.41/5.74 % (10510)Instructions burned: 285 (million)
% 30.41/5.74 % (10510)------------------------------
% 30.41/5.74 % (10510)------------------------------
% 30.41/5.75 % (10512)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_9951 for (2958ds/4528Mi)
% 31.40/5.84 % (10492)Instruction limit reached!
% 31.40/5.84 % (10492)------------------------------
% 31.40/5.84 % (10492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.40/5.84 % (10492)Termination reason: Unknown
% 31.40/5.84 % (10492)Termination phase: Saturation
% 31.40/5.84
% 31.40/5.84 % (10492)Memory used [KB]: 12792
% 31.40/5.84 % (10492)Time elapsed: 1.026 s
% 31.40/5.84 % (10492)Instructions burned: 3374 (million)
% 31.40/5.84 % (10492)------------------------------
% 31.40/5.84 % (10492)------------------------------
% 31.40/5.84 % (10505)Instruction limit reached!
% 31.40/5.84 % (10505)------------------------------
% 31.40/5.84 % (10505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.40/5.84 % (10505)Termination reason: Unknown
% 31.40/5.84 % (10505)Termination phase: Saturation
% 31.40/5.84
% 31.40/5.84 % (10505)Memory used [KB]: 18038
% 31.40/5.84 % (10505)Time elapsed: 0.429 s
% 31.40/5.84 % (10505)Instructions burned: 1673 (million)
% 31.40/5.84 % (10505)------------------------------
% 31.40/5.84 % (10505)------------------------------
% 31.40/5.85 % (10513)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_9951 for (2957ds/1001Mi)
% 31.40/5.85 % (10514)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_9951 for (2957ds/102Mi)
% 31.40/5.88 % (10514)Instruction limit reached!
% 31.40/5.88 % (10514)------------------------------
% 31.40/5.88 % (10514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.40/5.88 % (10514)Termination reason: Unknown
% 31.40/5.88 % (10514)Termination phase: Property scanning
% 31.40/5.88
% 31.40/5.88 % (10514)Memory used [KB]: 2686
% 31.40/5.88 % (10514)Time elapsed: 0.029 s
% 31.40/5.88 % (10514)Instructions burned: 104 (million)
% 31.40/5.88 % (10514)------------------------------
% 31.40/5.88 % (10514)------------------------------
% 31.40/5.89 % (10515)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_9951 for (2957ds/952Mi)
% 32.14/5.91 % (10476)Instruction limit reached!
% 32.14/5.91 % (10476)------------------------------
% 32.14/5.91 % (10476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.14/5.91 % (10476)Termination reason: Unknown
% 32.14/5.91 % (10476)Termination phase: Saturation
% 32.14/5.91
% 32.14/5.91 % (10476)Memory used [KB]: 16247
% 32.14/5.91 % (10476)Time elapsed: 1.702 s
% 32.14/5.91 % (10476)Instructions burned: 5414 (million)
% 32.14/5.91 % (10476)------------------------------
% 32.14/5.91 % (10476)------------------------------
% 32.14/5.92 % (10516)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_9951 for (2957ds/578Mi)
% 32.14/5.95 % (10512)Refutation not found, incomplete strategy
% 32.14/5.95 % (10512)------------------------------
% 32.14/5.95 % (10512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.14/5.95 % (10512)Termination reason: Refutation not found, incomplete strategy
% 32.14/5.95
% 32.14/5.95
% 32.14/5.95 % (10512)Memory used [KB]: 3070
% 32.14/5.95 % (10512)Time elapsed: 0.200 s
% 32.14/5.95 % (10512)Instructions burned: 769 (million)
% 32.14/5.95 % (10512)------------------------------
% 32.14/5.95 % (10512)------------------------------
% 32.14/5.96 % (10511)Instruction limit reached!
% 32.14/5.96 % (10511)------------------------------
% 32.14/5.96 % (10511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.14/5.96 % (10511)Termination reason: Unknown
% 32.14/5.96 % (10511)Termination phase: Saturation
% 32.14/5.96
% 32.14/5.96 % (10511)Memory used [KB]: 8059
% 32.14/5.96 % (10511)Time elapsed: 0.232 s
% 32.14/5.96 % (10511)Instructions burned: 867 (million)
% 32.14/5.96 % (10511)------------------------------
% 32.14/5.96 % (10511)------------------------------
% 32.14/5.96 % (10517)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_9951 for (2956ds/643Mi)
% 32.14/5.97 % (10518)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_9951 for (2956ds/865Mi)
% 32.14/6.01 % (10464)Instruction limit reached!
% 32.14/6.01 % (10464)------------------------------
% 32.14/6.01 % (10464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.14/6.01 % (10464)Termination reason: Unknown
% 32.14/6.01 % (10464)Termination phase: Saturation
% 32.14/6.01
% 32.14/6.01 % (10464)Memory used [KB]: 25713
% 32.14/6.01 % (10464)Time elapsed: 2.652 s
% 32.14/6.01 % (10464)Instructions burned: 8250 (million)
% 32.14/6.01 % (10464)------------------------------
% 32.14/6.01 % (10464)------------------------------
% 32.14/6.02 % (10519)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_9951 for (2956ds/1174Mi)
% 33.69/6.06 % (10516)Instruction limit reached!
% 33.69/6.06 % (10516)------------------------------
% 33.69/6.06 % (10516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.69/6.06 % (10516)Termination reason: Unknown
% 33.69/6.06 % (10516)Termination phase: Saturation
% 33.69/6.06
% 33.69/6.06 % (10516)Memory used [KB]: 10874
% 33.69/6.06 % (10516)Time elapsed: 0.142 s
% 33.69/6.06 % (10516)Instructions burned: 580 (million)
% 33.69/6.06 % (10516)------------------------------
% 33.69/6.06 % (10516)------------------------------
% 33.69/6.07 % (10520)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_9951 for (2955ds/644Mi)
% 33.69/6.12 % (10517)Instruction limit reached!
% 33.69/6.12 % (10517)------------------------------
% 33.69/6.12 % (10517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.69/6.12 % (10517)Termination reason: Unknown
% 33.69/6.12 % (10517)Termination phase: Saturation
% 33.69/6.12
% 33.69/6.12 % (10517)Memory used [KB]: 7675
% 33.69/6.12 % (10517)Time elapsed: 0.161 s
% 33.69/6.12 % (10517)Instructions burned: 643 (million)
% 33.69/6.12 % (10517)------------------------------
% 33.69/6.12 % (10517)------------------------------
% 34.11/6.13 % (10521)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_9951 for (2954ds/1201Mi)
% 34.11/6.15 % (10513)Instruction limit reached!
% 34.11/6.15 % (10513)------------------------------
% 34.11/6.15 % (10513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.11/6.15 % (10513)Termination reason: Unknown
% 34.11/6.15 % (10513)Termination phase: Saturation
% 34.11/6.15
% 34.11/6.15 % (10513)Memory used [KB]: 11257
% 34.11/6.15 % (10513)Time elapsed: 0.302 s
% 34.11/6.15 % (10513)Instructions burned: 1001 (million)
% 34.11/6.15 % (10513)------------------------------
% 34.11/6.15 % (10513)------------------------------
% 34.11/6.16 % (10522)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_9951 for (2954ds/1046Mi)
% 34.11/6.17 % (10515)Instruction limit reached!
% 34.11/6.17 % (10515)------------------------------
% 34.11/6.17 % (10515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.11/6.17 % (10515)Termination reason: Unknown
% 34.11/6.17 % (10515)Termination phase: Saturation
% 34.11/6.17
% 34.11/6.17 % (10515)Memory used [KB]: 10362
% 34.11/6.17 % (10515)Time elapsed: 0.281 s
% 34.11/6.17 % (10515)Instructions burned: 954 (million)
% 34.11/6.17 % (10515)------------------------------
% 34.11/6.17 % (10515)------------------------------
% 34.11/6.18 % (10523)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_9951 for (2954ds/222Mi)
% 34.52/6.20 % (10518)Instruction limit reached!
% 34.52/6.20 % (10518)------------------------------
% 34.52/6.20 % (10518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.52/6.20 % (10518)Termination reason: Unknown
% 34.52/6.20 % (10518)Termination phase: Saturation
% 34.52/6.20
% 34.52/6.20 % (10518)Memory used [KB]: 7803
% 34.52/6.20 % (10518)Time elapsed: 0.234 s
% 34.52/6.20 % (10518)Instructions burned: 866 (million)
% 34.52/6.20 % (10518)------------------------------
% 34.52/6.20 % (10518)------------------------------
% 34.52/6.21 % (10524)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_9951 for (2954ds/68Mi)
% 34.52/6.23 % (10524)Instruction limit reached!
% 34.52/6.23 % (10524)------------------------------
% 34.52/6.23 % (10524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.52/6.23 % (10524)Termination reason: Unknown
% 34.52/6.23 % (10524)Termination phase: Property scanning
% 34.52/6.23
% 34.52/6.23 % (10524)Memory used [KB]: 2558
% 34.52/6.23 % (10524)Time elapsed: 0.020 s
% 34.52/6.23 % (10524)Instructions burned: 71 (million)
% 34.52/6.23 % (10524)------------------------------
% 34.52/6.23 % (10524)------------------------------
% 34.52/6.24 % (10523)Instruction limit reached!
% 34.52/6.24 % (10523)------------------------------
% 34.52/6.24 % (10523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.52/6.24 % (10523)Termination reason: Unknown
% 34.52/6.24 % (10523)Termination phase: Saturation
% 34.52/6.24
% 34.52/6.24 % (10523)Memory used [KB]: 7419
% 34.52/6.24 % (10523)Time elapsed: 0.056 s
% 34.52/6.24 % (10523)Instructions burned: 222 (million)
% 34.52/6.24 % (10523)------------------------------
% 34.52/6.24 % (10523)------------------------------
% 34.52/6.24 % (10525)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_9951 for (2953ds/454Mi)
% 34.52/6.25 % (10526)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_9951 for (2953ds/360Mi)
% 34.52/6.25 % (10520)Instruction limit reached!
% 34.52/6.25 % (10520)------------------------------
% 34.52/6.25 % (10520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.52/6.25 % (10520)Termination reason: Unknown
% 34.52/6.25 % (10520)Termination phase: Saturation
% 34.52/6.25
% 34.52/6.25 % (10520)Memory used [KB]: 8443
% 34.52/6.25 % (10520)Time elapsed: 0.204 s
% 34.52/6.25 % (10520)Instructions burned: 644 (million)
% 34.52/6.25 % (10520)------------------------------
% 34.52/6.25 % (10520)------------------------------
% 34.52/6.26 % (10527)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_9951 for (2953ds/157Mi)
% 34.91/6.30 % (10527)Instruction limit reached!
% 34.91/6.30 % (10527)------------------------------
% 34.91/6.30 % (10527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.91/6.30 % (10527)Termination reason: Unknown
% 34.91/6.30 % (10527)Termination phase: Property scanning
% 34.91/6.30
% 34.91/6.30 % (10527)Memory used [KB]: 2686
% 34.91/6.30 % (10527)Time elapsed: 0.040 s
% 34.91/6.30 % (10527)Instructions burned: 157 (million)
% 34.91/6.30 % (10527)------------------------------
% 34.91/6.30 % (10527)------------------------------
% 34.91/6.31 % (10528)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_9951 for (2953ds/5061Mi)
% 34.91/6.34 % (10526)Instruction limit reached!
% 34.91/6.34 % (10526)------------------------------
% 34.91/6.34 % (10526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.91/6.34 % (10526)Termination reason: Unknown
% 34.91/6.34 % (10526)Termination phase: Saturation
% 34.91/6.34
% 34.91/6.34 % (10526)Memory used [KB]: 7547
% 34.91/6.34 % (10526)Time elapsed: 0.090 s
% 34.91/6.34 % (10526)Instructions burned: 361 (million)
% 34.91/6.34 % (10526)------------------------------
% 34.91/6.34 % (10526)------------------------------
% 34.91/6.34 % (10529)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_9951 for (2952ds/2401Mi)
% 34.91/6.35 % (10519)Refutation not found, non-redundant clauses discarded% (10519)------------------------------
% 34.91/6.35 % (10519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.91/6.35 % (10519)Termination reason: Refutation not found, non-redundant clauses discarded
% 34.91/6.35
% 34.91/6.35 % (10519)Memory used [KB]: 10234
% 34.91/6.35 % (10519)Time elapsed: 0.328 s
% 34.91/6.35 % (10519)Instructions burned: 1112 (million)
% 34.91/6.35 % (10519)------------------------------
% 34.91/6.35 % (10519)------------------------------
% 34.91/6.35 % (10525)Instruction limit reached!
% 34.91/6.35 % (10525)------------------------------
% 34.91/6.35 % (10525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.91/6.35 % (10525)Termination reason: Unknown
% 34.91/6.35 % (10525)Termination phase: Saturation
% 34.91/6.35
% 34.91/6.35 % (10525)Memory used [KB]: 12025
% 34.91/6.35 % (10525)Time elapsed: 0.114 s
% 34.91/6.35 % (10525)Instructions burned: 457 (million)
% 34.91/6.35 % (10525)------------------------------
% 34.91/6.35 % (10525)------------------------------
% 34.91/6.36 % (10531)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_9951 for (2952ds/346Mi)
% 34.91/6.37 % (10530)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_9951 for (2952ds/5798Mi)
% 35.63/6.42 % (10522)Instruction limit reached!
% 35.63/6.42 % (10522)------------------------------
% 35.63/6.42 % (10522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.63/6.42 % (10522)Termination reason: Unknown
% 35.63/6.42 % (10522)Termination phase: Saturation
% 35.63/6.42
% 35.63/6.42 % (10522)Memory used [KB]: 7675
% 35.63/6.42 % (10522)Time elapsed: 0.259 s
% 35.63/6.42 % (10522)Instructions burned: 1049 (million)
% 35.63/6.42 % (10522)------------------------------
% 35.63/6.42 % (10522)------------------------------
% 35.63/6.43 % (10532)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_9951 for (2952ds/1321Mi)
% 35.63/6.45 % (10531)Instruction limit reached!
% 35.63/6.45 % (10531)------------------------------
% 35.63/6.45 % (10531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.63/6.45 % (10531)Termination reason: Unknown
% 35.63/6.45 % (10531)Termination phase: Saturation
% 35.63/6.45
% 35.63/6.45 % (10531)Memory used [KB]: 7547
% 35.63/6.45 % (10531)Time elapsed: 0.087 s
% 35.63/6.45 % (10531)Instructions burned: 346 (million)
% 35.63/6.45 % (10531)------------------------------
% 35.63/6.45 % (10531)------------------------------
% 35.63/6.45 % (10521)Instruction limit reached!
% 35.63/6.45 % (10521)------------------------------
% 35.63/6.45 % (10521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.63/6.45 % (10521)Termination reason: Unknown
% 35.63/6.45 % (10521)Termination phase: Saturation
% 35.63/6.45
% 35.63/6.45 % (10521)Memory used [KB]: 11001
% 35.63/6.45 % (10521)Time elapsed: 0.316 s
% 35.63/6.45 % (10521)Instructions burned: 1203 (million)
% 35.63/6.45 % (10521)------------------------------
% 35.63/6.45 % (10521)------------------------------
% 35.63/6.46 % (10533)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_9951 for (2951ds/1312Mi)
% 35.63/6.46 % (10534)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_9951 for (2951ds/672Mi)
% 36.52/6.66 % (10534)Instruction limit reached!
% 36.52/6.66 % (10534)------------------------------
% 36.52/6.66 % (10534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.52/6.66 % (10534)Termination reason: Unknown
% 36.52/6.66 % (10534)Termination phase: Saturation
% 36.52/6.66
% 36.52/6.66 % (10534)Memory used [KB]: 11001
% 36.52/6.66 % (10534)Time elapsed: 0.204 s
% 36.52/6.66 % (10534)Instructions burned: 674 (million)
% 36.52/6.66 % (10534)------------------------------
% 36.52/6.66 % (10534)------------------------------
% 36.52/6.67 % (10535)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_9951 for (2949ds/1897Mi)
% 36.82/6.79 % (10533)Instruction limit reached!
% 36.82/6.79 % (10533)------------------------------
% 36.82/6.79 % (10533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.82/6.79 % (10533)Termination reason: Unknown
% 36.82/6.79 % (10533)Termination phase: Saturation
% 36.82/6.79
% 36.82/6.79 % (10533)Memory used [KB]: 16758
% 36.82/6.79 % (10533)Time elapsed: 0.331 s
% 36.82/6.79 % (10533)Instructions burned: 1312 (million)
% 36.82/6.79 % (10533)------------------------------
% 36.82/6.79 % (10533)------------------------------
% 37.27/6.80 % (10536)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_9951 for (2948ds/1202Mi)
% 37.27/6.82 % (10532)Instruction limit reached!
% 37.27/6.82 % (10532)------------------------------
% 37.27/6.82 % (10532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.27/6.82 % (10532)Termination reason: Unknown
% 37.27/6.82 % (10532)Termination phase: Saturation
% 37.27/6.82
% 37.27/6.82 % (10532)Memory used [KB]: 10234
% 37.27/6.82 % (10532)Time elapsed: 0.392 s
% 37.27/6.82 % (10532)Instructions burned: 1323 (million)
% 37.27/6.82 % (10532)------------------------------
% 37.27/6.82 % (10532)------------------------------
% 37.27/6.83 % (10537)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_9951 for (2948ds/1493Mi)
% 40.68/7.07 % (10529)Instruction limit reached!
% 40.68/7.07 % (10529)------------------------------
% 40.68/7.07 % (10529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.68/7.07 % (10529)Termination reason: Unknown
% 40.68/7.07 % (10529)Termination phase: Saturation
% 40.68/7.07
% 40.68/7.07 % (10529)Memory used [KB]: 9722
% 40.68/7.07 % (10529)Time elapsed: 0.723 s
% 40.68/7.07 % (10529)Instructions burned: 2401 (million)
% 40.68/7.07 % (10529)------------------------------
% 40.68/7.07 % (10529)------------------------------
% 40.68/7.08 % (10538)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_9951 for (2945ds/7679Mi)
% 41.35/7.13 % (10536)Instruction limit reached!
% 41.35/7.13 % (10536)------------------------------
% 41.35/7.13 % (10536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.35/7.13 % (10536)Termination reason: Unknown
% 41.35/7.13 % (10536)Termination phase: Saturation
% 41.35/7.13
% 41.35/7.13 % (10536)Memory used [KB]: 9466
% 41.35/7.13 % (10536)Time elapsed: 0.338 s
% 41.35/7.13 % (10536)Instructions burned: 1205 (million)
% 41.35/7.13 % (10536)------------------------------
% 41.35/7.13 % (10536)------------------------------
% 41.35/7.14 % (10539)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_9951 for (2944ds/340Mi)
% 41.77/7.20 % (10537)Instruction limit reached!
