%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU796^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 09:37:16 AM UTC 2026
% Result : Theorem 23.42s 4.72s
% Output : Refutation 23.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 6005 (1689 equ; 0 cnn)
% Maximal formula atoms : 315 ( 139 avg)
% Number of connectives : 3050 ( 74 ~; 64 |; 972 &; 364 @)
% ( 7 <=>;1569 =>; 0 <=; 0 <~>)
% Maximal formula depth : 322 ( 63 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 565 ( 562 usr; 322 con; 0-6 aty)
% Number of variables : 140 ( 32 ^; 74 !; 34 ?; 140 :)
% 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_325,type,
breln1Set: $i > $i ).
thf(func_def_327,type,
transitive: $i > $i > $o ).
thf(func_def_328,type,
antisymmetric: $i > $i > $o ).
thf(func_def_329,type,
reflexive: $i > $i > $o ).
thf(func_def_330,type,
refltransitive: $i > $i > $o ).
thf(func_def_331,type,
refllinearorder: $i > $i > $o ).
thf(func_def_332,type,
reflwellordering: $i > $i > $o ).
thf(func_def_338,type,
breln1invset: $i > $i > $i ).
thf(func_def_342,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_360,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_376,type,
sP0: $i > $i > $i > $o ).
thf(func_def_378,type,
sP2: $i > $i > $o ).
thf(func_def_379,type,
sP3: $i > $o ).
thf(func_def_380,type,
sP4: $i > $i > $o ).
thf(func_def_381,type,
sP5: $i > $i > $o ).
thf(func_def_382,type,
sP6: $i > $i > $i > $i > $o ).
thf(func_def_388,type,
sP12: $i > $i > $i > $o ).
thf(func_def_393,type,
sP17: $i > $o > $i > $i > $o ).
thf(func_def_396,type,
sK20: $i > $o ).
thf(func_def_398,type,
sK22: ( $i > $o ) > $i > $i > $i ).
thf(func_def_399,type,
sK23: ( $i > $o ) > $i > $i > $i ).
thf(func_def_400,type,
sK24: $i > $o ).
thf(func_def_403,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_404,type,
sK28: $i > $i > $i > $i ).
thf(func_def_405,type,
sK29: $i > $i > $i > $i ).
thf(func_def_418,type,
sK42: $i > $i ).
thf(func_def_419,type,
sK43: $i > $i ).
thf(func_def_421,type,
sK45: $i > $o ).
thf(func_def_422,type,
sK46: $i > $i ).
thf(func_def_423,type,
sK47: ( $i > $o ) > $i ).
thf(func_def_433,type,
sK57: $i > $i > $i ).
thf(func_def_465,type,
sK89: ( $i > $o ) > $i > $i > $i ).
thf(func_def_466,type,
sK90: ( $i > $o ) > $i > $i > $i ).
thf(func_def_469,type,
sK93: $i > $o ).
thf(func_def_495,type,
sK119: $i > $i > $i > $i ).
thf(func_def_499,type,
sK123: $o > $i > $i > $i ).
thf(func_def_523,type,
sK147: $i > $o ).
thf(func_def_525,type,
sK149: ( $i > $o ) > $i > $i ).
thf(func_def_564,type,
sK188: $i > $i > $i > $i > $i ).
thf(func_def_579,type,
sK203: $i > $o ).
thf(func_def_602,type,
sK226: $i > $o ).
thf(func_def_603,type,
sK227: $i > $o ).
thf(func_def_604,type,
sK228: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_605,type,
sK229: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_618,type,
sK242: $i > $o ).
thf(func_def_619,type,
sK243: ( $i > $o ) > $i > $i > $i ).
thf(func_def_622,type,
sK246: $i > $o ).
thf(func_def_627,type,
sK251: $i > $i > $i ).
thf(func_def_628,type,
sK252: $i > $i > $i ).
thf(func_def_629,type,
sK253: $i > $i > $i ).
thf(func_def_630,type,
sK254: $i > $i > $i ).
thf(func_def_631,type,
sK255: $i > $i > $i ).
thf(func_def_632,type,
sK256: $i > $i > $i > $i ).
thf(func_def_633,type,
sK257: $i > $i ).
thf(func_def_634,type,
sK258: $i > $i ).