% 41.77/7.20 % (10537)------------------------------
% 41.77/7.20 % (10537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.77/7.20 % (10537)Termination reason: Unknown
% 41.77/7.20 % (10537)Termination phase: Saturation
% 41.77/7.20
% 41.77/7.20 % (10537)Memory used [KB]: 8059
% 41.77/7.20 % (10537)Time elapsed: 0.369 s
% 41.77/7.20 % (10537)Instructions burned: 1495 (million)
% 41.77/7.20 % (10537)------------------------------
% 41.77/7.20 % (10537)------------------------------
% 41.77/7.21 % (10540)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_9951 for (2944ds/3672Mi)
% 41.77/7.24 % (10539)Instruction limit reached!
% 41.77/7.24 % (10539)------------------------------
% 41.77/7.24 % (10539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.77/7.24 % (10539)Termination reason: Unknown
% 41.77/7.24 % (10539)Termination phase: Saturation
% 41.77/7.24
% 41.77/7.24 % (10539)Memory used [KB]: 11001
% 41.77/7.24 % (10539)Time elapsed: 0.099 s
% 41.77/7.24 % (10539)Instructions burned: 342 (million)
% 41.77/7.24 % (10539)------------------------------
% 41.77/7.24 % (10539)------------------------------
% 41.77/7.25 % (10541)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_9951 for (2943ds/1535Mi)
% 41.77/7.27 % (10535)Instruction limit reached!
% 41.77/7.27 % (10535)------------------------------
% 41.77/7.27 % (10535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.77/7.27 % (10535)Termination reason: Unknown
% 41.77/7.27 % (10535)Termination phase: Saturation
% 41.77/7.27
% 41.77/7.27 % (10535)Memory used [KB]: 13816
% 41.77/7.27 % (10535)Time elapsed: 0.601 s
% 41.77/7.27 % (10535)Instructions burned: 1899 (million)
% 41.77/7.27 % (10535)------------------------------
% 41.77/7.27 % (10535)------------------------------
% 41.77/7.28 % (10542)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_9951 for (2943ds/4637Mi)
% 42.87/7.56 % (10528)Instruction limit reached!
% 42.87/7.56 % (10528)------------------------------
% 42.87/7.56 % (10528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.87/7.56 % (10528)Termination reason: Unknown
% 42.87/7.56 % (10528)Termination phase: Saturation
% 42.87/7.56
% 42.87/7.56 % (10528)Memory used [KB]: 7931
% 42.87/7.56 % (10528)Time elapsed: 1.255 s
% 42.87/7.56 % (10528)Instructions burned: 5065 (million)
% 42.87/7.56 % (10528)------------------------------
% 42.87/7.56 % (10528)------------------------------
% 42.87/7.57 % (10544)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_9951 for (2940ds/3174Mi)
% 42.87/7.59 % (10509)Instruction limit reached!
% 42.87/7.59 % (10509)------------------------------
% 42.87/7.59 % (10509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.87/7.59 % (10509)Termination reason: Unknown
% 42.87/7.59 % (10509)Termination phase: Saturation
% 42.87/7.59
% 42.87/7.59 % (10509)Memory used [KB]: 14328
% 42.87/7.59 % (10509)Time elapsed: 2.013 s
% 42.87/7.59 % (10509)Instructions burned: 6457 (million)
% 42.87/7.59 % (10509)------------------------------
% 42.87/7.59 % (10509)------------------------------
% 43.14/7.60 % (10545)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_9951 for (2940ds/307Mi)
% 43.14/7.63 % (10541)Instruction limit reached!
% 43.14/7.63 % (10541)------------------------------
% 43.14/7.63 % (10541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.14/7.63 % (10541)Termination reason: Unknown
% 43.14/7.63 % (10541)Termination phase: Saturation
% 43.14/7.63
% 43.14/7.63 % (10541)Memory used [KB]: 16375
% 43.14/7.63 % (10541)Time elapsed: 0.376 s
% 43.14/7.63 % (10541)Instructions burned: 1537 (million)
% 43.14/7.63 % (10541)------------------------------
% 43.14/7.63 % (10541)------------------------------
% 43.14/7.64 % (10546)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_9951 for (2940ds/3619Mi)
% 43.14/7.68 % (10545)Instruction limit reached!
% 43.14/7.68 % (10545)------------------------------
% 43.14/7.68 % (10545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.14/7.68 % (10545)Termination reason: Unknown
% 43.14/7.68 % (10545)Termination phase: Saturation
% 43.14/7.68
% 43.14/7.68 % (10545)Memory used [KB]: 7547
% 43.14/7.68 % (10545)Time elapsed: 0.079 s
% 43.14/7.68 % (10545)Instructions burned: 308 (million)
% 43.14/7.68 % (10545)------------------------------
% 43.14/7.68 % (10545)------------------------------
% 43.14/7.69 % (10547)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_9951 for (2939ds/2325Mi)
% 47.67/8.10 % (10544)Refutation not found, non-redundant clauses discarded% (10544)------------------------------
% 47.67/8.10 % (10544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.67/8.10 % (10544)Termination reason: Refutation not found, non-redundant clauses discarded
% 47.67/8.10
% 47.67/8.10 % (10544)Memory used [KB]: 16886
% 47.67/8.10 % (10544)Time elapsed: 0.524 s
% 47.67/8.10 % (10544)Instructions burned: 1762 (million)
% 47.67/8.10 % (10544)------------------------------
% 47.67/8.10 % (10544)------------------------------
% 47.67/8.11 % (10548)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_9951 for (2935ds/2341Mi)
% 48.36/8.12 % (10547)Refutation not found, non-redundant clauses discarded% (10547)------------------------------
% 48.36/8.12 % (10547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.36/8.12 % (10547)Termination reason: Refutation not found, non-redundant clauses discarded
% 48.36/8.12
% 48.36/8.12 % (10547)Memory used [KB]: 15735
% 48.36/8.12 % (10547)Time elapsed: 0.434 s
% 48.36/8.12 % (10547)Instructions burned: 1478 (million)
% 48.36/8.12 % (10547)------------------------------
% 48.36/8.12 % (10547)------------------------------
% 48.36/8.13 % (10549)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_9951 for (2935ds/7257Mi)
% 48.78/8.28 % (10530)Instruction limit reached!
% 48.78/8.28 % (10530)------------------------------
% 48.78/8.28 % (10530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.78/8.28 % (10530)Termination reason: Unknown
% 48.78/8.28 % (10530)Termination phase: Saturation
% 48.78/8.28
% 48.78/8.28 % (10530)Memory used [KB]: 13048
% 48.78/8.28 % (10530)Time elapsed: 1.904 s
% 48.78/8.28 % (10530)Instructions burned: 5799 (million)
% 48.78/8.28 % (10530)------------------------------
% 48.78/8.28 % (10530)------------------------------
% 48.78/8.29 % (10550)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_9951 for (2933ds/3710Mi)
% 49.28/8.34 % (10540)Instruction limit reached!
% 49.28/8.34 % (10540)------------------------------
% 49.28/8.34 % (10540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.28/8.34 % (10540)Termination reason: Unknown
% 49.28/8.34 % (10540)Termination phase: Saturation
% 49.28/8.34
% 49.28/8.34 % (10540)Memory used [KB]: 12920
% 49.28/8.34 % (10540)Time elapsed: 1.132 s
% 49.28/8.34 % (10540)Instructions burned: 3674 (million)
% 49.28/8.34 % (10540)------------------------------
% 49.28/8.34 % (10540)------------------------------
% 49.28/8.35 % (10551)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_9951 for (2932ds/326Mi)
% 49.65/8.43 % (10551)Instruction limit reached!
% 49.65/8.43 % (10551)------------------------------
% 49.65/8.43 % (10551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.65/8.43 % (10551)Termination reason: Unknown
% 49.65/8.43 % (10551)Termination phase: Saturation
% 49.65/8.43
% 49.65/8.43 % (10551)Memory used [KB]: 8571
% 49.65/8.43 % (10551)Time elapsed: 0.086 s
% 49.65/8.43 % (10551)Instructions burned: 327 (million)
% 49.65/8.43 % (10551)------------------------------
% 49.65/8.43 % (10551)------------------------------
% 49.65/8.44 % (10552)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_9951 for (2931ds/1100Mi)
% 50.34/8.69 % (10546)Instruction limit reached!
% 50.34/8.69 % (10546)------------------------------
% 50.34/8.69 % (10546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.34/8.69 % (10546)Termination reason: Unknown
% 50.34/8.69 % (10546)Termination phase: Saturation
% 50.34/8.69
% 50.34/8.69 % (10546)Memory used [KB]: 15991
% 50.34/8.69 % (10546)Time elapsed: 1.059 s
% 50.34/8.69 % (10546)Instructions burned: 3619 (million)
% 50.34/8.69 % (10546)------------------------------
% 50.34/8.69 % (10546)------------------------------
% 50.65/8.71 % (10553)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_9951 for (2929ds/406Mi)
% 50.65/8.72 % (10542)Instruction limit reached!
% 50.65/8.72 % (10542)------------------------------
% 50.65/8.72 % (10542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.65/8.72 % (10542)Termination reason: Unknown
% 50.65/8.72 % (10542)Termination phase: Saturation
% 50.65/8.72
% 50.65/8.72 % (10542)Memory used [KB]: 11641
% 50.65/8.72 % (10542)Time elapsed: 1.436 s
% 50.65/8.72 % (10542)Instructions burned: 4638 (million)
% 50.65/8.72 % (10542)------------------------------
% 50.65/8.72 % (10542)------------------------------
% 50.65/8.73 % (10554)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_9951 for (2929ds/1871Mi)
% 50.65/8.79 % (10552)Instruction limit reached!
% 50.65/8.79 % (10552)------------------------------
% 50.65/8.79 % (10552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.65/8.79 % (10552)Termination reason: Unknown
% 50.65/8.79 % (10552)Termination phase: Saturation
% 50.65/8.79
% 50.65/8.79 % (10552)Memory used [KB]: 14967
% 50.65/8.79 % (10552)Time elapsed: 0.346 s
% 50.65/8.79 % (10552)Instructions burned: 1100 (million)
% 50.65/8.79 % (10552)------------------------------
% 50.65/8.79 % (10552)------------------------------
% 51.13/8.80 % (10555)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_9951 for (2928ds/1194Mi)
% 51.13/8.82 % (10553)Instruction limit reached!
% 51.13/8.82 % (10553)------------------------------
% 51.13/8.82 % (10553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.13/8.82 % (10553)Termination reason: Unknown
% 51.13/8.82 % (10553)Termination phase: Saturation
% 51.13/8.82
% 51.13/8.82 % (10553)Memory used [KB]: 7931
% 51.13/8.82 % (10553)Time elapsed: 0.113 s
% 51.13/8.82 % (10553)Instructions burned: 408 (million)
% 51.13/8.82 % (10553)------------------------------
% 51.13/8.82 % (10553)------------------------------
% 51.13/8.83 % (10556)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_9951 for (2928ds/474Mi)
% 51.13/8.83 % (10548)Instruction limit reached!
% 51.13/8.83 % (10548)------------------------------
% 51.13/8.83 % (10548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.13/8.83 % (10548)Termination reason: Unknown
% 51.13/8.83 % (10548)Termination phase: Saturation
% 51.13/8.83
% 51.13/8.83 % (10548)Memory used [KB]: 11257
% 51.13/8.83 % (10548)Time elapsed: 0.722 s
% 51.13/8.83 % (10548)Instructions burned: 2343 (million)
% 51.13/8.83 % (10548)------------------------------
% 51.13/8.83 % (10548)------------------------------
% 51.13/8.84 % (10557)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_9951 for (2928ds/3115Mi)
% 52.08/8.95 % (10556)Instruction limit reached!
% 52.08/8.95 % (10556)------------------------------
% 52.08/8.95 % (10556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.08/8.95 % (10556)Termination reason: Unknown
% 52.08/8.95 % (10556)Termination phase: Saturation
% 52.08/8.95
% 52.08/8.95 % (10556)Memory used [KB]: 7675
% 52.08/8.95 % (10556)Time elapsed: 0.123 s
% 52.08/8.95 % (10556)Instructions burned: 477 (million)
% 52.08/8.95 % (10556)------------------------------
% 52.08/8.95 % (10556)------------------------------
% 52.08/8.96 % (10558)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_9951 for (2926ds/831Mi)
% 55.34/9.17 % (10555)Instruction limit reached!
% 55.34/9.17 % (10555)------------------------------
% 55.34/9.17 % (10555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.34/9.17 % (10555)Termination reason: Unknown
% 55.34/9.17 % (10555)Termination phase: Saturation
% 55.34/9.17
% 55.34/9.17 % (10555)Memory used [KB]: 12792
% 55.34/9.17 % (10555)Time elapsed: 0.375 s
% 55.34/9.17 % (10555)Instructions burned: 1196 (million)
% 55.34/9.17 % (10555)------------------------------
% 55.34/9.17 % (10555)------------------------------
% 55.34/9.18 % (10559)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_9951 for (2924ds/1188Mi)
% 55.93/9.21 % (10558)Instruction limit reached!
% 55.93/9.21 % (10558)------------------------------
% 55.93/9.21 % (10558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.93/9.21 % (10558)Termination reason: Unknown
% 55.93/9.21 % (10558)Termination phase: Saturation
% 55.93/9.21
% 55.93/9.21 % (10558)Memory used [KB]: 10106
% 55.93/9.21 % (10558)Time elapsed: 0.271 s
% 55.93/9.21 % (10558)Instructions burned: 834 (million)
% 55.93/9.21 % (10558)------------------------------
% 55.93/9.21 % (10558)------------------------------
% 55.93/9.22 % (10560)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_9951 for (2924ds/2868Mi)
% 55.93/9.27 % (10550)Instruction limit reached!
% 55.93/9.27 % (10550)------------------------------
% 55.93/9.27 % (10550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.93/9.27 % (10550)Termination reason: Unknown
% 55.93/9.27 % (10550)Termination phase: Saturation
% 55.93/9.27
% 55.93/9.27 % (10550)Memory used [KB]: 17910
% 55.93/9.27 % (10550)Time elapsed: 0.986 s
% 55.93/9.27 % (10550)Instructions burned: 3713 (million)
% 55.93/9.27 % (10550)------------------------------
% 55.93/9.27 % (10550)------------------------------
% 55.93/9.28 % (10561)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_9951 for (2923ds/1516Mi)
% 56.43/9.31 % (10554)Instruction limit reached!
% 56.43/9.31 % (10554)------------------------------
% 56.43/9.31 % (10554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.43/9.31 % (10554)Termination reason: Unknown
% 56.43/9.31 % (10554)Termination phase: Saturation
% 56.43/9.31
% 56.43/9.31 % (10554)Memory used [KB]: 19701
% 56.43/9.31 % (10554)Time elapsed: 0.582 s
% 56.43/9.31 % (10554)Instructions burned: 1872 (million)
% 56.43/9.31 % (10554)------------------------------
% 56.43/9.31 % (10554)------------------------------
% 56.43/9.32 % (10562)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_9951 for (2923ds/2321Mi)
% 56.43/9.39 % (10538)Instruction limit reached!
% 56.43/9.39 % (10538)------------------------------
% 56.43/9.39 % (10538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.43/9.39 % (10538)Termination reason: Unknown
% 56.43/9.39 % (10538)Termination phase: Saturation
% 56.43/9.39
% 56.43/9.39 % (10538)Memory used [KB]: 18549
% 56.43/9.39 % (10538)Time elapsed: 2.310 s
% 56.43/9.39 % (10538)Instructions burned: 7681 (million)
% 56.43/9.39 % (10538)------------------------------
% 56.43/9.39 % (10538)------------------------------
% 56.76/9.40 % (10563)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_9951 for (2922ds/2812Mi)
% 56.76/9.48 % (10559)Instruction limit reached!
% 56.76/9.48 % (10559)------------------------------
% 56.76/9.48 % (10559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.76/9.48 % (10559)Termination reason: Unknown
% 56.76/9.48 % (10559)Termination phase: Saturation
% 56.76/9.48
% 56.76/9.48 % (10559)Memory used [KB]: 17526
% 56.76/9.48 % (10559)Time elapsed: 0.301 s
% 56.76/9.48 % (10559)Instructions burned: 1188 (million)
% 56.76/9.48 % (10559)------------------------------
% 56.76/9.48 % (10559)------------------------------
% 56.76/9.49 % (10564)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_9951 for (2921ds/4604Mi)
% 57.47/9.63 % (10557)Instruction limit reached!
% 57.47/9.63 % (10557)------------------------------
% 57.47/9.63 % (10557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.47/9.63 % (10557)Termination reason: Unknown
% 57.47/9.63 % (10557)Termination phase: Saturation
% 57.47/9.63
% 57.47/9.63 % (10557)Memory used [KB]: 16630
% 57.47/9.63 % (10557)Time elapsed: 0.792 s
% 57.47/9.63 % (10557)Instructions burned: 3117 (million)
% 57.47/9.63 % (10557)------------------------------
% 57.47/9.63 % (10557)------------------------------
% 57.47/9.64 % (10565)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_9951 for (2920ds/2678Mi)
% 57.61/9.75 % (10561)Instruction limit reached!
% 57.61/9.75 % (10561)------------------------------
% 57.61/9.75 % (10561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.61/9.75 % (10561)Termination reason: Unknown
% 57.61/9.75 % (10561)Termination phase: Saturation
% 57.61/9.75
% 57.61/9.75 % (10561)Memory used [KB]: 12281
% 57.61/9.75 % (10561)Time elapsed: 0.501 s
% 57.61/9.75 % (10561)Instructions burned: 1518 (million)
% 57.61/9.75 % (10561)------------------------------
% 57.61/9.75 % (10561)------------------------------
% 57.61/9.76 % (10566)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_9951 for (2918ds/643Mi)
% 58.31/9.90 % (10562)Instruction limit reached!
% 58.31/9.90 % (10562)------------------------------
% 58.31/9.90 % (10562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.31/9.90 % (10562)Termination reason: Unknown
% 58.31/9.90 % (10562)Termination phase: Saturation
% 58.31/9.90
% 58.31/9.90 % (10562)Memory used [KB]: 16247
% 58.31/9.90 % (10562)Time elapsed: 0.607 s
% 58.31/9.90 % (10562)Instructions burned: 2321 (million)
% 58.31/9.90 % (10562)------------------------------
% 58.31/9.90 % (10562)------------------------------
% 58.31/9.91 % (10567)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_9951 for (2917ds/458Mi)
% 58.31/9.93 % (10566)Instruction limit reached!
% 58.31/9.93 % (10566)------------------------------
% 58.31/9.93 % (10566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.31/9.93 % (10566)Termination reason: Unknown
% 58.31/9.93 % (10566)Termination phase: Saturation
% 58.31/9.93
% 58.31/9.93 % (10566)Memory used [KB]: 7675
% 58.31/9.93 % (10566)Time elapsed: 0.162 s
% 58.31/9.93 % (10566)Instructions burned: 644 (million)
% 58.31/9.93 % (10566)------------------------------
% 58.31/9.93 % (10566)------------------------------
% 58.31/9.93 % (10568)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_9951 for (2916ds/2546Mi)
% 58.31/9.94 % (10560)Instruction limit reached!
% 58.31/9.94 % (10560)------------------------------
% 58.31/9.94 % (10560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.31/9.94 % (10560)Termination reason: Unknown
% 58.31/9.94 % (10560)Termination phase: Saturation
% 58.31/9.94
% 58.31/9.94 % (10560)Memory used [KB]: 7675
% 58.31/9.94 % (10560)Time elapsed: 0.726 s
% 58.31/9.94 % (10560)Instructions burned: 2870 (million)
% 58.31/9.94 % (10560)------------------------------
% 58.31/9.94 % (10560)------------------------------
% 58.31/9.95 % (10569)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_9951 for (2916ds/1432Mi)
% 61.65/10.03 % (10567)Instruction limit reached!
% 61.65/10.03 % (10567)------------------------------
% 61.65/10.03 % (10567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.65/10.03 % (10567)Termination reason: Unknown
% 61.65/10.03 % (10567)Termination phase: Saturation
% 61.65/10.03
% 61.65/10.03 % (10567)Memory used [KB]: 7547
% 61.65/10.03 % (10567)Time elapsed: 0.115 s
% 61.65/10.03 % (10567)Instructions burned: 461 (million)
% 61.65/10.03 % (10567)------------------------------
% 61.65/10.03 % (10567)------------------------------
% 61.65/10.04 % (10570)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_9951 for (2916ds/386Mi)
% 62.29/10.13 % (10570)Instruction limit reached!
% 62.29/10.13 % (10570)------------------------------
% 62.29/10.13 % (10570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.29/10.13 % (10570)Termination reason: Unknown
% 62.29/10.13 % (10570)Termination phase: Saturation
% 62.29/10.13
% 62.29/10.13 % (10570)Memory used [KB]: 7547
% 62.29/10.13 % (10570)Time elapsed: 0.097 s
% 62.29/10.13 % (10570)Instructions burned: 388 (million)
% 62.29/10.13 % (10570)------------------------------
% 62.29/10.13 % (10570)------------------------------
% 62.29/10.14 % (10571)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_9951 for (2914ds/360Mi)
% 62.90/10.23 % (10571)Instruction limit reached!
% 62.90/10.23 % (10571)------------------------------
% 62.90/10.23 % (10571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.90/10.23 % (10571)Termination reason: Unknown
% 62.90/10.23 % (10571)Termination phase: Saturation
% 62.90/10.23
% 62.90/10.23 % (10571)Memory used [KB]: 7547
% 62.90/10.23 % (10571)Time elapsed: 0.091 s
% 62.90/10.23 % (10571)Instructions burned: 362 (million)
% 62.90/10.23 % (10571)------------------------------
% 62.90/10.23 % (10571)------------------------------
% 62.90/10.24 % (10572)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_9951 for (2913ds/5446Mi)
% 62.90/10.26 % (10563)Instruction limit reached!
% 62.90/10.26 % (10563)------------------------------
% 62.90/10.26 % (10563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.90/10.26 % (10563)Termination reason: Unknown
% 62.90/10.26 % (10563)Termination phase: Saturation
% 62.90/10.26
% 62.90/10.26 % (10563)Memory used [KB]: 13176
% 62.90/10.26 % (10563)Time elapsed: 0.884 s
% 62.90/10.26 % (10563)Instructions burned: 2814 (million)
% 62.90/10.26 % (10563)------------------------------
% 62.90/10.26 % (10563)------------------------------
% 62.90/10.27 % (10573)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_9951 for (2913ds/2573Mi)
% 62.90/10.29 % (10565)Instruction limit reached!
% 62.90/10.29 % (10565)------------------------------
% 62.90/10.29 % (10565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.90/10.29 % (10565)Termination reason: Unknown
% 62.90/10.29 % (10565)Termination phase: Saturation
% 62.90/10.29
% 62.90/10.29 % (10565)Memory used [KB]: 25202
% 62.90/10.29 % (10565)Time elapsed: 0.654 s
% 62.90/10.29 % (10565)Instructions burned: 2679 (million)
% 62.90/10.29 % (10565)------------------------------
% 62.90/10.29 % (10565)------------------------------
% 63.58/10.30 % (10569)Instruction limit reached!
% 63.58/10.30 % (10569)------------------------------
% 63.58/10.30 % (10569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.58/10.30 % (10569)Termination reason: Unknown
% 63.58/10.30 % (10569)Termination phase: Saturation
% 63.58/10.30
% 63.58/10.30 % (10569)Memory used [KB]: 22259
% 63.58/10.30 % (10569)Time elapsed: 0.350 s
% 63.58/10.30 % (10569)Instructions burned: 1435 (million)
% 63.58/10.30 % (10569)------------------------------
% 63.58/10.30 % (10569)------------------------------
% 63.58/10.31 % (10574)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_9951 for (2913ds/2655Mi)
% 63.58/10.31 % (10575)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_9951 for (2913ds/2781Mi)
% 63.58/10.36 % (10549)Instruction limit reached!
% 63.58/10.36 % (10549)------------------------------
% 63.58/10.36 % (10549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.58/10.36 % (10549)Termination reason: Unknown
% 63.58/10.36 % (10549)Termination phase: Saturation
% 63.58/10.36
% 63.58/10.36 % (10549)Memory used [KB]: 10746
% 63.58/10.36 % (10549)Time elapsed: 2.229 s
% 63.58/10.36 % (10549)Instructions burned: 7259 (million)
% 63.58/10.36 % (10549)------------------------------
% 63.58/10.36 % (10549)------------------------------
% 63.58/10.37 % (10576)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_9951 for (2912ds/307Mi)
% 63.88/10.44 % (10576)Instruction limit reached!
% 63.88/10.44 % (10576)------------------------------
% 63.88/10.44 % (10576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.88/10.44 % (10576)Termination reason: Unknown
% 63.88/10.44 % (10576)Termination phase: Saturation
% 63.88/10.44
% 63.88/10.44 % (10576)Memory used [KB]: 7547
% 63.88/10.44 % (10576)Time elapsed: 0.077 s
% 63.88/10.44 % (10576)Instructions burned: 309 (million)
% 63.88/10.44 % (10576)------------------------------
% 63.88/10.44 % (10576)------------------------------
% 63.88/10.45 % (10577)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_9951 for (2911ds/1548Mi)
% 64.56/10.77 % (10568)Instruction limit reached!
% 64.56/10.77 % (10568)------------------------------
% 64.56/10.77 % (10568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.56/10.77 % (10568)Termination reason: Unknown
% 64.56/10.77 % (10568)Termination phase: Saturation
% 64.56/10.77
% 64.56/10.77 % (10568)Memory used [KB]: 10874
% 64.56/10.77 % (10568)Time elapsed: 0.840 s
% 64.56/10.77 % (10568)Instructions burned: 2546 (million)
% 64.56/10.77 % (10568)------------------------------
% 64.56/10.77 % (10568)------------------------------
% 64.56/10.79 % (10578)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_9951 for (2908ds/5214Mi)
% 64.85/10.91 % (10564)Instruction limit reached!
% 64.85/10.91 % (10564)------------------------------
% 64.85/10.91 % (10564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.85/10.91 % (10564)Termination reason: Unknown
% 64.85/10.91 % (10564)Termination phase: Saturation
% 64.85/10.91
% 64.85/10.91 % (10564)Memory used [KB]: 14072
% 64.85/10.91 % (10564)Time elapsed: 1.445 s
% 64.85/10.91 % (10564)Instructions burned: 4605 (million)
% 64.85/10.91 % (10564)------------------------------
% 64.85/10.91 % (10564)------------------------------
% 64.85/10.92 % (10579)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_9951 for (2907ds/3201Mi)
% 64.85/10.93 % (10573)Instruction limit reached!
% 64.85/10.93 % (10573)------------------------------
% 64.85/10.93 % (10573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.85/10.93 % (10573)Termination reason: Unknown
% 64.85/10.93 % (10573)Termination phase: Saturation
% 64.85/10.93
% 64.85/10.93 % (10573)Memory used [KB]: 18421
% 64.85/10.93 % (10573)Time elapsed: 0.666 s
% 64.85/10.93 % (10573)Instructions burned: 2577 (million)
% 64.85/10.93 % (10573)------------------------------
% 64.85/10.93 % (10573)------------------------------
% 64.85/10.93 % (10577)Instruction limit reached!
% 64.85/10.93 % (10577)------------------------------
% 64.85/10.93 % (10577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.85/10.93 % (10577)Termination reason: Unknown
% 64.85/10.93 % (10577)Termination phase: Saturation
% 64.85/10.93
% 64.85/10.93 % (10577)Memory used [KB]: 11129
% 64.85/10.93 % (10577)Time elapsed: 0.482 s
% 64.85/10.93 % (10577)Instructions burned: 1549 (million)
% 64.85/10.93 % (10577)------------------------------
% 64.85/10.93 % (10577)------------------------------
% 64.85/10.94 % (10580)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_9951 for (2906ds/454Mi)
% 64.85/10.94 % (10581)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_9951 for (2906ds/3049Mi)
% 64.85/11.00 % (10574)Instruction limit reached!
% 64.85/11.00 % (10574)------------------------------
% 64.85/11.00 % (10574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.85/11.00 % (10574)Termination reason: Unknown
% 64.85/11.00 % (10574)Termination phase: Saturation
% 64.85/11.00
% 64.85/11.00 % (10574)Memory used [KB]: 5884
% 64.85/11.00 % (10574)Time elapsed: 0.691 s
% 64.85/11.00 % (10574)Instructions burned: 2655 (million)
% 64.85/11.00 % (10574)------------------------------
% 64.85/11.00 % (10574)------------------------------
% 64.85/11.02 % (10582)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_9951 for (2906ds/7311Mi)
% 68.73/11.06 % (10580)Instruction limit reached!
% 68.73/11.06 % (10580)------------------------------
% 68.73/11.06 % (10580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.73/11.06 % (10580)Termination reason: Unknown
% 68.73/11.06 % (10580)Termination phase: Saturation
% 68.73/11.06
% 68.73/11.06 % (10580)Memory used [KB]: 12025
% 68.73/11.06 % (10580)Time elapsed: 0.113 s
% 68.73/11.06 % (10580)Instructions burned: 456 (million)
% 68.73/11.06 % (10580)------------------------------
% 68.73/11.06 % (10580)------------------------------
% 68.73/11.07 % (10583)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_9951 for (2905ds/6804Mi)
% 69.30/11.16 % (10575)Instruction limit reached!
% 69.30/11.16 % (10575)------------------------------
% 69.30/11.16 % (10575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.30/11.16 % (10575)Termination reason: Unknown
% 69.30/11.16 % (10575)Termination phase: Saturation
% 69.30/11.16
% 69.30/11.16 % (10575)Memory used [KB]: 9210
% 69.30/11.16 % (10575)Time elapsed: 0.849 s
% 69.30/11.16 % (10575)Instructions burned: 2781 (million)
% 69.30/11.16 % (10575)------------------------------
% 69.30/11.16 % (10575)------------------------------
% 69.30/11.17 % (10584)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_9951 for (2904ds/1683Mi)
% 71.24/11.63 % (10584)Instruction limit reached!
% 71.24/11.63 % (10584)------------------------------
% 71.24/11.63 % (10584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.24/11.63 % (10584)Termination reason: Unknown
% 71.24/11.63 % (10584)Termination phase: Saturation
% 71.24/11.63
% 71.24/11.63 % (10584)Memory used [KB]: 20724
% 71.24/11.63 % (10584)Time elapsed: 0.462 s
% 71.24/11.63 % (10584)Instructions burned: 1684 (million)
% 71.24/11.63 % (10584)------------------------------
% 71.24/11.63 % (10584)------------------------------
% 71.24/11.64 % (10585)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_9951 for (2899ds/4688Mi)
% 72.51/11.86 % (10581)Instruction limit reached!
% 72.51/11.86 % (10581)------------------------------
% 72.51/11.86 % (10581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.51/11.86 % (10581)Termination reason: Unknown
% 72.51/11.86 % (10581)Termination phase: Saturation
% 72.51/11.86
% 72.51/11.86 % (10581)Memory used [KB]: 11129
% 72.51/11.86 % (10581)Time elapsed: 0.943 s
% 72.51/11.86 % (10581)Instructions burned: 3050 (million)
% 72.51/11.86 % (10581)------------------------------
% 72.51/11.86 % (10581)------------------------------
% 72.51/11.88 % (10586)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_9951 for (2897ds/2207Mi)
% 72.88/11.90 % (10579)Instruction limit reached!
% 72.88/11.90 % (10579)------------------------------
% 72.88/11.90 % (10579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.88/11.90 % (10579)Termination reason: Unknown
% 72.88/11.90 % (10579)Termination phase: Saturation
% 72.88/11.90
% 72.88/11.90 % (10579)Memory used [KB]: 12281
% 72.88/11.90 % (10579)Time elapsed: 0.979 s
% 72.88/11.90 % (10579)Instructions burned: 3201 (million)
% 72.88/11.90 % (10579)------------------------------
% 72.88/11.90 % (10579)------------------------------
% 72.88/11.91 % (10587)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_9951 for (2897ds/8216Mi)
% 72.88/11.96 % (10572)Instruction limit reached!
% 72.88/11.96 % (10572)------------------------------
% 72.88/11.96 % (10572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.88/11.96 % (10572)Termination reason: Unknown
% 72.88/11.96 % (10572)Termination phase: Saturation
% 72.88/11.96
% 72.88/11.96 % (10572)Memory used [KB]: 15991
% 72.88/11.96 % (10572)Time elapsed: 1.715 s
% 72.88/11.96 % (10572)Instructions burned: 5446 (million)
% 72.88/11.96 % (10572)------------------------------
% 72.88/11.96 % (10572)------------------------------
% 72.88/11.97 % (10588)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_9951 for (2896ds/430Mi)
% 75.74/12.07 % (10588)Instruction limit reached!
% 75.74/12.07 % (10588)------------------------------
% 75.74/12.07 % (10588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.74/12.07 % (10588)Termination reason: Unknown
% 75.74/12.07 % (10588)Termination phase: Saturation
% 75.74/12.07
% 75.74/12.07 % (10588)Memory used [KB]: 7547
% 75.74/12.07 % (10588)Time elapsed: 0.107 s
% 75.74/12.07 % (10588)Instructions burned: 430 (million)
% 75.74/12.07 % (10588)------------------------------
% 75.74/12.07 % (10588)------------------------------
% 75.74/12.08 % (10589)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_9951 for (2895ds/2012Mi)
% 77.47/12.35 % (10578)Instruction limit reached!
% 77.47/12.35 % (10578)------------------------------
% 77.47/12.35 % (10578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.47/12.35 % (10578)Termination reason: Unknown
% 77.47/12.35 % (10578)Termination phase: Saturation
% 77.47/12.35
% 77.47/12.35 % (10578)Memory used [KB]: 11385
% 77.47/12.35 % (10578)Time elapsed: 1.566 s
% 77.47/12.35 % (10578)Instructions burned: 5214 (million)
% 77.47/12.35 % (10578)------------------------------
% 77.47/12.35 % (10578)------------------------------
% 77.47/12.36 % (10590)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_9951 for (2892ds/631Mi)
% 78.55/12.54 % (10590)Instruction limit reached!
% 78.55/12.54 % (10590)------------------------------
% 78.55/12.54 % (10590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.55/12.54 % (10590)Termination reason: Unknown
% 78.55/12.54 % (10590)Termination phase: Saturation
% 78.55/12.54
% 78.55/12.54 % (10590)Memory used [KB]: 8443
% 78.55/12.54 % (10590)Time elapsed: 0.180 s
% 78.55/12.54 % (10590)Instructions burned: 633 (million)
% 78.55/12.54 % (10590)------------------------------
% 78.55/12.54 % (10590)------------------------------
% 78.55/12.55 % (10591)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_9951 for (2890ds/8785Mi)
% 78.55/12.55 % (10586)Instruction limit reached!
% 78.55/12.55 % (10586)------------------------------
% 78.55/12.55 % (10586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.55/12.55 % (10586)Termination reason: Unknown
% 78.55/12.55 % (10586)Termination phase: Saturation
% 78.55/12.55
% 78.55/12.55 % (10586)Memory used [KB]: 11257
% 78.55/12.55 % (10586)Time elapsed: 0.677 s
% 78.55/12.55 % (10586)Instructions burned: 2207 (million)
% 78.55/12.55 % (10586)------------------------------
% 78.55/12.55 % (10586)------------------------------
% 78.55/12.56 % (10592)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_9951 for (2890ds/739Mi)
% 78.55/12.59 % (10589)Instruction limit reached!
% 78.55/12.59 % (10589)------------------------------
% 78.55/12.59 % (10589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.55/12.59 % (10589)Termination reason: Unknown
% 78.55/12.59 % (10589)Termination phase: Saturation
% 78.55/12.59
% 78.55/12.59 % (10589)Memory used [KB]: 12153
% 78.55/12.59 % (10589)Time elapsed: 0.513 s
% 78.55/12.59 % (10589)Instructions burned: 2012 (million)
% 78.55/12.59 % (10589)------------------------------
% 78.55/12.59 % (10589)------------------------------
% 79.72/12.60 % (10593)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_9951 for (2890ds/5473Mi)
% 80.11/12.79 % (10592)Instruction limit reached!
% 80.11/12.79 % (10592)------------------------------
% 80.11/12.79 % (10592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.11/12.79 % (10592)Termination reason: Unknown
% 80.11/12.79 % (10592)Termination phase: Saturation
% 80.11/12.79
% 80.11/12.79 % (10592)Memory used [KB]: 13560
% 80.11/12.79 % (10592)Time elapsed: 0.229 s
% 80.11/12.79 % (10592)Instructions burned: 739 (million)
% 80.11/12.79 % (10592)------------------------------
% 80.11/12.79 % (10592)------------------------------
% 80.75/12.80 % (10594)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_9951 for (2888ds/43570Mi)
% 82.76/13.05 % (10585)Instruction limit reached!
% 82.76/13.05 % (10585)------------------------------
% 82.76/13.05 % (10585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.76/13.05 % (10585)Termination reason: Unknown
% 82.76/13.05 % (10585)Termination phase: Saturation
% 82.76/13.05
% 82.76/13.05 % (10585)Memory used [KB]: 14328
% 82.76/13.05 % (10585)Time elapsed: 1.415 s
% 82.76/13.05 % (10585)Instructions burned: 4688 (million)
% 82.76/13.05 % (10585)------------------------------
% 82.76/13.05 % (10585)------------------------------
% 82.76/13.07 % (10595)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_9951 for (2885ds/8382Mi)
% 83.41/13.17 % (10583)Instruction limit reached!
% 83.41/13.17 % (10583)------------------------------
% 83.41/13.17 % (10583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.41/13.17 % (10583)Termination reason: Unknown
% 83.41/13.17 % (10583)Termination phase: Saturation
% 83.41/13.17
% 83.41/13.17 % (10583)Memory used [KB]: 19061
% 83.41/13.17 % (10583)Time elapsed: 2.107 s
% 83.41/13.17 % (10583)Instructions burned: 6804 (million)
% 83.41/13.17 % (10583)------------------------------
% 83.41/13.17 % (10583)------------------------------
% 83.41/13.18 % (10596)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_9951 for (2884ds/407Mi)
% 83.85/13.29 % (10596)Instruction limit reached!