thf(func_def_635,type,
sK259: $i > $i ).
thf(func_def_636,type,
sK260: $i > $i ).
thf(func_def_637,type,
sK261: $i > $i > $i > $i ).
thf(func_def_638,type,
sK262: $i > $i > $i > $i ).
thf(func_def_639,type,
sK263: $i > $i > $i ).
thf(func_def_640,type,
sK264: $i > $i > $i ).
thf(func_def_641,type,
sK265: $i > $i > $i ).
thf(func_def_642,type,
sK266: $i > $i ).
thf(func_def_644,type,
sK268: $i > $i ).
thf(func_def_645,type,
sK269: $i > $i ).
thf(func_def_646,type,
sK270: ( $i > $i ) > $i > $i > $i ).
thf(func_def_649,type,
sK273: $i > $i ).
thf(func_def_666,type,
sK290: $i > $o ).
thf(func_def_677,type,
sK301: $i > $i > $o ).
thf(func_def_682,type,
sK306: $i > $i > $o ).
thf(func_def_698,type,
sK322: $i > $i > $i > $i > $i ).
thf(func_def_699,type,
sK323: $i > $i > $i > $i > $i ).
thf(func_def_700,type,
sK324: $i > $i > $i > $i > $i ).
thf(func_def_701,type,
sK325: $i > $i > $i > $i > $i ).
thf(func_def_708,type,
sK332: $i > $o ).
thf(func_def_737,type,
sK361: $i > $i > $i > $i > $i ).
thf(func_def_756,type,
sK380: $o > $i > $i > $i > $i > $i > $i ).
thf(func_def_761,type,
sK385: $i > $o ).
thf(func_def_764,type,
sK388: $i > ( $i > $o ) > $i ).
thf(func_def_765,type,
sK389: $i > ( $i > $o ) > $i ).
thf(func_def_774,type,
sK398: $i > $i > $i > $i ).
thf(func_def_775,type,
sK399: $i > $i > $i > $i ).
thf(func_def_794,type,
sK418: $i > ( $i > $i ) > $i > $i ).
thf(func_def_796,type,
sK420: $i > $i ).
thf(func_def_800,type,
sK424: $i > $i > $o ).
thf(func_def_801,type,
sK425: $i > $i ).
thf(func_def_804,type,
sK428: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_822,type,
sK446: $i > $i ).
thf(func_def_825,type,
sK449: $i > $i > ( $i > $i ) > $i ).
thf(func_def_835,type,
sK459: $i > $i > $i > $i ).
thf(func_def_836,type,
sK460: $i > $i > $i > $i ).
thf(func_def_853,type,
sK477: $i > $i ).
thf(func_def_855,type,
sK479: $i > $i ).
thf(func_def_856,type,
sK480: $i > $i ).
thf(func_def_857,type,
sK481: $i > ( $i > $i ) > $i ).
thf(func_def_858,type,
sK482: $i > $i > ( $i > $i ) > $i ).
thf(func_def_863,type,
sK487: $i > $i > $i ).
thf(func_def_864,type,
sK488: $i > $i > $i ).
thf(func_def_870,type,
sK494: $i > $i > $i ).
thf(func_def_885,type,
sK509: ( $i > $o ) > $i > $i ).
thf(func_def_887,type,
sK511: $i > $o ).
thf(func_def_890,type,
sK514: $i > $i ).
thf(func_def_892,type,
sK516: ( $i > $i ) > $i > $i > $i ).
thf(func_def_894,type,
sK518: $i > $i > $o ).
thf(func_def_895,type,
sK519: $i > $i ).
thf(func_def_896,type,
sK520: $i > $i ).
thf(func_def_897,type,
sK521: ( $i > $i > $o ) > $i > $i ).
thf(func_def_898,type,
sK522: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_899,type,
sK523: ( $i > $i > $o ) > $i > $i ).
thf(func_def_904,type,
sK528: $i > $i > $i ).
thf(func_def_921,type,
sK545: $i > $i > $o ).
thf(func_def_925,type,
sK549: $i > $i > $o ).
thf(func_def_956,type,
sK580: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_957,type,
sK581: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_958,type,
sK582: $i > $o ).
thf(func_def_959,type,
sK583: $i > $o ).