% 83.85/13.29 % (10596)------------------------------
% 83.85/13.29 % (10596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.85/13.29 % (10596)Termination reason: Unknown
% 83.85/13.29 % (10596)Termination phase: Saturation
% 83.85/13.29
% 83.85/13.29 % (10596)Memory used [KB]: 9722
% 83.85/13.29 % (10596)Time elapsed: 0.112 s
% 83.85/13.29 % (10596)Instructions burned: 407 (million)
% 83.85/13.29 % (10596)------------------------------
% 83.85/13.29 % (10596)------------------------------
% 84.48/13.30 % (10597)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_9951 for (2883ds/2971Mi)
% 84.48/13.34 % (10582)Instruction limit reached!
% 84.48/13.34 % (10582)------------------------------
% 84.48/13.34 % (10582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.48/13.34 % (10582)Termination reason: Unknown
% 84.48/13.34 % (10582)Termination phase: Saturation
% 84.48/13.34
% 84.48/13.34 % (10582)Memory used [KB]: 18421
% 84.48/13.34 % (10582)Time elapsed: 2.325 s
% 84.48/13.34 % (10582)Instructions burned: 7312 (million)
% 84.48/13.34 % (10582)------------------------------
% 84.48/13.34 % (10582)------------------------------
% 84.48/13.35 % (10598)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_9951 for (2882ds/9822Mi)
% 86.56/13.89 % (10587)Instruction limit reached!
% 86.56/13.89 % (10587)------------------------------
% 86.56/13.89 % (10587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.56/13.89 % (10587)Termination reason: Unknown
% 86.56/13.89 % (10587)Termination phase: Saturation
% 86.56/13.89
% 86.56/13.89 % (10587)Memory used [KB]: 7931
% 86.56/13.89 % (10587)Time elapsed: 1.980 s
% 86.56/13.89 % (10587)Instructions burned: 8217 (million)
% 86.56/13.89 % (10587)------------------------------
% 86.56/13.89 % (10587)------------------------------
% 86.97/13.90 % (10599)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_9951 for (2877ds/8425Mi)
% 89.81/14.04 % (10597)Instruction limit reached!
% 89.81/14.04 % (10597)------------------------------
% 89.81/14.04 % (10597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.81/14.04 % (10597)Termination reason: Unknown
% 89.81/14.04 % (10597)Termination phase: Saturation
% 89.81/14.04
% 89.81/14.04 % (10597)Memory used [KB]: 7675
% 89.81/14.04 % (10597)Time elapsed: 0.742 s
% 89.81/14.04 % (10597)Instructions burned: 2973 (million)
% 89.81/14.04 % (10597)------------------------------
% 89.81/14.04 % (10597)------------------------------
% 89.81/14.05 % (10601)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_9951 for (2875ds/3107Mi)
% 90.88/14.26 % (10593)Instruction limit reached!
% 90.88/14.26 % (10593)------------------------------
% 90.88/14.26 % (10593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.88/14.26 % (10593)Termination reason: Unknown
% 90.88/14.26 % (10593)Termination phase: Saturation
% 90.88/14.26
% 90.88/14.26 % (10593)Memory used [KB]: 13560
% 90.88/14.26 % (10593)Time elapsed: 1.653 s
% 90.88/14.26 % (10593)Instructions burned: 5476 (million)
% 90.88/14.26 % (10593)------------------------------
% 90.88/14.26 % (10593)------------------------------
% 90.88/14.27 % (10658)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_9951 for (2873ds/7967Mi)
% 94.47/14.99 % (10601)Instruction limit reached!
% 94.47/14.99 % (10601)------------------------------
% 94.47/14.99 % (10601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.47/14.99 % (10601)Termination reason: Unknown
% 94.47/14.99 % (10601)Termination phase: Saturation
% 94.47/14.99
% 94.47/14.99 % (10601)Memory used [KB]: 21492
% 94.47/14.99 % (10601)Time elapsed: 0.938 s
% 94.47/14.99 % (10601)Instructions burned: 3110 (million)
% 94.47/14.99 % (10601)------------------------------
% 94.47/14.99 % (10601)------------------------------
% 94.47/15.00 % (10976)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_9951 for (2866ds/3629Mi)
% 98.05/15.29 % (10591)Instruction limit reached!
% 98.05/15.29 % (10591)------------------------------
% 98.05/15.29 % (10591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.05/15.29 % (10591)Termination reason: Unknown
% 98.05/15.29 % (10591)Termination phase: Saturation
% 98.05/15.29
% 98.05/15.29 % (10591)Memory used [KB]: 21364
% 98.05/15.29 % (10591)Time elapsed: 2.747 s
% 98.05/15.29 % (10591)Instructions burned: 8787 (million)
% 98.05/15.29 % (10591)------------------------------
% 98.05/15.29 % (10591)------------------------------
% 96.00/15.31 % (11062)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_9951 for (2863ds/939Mi)
% 96.00/15.32 % (10595)Instruction limit reached!
% 96.00/15.32 % (10595)------------------------------
% 96.00/15.32 % (10595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.00/15.32 % (10595)Termination reason: Unknown
% 96.00/15.32 % (10595)Termination phase: Saturation
% 96.00/15.32
% 96.00/15.32 % (10595)Memory used [KB]: 14583
% 96.00/15.32 % (10595)Time elapsed: 2.259 s
% 96.00/15.32 % (10595)Instructions burned: 8384 (million)
% 96.00/15.32 % (10595)------------------------------
% 96.00/15.32 % (10595)------------------------------
% 96.00/15.34 % (11067)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_9951 for (2862ds/1188Mi)
% 100.30/15.63 % (11062)Instruction limit reached!
% 100.30/15.63 % (11062)------------------------------
% 100.30/15.63 % (11062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.30/15.63 % (11062)Termination reason: Unknown
% 100.30/15.63 % (11062)Termination phase: Saturation
% 100.30/15.63
% 100.30/15.63 % (11062)Memory used [KB]: 10106
% 100.30/15.63 % (11062)Time elapsed: 0.324 s
% 100.30/15.63 % (11062)Instructions burned: 940 (million)
% 100.30/15.63 % (11062)------------------------------
% 100.30/15.63 % (11062)------------------------------
% 100.30/15.64 % (11067)Instruction limit reached!
% 100.30/15.64 % (11067)------------------------------
% 100.30/15.64 % (11067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.30/15.64 % (11067)Termination reason: Unknown
% 100.30/15.64 % (11067)Termination phase: Saturation
% 100.30/15.64
% 100.30/15.64 % (11067)Memory used [KB]: 17398
% 100.30/15.64 % (11067)Time elapsed: 0.302 s
% 100.30/15.64 % (11067)Instructions burned: 1188 (million)
% 100.30/15.64 % (11067)------------------------------
% 100.30/15.64 % (11067)------------------------------
% 100.30/15.64 % (11072)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_9951 for (2859ds/3205Mi)
% 100.30/15.65 % (11073)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_9951 for (2859ds/865Mi)
% 102.46/15.90 % (11073)Instruction limit reached!
% 102.46/15.90 % (11073)------------------------------
% 102.46/15.90 % (11073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.46/15.90 % (11073)Termination reason: Unknown
% 102.46/15.90 % (11073)Termination phase: Saturation
% 102.46/15.90
% 102.46/15.90 % (11073)Memory used [KB]: 7803
% 102.46/15.90 % (11073)Time elapsed: 0.255 s
% 102.46/15.90 % (11073)Instructions burned: 865 (million)
% 102.46/15.90 % (11073)------------------------------
% 102.46/15.90 % (11073)------------------------------
% 102.46/15.92 % (11074)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_9951 for (2857ds/7469Mi)
% 102.46/15.95 % (10976)Instruction limit reached!
% 102.46/15.95 % (10976)------------------------------
% 102.46/15.95 % (10976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.46/15.95 % (10976)Termination reason: Unknown
% 102.46/15.95 % (10976)Termination phase: Saturation
% 102.46/15.95
% 102.46/15.95 % (10976)Memory used [KB]: 7803
% 102.46/15.95 % (10976)Time elapsed: 0.944 s
% 102.46/15.95 % (10976)Instructions burned: 3630 (million)
% 102.46/15.95 % (10976)------------------------------
% 102.46/15.95 % (10976)------------------------------
% 102.46/15.96 % (11077)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_9951 for (2856ds/4165Mi)
% 105.06/16.22 % (10598)Refutation not found, non-redundant clauses discarded% (10598)------------------------------
% 105.06/16.22 % (10598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.06/16.22 % (10598)Termination reason: Refutation not found, non-redundant clauses discarded
% 105.06/16.22
% 105.06/16.22 % (10598)Memory used [KB]: 21364
% 105.06/16.22 % (10598)Time elapsed: 2.864 s
% 105.06/16.22 % (10598)Instructions burned: 9233 (million)
% 105.06/16.22 % (10598)------------------------------
% 105.06/16.22 % (10598)------------------------------
% 105.06/16.23 % (11078)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_9951 for (2854ds/13468Mi)
% 105.70/16.38 % (10658)Instruction limit reached!
% 105.70/16.38 % (10658)------------------------------
% 105.70/16.38 % (10658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.70/16.38 % (10658)Termination reason: Unknown
% 105.70/16.38 % (10658)Termination phase: Saturation
% 105.70/16.38
% 105.70/16.38 % (10658)Memory used [KB]: 16375
% 105.70/16.38 % (10658)Time elapsed: 2.118 s
% 105.70/16.38 % (10658)Instructions burned: 7969 (million)
% 105.70/16.38 % (10658)------------------------------
% 105.70/16.38 % (10658)------------------------------
% 105.70/16.39 % (11084)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_9951 for (2852ds/2635Mi)
% 106.79/16.59 % (10599)Instruction limit reached!
% 106.79/16.59 % (10599)------------------------------
% 106.79/16.59 % (10599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.79/16.59 % (10599)Termination reason: Unknown
% 106.79/16.59 % (10599)Termination phase: Saturation
% 106.79/16.59
% 106.79/16.59 % (10599)Memory used [KB]: 12281
% 106.79/16.59 % (10599)Time elapsed: 2.696 s
% 106.79/16.59 % (10599)Instructions burned: 8426 (million)
% 106.79/16.59 % (10599)------------------------------
% 106.79/16.59 % (10599)------------------------------
% 104.59/16.61 % (11118)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_9951 for (2850ds/631Mi)
% 108.12/16.85 % (11118)Instruction limit reached!
% 108.12/16.85 % (11118)------------------------------
% 108.12/16.85 % (11118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.12/16.85 % (11118)Termination reason: Unknown
% 108.12/16.85 % (11118)Termination phase: Saturation
% 108.12/16.85
% 108.12/16.85 % (11118)Memory used [KB]: 7675
% 108.12/16.85 % (11118)Time elapsed: 0.239 s
% 108.12/16.85 % (11118)Instructions burned: 631 (million)
% 108.12/16.85 % (11118)------------------------------
% 108.12/16.85 % (11118)------------------------------
% 108.12/16.86 % (11131)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_9951 for (2847ds/15557Mi)
% 108.77/16.95 % (11072)Instruction limit reached!
% 108.77/16.95 % (11072)------------------------------
% 108.77/16.95 % (11072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.77/16.95 % (11072)Termination reason: Unknown
% 108.77/16.95 % (11072)Termination phase: Saturation
% 108.77/16.95
% 108.77/16.95 % (11072)Memory used [KB]: 15735
% 108.77/16.95 % (11072)Time elapsed: 1.312 s
% 108.77/16.95 % (11072)Instructions burned: 3206 (million)
% 108.77/16.95 % (11072)------------------------------
% 108.77/16.95 % (11072)------------------------------
% 108.77/16.97 % (11141)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_9951 for (2846ds/2142Mi)
% 114.14/17.58 % (11084)Instruction limit reached!
% 114.14/17.58 % (11084)------------------------------
% 114.14/17.58 % (11084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.14/17.58 % (11084)Termination reason: Unknown
% 114.14/17.58 % (11084)Termination phase: Saturation
% 114.14/17.58
% 114.14/17.58 % (11084)Memory used [KB]: 12281
% 114.14/17.58 % (11084)Time elapsed: 1.184 s
% 114.14/17.58 % (11084)Instructions burned: 2635 (million)
% 114.14/17.58 % (11084)------------------------------
% 114.14/17.58 % (11084)------------------------------
% 114.14/17.59 % (11181)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_9951 for (2840ds/5624Mi)
% 116.03/17.80 % (11077)Instruction limit reached!
% 116.03/17.80 % (11077)------------------------------
% 116.03/17.80 % (11077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.03/17.80 % (11077)Termination reason: Unknown
% 116.03/17.80 % (11077)Termination phase: Saturation
% 116.03/17.80
% 116.03/17.80 % (11077)Memory used [KB]: 26225
% 116.03/17.80 % (11077)Time elapsed: 1.844 s
% 116.03/17.80 % (11077)Instructions burned: 4165 (million)
% 116.03/17.80 % (11077)------------------------------
% 116.03/17.80 % (11077)------------------------------
% 116.03/17.81 % (11191)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_9951 for (2838ds/1665Mi)
% 116.03/17.85 % (11141)Instruction limit reached!
% 116.03/17.85 % (11141)------------------------------
% 116.03/17.85 % (11141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.03/17.85 % (11141)Termination reason: Unknown
% 116.03/17.85 % (11141)Termination phase: Saturation
% 116.03/17.85
% 116.03/17.85 % (11141)Memory used [KB]: 11129
% 116.03/17.85 % (11141)Time elapsed: 0.882 s
% 116.03/17.85 % (11141)Instructions burned: 2142 (million)
% 116.03/17.85 % (11141)------------------------------
% 116.03/17.85 % (11141)------------------------------
% 116.03/17.87 % (11192)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_9951 for (2837ds/64912Mi)
% 119.73/18.34 % (11191)Instruction limit reached!
% 119.73/18.34 % (11191)------------------------------
% 119.73/18.34 % (11191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.73/18.34 % (11191)Termination reason: Unknown
% 119.73/18.34 % (11191)Termination phase: Saturation
% 119.73/18.34
% 119.73/18.34 % (11191)Memory used [KB]: 16119
% 119.73/18.34 % (11191)Time elapsed: 0.531 s
% 119.73/18.34 % (11191)Instructions burned: 1665 (million)
% 119.73/18.34 % (11191)------------------------------
% 119.73/18.34 % (11191)------------------------------
% 119.73/18.35 % (11202)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_9951 for (2832ds/7801Mi)
% 122.82/18.84 % (11074)Instruction limit reached!
% 122.82/18.84 % (11074)------------------------------
% 122.82/18.84 % (11074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 122.82/18.84 % (11074)Termination reason: Unknown
% 122.82/18.84 % (11074)Termination phase: Saturation
% 122.82/18.84
% 122.82/18.84 % (11074)Memory used [KB]: 13048
% 122.82/18.84 % (11074)Time elapsed: 2.925 s
% 122.82/18.84 % (11074)Instructions burned: 7470 (million)
% 122.82/18.84 % (11074)------------------------------
% 122.82/18.84 % (11074)------------------------------
% 122.82/18.86 % (11214)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_9951 for (2827ds/15194Mi)
% 129.55/19.77 % (11181)Instruction limit reached!
% 129.55/19.77 % (11181)------------------------------
% 129.55/19.77 % (11181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 129.55/19.77 % (11181)Termination reason: Unknown
% 129.55/19.77 % (11181)Termination phase: Saturation
% 129.55/19.77
% 129.55/19.77 % (11181)Memory used [KB]: 14839
% 129.55/19.77 % (11181)Time elapsed: 2.178 s
% 129.55/19.77 % (11181)Instructions burned: 5624 (million)
% 129.55/19.77 % (11181)------------------------------
% 129.55/19.77 % (11181)------------------------------
% 129.55/19.78 % (11450)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_9951 for (2818ds/6753Mi)
% 132.56/20.14 % (11078)Instruction limit reached!
% 132.56/20.14 % (11078)------------------------------
% 132.56/20.14 % (11078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 132.56/20.14 % (11078)Termination reason: Unknown
% 132.56/20.14 % (11078)Termination phase: Saturation
% 132.56/20.14
% 132.56/20.14 % (11078)Memory used [KB]: 10874
% 132.56/20.14 % (11078)Time elapsed: 3.934 s
% 132.56/20.14 % (11078)Instructions burned: 13471 (million)
% 132.56/20.14 % (11078)------------------------------
% 132.56/20.14 % (11078)------------------------------
% 132.56/20.15 % (11451)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_9951 for (2814ds/1003Mi)
% 134.24/20.40 % (11451)Instruction limit reached!
% 134.24/20.40 % (11451)------------------------------
% 134.24/20.40 % (11451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 134.24/20.40 % (11451)Termination reason: Unknown
% 134.24/20.40 % (11451)Termination phase: Saturation
% 134.24/20.40
% 134.24/20.40 % (11451)Memory used [KB]: 7675
% 134.24/20.40 % (11451)Time elapsed: 0.250 s
% 134.24/20.40 % (11451)Instructions burned: 1003 (million)
% 134.24/20.40 % (11451)------------------------------
% 134.24/20.40 % (11451)------------------------------
% 134.24/20.41 % (11452)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_9951 for (2812ds/13018Mi)
% 136.91/20.82 % (11202)Instruction limit reached!
% 136.91/20.82 % (11202)------------------------------
% 136.91/20.82 % (11202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 136.91/20.82 % (11202)Termination reason: Unknown
% 136.91/20.82 % (11202)Termination phase: Saturation
% 136.91/20.82
% 136.91/20.82 % (11202)Memory used [KB]: 13432
% 136.91/20.82 % (11202)Time elapsed: 2.472 s
% 136.91/20.82 % (11202)Instructions burned: 7801 (million)
% 136.91/20.82 % (11202)------------------------------
% 136.91/20.82 % (11202)------------------------------
% 136.91/20.83 % (11453)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_9951 for (2807ds/1267Mi)
% 139.59/21.19 % (11131)Instruction limit reached!
% 139.59/21.19 % (11131)------------------------------
% 139.59/21.19 % (11131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.59/21.19 % (11131)Termination reason: Unknown
% 139.59/21.19 % (11131)Termination phase: Saturation
% 139.59/21.19
% 139.59/21.19 % (11131)Memory used [KB]: 17270
% 139.59/21.19 % (11131)Time elapsed: 4.331 s
% 139.59/21.19 % (11131)Instructions burned: 15557 (million)
% 139.59/21.19 % (11131)------------------------------
% 139.59/21.19 % (11131)------------------------------
% 140.11/21.20 % (11454)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_9951 for (2804ds/2570Mi)
% 140.11/21.22 % (11453)Instruction limit reached!
% 140.11/21.22 % (11453)------------------------------
% 140.11/21.22 % (11453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 140.11/21.22 % (11453)Termination reason: Unknown
% 140.11/21.22 % (11453)Termination phase: Saturation
% 140.11/21.22
% 140.11/21.22 % (11453)Memory used [KB]: 12025
% 140.11/21.22 % (11453)Time elapsed: 0.390 s
% 140.11/21.22 % (11453)Instructions burned: 1267 (million)
% 140.11/21.22 % (11453)------------------------------
% 140.11/21.22 % (11453)------------------------------
% 140.11/21.23 % (11455)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_9951 for (2803ds/13163Mi)
% 143.16/21.83 % (11454)Instruction limit reached!
% 143.16/21.83 % (11454)------------------------------
% 143.16/21.83 % (11454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 143.16/21.83 % (11454)Termination reason: Unknown
% 143.16/21.83 % (11454)Termination phase: Saturation
% 143.16/21.83
% 143.16/21.83 % (11454)Memory used [KB]: 25074
% 143.16/21.83 % (11454)Time elapsed: 0.632 s
% 143.16/21.83 % (11454)Instructions burned: 2573 (million)
% 143.16/21.83 % (11454)------------------------------
% 143.16/21.83 % (11454)------------------------------
% 143.16/21.85 % (11456)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_9951 for (2797ds/5087Mi)
% 143.16/21.86 % (11450)Instruction limit reached!
% 143.16/21.86 % (11450)------------------------------
% 143.16/21.86 % (11450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 143.16/21.86 % (11450)Termination reason: Unknown
% 143.16/21.86 % (11450)Termination phase: Saturation
% 143.16/21.86
% 143.16/21.86 % (11450)Memory used [KB]: 17014
% 143.16/21.86 % (11450)Time elapsed: 2.102 s
% 143.16/21.86 % (11450)Instructions burned: 6754 (million)
% 143.16/21.86 % (11450)------------------------------
% 143.16/21.86 % (11450)------------------------------
% 143.16/21.87 % (11457)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_9951 for (2797ds/10380Mi)
% 155.58/23.45 % (11214)Instruction limit reached!
% 155.58/23.45 % (11214)------------------------------
% 155.58/23.45 % (11214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.58/23.45 % (11214)Termination reason: Unknown
% 155.58/23.45 % (11214)Termination phase: Saturation
% 155.58/23.45
% 155.58/23.45 % (11214)Memory used [KB]: 22131
% 155.58/23.45 % (11214)Time elapsed: 4.592 s
% 155.58/23.45 % (11214)Instructions burned: 15196 (million)
% 155.58/23.45 % (11214)------------------------------
% 155.58/23.45 % (11214)------------------------------
% 155.58/23.46 % (11458)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_9951 for (2781ds/4218Mi)
% 155.58/23.47 % (11456)Instruction limit reached!
% 155.58/23.47 % (11456)------------------------------
% 155.58/23.47 % (11456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.58/23.47 % (11456)Termination reason: Unknown
% 155.58/23.47 % (11456)Termination phase: Saturation
% 155.58/23.47
% 155.58/23.47 % (11456)Memory used [KB]: 14072
% 155.58/23.47 % (11456)Time elapsed: 1.628 s
% 155.58/23.47 % (11456)Instructions burned: 5089 (million)
% 155.58/23.47 % (11456)------------------------------
% 155.58/23.47 % (11456)------------------------------
% 155.58/23.48 % (11459)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_9951 for (2781ds/3971Mi)
% 162.59/24.44 % (11457)Instruction limit reached!
% 162.59/24.44 % (11457)------------------------------
% 162.59/24.44 % (11457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 162.59/24.44 % (11457)Termination reason: Unknown
% 162.59/24.44 % (11457)Termination phase: Saturation
% 162.59/24.44
% 162.59/24.44 % (11457)Memory used [KB]: 7803
% 162.59/24.44 % (11457)Time elapsed: 2.572 s
% 162.59/24.44 % (11457)Instructions burned: 10382 (million)
% 162.59/24.44 % (11457)------------------------------
% 162.59/24.44 % (11457)------------------------------
% 162.59/24.45 % (11460)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_9951 for (2771ds/14014Mi)
% 163.84/24.62 % (11452)Instruction limit reached!
% 163.84/24.62 % (11452)------------------------------
% 163.84/24.62 % (11452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.84/24.62 % (11452)Termination reason: Unknown
% 163.84/24.62 % (11452)Termination phase: Saturation
% 163.84/24.62
% 163.84/24.62 % (11452)Memory used [KB]: 41065
% 163.84/24.62 % (11452)Time elapsed: 4.211 s
% 163.84/24.62 % (11452)Instructions burned: 13019 (million)
% 163.84/24.62 % (11452)------------------------------
% 163.84/24.62 % (11452)------------------------------
% 163.84/24.63 % (11461)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_9951 for (2770ds/8517Mi)
% 163.84/24.68 % (11459)Instruction limit reached!
% 163.84/24.68 % (11459)------------------------------
% 163.84/24.68 % (11459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.84/24.68 % (11459)Termination reason: Unknown
% 163.84/24.68 % (11459)Termination phase: Saturation
% 163.84/24.68
% 163.84/24.68 % (11459)Memory used [KB]: 15223
% 163.84/24.68 % (11459)Time elapsed: 1.196 s
% 163.84/24.68 % (11459)Instructions burned: 3973 (million)
% 163.84/24.68 % (11459)------------------------------
% 163.84/24.68 % (11459)------------------------------
% 163.84/24.69 % (11462)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_9951 for (2769ds/10148Mi)
% 164.36/24.74 % (11458)Instruction limit reached!
% 164.36/24.74 % (11458)------------------------------
% 164.36/24.74 % (11458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.36/24.74 % (11458)Termination reason: Unknown
% 164.36/24.74 % (11458)Termination phase: Saturation
% 164.36/24.74
% 164.36/24.74 % (11458)Memory used [KB]: 13688
% 164.36/24.74 % (11458)Time elapsed: 1.286 s
% 164.36/24.74 % (11458)Instructions burned: 4218 (million)
% 164.36/24.74 % (11458)------------------------------
% 164.36/24.74 % (11458)------------------------------
% 164.36/24.75 % (11463)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_9951 for (2768ds/9078Mi)
% 168.19/25.29 % (11455)Instruction limit reached!
% 168.19/25.29 % (11455)------------------------------
% 168.19/25.29 % (11455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 168.19/25.29 % (11455)Termination reason: Unknown
% 168.19/25.29 % (11455)Termination phase: Saturation
% 168.19/25.29
% 168.19/25.29 % (11455)Memory used [KB]: 26609
% 168.19/25.29 % (11455)Time elapsed: 4.056 s
% 168.19/25.29 % (11455)Instructions burned: 13164 (million)
% 168.19/25.29 % (11455)------------------------------
% 168.19/25.29 % (11455)------------------------------
% 168.90/25.30 % (11464)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_9951 for (2763ds/16164Mi)
% 181.01/27.11 % (10594)Instruction limit reached!
% 181.01/27.11 % (10594)------------------------------
% 181.01/27.11 % (10594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 181.01/27.11 % (10594)Termination reason: Unknown
% 181.01/27.11 % (10594)Termination phase: Saturation
% 181.01/27.11
% 181.01/27.11 % (10594)Memory used [KB]: 38762
% 181.01/27.11 % (10594)Time elapsed: 14.304 s
% 181.01/27.11 % (10594)Instructions burned: 43570 (million)
% 181.01/27.11 % (10594)------------------------------
% 181.01/27.11 % (10594)------------------------------
% 181.01/27.12 % (11465)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_9951 for (2745ds/6102Mi)
% 182.78/27.31 % (11462)First to succeed.
% 182.78/27.32 % (11462)Refutation found. Thanks to Tanya!
% 182.78/27.32 % SZS status Theorem for DTF2THF_9951
% 182.78/27.32 % SZS output start Proof for DTF2THF_9951
% 182.78/27.32 thf(func_def_0, type, in: $i > $i > $o).
% 182.78/27.32 thf(func_def_1, type, exu: ($i > $o) > $o).
% 182.78/27.32 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 182.78/27.32 thf(func_def_8, type, powerset: $i > $i).
% 182.78/27.32 thf(func_def_10, type, setunion: $i > $i).
% 182.78/27.32 thf(func_def_19, type, descr: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_26, type, prop2set: $o > $i).
% 182.78/27.32 thf(func_def_36, type, nonempty: $i > $o).
% 182.78/27.32 thf(func_def_69, type, set2prop: $i > $o).
% 182.78/27.32 thf(func_def_88, type, subset: $i > $i > $o).
% 182.78/27.32 thf(func_def_89, type, disjoint: $i > $i > $o).
% 182.78/27.32 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 182.78/27.32 thf(func_def_114, type, binunion: $i > $i > $i).
% 182.78/27.32 thf(func_def_122, type, binintersect: $i > $i > $i).
% 182.78/27.32 thf(func_def_135, type, regular: $i > $o).
% 182.78/27.32 thf(func_def_136, type, setminus: $i > $i > $i).
% 182.78/27.32 thf(func_def_147, type, symdiff: $i > $i > $i).
% 182.78/27.32 thf(func_def_153, type, iskpair: $i > $o).
% 182.78/27.32 thf(func_def_158, type, kpair: $i > $i > $i).
% 182.78/27.32 thf(func_def_160, type, cartprod: $i > $i > $i).
% 182.78/27.32 thf(func_def_177, type, singleton: $i > $o).
% 182.78/27.32 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 182.78/27.32 thf(func_def_184, type, atmost1p: $i > $o).
% 182.78/27.32 thf(func_def_185, type, atleast2p: $i > $o).
% 182.78/27.32 thf(func_def_186, type, atmost2p: $i > $o).
% 182.78/27.32 thf(func_def_187, type, upairsetp: $i > $o).
% 182.78/27.32 thf(func_def_191, type, kfst: $i > $i).
% 182.78/27.32 thf(func_def_203, type, ksnd: $i > $i).
% 182.78/27.32 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 182.78/27.32 thf(func_def_222, type, func: $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_223, type, funcSet: $i > $i > $i).
% 182.78/27.32 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 182.78/27.32 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 182.78/27.32 thf(func_def_323, type, breln1: $i > $i > $o).
% 182.78/27.32 thf(func_def_337, type, sP0: $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_338, type, sP1: $i > $i > $o).
% 182.78/27.32 thf(func_def_342, type, sP5: $i > ($i > $o) > $o).
% 182.78/27.32 thf(func_def_355, type, sP18: $i > $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_357, type, sP20: $i > $o > $i > $i > $o).
% 182.78/27.32 thf(func_def_359, type, sP22: $i > $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_360, type, sP23: $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_361, type, sP24: $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_362, type, sP25: $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_363, type, sP26: $i > $i > $o).
% 182.78/27.32 thf(func_def_364, type, sP27: $i > $o).
% 182.78/27.32 thf(func_def_365, type, sP28: $i > $i > $o).
% 182.78/27.32 thf(func_def_366, type, sP29: $i > $i > $o).
% 182.78/27.32 thf(func_def_370, type, sP33: ($i > $i > $o) > $i > $o).
% 182.78/27.32 thf(func_def_375, type, sP38: $i > ($i > $o) > $o).
% 182.78/27.32 thf(func_def_388, type, sK51: $i > $i > $i).
% 182.78/27.32 thf(func_def_389, type, sK52: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_390, type, sK53: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_409, type, sK72: $i > $o).
% 182.78/27.32 thf(func_def_411, type, sK74: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_412, type, sK75: $i > $o).
% 182.78/27.32 thf(func_def_414, type, sK77: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_422, type, sK85: $i > $o).
% 182.78/27.32 thf(func_def_452, type, sK115: $i > $i).
% 182.78/27.32 thf(func_def_456, type, sK119: $i > $o).
% 182.78/27.32 thf(func_def_458, type, sK121: ($i > $o) > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_459, type, sK122: ($i > $o) > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_467, type, sK130: $i > $o).
% 182.78/27.32 thf(func_def_470, type, sK133: $i > $o).
% 182.78/27.32 thf(func_def_478, type, sK141: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_483, type, sK146: ($i > $o) > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_484, type, sK147: ($i > $o) > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_485, type, sK148: $i > $o).
% 182.78/27.32 thf(func_def_486, type, sK149: $i > $o).
% 182.78/27.32 thf(func_def_503, type, sK166: $i > $o).
% 182.78/27.32 thf(func_def_504, type, sK167: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_505, type, sK168: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_507, type, sK170: $i > $o).
% 182.78/27.32 thf(func_def_526, type, sK189: $i > $i).
% 182.78/27.32 thf(func_def_532, type, sK195: $i > $o).
% 182.78/27.32 thf(func_def_534, type, sK197: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_555, type, sK218: $i > $o).
% 182.78/27.32 thf(func_def_557, type, sK220: ($i > $o) > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_558, type, sK221: ($i > $o) > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_563, type, sK226: $i > $i > $i).
% 182.78/27.32 thf(func_def_564, type, sK227: $i > $i > $i).
% 182.78/27.32 thf(func_def_567, type, sK230: $i > $o).
% 182.78/27.32 thf(func_def_568, type, sK231: $i > $o).
% 182.78/27.32 thf(func_def_569, type, sK232: ($i > $o) > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_570, type, sK233: ($i > $o) > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_572, type, sK235: $i > $o).
% 182.78/27.32 thf(func_def_576, type, sK239: $i > $i > $i).
% 182.78/27.32 thf(func_def_589, type, sK252: $i > $i).
% 182.78/27.32 thf(func_def_592, type, sK255: $i > ($i > $i) > $i > $i).
% 182.78/27.32 thf(func_def_610, type, sK273: $i > $o).
% 182.78/27.32 thf(func_def_611, type, sK274: $i > $o).
% 182.78/27.32 thf(func_def_614, type, sK277: $i > $i > $o).
% 182.78/27.32 thf(func_def_622, type, sK285: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_623, type, sK286: $i > $o).
% 182.78/27.32 thf(func_def_628, type, sK291: $i > $o).
% 182.78/27.32 thf(func_def_636, type, sK299: $i > $i > $i).
% 182.78/27.32 thf(func_def_647, type, sK310: $i > $i > $i).
% 182.78/27.32 thf(func_def_672, type, sK335: $i > $o).
% 182.78/27.32 thf(func_def_678, type, sK341: $i > $o).
% 182.78/27.32 thf(func_def_679, type, sK342: $i > $o).
% 182.78/27.32 thf(func_def_680, type, sK343: ($i > $o) > ($i > $o) > $i > $i > $i).
% 182.78/27.32 thf(func_def_681, type, sK344: ($i > $o) > ($i > $o) > $i > $i > $i).
% 182.78/27.32 thf(func_def_719, type, sK382: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_723, type, sK386: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_724, type, sK387: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_734, type, sK397: $i > $i).
% 182.78/27.32 thf(func_def_735, type, sK398: $i > $i).
% 182.78/27.32 thf(func_def_750, type, sK413: $i > $o).
% 182.78/27.32 thf(func_def_755, type, sK418: $i > $i > $i).
% 182.78/27.32 thf(func_def_763, type, sK426: $i > $o).
% 182.78/27.32 thf(func_def_765, type, sK428: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_781, type, sK444: $o > $i > $i > $i).
% 182.78/27.32 thf(func_def_787, type, sK450: $i > $i > $o).
% 182.78/27.32 thf(func_def_798, type, sK461: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_799, type, sK462: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_800, type, sK463: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_835, type, sK498: $i > $i > $o).
% 182.78/27.32 thf(func_def_843, type, sK506: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_844, type, sK507: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_845, type, sK508: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_846, type, sK509: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_847, type, sK510: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_855, type, sK518: $i > ($i > $i) > $i > $i).
% 182.78/27.32 thf(func_def_857, type, sK520: $i > $i).
% 182.78/27.32 thf(func_def_865, type, sK528: $i > $i > $o).
% 182.78/27.32 thf(func_def_869, type, sK532: $i > $o).
% 182.78/27.32 thf(func_def_893, type, sK556: $i > $i > $i > $o).
% 182.78/27.32 thf(func_def_894, type, sK557: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_916, type, sK579: $i > $i).
% 182.78/27.32 thf(func_def_917, type, sK580: $i > $i).
% 182.78/27.32 thf(func_def_918, type, sK581: $i > $i).
% 182.78/27.32 thf(func_def_919, type, sK582: $i > $i > $i).
% 182.78/27.32 thf(func_def_920, type, sK583: $i > $i > $i).
% 182.78/27.32 thf(func_def_921, type, sK584: $i > $i > $i).
% 182.78/27.32 thf(func_def_922, type, sK585: $i > $i > $i).
% 182.78/27.32 thf(func_def_923, type, sK586: $i > $i > $i).
% 182.78/27.32 thf(func_def_924, type, sK587: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_925, type, sK588: $i > $i).
% 182.78/27.32 thf(func_def_926, type, sK589: $i > $i).
% 182.78/27.32 thf(func_def_927, type, sK590: $i > $i).
% 182.78/27.32 thf(func_def_928, type, sK591: $i > $i).
% 182.78/27.32 thf(func_def_929, type, sK592: $i > $i > $i).
% 182.78/27.32 thf(func_def_930, type, sK593: $i > $i > $i).
% 182.78/27.32 thf(func_def_931, type, sK594: $i > $i > $i).
% 182.78/27.32 thf(func_def_932, type, sK595: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_933, type, sK596: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_971, type, sK634: $i > $o).
% 182.78/27.32 thf(func_def_973, type, sK636: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_975, type, sK638: $i > $i > $o).
% 182.78/27.32 thf(func_def_981, type, sK644: $i > $i > $i).
% 182.78/27.32 thf(func_def_984, type, sK647: $i > $o).
% 182.78/27.32 thf(func_def_986, type, sK649: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_991, type, sK654: $i > $i > $i).
% 182.78/27.32 thf(func_def_996, type, sK659: $i > ($i > $i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_997, type, sK660: $i > ($i > $i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_998, type, sK661: ($i > $i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_999, type, sK662: $i > ($i > $i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1001, type, sK664: $i > $i > $o).
% 182.78/27.32 thf(func_def_1002, type, sK665: ($i > $i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1008, type, sK671: $i > $o).
% 182.78/27.32 thf(func_def_1019, type, sK682: $i > $o).
% 182.78/27.32 thf(func_def_1020, type, sK683: $i > $i).
% 182.78/27.32 thf(func_def_1021, type, sK684: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1041, type, sK704: $i > $o).
% 182.78/27.32 thf(func_def_1047, type, sK710: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_1054, type, sK717: $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_1060, type, sK723: $i > $i).
% 182.78/27.32 thf(func_def_1073, type, sK736: $i > $o).
% 182.78/27.32 thf(func_def_1075, type, sK738: $i > ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1083, type, sK746: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1084, type, sK747: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1086, type, sK749: $i > $o).
% 182.78/27.32 thf(func_def_1115, type, sK778: $i > $o).
% 182.78/27.32 thf(func_def_1118, type, sK781: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1142, type, sK805: $i > $i > $i).