thf(func_def_971,type,
sK595: $i > $i > $i ).
thf(func_def_987,type,
sK611: $i > $i ).
thf(func_def_999,type,
sK623: $i > $o ).
thf(func_def_1001,type,
sK625: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1002,type,
sK626: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1015,type,
sK639: $i > $i > $i ).
thf(func_def_1017,type,
sK641: $i > $o ).
thf(func_def_1021,type,
sK645: $i > $i > $o ).
thf(func_def_1026,type,
sK650: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1027,type,
sK651: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1031,type,
sK655: $i > $o ).
thf(func_def_1043,type,
sK667: $i > $i > $i ).
thf(func_def_1049,type,
sK673: $i > $o ).
thf(func_def_1057,type,
sK681: $i > $i ).
thf(func_def_1059,type,
sK683: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1064,type,
sK688: $i > ( $i > $o ) > $i ).
thf(func_def_1065,type,
sK689: $i > $o ).
thf(func_def_1076,type,
sK700: $i > ( $i > $o ) > $i ).
thf(func_def_1077,type,
sK701: $i > $o ).
thf(func_def_1079,type,
sK703: $i > $o ).
thf(func_def_1080,type,
sK704: $i > $i ).
thf(func_def_1081,type,
sK705: ( $i > $o ) > $i ).
thf(func_def_1099,type,
sK723: $i > $o ).
thf(func_def_1101,type,
sK725: $i > $o ).
thf(func_def_1125,type,
sK749: $i > $i ).
thf(func_def_1127,type,
sK751: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1137,type,
sK761: ( $i > $o ) > $i > $i ).
thf(func_def_1139,type,
sK763: $i > $o ).
thf(func_def_1142,type,
sK766: $i > $o ).
thf(func_def_1144,type,
sK768: $i > $i > $i ).
thf(func_def_1154,type,
sK778: $i > $i ).
thf(func_def_1159,type,
sK783: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1160,type,
sK784: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1161,type,
sK785: $i > $o ).
thf(func_def_1162,type,
sK786: $i > $o ).
thf(func_def_1182,type,
sK806: $i > $i > $i > $i ).
thf(func_def_1183,type,
sK807: $i > $i > $i > $i ).
thf(func_def_1184,type,
sK808: $i > $i > $i > $i ).
thf(func_def_1185,type,
sK809: $i > $i > $i > $i ).
thf(func_def_1192,type,
sK816: $i > $i > $o ).
thf(func_def_1197,type,
sK821: ( $i > $o ) > $i > $i ).
thf(func_def_1199,type,
sK823: $i > $o ).
thf(func_def_1201,type,
sK825: $i > $i > $o ).
thf(func_def_1219,type,
sK843: $i > $o ).
thf(func_def_1220,type,
sK844: ( $i > $o ) > $i ).
thf(func_def_1221,type,
sK845: $i > $i > $i > $i > $i ).
thf(func_def_1222,type,
sK846: $i > $i > $i > $i > $i ).
thf(func_def_1240,type,
sK864: $i > $o ).
thf(func_def_1242,type,
sK866: ( $i > $o ) > $i > $i ).
thf(func_def_1248,type,
sK872: $i > $o ).
thf(func_def_1252,type,
sK876: $i > $i ).
thf(func_def_1254,type,
sK878: $i > $i ).
thf(func_def_1263,type,
sK887: $i > $i ).
thf(func_def_1264,type,
sK888: $i > $o ).
thf(func_def_1285,type,
sK909: $i > $i > $o ).
thf(func_def_1298,type,
sK922: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1301,type,
sK925: $i > $i ).
thf(func_def_1314,type,
sK938: $i > $o ).
thf(func_def_1316,type,
sK940: ( $i > $o ) > $i > $i ).
thf(func_def_1317,type,
sK941: ( $i > $o ) > $i > $i ).
thf(func_def_1338,type,
sK962: $i > $i > $i ).
thf(func_def_1342,type,
sK966: $i > $o ).
thf(func_def_1349,type,
sK973: $i > $o ).
thf(func_def_1351,type,
sK975: ( $i > $o ) > $i > $i ).
thf(func_def_1359,type,
sK983: $i > $o ).
thf(func_def_1361,type,
sK985: ( $i > $o ) > $i ).