% 182.78/27.32 thf(func_def_1145, type, sK808: $i > $i).
% 182.78/27.32 thf(func_def_1146, type, sK809: ($i > $i) > $i > $i > $i).
% 182.78/27.32 thf(func_def_1147, type, sK810: $i > $i).
% 182.78/27.32 thf(func_def_1151, type, sK814: $i > $i > ($i > $i) > $i).
% 182.78/27.32 thf(func_def_1158, type, sK821: $i > $o).
% 182.78/27.32 thf(func_def_1160, type, sK823: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1161, type, sK824: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1163, type, sK826: $i > $o).
% 182.78/27.32 thf(func_def_1164, type, sK827: $i > $i).
% 182.78/27.32 thf(func_def_1165, type, sK828: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1170, type, sK833: $i > $i > $o).
% 182.78/27.32 thf(func_def_1176, type, sK839: $i > $i > $i).
% 182.78/27.32 thf(func_def_1183, type, sK846: $i > $i).
% 182.78/27.32 thf(func_def_1185, type, sK848: $i > $i).
% 182.78/27.32 thf(func_def_1188, type, sK851: $i > $i > ($i > $i) > $i).
% 182.78/27.32 thf(func_def_1204, type, sK867: $i > $o).
% 182.78/27.32 thf(func_def_1207, type, sK870: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1229, type, sK892: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_1230, type, sK893: $i > $i > $i > $i > $i).
% 182.78/27.32 thf(func_def_1241, type, sK904: $i > $i).
% 182.78/27.32 thf(func_def_1257, type, sK920: $i > $o).
% 182.78/27.32 thf(func_def_1259, type, sK922: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1265, type, sK928: $i > $o).
% 182.78/27.32 thf(func_def_1289, type, sK952: $i > $i > $o).
% 182.78/27.32 thf(func_def_1294, type, sK957: ($i > $i) > $i > $i > $i).
% 182.78/27.32 thf(func_def_1297, type, sK960: $i > $i).
% 182.78/27.32 thf(func_def_1302, type, sK965: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1303, type, sK966: $i > $i > ($i > $i > $o) > $i).
% 182.78/27.32 thf(func_def_1304, type, sK967: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1305, type, sK968: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1306, type, sK969: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1307, type, sK970: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1308, type, sK971: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1309, type, sK972: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1310, type, sK973: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1311, type, sK974: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1312, type, sK975: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1313, type, sK976: $i > $i).
% 182.78/27.32 thf(func_def_1315, type, sK978: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1316, type, sK979: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1317, type, sK980: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1318, type, sK981: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1319, type, sK982: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1320, type, sK983: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1323, type, sK986: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1324, type, sK987: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1325, type, sK988: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1326, type, sK989: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1327, type, sK990: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1328, type, sK991: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1329, type, sK992: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1330, type, sK993: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1331, type, sK994: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1332, type, sK995: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1333, type, sK996: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1334, type, sK997: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1335, type, sK998: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1336, type, sK999: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1337, type, sK1000: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1338, type, sK1001: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1339, type, sK1002: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1340, type, sK1003: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1341, type, sK1004: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1342, type, sK1005: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1344, type, sK1007: ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1345, type, sK1008: $i > ($i > $o) > $i).
% 182.78/27.32 thf(func_def_1346, type, sK1009: ($i > $o) > $i > $i).
% 182.78/27.32 thf(func_def_1347, type, sK1010: $i > $i).
% 182.78/27.32 thf(func_def_1348, type, sK1011: $i > $i).
% 182.78/27.32 thf(func_def_1349, type, ph1012: !>[X0: $tType]:(X0)).
% 182.78/27.32 thf(f25328,plain,(
% 182.78/27.32 $false),
% 182.78/27.32 inference(subsumption_resolution,[status(thm)],[f25327,f24431])).
% 182.78/27.32 thf(f24431,plain,(
% 182.78/27.32 ((in @ (kfst @ sK86) @ sK84) = $true)),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f24382])).
% 182.78/27.32 thf(f24382,plain,(
% 182.78/27.32 ((in @ (kfst @ sK86) @ sK84) = $true) | ($true != $true)),
% 182.78/27.32 inference(superposition,[status(thm)],[f5620,f24365])).
% 182.78/27.32 thf(f24365,plain,(
% 182.78/27.32 ($true = (in @ sK86 @ (cartprod @ sK84 @ sK84)))),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f24350])).
% 182.78/27.32 thf(f24350,plain,(
% 182.78/27.32 ($true != $true) | ($true = (in @ sK86 @ (cartprod @ sK84 @ sK84)))),
% 182.78/27.32 inference(superposition,[status(thm)],[f7075,f3077])).
% 182.78/27.32 thf(f3077,plain,(
% 182.78/27.32 ($true = (in @ sK86 @ sK83))),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1414])).
% 182.78/27.32 thf(f1414,plain,(
% 182.78/27.32 (setminusELneg = $true) & (lamProp = $true) & (kpairp = $true) & (setextT = $true) & (setminusEL = $true) & (cartprodsndin = $true) & (setukpairinjR11 = $true) & (disjointsetsI1 = $true) & (dpsetconstrI = $true) & (emptyinPowerset = $true) & (singletoninpowunion = $true) & (setminusSubset2 = $true) & (contrasubsetT2 = $true) & (doubleComplementI1 = $true) & (binunionLsub = $true) & (cartprodpairin = $true) & (setminusT_lem = $true) & (setadjoinIL = $true) & (dsetconstrEL = $true) & (funcImageSingleton = $true) & (prop2setE = $true) & (powersetE1 = $true) & (complementTE1 = $true) & (demorgan2a = $true) & (symdiffI1 = $true) & (exuI1 = $true) & (prop2set2propI = $true) & (binunionTEcontra = $true) & (binunionRsub = $true) & (setextAx = $true) & (eta2 = $true) & (contraSubsetComplement = $true) & (setext = $true) & (iftrueProp1 = $true) & (cartprodpairsurjEq = $true) & (descrp = $true) & (singletonsubset = $true) & (cartprodmempair1 = $true) & (subsetI2 = $true) & (foundationAx = $true) & (dsetconstrI = $true) & (woz1_2 = $true) & (vacuousDall = $true) & (complementUnionInPowersetComplement = $true) & (subbreln = $true) & (omega__Cong = $true) & (setadjoin__Cong = $true) & (dsetconstr__Cong = $true) & (setukpairinjR = $true) & (demorgan1a = $true) & (setunionsingleton1 = $true) & (apProp = $true) & (binintersectLsub = $true) & (cartprodmempair = $true) & (setukpairIR = $true) & (subsetI1 = $true) & (uniqinunit = $true) & (upairsetIL = $true) & (brelnall2 = $true) & (dpsetconstrERa = $true) & (binintersectSubset1 = $true) & (binunionE = $true) & (iffalse = $true) & (funcGraphProp2 = $true) & (iftrueProp2 = $true) & (inIntersectImpInUnion2 = $true) & (infuncsetfunc = $true) & (eqbreln = $true) & (powersetI = $true) & (upairsetE = $true) & (setukpairIL = $true) & (subsetTrans = $true) & (ap2p = $true) & (powersetTE1 = $true) & (powerset__Cong = $true) & (funcext2 = $true) & (($true = (breln1 @ sK84 @ sK83)) & ((((sK85 @ sK86) != $true) & ($true = (in @ sK86 @ sK83))) & ! [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK83)) | ($true = (sK85 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK84))) | ($true != (in @ X4 @ sK84))))) & (setukpairinjL2 = $true) & (upairset2IR = $true) & (brelnall1 = $true) & (setadjoinIR = $true) & (ap2apEq2 = $true) & (powersetsubset = $true) & (setadjoinAx = $true) & (iffalseProp1 = $true) & (binintersectEL = $true) & (cartprodpairmemER = $true) & (kfstpairEq = $true) & (complementImpComplementIntersect = $true) & (emptyinunitempty = $true) & (dsetconstrER = $true) & (notdexE = $true) & (ex1I2 = $true) & (nonemptyImpWitness = $true) & (subsetTI = $true) & (eqinunit = $true) & (demorgan2a2 = $true) & (app = $true) & (subsetemptysetimpeq = $true) & (demorgan2b2 = $true) & (setunionsingleton2 = $true) & (contrasubsetT = $true) & (setbeta = $true) & (setminusLsub = $true) & (funcGraphProp3 = $true) & (dpsetconstrEL1 = $true) & (setminusI = $true) & (woz13rule2 = $true) & (ksndsingleton = $true) & (inIntersectImpInIntersectUnions = $true) & (woz1_5 = $true) & (nonemptyI1 = $true) & (setOfPairsIsBReln = $true) & (binunionIR = $true) & (singletonsuniq = $true) & (exuEu = $true) & (woz13rule1 = $true) & (dpsetconstrER = $true) & (binintersectI = $true) & (setunionAx = $true) & (beta2 = $true) & (notdallE = $true) & (exuI2 = $true) & (setminusER = $true) & (iftrueorfalse = $true) & (quantDeMorgan2 = $true) & (setunion__Cong = $true) & (descr__Cong = $true) & (doubleComplementSub1 = $true) & (ex1E1 = $true) & (setukpairinjR2 = $true) & (lam2lamEq = $true) & (secondinupair = $true) & (eqimpsubset2 = $true) & (cartprodfstin = $true) & (cartprodsndpairEq = $true) & (exu__Cong = $true) & (notequalI2 = $true) & (setminusIRneg = $true) & (symdiffE = $true) & (setunionI = $true) & (nonemptyI = $true) & (setukpairinjL = $true) & (demorgan1 = $true) & (setminusILneg = $true) & (setunionE2 = $true) & (setadjoinSub = $true) & (emptyE1 = $true) & (woz13rule4 = $true) & (complementTnotintersectT = $true) & (doubleComplementE1 = $true) & (complementTcontraSubset = $true) & (dpsetconstrEL2 = $true) & (demorgan2 = $true) & (setminusERneg = $true) & (theeq = $true) & (emptyset__Cong = $true) & (setminusSubset1 = $true) & (contrasubsetT1 = $true) & (beta1 = $true) & (powersetI1 = $true) & (lam2p = $true) & (inComplementUnionImpInComplement1 = $true) & (omegaIndAx = $true) & (setoftrueEq = $true) & (prop2setI = $true) & (cartprodpairmemEL = $true) & (eta1 = $true) & (inPowerset = $true) & (complementTI1 = $true) & (exuI3 = $true) & (subset2powerset = $true) & (notinemptyset = $true) & (singletonprop = $true) & (upairequniteq = $true) & (upairsetIR = $true) & (replAx = $true) & (subsetE2 = $true) & (upairsubunion = $true) & (inIntersectImpInUnion = $true) & (binintersectRsub = $true) & (symdiffI2 = $true) & (binintersectT_lem = $true) & (noeltsimpempty = $true) & (iffalseProp2 = $true) & (ex1E2 = $true) & (quantDeMorgan3 = $true) & (ifSingleton = $true) & (doubleComplementSub2 = $true) & (ubforcartprodlem2 = $true) & (theprop = $true) & (complementSubsetComplementIntersect = $true) & (funcinfuncset = $true) & (nonemptyE1 = $true) & (woz13rule0 = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (kpairsurjEq = $true) & (upairinpowunion = $true) & (contrasubsetT3 = $true) & (demorgan2b = $true) & (subPowSU = $true) & (binunionTE = $true) & (demorgan1b = $true) & (intersectInPowersetIntersectUnions = $true) & (emptysetAx = $true) & (upairset2E = $true) & (exuE3u = $true) & (symdiffIneg1 = $true) & (complementT_lem = $true) & (subsetRefl = $true) & (funcext = $true) & (exuE3e = $true) & (singletoninpowerset = $true) & (ifp = $true) & (notsubsetI = $true) & (setadjoinE = $true) & (funcGraphProp1 = $true) & (inComplementUnionImpNotIn1 = $true) & (bs114d = $true) & (binintersectSubset3 = $true) & (eqimpsubset1 = $true) & (dpsetconstrSub = $true) & (woz1_4 = $true) & (binintersectTERcontra = $true) & (binunionTIRcontra = $true) & (binunionT_lem = $true) & (binintersectSubset5 = $true) & (lamp = $true) & (binintersectSubset2 = $true) & (binunionIL = $true) & (setukpairinjR12 = $true) & (setextsub = $true) & (ubforcartprodlem1 = $true) & (binintersectER = $true) & (cartprodmempaircEq = $true) & (setunionsingleton = $true) & (emptyInPowerset = $true) & (notinsingleton = $true) & (emptysetimpfalse = $true) & (funcextLem = $true) & (notequalI1 = $true) & (emptysetsubset = $true) & (setadjoinSub2 = $true) & (kfstsingleton = $true) & (ex1I = $true) & (exuE2 = $true) & (emptysetE = $true) & (powersetT_lem = $true) & (symdiffIneg2 = $true) & (omega0Ax = $true) & (exuE1 = $true) & (binunionTILcontra = $true) & (in__Cong = $true) & (kpairiskpair = $true) & (setadjoinOr = $true) & (woz1_3 = $true) & (singletonsswitch = $true) & (cartprodfstpairEq = $true) & (setukpairinjR1 = $true) & (ap2apEq1 = $true) & (binunionEcases = $true) & (woz13rule3 = $true) & (ksndpairEq = $true) & (setunionE = $true) & (doubleComplementEq = $true) & (powersetTI1 = $true) & (ubforcartprodlem3 = $true) & (sepInPowerset = $true) & (omegaSAx = $true) & (subsetE = $true) & (powersetAx = $true) & (quantDeMorgan4 = $true) & (sepSubset = $true) & (binintersectSubset4 = $true) & (woz1_1 = $true) & (inCongP = $true) & (iftrue = $true) & (funcGraphProp4 = $true) & (binintersectTELcontra = $true) & (demorgan2a1 = $true) & (powersetE = $true) & (wellorderingAx = $true) & (complementInPowersetComplementIntersect = $true) & (emptyI = $true)),
% 182.78/27.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK83,sK84,sK85,sK86])],[f1410,f1413,f1412,f1411])).
% 182.78/27.32 thf(f1411,plain,(
% 182.78/27.32 ? [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) & ? [X2 : $i > $o] : (? [X3 : $i] : (($true != (X2 @ X3)) & ($true = (in @ X3 @ X0))) & ! [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ X0) != $true) | ($true = (X2 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ X1))) | ($true != (in @ X4 @ X1))))) => (($true = (breln1 @ sK84 @ sK83)) & ? [X2 : $i > $o] : (? [X3 : $i] : (($true != (X2 @ X3)) & ($true = (in @ X3 @ sK83))) & ! [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK83)) | ($true = (X2 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK84))) | ($true != (in @ X4 @ sK84)))))),
% 182.78/27.32 introduced(definition,[],[choice_axiom])).
% 182.78/27.32 thf(f1412,plain,(
% 182.78/27.32 ? [X2 : $i > $o] : (? [X3 : $i] : (($true != (X2 @ X3)) & ($true = (in @ X3 @ sK83))) & ! [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK83)) | ($true = (X2 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK84))) | ($true != (in @ X4 @ sK84)))) => (? [X3 : $i] : (($true != (sK85 @ X3)) & ($true = (in @ X3 @ sK83))) & ! [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK83)) | ($true = (sK85 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK84))) | ($true != (in @ X4 @ sK84))))),
% 182.78/27.32 introduced(definition,[],[choice_axiom])).
% 182.78/27.32 thf(f1413,plain,(
% 182.78/27.32 ? [X3 : $i] : (($true != (sK85 @ X3)) & ($true = (in @ X3 @ sK83))) => (((sK85 @ sK86) != $true) & ($true = (in @ sK86 @ sK83)))),
% 182.78/27.32 introduced(definition,[],[choice_axiom])).