thf(func_def_1362,type,
sK986: ( $i > $o ) > $i ).
thf(func_def_1371,type,
sK995: $i > $i > $i > $i ).
thf(func_def_1374,type,
sK998: $i > $i > $i > $i > $i ).
thf(func_def_1379,type,
sK1003: $i > $i ).
thf(func_def_1389,type,
sK1013: $i > $i > $i > $i > $i > $i ).
thf(func_def_1390,type,
sK1014: $i > $i ).
thf(func_def_1415,type,
sK1039: $i > $o ).
thf(func_def_1433,type,
ph1057:
!>[X0: $tType] : X0 ).
thf(func_def_1434,type,
sK1058: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1435,type,
sK1059: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1436,type,
sK1060: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1437,type,
sK1061: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1438,type,
sK1062: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1439,type,
sK1063: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1440,type,
sK1064: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1441,type,
sK1065: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1442,type,
sK1066: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1443,type,
sK1067: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1444,type,
sK1068: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1445,type,
sK1069: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1446,type,
sK1070: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1447,type,
sK1071: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1448,type,
sK1072: $i > ( $i > $i ) > $i > $i ).
thf(f24522,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f9067,f11267,f12733,f24521]) ).
thf(f24521,plain,
( ~ spl1056_905
| ~ spl1056_1360 ),
inference(avatar_contradiction_clause,[status(thm)],[f24520]) ).
thf(f24520,plain,
( $false
| ~ spl1056_905
| ~ spl1056_1360 ),
inference(subsumption_resolution,[status(thm)],[f24516,f18305]) ).
thf(f18305,plain,
( ( ( sK42 @ ( sK516 @ sK42 @ sK41 @ sK40 ) )
= sK41 )
| ~ spl1056_1360 ),
inference(trivial_inequality_removal,[status(thm)],[f18266]) ).
thf(f18266,plain,
( ( $true != $true )
| ( ( sK42 @ ( sK516 @ sK42 @ sK41 @ sK40 ) )
= sK41 )
| ~ spl1056_1360 ),
inference(superposition,[status(thm)],[f11266,f4831]) ).
thf(f4831,plain,
( $true
= ( in @ sK41 @ ( image1 @ sK40 @ sK42 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3323]) ).
thf(f3323,plain,
( ( in @ sK41
@ ( image1 @ sK40
@ ^ [Y0: $i] : ( sK42 @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1444]) ).
thf(f1444,plain,
( ( binunionT_lem = $true )
& ( setadjoinE = $true )
& ( powersetE1 = $true )
& ( eqinunit = $true )
& ( cartprodpairin = $true )
& ( complementT_lem = $true )
& ( cartprodmempaircEq = $true )
& ( notinemptyset = $true )
& ( binintersectSubset1 = $true )
& ( omega0Ax = $true )
& ( setadjoinIR = $true )
& ( eqbreln = $true )
& ( iffalseProp1 = $true )
& ( binintersectSubset3 = $true )
& ( binunionIR = $true )
& ( cartprodfstin = $true )
& ( funcGraphProp2 = $true )
& ( breln1all1 = $true )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( contrasubsetT3 = $true )
& ( ap2apEq2 = $true )
& ( inCongP = $true )
& ( ubforcartprodlem1 = $true )
& ( ( in @ sK41
@ ( image1 @ sK40
@ ^ [Y0: $i] : ( sK42 @ Y0 ) ) )
= $true )
& ! [X3: $i] :
( ( ( sK42 @ X3 )
!= sK41 )
| ( ( in @ X3 @ sK40 )
!= $true ) )
& ( inIntersectImpInUnion = $true )
& ( binintersectT_lem = $true )
& ( demorgan2b = $true )
& ( disjointsetsI1 = $true )
& ( emptyinPowerset = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( breln1compI = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( dpsetconstrSub = $true )
& ( woz13rule3 = $true )