% 182.78/27.32 thf(f1410,plain,(
% 182.78/27.32 (setminusELneg = $true) & (lamProp = $true) & (kpairp = $true) & (setextT = $true) & (setminusEL = $true) & (cartprodsndin = $true) & (setukpairinjR11 = $true) & (disjointsetsI1 = $true) & (dpsetconstrI = $true) & (emptyinPowerset = $true) & (singletoninpowunion = $true) & (setminusSubset2 = $true) & (contrasubsetT2 = $true) & (doubleComplementI1 = $true) & (binunionLsub = $true) & (cartprodpairin = $true) & (setminusT_lem = $true) & (setadjoinIL = $true) & (dsetconstrEL = $true) & (funcImageSingleton = $true) & (prop2setE = $true) & (powersetE1 = $true) & (complementTE1 = $true) & (demorgan2a = $true) & (symdiffI1 = $true) & (exuI1 = $true) & (prop2set2propI = $true) & (binunionTEcontra = $true) & (binunionRsub = $true) & (setextAx = $true) & (eta2 = $true) & (contraSubsetComplement = $true) & (setext = $true) & (iftrueProp1 = $true) & (cartprodpairsurjEq = $true) & (descrp = $true) & (singletonsubset = $true) & (cartprodmempair1 = $true) & (subsetI2 = $true) & (foundationAx = $true) & (dsetconstrI = $true) & (woz1_2 = $true) & (vacuousDall = $true) & (complementUnionInPowersetComplement = $true) & (subbreln = $true) & (omega__Cong = $true) & (setadjoin__Cong = $true) & (dsetconstr__Cong = $true) & (setukpairinjR = $true) & (demorgan1a = $true) & (setunionsingleton1 = $true) & (apProp = $true) & (binintersectLsub = $true) & (cartprodmempair = $true) & (setukpairIR = $true) & (subsetI1 = $true) & (uniqinunit = $true) & (upairsetIL = $true) & (brelnall2 = $true) & (dpsetconstrERa = $true) & (binintersectSubset1 = $true) & (binunionE = $true) & (iffalse = $true) & (funcGraphProp2 = $true) & (iftrueProp2 = $true) & (inIntersectImpInUnion2 = $true) & (infuncsetfunc = $true) & (eqbreln = $true) & (powersetI = $true) & (upairsetE = $true) & (setukpairIL = $true) & (subsetTrans = $true) & (ap2p = $true) & (powersetTE1 = $true) & (powerset__Cong = $true) & (funcext2 = $true) & ? [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) & ? [X2 : $i > $o] : (? [X3 : $i] : (($true != (X2 @ X3)) & ($true = (in @ X3 @ X0))) & ! [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ X0) != $true) | ($true = (X2 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ X1))) | ($true != (in @ X4 @ X1))))) & (setukpairinjL2 = $true) & (upairset2IR = $true) & (brelnall1 = $true) & (setadjoinIR = $true) & (ap2apEq2 = $true) & (powersetsubset = $true) & (setadjoinAx = $true) & (iffalseProp1 = $true) & (binintersectEL = $true) & (cartprodpairmemER = $true) & (kfstpairEq = $true) & (complementImpComplementIntersect = $true) & (emptyinunitempty = $true) & (dsetconstrER = $true) & (notdexE = $true) & (ex1I2 = $true) & (nonemptyImpWitness = $true) & (subsetTI = $true) & (eqinunit = $true) & (demorgan2a2 = $true) & (app = $true) & (subsetemptysetimpeq = $true) & (demorgan2b2 = $true) & (setunionsingleton2 = $true) & (contrasubsetT = $true) & (setbeta = $true) & (setminusLsub = $true) & (funcGraphProp3 = $true) & (dpsetconstrEL1 = $true) & (setminusI = $true) & (woz13rule2 = $true) & (ksndsingleton = $true) & (inIntersectImpInIntersectUnions = $true) & (woz1_5 = $true) & (nonemptyI1 = $true) & (setOfPairsIsBReln = $true) & (binunionIR = $true) & (singletonsuniq = $true) & (exuEu = $true) & (woz13rule1 = $true) & (dpsetconstrER = $true) & (binintersectI = $true) & (setunionAx = $true) & (beta2 = $true) & (notdallE = $true) & (exuI2 = $true) & (setminusER = $true) & (iftrueorfalse = $true) & (quantDeMorgan2 = $true) & (setunion__Cong = $true) & (descr__Cong = $true) & (doubleComplementSub1 = $true) & (ex1E1 = $true) & (setukpairinjR2 = $true) & (lam2lamEq = $true) & (secondinupair = $true) & (eqimpsubset2 = $true) & (cartprodfstin = $true) & (cartprodsndpairEq = $true) & (exu__Cong = $true) & (notequalI2 = $true) & (setminusIRneg = $true) & (symdiffE = $true) & (setunionI = $true) & (nonemptyI = $true) & (setukpairinjL = $true) & (demorgan1 = $true) & (setminusILneg = $true) & (setunionE2 = $true) & (setadjoinSub = $true) & (emptyE1 = $true) & (woz13rule4 = $true) & (complementTnotintersectT = $true) & (doubleComplementE1 = $true) & (complementTcontraSubset = $true) & (dpsetconstrEL2 = $true) & (demorgan2 = $true) & (setminusERneg = $true) & (theeq = $true) & (emptyset__Cong = $true) & (setminusSubset1 = $true) & (contrasubsetT1 = $true) & (beta1 = $true) & (powersetI1 = $true) & (lam2p = $true) & (inComplementUnionImpInComplement1 = $true) & (omegaIndAx = $true) & (setoftrueEq = $true) & (prop2setI = $true) & (cartprodpairmemEL = $true) & (eta1 = $true) & (inPowerset = $true) & (complementTI1 = $true) & (exuI3 = $true) & (subset2powerset = $true) & (notinemptyset = $true) & (singletonprop = $true) & (upairequniteq = $true) & (upairsetIR = $true) & (replAx = $true) & (subsetE2 = $true) & (upairsubunion = $true) & (inIntersectImpInUnion = $true) & (binintersectRsub = $true) & (symdiffI2 = $true) & (binintersectT_lem = $true) & (noeltsimpempty = $true) & (iffalseProp2 = $true) & (ex1E2 = $true) & (quantDeMorgan3 = $true) & (ifSingleton = $true) & (doubleComplementSub2 = $true) & (ubforcartprodlem2 = $true) & (theprop = $true) & (complementSubsetComplementIntersect = $true) & (funcinfuncset = $true) & (nonemptyE1 = $true) & (woz13rule0 = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (kpairsurjEq = $true) & (upairinpowunion = $true) & (contrasubsetT3 = $true) & (demorgan2b = $true) & (subPowSU = $true) & (binunionTE = $true) & (demorgan1b = $true) & (intersectInPowersetIntersectUnions = $true) & (emptysetAx = $true) & (upairset2E = $true) & (exuE3u = $true) & (symdiffIneg1 = $true) & (complementT_lem = $true) & (subsetRefl = $true) & (funcext = $true) & (exuE3e = $true) & (singletoninpowerset = $true) & (ifp = $true) & (notsubsetI = $true) & (setadjoinE = $true) & (funcGraphProp1 = $true) & (inComplementUnionImpNotIn1 = $true) & (bs114d = $true) & (binintersectSubset3 = $true) & (eqimpsubset1 = $true) & (dpsetconstrSub = $true) & (woz1_4 = $true) & (binintersectTERcontra = $true) & (binunionTIRcontra = $true) & (binunionT_lem = $true) & (binintersectSubset5 = $true) & (lamp = $true) & (binintersectSubset2 = $true) & (binunionIL = $true) & (setukpairinjR12 = $true) & (setextsub = $true) & (ubforcartprodlem1 = $true) & (binintersectER = $true) & (cartprodmempaircEq = $true) & (setunionsingleton = $true) & (emptyInPowerset = $true) & (notinsingleton = $true) & (emptysetimpfalse = $true) & (funcextLem = $true) & (notequalI1 = $true) & (emptysetsubset = $true) & (setadjoinSub2 = $true) & (kfstsingleton = $true) & (ex1I = $true) & (exuE2 = $true) & (emptysetE = $true) & (powersetT_lem = $true) & (symdiffIneg2 = $true) & (omega0Ax = $true) & (exuE1 = $true) & (binunionTILcontra = $true) & (in__Cong = $true) & (kpairiskpair = $true) & (setadjoinOr = $true) & (woz1_3 = $true) & (singletonsswitch = $true) & (cartprodfstpairEq = $true) & (setukpairinjR1 = $true) & (ap2apEq1 = $true) & (binunionEcases = $true) & (woz13rule3 = $true) & (ksndpairEq = $true) & (setunionE = $true) & (doubleComplementEq = $true) & (powersetTI1 = $true) & (ubforcartprodlem3 = $true) & (sepInPowerset = $true) & (omegaSAx = $true) & (subsetE = $true) & (powersetAx = $true) & (quantDeMorgan4 = $true) & (sepSubset = $true) & (binintersectSubset4 = $true) & (woz1_1 = $true) & (inCongP = $true) & (iftrue = $true) & (funcGraphProp4 = $true) & (binintersectTELcontra = $true) & (demorgan2a1 = $true) & (powersetE = $true) & (wellorderingAx = $true) & (complementInPowersetComplementIntersect = $true) & (emptyI = $true)),
% 182.78/27.32 inference(rectify,[status(thm)],[f1251])).
% 182.78/27.32 thf(f1251,plain,(
% 182.78/27.32 (setminusELneg = $true) & (lamProp = $true) & (kpairp = $true) & (setextT = $true) & (setminusEL = $true) & (cartprodsndin = $true) & (setukpairinjR11 = $true) & (disjointsetsI1 = $true) & (dpsetconstrI = $true) & (emptyinPowerset = $true) & (singletoninpowunion = $true) & (setminusSubset2 = $true) & (contrasubsetT2 = $true) & (doubleComplementI1 = $true) & (binunionLsub = $true) & (cartprodpairin = $true) & (setminusT_lem = $true) & (setadjoinIL = $true) & (dsetconstrEL = $true) & (funcImageSingleton = $true) & (prop2setE = $true) & (powersetE1 = $true) & (complementTE1 = $true) & (demorgan2a = $true) & (symdiffI1 = $true) & (exuI1 = $true) & (prop2set2propI = $true) & (binunionTEcontra = $true) & (binunionRsub = $true) & (setextAx = $true) & (eta2 = $true) & (contraSubsetComplement = $true) & (setext = $true) & (iftrueProp1 = $true) & (cartprodpairsurjEq = $true) & (descrp = $true) & (singletonsubset = $true) & (cartprodmempair1 = $true) & (subsetI2 = $true) & (foundationAx = $true) & (dsetconstrI = $true) & (woz1_2 = $true) & (vacuousDall = $true) & (complementUnionInPowersetComplement = $true) & (subbreln = $true) & (omega__Cong = $true) & (setadjoin__Cong = $true) & (dsetconstr__Cong = $true) & (setukpairinjR = $true) & (demorgan1a = $true) & (setunionsingleton1 = $true) & (apProp = $true) & (binintersectLsub = $true) & (cartprodmempair = $true) & (setukpairIR = $true) & (subsetI1 = $true) & (uniqinunit = $true) & (upairsetIL = $true) & (brelnall2 = $true) & (dpsetconstrERa = $true) & (binintersectSubset1 = $true) & (binunionE = $true) & (iffalse = $true) & (funcGraphProp2 = $true) & (iftrueProp2 = $true) & (inIntersectImpInUnion2 = $true) & (infuncsetfunc = $true) & (eqbreln = $true) & (powersetI = $true) & (upairsetE = $true) & (setukpairIL = $true) & (subsetTrans = $true) & (ap2p = $true) & (powersetTE1 = $true) & (powerset__Cong = $true) & (funcext2 = $true) & ? [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) & ? [X2 : $i > $o] : (? [X5 : $i] : (($true != (X2 @ X5)) & ((in @ X5 @ X0) = $true)) & ! [X3 : $i] : (! [X4 : $i] : (((in @ (kpair @ X3 @ X4) @ X0) != $true) | ($true = (X2 @ (kpair @ X3 @ X4))) | ($true != (in @ X4 @ X1))) | ((in @ X3 @ X1) != $true)))) & (setukpairinjL2 = $true) & (upairset2IR = $true) & (brelnall1 = $true) & (setadjoinIR = $true) & (ap2apEq2 = $true) & (powersetsubset = $true) & (setadjoinAx = $true) & (iffalseProp1 = $true) & (binintersectEL = $true) & (cartprodpairmemER = $true) & (kfstpairEq = $true) & (complementImpComplementIntersect = $true) & (emptyinunitempty = $true) & (dsetconstrER = $true) & (notdexE = $true) & (ex1I2 = $true) & (nonemptyImpWitness = $true) & (subsetTI = $true) & (eqinunit = $true) & (demorgan2a2 = $true) & (app = $true) & (subsetemptysetimpeq = $true) & (demorgan2b2 = $true) & (setunionsingleton2 = $true) & (contrasubsetT = $true) & (setbeta = $true) & (setminusLsub = $true) & (funcGraphProp3 = $true) & (dpsetconstrEL1 = $true) & (setminusI = $true) & (woz13rule2 = $true) & (ksndsingleton = $true) & (inIntersectImpInIntersectUnions = $true) & (woz1_5 = $true) & (nonemptyI1 = $true) & (setOfPairsIsBReln = $true) & (binunionIR = $true) & (singletonsuniq = $true) & (exuEu = $true) & (woz13rule1 = $true) & (dpsetconstrER = $true) & (binintersectI = $true) & (setunionAx = $true) & (beta2 = $true) & (notdallE = $true) & (exuI2 = $true) & (setminusER = $true) & (iftrueorfalse = $true) & (quantDeMorgan2 = $true) & (setunion__Cong = $true) & (descr__Cong = $true) & (doubleComplementSub1 = $true) & (ex1E1 = $true) & (setukpairinjR2 = $true) & (lam2lamEq = $true) & (secondinupair = $true) & (eqimpsubset2 = $true) & (cartprodfstin = $true) & (cartprodsndpairEq = $true) & (exu__Cong = $true) & (notequalI2 = $true) & (setminusIRneg = $true) & (symdiffE = $true) & (setunionI = $true) & (nonemptyI = $true) & (setukpairinjL = $true) & (demorgan1 = $true) & (setminusILneg = $true) & (setunionE2 = $true) & (setadjoinSub = $true) & (emptyE1 = $true) & (woz13rule4 = $true) & (complementTnotintersectT = $true) & (doubleComplementE1 = $true) & (complementTcontraSubset = $true) & (dpsetconstrEL2 = $true) & (demorgan2 = $true) & (setminusERneg = $true) & (theeq = $true) & (emptyset__Cong = $true) & (setminusSubset1 = $true) & (contrasubsetT1 = $true) & (beta1 = $true) & (powersetI1 = $true) & (lam2p = $true) & (inComplementUnionImpInComplement1 = $true) & (omegaIndAx = $true) & (setoftrueEq = $true) & (prop2setI = $true) & (cartprodpairmemEL = $true) & (eta1 = $true) & (inPowerset = $true) & (complementTI1 = $true) & (exuI3 = $true) & (subset2powerset = $true) & (notinemptyset = $true) & (singletonprop = $true) & (upairequniteq = $true) & (upairsetIR = $true) & (replAx = $true) & (subsetE2 = $true) & (upairsubunion = $true) & (inIntersectImpInUnion = $true) & (binintersectRsub = $true) & (symdiffI2 = $true) & (binintersectT_lem = $true) & (noeltsimpempty = $true) & (iffalseProp2 = $true) & (ex1E2 = $true) & (quantDeMorgan3 = $true) & (ifSingleton = $true) & (doubleComplementSub2 = $true) & (ubforcartprodlem2 = $true) & (theprop = $true) & (complementSubsetComplementIntersect = $true) & (funcinfuncset = $true) & (nonemptyE1 = $true) & (woz13rule0 = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (kpairsurjEq = $true) & (upairinpowunion = $true) & (contrasubsetT3 = $true) & (demorgan2b = $true) & (subPowSU = $true) & (binunionTE = $true) & (demorgan1b = $true) & (intersectInPowersetIntersectUnions = $true) & (emptysetAx = $true) & (upairset2E = $true) & (exuE3u = $true) & (symdiffIneg1 = $true) & (complementT_lem = $true) & (subsetRefl = $true) & (funcext = $true) & (exuE3e = $true) & (singletoninpowerset = $true) & (ifp = $true) & (notsubsetI = $true) & (setadjoinE = $true) & (funcGraphProp1 = $true) & (inComplementUnionImpNotIn1 = $true) & (bs114d = $true) & (binintersectSubset3 = $true) & (eqimpsubset1 = $true) & (dpsetconstrSub = $true) & (woz1_4 = $true) & (binintersectTERcontra = $true) & (binunionTIRcontra = $true) & (binunionT_lem = $true) & (binintersectSubset5 = $true) & (lamp = $true) & (binintersectSubset2 = $true) & (binunionIL = $true) & (setukpairinjR12 = $true) & (setextsub = $true) & (ubforcartprodlem1 = $true) & (binintersectER = $true) & (cartprodmempaircEq = $true) & (setunionsingleton = $true) & (emptyInPowerset = $true) & (notinsingleton = $true) & (emptysetimpfalse = $true) & (funcextLem = $true) & (notequalI1 = $true) & (emptysetsubset = $true) & (setadjoinSub2 = $true) & (kfstsingleton = $true) & (ex1I = $true) & (exuE2 = $true) & (emptysetE = $true) & (powersetT_lem = $true) & (symdiffIneg2 = $true) & (omega0Ax = $true) & (exuE1 = $true) & (binunionTILcontra = $true) & (in__Cong = $true) & (kpairiskpair = $true) & (setadjoinOr = $true) & (woz1_3 = $true) & (singletonsswitch = $true) & (cartprodfstpairEq = $true) & (setukpairinjR1 = $true) & (ap2apEq1 = $true) & (binunionEcases = $true) & (woz13rule3 = $true) & (ksndpairEq = $true) & (setunionE = $true) & (doubleComplementEq = $true) & (powersetTI1 = $true) & (ubforcartprodlem3 = $true) & (sepInPowerset = $true) & (omegaSAx = $true) & (subsetE = $true) & (powersetAx = $true) & (quantDeMorgan4 = $true) & (sepSubset = $true) & (binintersectSubset4 = $true) & (woz1_1 = $true) & (inCongP = $true) & (iftrue = $true) & (funcGraphProp4 = $true) & (binintersectTELcontra = $true) & (demorgan2a1 = $true) & (powersetE = $true) & (wellorderingAx = $true) & (complementInPowersetComplementIntersect = $true) & (emptyI = $true)),
% 182.78/27.32 inference(flattening,[status(thm)],[f1250])).
% 182.78/27.32 thf(f1250,plain,(
% 182.78/27.32 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X5 : $i] : (($true != (X2 @ X5)) & ((in @ X5 @ X0) = $true)) & ! [X3 : $i] : (! [X4 : $i] : ((($true = (X2 @ (kpair @ X3 @ X4))) | ((in @ (kpair @ X3 @ X4) @ X0) != $true)) | ($true != (in @ X4 @ X1))) | ((in @ X3 @ X1) != $true))) & ((breln1 @ X1 @ X0) = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 182.78/27.32 inference(ennf_transformation,[status(thm)],[f539])).
% 182.78/27.32 thf(f539,plain,(
% 182.78/27.32 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ! [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) => ! [X2 : $i > $o] : (! [X3 : $i] : (((in @ X3 @ X1) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X1)) => (((in @ (kpair @ X3 @ X4) @ X0) = $true) => ($true = (X2 @ (kpair @ X3 @ X4)))))) => ! [X5 : $i] : (((in @ X5 @ X0) = $true) => ($true = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 182.78/27.32 inference(fool_elimination,[status(thm)],[f538])).
% 182.78/27.32 thf(f538,plain,(
% 182.78/27.32 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i > $o] : (! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X0) => (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 182.78/27.32 inference(rectify,[status(thm)],[f291])).
% 182.78/27.32 thf(f291,negated_conjecture,(
% 182.78/27.32 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => ! [X13 : $i,X3 : $i] : ((breln1 @ X3 @ X13) => ! [X0 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ X13) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1 : $i] : ((in @ X1 @ X13) => (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 182.78/27.32 inference(negated_conjecture,[status(cth)],[f290])).
% 182.78/27.32 thf(f290,conjecture,(
% 182.78/27.32 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => ! [X13 : $i,X3 : $i] : ((breln1 @ X3 @ X13) => ! [X0 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ X13) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1 : $i] : ((in @ X1 @ X13) => (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 182.78/27.32 file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',breln1all2)).
% 182.78/27.32 thf(f7075,plain,(
% 182.78/27.32 ( ! [X0 : $i] : (((in @ X0 @ sK83) != $true) | ((in @ X0 @ (cartprod @ sK84 @ sK84)) = $true)) )),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f7071])).
% 182.78/27.32 thf(f7071,plain,(
% 182.78/27.32 ( ! [X0 : $i] : (((in @ X0 @ (cartprod @ sK84 @ sK84)) = $true) | ((in @ X0 @ sK83) != $true) | ($true != $true)) )),
% 182.78/27.32 inference(superposition,[status(thm)],[f5637,f6017])).
% 182.78/27.32 thf(f6017,plain,(
% 182.78/27.32 ($true = (subset @ sK83 @ (cartprod @ sK84 @ sK84)))),
% 182.78/27.32 inference(beta_eta_normalization,[status(thm)],[f4456])).
% 182.78/27.32 thf(f4456,plain,(
% 182.78/27.32 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK84 @ sK83))),
% 182.78/27.32 inference(definition_unfolding,[status(thm)],[f3079,f4420])).
% 182.78/27.32 thf(f4420,plain,(
% 182.78/27.32 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 182.78/27.32 inference(definition_unfolding,[status(thm)],[f3812,f4394])).
% 182.78/27.32 thf(f4394,plain,(
% 182.78/27.32 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f799])).
% 182.78/27.32 thf(f799,plain,(
% 182.78/27.32 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 182.78/27.32 inference(fool_elimination,[status(thm)],[f798])).
% 182.78/27.32 thf(f798,plain,(
% 182.78/27.32 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 182.78/27.32 inference(rectify,[status(thm)],[f185])).
% 182.78/27.32 thf(f185,axiom,(
% 182.78/27.32 (breln = (^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))))),
% 182.78/27.32 file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',breln)).
% 182.78/27.32 thf(f3812,plain,(
% 182.78/27.32 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f801])).
% 182.78/27.32 thf(f801,plain,(
% 182.78/27.32 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 182.78/27.32 inference(fool_elimination,[status(thm)],[f800])).
% 182.78/27.32 thf(f800,plain,(
% 182.78/27.32 ((^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)) = breln1)),
% 182.78/27.32 inference(rectify,[status(thm)],[f289])).
% 182.78/27.32 thf(f289,axiom,(
% 182.78/27.32 ((^[X3 : $i, X13 : $i] : (breln @ X3 @ X3 @ X13)) = breln1)),
% 182.78/27.32 file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',breln1)).
% 182.78/27.32 thf(f3079,plain,(
% 182.78/27.32 ($true = (breln1 @ sK84 @ sK83))),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1414])).
% 182.78/27.32 thf(f5637,plain,(
% 182.78/27.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X1) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true)) )),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f5128])).
% 182.78/27.32 thf(f5128,plain,(
% 182.78/27.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true) | ((subset @ X2 @ X1) != $true)) )),
% 182.78/27.32 inference(definition_unfolding,[status(thm)],[f3996,f2937])).
% 182.78/27.32 thf(f2937,plain,(
% 182.78/27.32 (notsubsetI = $true)),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1414])).
% 182.78/27.32 thf(f3996,plain,(
% 182.78/27.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | (notsubsetI != $true)) )),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f2343])).
% 182.78/27.32 thf(f2343,plain,(
% 182.78/27.32 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true)) | (notsubsetI != $true)) & ((notsubsetI = $true) | (($true = (subset @ sK675 @ sK674)) & ((in @ sK673 @ sK675) = $true) & ((in @ sK673 @ sK674) != $true)))),
% 182.78/27.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK673,sK674,sK675])],[f2341,f2342])).
% 182.78/27.32 thf(f2342,plain,(
% 182.78/27.32 ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X4) = $true) & ($true = (in @ X3 @ X5)) & ((in @ X3 @ X4) != $true)) => (($true = (subset @ sK675 @ sK674)) & ((in @ sK673 @ sK675) = $true) & ((in @ sK673 @ sK674) != $true))),
% 182.78/27.32 introduced(definition,[],[choice_axiom])).
% 182.78/27.32 thf(f2341,plain,(
% 182.78/27.32 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true)) | (notsubsetI != $true)) & ((notsubsetI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X4) = $true) & ($true = (in @ X3 @ X5)) & ((in @ X3 @ X4) != $true)))),
% 182.78/27.32 inference(rectify,[status(thm)],[f2340])).
% 182.78/27.32 thf(f2340,plain,(
% 182.78/27.32 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true)) | (notsubsetI != $true)) & ((notsubsetI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) = $true) & ((in @ X0 @ X2) = $true) & ((in @ X0 @ X1) != $true)))),
% 182.78/27.32 inference(nnf_transformation,[status(thm)],[f1203])).
% 182.78/27.32 thf(f1203,plain,(
% 182.78/27.32 ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) != $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true)) <=> (notsubsetI = $true)),
% 182.78/27.32 inference(flattening,[status(thm)],[f1202])).
% 182.78/27.32 thf(f1202,plain,(
% 182.78/27.32 (notsubsetI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X2 @ X1) != $true) | ((in @ X0 @ X1) = $true)) | ((in @ X0 @ X2) != $true))),
% 182.78/27.32 inference(ennf_transformation,[status(thm)],[f874])).
% 182.78/27.32 thf(f874,plain,(
% 182.78/27.32 (notsubsetI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (((in @ X0 @ X1) != $true) => ((subset @ X2 @ X1) != $true)))),
% 182.78/27.32 inference(flattening,[status(thm)],[f381])).
% 182.78/27.32 thf(f381,plain,(
% 182.78/27.32 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (~((in @ X0 @ X1) = $true) => ~((subset @ X2 @ X1) = $true))) <=> (notsubsetI = $true)),
% 182.78/27.32 inference(fool_elimination,[status(thm)],[f380])).
% 182.78/27.32 thf(f380,plain,(
% 182.78/27.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => ~(subset @ X2 @ X1))) = notsubsetI)),
% 182.78/27.32 inference(rectify,[status(thm)],[f85])).
% 182.78/27.32 thf(f85,axiom,(
% 182.78/27.32 (! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(subset @ X3 @ X4))) = notsubsetI)),
% 182.78/27.32 file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',notsubsetI)).
% 182.78/27.32 thf(f5620,plain,(
% 182.78/27.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (cartprod @ X5 @ X3))) | ($true = (in @ (kfst @ X4) @ X5))) )),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f5238])).
% 182.78/27.32 thf(f5238,plain,(
% 182.78/27.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != (in @ X4 @ (cartprod @ X5 @ X3))) | ($true = (in @ (kfst @ X4) @ X5))) )),
% 182.78/27.32 inference(definition_unfolding,[status(thm)],[f4126,f3018])).
% 182.78/27.32 thf(f3018,plain,(
% 182.78/27.32 (cartprodfstin = $true)),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1414])).
% 182.78/27.32 thf(f4126,plain,(
% 182.78/27.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ (kfst @ X4) @ X5)) | ($true != (in @ X4 @ (cartprod @ X5 @ X3))) | (cartprodfstin != $true)) )),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f2489])).
% 182.78/27.32 thf(f2489,plain,(
% 182.78/27.32 ((cartprodfstin = $true) | (($true != (in @ (kfst @ sK761) @ sK762)) & ((in @ sK761 @ (cartprod @ sK762 @ sK760)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ (kfst @ X4) @ X5)) | ($true != (in @ X4 @ (cartprod @ X5 @ X3)))) | (cartprodfstin != $true))),
% 182.78/27.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK760,sK761,sK762])],[f2487,f2488])).
% 182.78/27.32 thf(f2488,plain,(
% 182.78/27.32 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (kfst @ X1) @ X2)) & ((in @ X1 @ (cartprod @ X2 @ X0)) = $true)) => (($true != (in @ (kfst @ sK761) @ sK762)) & ((in @ sK761 @ (cartprod @ sK762 @ sK760)) = $true))),
% 182.78/27.32 introduced(definition,[],[choice_axiom])).
% 182.78/27.32 thf(f2487,plain,(
% 182.78/27.32 ((cartprodfstin = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (kfst @ X1) @ X2)) & ((in @ X1 @ (cartprod @ X2 @ X0)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ (kfst @ X4) @ X5)) | ($true != (in @ X4 @ (cartprod @ X5 @ X3)))) | (cartprodfstin != $true))),
% 182.78/27.32 inference(rectify,[status(thm)],[f2486])).
% 182.78/27.32 thf(f2486,plain,(
% 182.78/27.32 ((cartprodfstin = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (kfst @ X1) @ X2)) & ((in @ X1 @ (cartprod @ X2 @ X0)) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (kfst @ X1) @ X2)) | ((in @ X1 @ (cartprod @ X2 @ X0)) != $true)) | (cartprodfstin != $true))),
% 182.78/27.32 inference(nnf_transformation,[status(thm)],[f1160])).
% 182.78/27.32 thf(f1160,plain,(
% 182.78/27.32 (cartprodfstin = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (kfst @ X1) @ X2)) | ((in @ X1 @ (cartprod @ X2 @ X0)) != $true))),
% 182.78/27.32 inference(ennf_transformation,[status(thm)],[f429])).
% 182.78/27.32 thf(f429,plain,(
% 182.78/27.32 (cartprodfstin = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (cartprod @ X2 @ X0)) = $true) => ($true = (in @ (kfst @ X1) @ X2)))),
% 182.78/27.32 inference(fool_elimination,[status(thm)],[f428])).
% 182.78/27.32 thf(f428,plain,(
% 182.78/27.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (in @ (kfst @ X1) @ X2)) = cartprodfstin)),
% 182.78/27.32 inference(rectify,[status(thm)],[f166])).
% 182.78/27.32 thf(f166,axiom,(
% 182.78/27.32 (! [X4 : $i,X10 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (kfst @ X10) @ X3)) = cartprodfstin)),
% 182.78/27.32 file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',cartprodfstin)).
% 182.78/27.32 thf(f25327,plain,(
% 182.78/27.32 ((in @ (kfst @ sK86) @ sK84) != $true)),
% 182.78/27.32 inference(subsumption_resolution,[status(thm)],[f25326,f3078])).
% 182.78/27.32 thf(f3078,plain,(
% 182.78/27.32 ((sK85 @ sK86) != $true)),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1414])).
% 182.78/27.32 thf(f25326,plain,(
% 182.78/27.32 ((sK85 @ sK86) = $true) | ((in @ (kfst @ sK86) @ sK84) != $true)),
% 182.78/27.32 inference(subsumption_resolution,[status(thm)],[f25325,f24436])).
% 182.78/27.32 thf(f24436,plain,(
% 182.78/27.32 ($true = (in @ (ksnd @ sK86) @ sK84))),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f24381])).
% 182.78/27.32 thf(f24381,plain,(
% 182.78/27.32 ($true != $true) | ($true = (in @ (ksnd @ sK86) @ sK84))),
% 182.78/27.32 inference(superposition,[status(thm)],[f6148,f24365])).
% 182.78/27.32 thf(f6148,plain,(
% 182.78/27.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | ($true = (in @ (ksnd @ X2) @ X1))) )),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f4873])).
% 182.78/27.32 thf(f4873,plain,(
% 182.78/27.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (ksnd @ X2) @ X1)) | ($true != $true) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) )),
% 182.78/27.32 inference(definition_unfolding,[status(thm)],[f3644,f3150])).
% 182.78/27.32 thf(f3150,plain,(
% 182.78/27.32 (cartprodsndin = $true)),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1414])).
% 182.78/27.32 thf(f3644,plain,(
% 182.78/27.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ (ksnd @ X2) @ X1)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true) | (cartprodsndin != $true)) )),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1961])).
% 182.78/27.32 thf(f1961,plain,(
% 182.78/27.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (ksnd @ X2) @ X1)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) | (cartprodsndin != $true)) & ((cartprodsndin = $true) | (((in @ (ksnd @ sK433) @ sK432) != $true) & ($true = (in @ sK433 @ (cartprod @ sK431 @ sK432)))))),
% 182.78/27.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK431,sK432,sK433])],[f1959,f1960])).
% 182.78/27.32 thf(f1960,plain,(
% 182.78/27.32 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ (ksnd @ X5) @ X4) != $true) & ((in @ X5 @ (cartprod @ X3 @ X4)) = $true)) => (((in @ (ksnd @ sK433) @ sK432) != $true) & ($true = (in @ sK433 @ (cartprod @ sK431 @ sK432))))),
% 182.78/27.32 introduced(definition,[],[choice_axiom])).
% 182.78/27.32 thf(f1959,plain,(
% 182.78/27.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (ksnd @ X2) @ X1)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) | (cartprodsndin != $true)) & ((cartprodsndin = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ (ksnd @ X5) @ X4) != $true) & ((in @ X5 @ (cartprod @ X3 @ X4)) = $true)))),
% 182.78/27.32 inference(rectify,[status(thm)],[f1958])).
% 182.78/27.32 thf(f1958,plain,(
% 182.78/27.32 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (ksnd @ X2) @ X1)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) | (cartprodsndin != $true)) & ((cartprodsndin = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (ksnd @ X2) @ X1)) & ((in @ X2 @ (cartprod @ X0 @ X1)) = $true)))),
% 182.78/27.32 inference(nnf_transformation,[status(thm)],[f1179])).
% 182.78/27.32 thf(f1179,plain,(
% 182.78/27.32 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (ksnd @ X2) @ X1)) | ((in @ X2 @ (cartprod @ X0 @ X1)) != $true)) <=> (cartprodsndin = $true)),
% 182.78/27.32 inference(ennf_transformation,[status(thm)],[f553])).
% 182.78/27.32 thf(f553,plain,(
% 182.78/27.32 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (cartprod @ X0 @ X1)) = $true) => ($true = (in @ (ksnd @ X2) @ X1))) <=> (cartprodsndin = $true)),
% 182.78/27.32 inference(fool_elimination,[status(thm)],[f552])).
% 182.78/27.32 thf(f552,plain,(
% 182.78/27.32 (cartprodsndin = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (ksnd @ X2) @ X1)))),
% 182.78/27.32 inference(rectify,[status(thm)],[f178])).
% 182.78/27.32 thf(f178,axiom,(
% 182.78/27.32 (cartprodsndin = ! [X3 : $i,X4 : $i,X10 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4)))),
% 182.78/27.32 file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',cartprodsndin)).
% 182.78/27.32 thf(f25325,plain,(
% 182.78/27.32 ($true != (in @ (ksnd @ sK86) @ sK84)) | ((sK85 @ sK86) = $true) | ((in @ (kfst @ sK86) @ sK84) != $true)),
% 182.78/27.32 inference(subsumption_resolution,[status(thm)],[f25306,f3077])).
% 182.78/27.32 thf(f25306,plain,(
% 182.78/27.32 ($true != (in @ sK86 @ sK83)) | ((sK85 @ sK86) = $true) | ((in @ (kfst @ sK86) @ sK84) != $true) | ($true != (in @ (ksnd @ sK86) @ sK84))),
% 182.78/27.32 inference(superposition,[status(thm)],[f3076,f24458])).
% 182.78/27.32 thf(f24458,plain,(
% 182.78/27.32 ((kpair @ (kfst @ sK86) @ (ksnd @ sK86)) = sK86)),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f24380])).
% 182.78/27.32 thf(f24380,plain,(
% 182.78/27.32 ($true != $true) | ((kpair @ (kfst @ sK86) @ (ksnd @ sK86)) = sK86)),
% 182.78/27.32 inference(superposition,[status(thm)],[f5624,f24365])).
% 182.78/27.32 thf(f5624,plain,(
% 182.78/27.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (cartprod @ X4 @ X3)) != $true) | ((kpair @ (kfst @ X5) @ (ksnd @ X5)) = X5)) )),
% 182.78/27.32 inference(trivial_inequality_removal,[status(thm)],[f5034])).
% 182.78/27.32 thf(f5034,plain,(
% 182.78/27.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (cartprod @ X4 @ X3)) != $true) | ((kpair @ (kfst @ X5) @ (ksnd @ X5)) = X5) | ($true != $true)) )),
% 182.78/27.32 inference(definition_unfolding,[status(thm)],[f3847,f3121])).
% 182.78/27.32 thf(f3121,plain,(
% 182.78/27.32 (cartprodpairsurjEq = $true)),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1414])).
% 182.78/27.32 thf(f3847,plain,(
% 182.78/27.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (cartprod @ X4 @ X3)) != $true) | ((kpair @ (kfst @ X5) @ (ksnd @ X5)) = X5) | (cartprodpairsurjEq != $true)) )),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f2174])).
% 182.78/27.32 thf(f2174,plain,(
% 182.78/27.32 ((cartprodpairsurjEq = $true) | (($true = (in @ sK575 @ (cartprod @ sK574 @ sK573))) & ((kpair @ (kfst @ sK575) @ (ksnd @ sK575)) != sK575))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (cartprod @ X4 @ X3)) != $true) | ((kpair @ (kfst @ X5) @ (ksnd @ X5)) = X5)) | (cartprodpairsurjEq != $true))),
% 182.78/27.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK573,sK574,sK575])],[f2172,f2173])).
% 182.78/27.32 thf(f2173,plain,(
% 182.78/27.32 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) & ((kpair @ (kfst @ X2) @ (ksnd @ X2)) != X2)) => (($true = (in @ sK575 @ (cartprod @ sK574 @ sK573))) & ((kpair @ (kfst @ sK575) @ (ksnd @ sK575)) != sK575))),
% 182.78/27.32 introduced(definition,[],[choice_axiom])).
% 182.78/27.32 thf(f2172,plain,(
% 182.78/27.32 ((cartprodpairsurjEq = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) & ((kpair @ (kfst @ X2) @ (ksnd @ X2)) != X2))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (cartprod @ X4 @ X3)) != $true) | ((kpair @ (kfst @ X5) @ (ksnd @ X5)) = X5)) | (cartprodpairsurjEq != $true))),
% 182.78/27.32 inference(rectify,[status(thm)],[f2171])).
% 182.78/27.32 thf(f2171,plain,(
% 182.78/27.32 ((cartprodpairsurjEq = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) & ((kpair @ (kfst @ X2) @ (ksnd @ X2)) != X2))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (cartprod @ X1 @ X0)) != $true) | ((kpair @ (kfst @ X2) @ (ksnd @ X2)) = X2)) | (cartprodpairsurjEq != $true))),
% 182.78/27.32 inference(nnf_transformation,[status(thm)],[f1224])).
% 182.78/27.32 thf(f1224,plain,(
% 182.78/27.32 (cartprodpairsurjEq = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (cartprod @ X1 @ X0)) != $true) | ((kpair @ (kfst @ X2) @ (ksnd @ X2)) = X2))),
% 182.78/27.32 inference(ennf_transformation,[status(thm)],[f395])).
% 182.78/27.32 thf(f395,plain,(
% 182.78/27.32 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) => ((kpair @ (kfst @ X2) @ (ksnd @ X2)) = X2)) <=> (cartprodpairsurjEq = $true)),
% 182.78/27.32 inference(fool_elimination,[status(thm)],[f394])).
% 182.78/27.32 thf(f394,plain,(
% 182.78/27.32 (cartprodpairsurjEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X1 @ X0)) => ((kpair @ (kfst @ X2) @ (ksnd @ X2)) = X2)))),
% 182.78/27.32 inference(rectify,[status(thm)],[f184])).
% 182.78/27.32 thf(f184,axiom,(
% 182.78/27.32 (cartprodpairsurjEq = ! [X4 : $i,X3 : $i,X10 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)))),
% 182.78/27.32 file('/export/starexec/sandbox2/tmp/tmp.XkInnqrZgy/DTF2THF_9951.p',cartprodpairsurjEq)).
% 182.78/27.32 thf(f3076,plain,(
% 182.78/27.32 ( ! [X4 : $i,X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ sK83)) | ($true != (in @ X4 @ sK84)) | ($true = (sK85 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK84))) )),
% 182.78/27.32 inference(cnf_transformation,[status(thm)],[f1414])).
% 182.78/27.32 % SZS output end Proof for DTF2THF_9951
% 182.78/27.32 % (11462)------------------------------
% 182.78/27.32 % (11462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 182.78/27.32 % (11462)Termination reason: Refutation
% 182.78/27.32
% 182.78/27.32 % (11462)Memory used [KB]: 18293
% 182.78/27.32 % (11462)Time elapsed: 2.625 s
% 182.78/27.32 % (11462)Instructions burned: 8119 (million)
% 182.78/27.32 % (11462)------------------------------
% 182.78/27.32 % (11462)------------------------------
% 182.78/27.32 % (10196)Success in time 25.697 s
%------------------------------------------------------------------------------