& ( binunionEcases = $true )
& ( singletonsswitch = $true )
& ( complementTE1 = $true )
& ( setunionsingleton1 = $true )
& ( exuI3 = $true )
& ( powersetI1 = $true )
& ( setukpairinjR1 = $true )
& ( demorgan2a2 = $true )
& ( ubforcartprodlem3 = $true )
& ( image1Equiv = $true )
& ( subsetRefl = $true )
& ( symdiffI2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( kfstpairEq = $true )
& ( quantDeMorgan2 = $true )
& ( setminusI = $true )
& ( contraSubsetComplement = $true )
& ( woz2W = $true )
& ( demorgan1b = $true )
& ( notsubsetI = $true )
& ( woz1_5 = $true )
& ( breln1SetBreln1 = $true )
& ( setunionE = $true )
& ( symdiffE = $true )
& ( setadjoinAx = $true )
& ( upairset2IR = $true )
& ( contrasubsetT = $true )
& ( binintersectSubset4 = $true )
& ( exuI2 = $true )
& ( upairset2E = $true )
& ( theprop = $true )
& ( breln1compE = $true )
& ( notequalI2 = $true )
& ( setukpairinjR11 = $true )
& ( exuI1 = $true )
& ( exuE1 = $true )
& ( contrasubsetT1 = $true )
& ( demorgan2b2 = $true )
& ( emptyI = $true )
& ( cartprodpairmemEL = $true )
& ( emptyE1 = $true )
& ( emptysetAx = $true )
& ( setunion__Cong = $true )
& ( brelnall2 = $true )
& ( funcinfuncset = $true )
& ( exu__Cong = $true )
& ( woz1_4 = $true )
& ( powersetAx = $true )
& ( image1Ex1 = $true )
& ( lamp = $true )
& ( powersetTI1 = $true )
& ( setextT = $true )
& ( cartprodsndin = $true )
& ( powersetT_lem = $true )
& ( complementImpComplementIntersect = $true )
& ( binunionLsub = $true )
& ( binintersectER = $true )
& ( singletoninpowunion = $true )
& ( eta2 = $true )
& ( ap2p = $true )
& ( subPowSU = $true )
& ( ex1I = $true )
& ( beta2 = $true )
& ( ifSingleton = $true )
& ( kpairp = $true )
& ( vacuousDall = $true )
& ( binunionE = $true )
& ( subsetI2 = $true )
& ( emptysetimpfalse = $true )
& ( setunionI = $true )
& ( image1Ex = $true )
& ( omega__Cong = $true )
& ( iffalseProp2 = $true )
& ( replAx = $true )
& ( cartprodpairsurjEq = $true )
& ( setadjoinSub = $true )
& ( setOfPairsIsBReln = $true )
& ( iftrueProp2 = $true )
& ( nonemptyI1 = $true )
& ( exuE3e = $true )
& ( subset2powerset = $true )
& ( binunionTE = $true )
& ( wellorderingAx = $true )
& ( upairequniteq = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjL1 = $true )
& ( woz1_1 = $true )
& ( setminusILneg = $true )
& ( subsetTI = $true )
& ( woz2A = $true )
& ( setukpairIL = $true )
& ( setOfPairsIsBReln1 = $true )
& ( setminusER = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setextsub = $true )
& ( setunionAx = $true )
& ( doubleComplementI1 = $true )
& ( complementTnotintersectT = $true )
& ( demorgan2 = $true )
& ( setext = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( breln1unionCommutes = $true )
& ( quantDeMorgan4 = $true )
& ( upairinpowunion = $true )
& ( ksndsingleton = $true )
& ( funcext2 = $true )
& ( lam2p = $true )
& ( binintersectTERcontra = $true )
& ( breln1unionEcases = $true )
& ( subsetTrans = $true )
& ( exuE2 = $true )
& ( doubleComplementE1 = $true )
& ( breln1invE = $true )
& ( setminusERneg = $true )
& ( theeq = $true )
& ( setukpairinjR12 = $true )
& ( demorgan2a = $true )
& ( setbeta = $true )
& ( powerset__Cong = $true )
& ( ap2apEq1 = $true )
& ( woz2B = $true )
& ( ubforcartprodlem2 = $true )
& ( dpsetconstrEL1 = $true )
& ( funcext = $true )
& ( binintersectTELcontra = $true )
& ( setminusIRneg = $true )
& ( doubleComplementSub1 = $true )
& ( funcGraphProp3 = $true )
& ( setukpairinjR = $true )
& ( brelnall1 = $true )
& ( notequalI1 = $true )
& ( nonemptyI = $true )
& ( eqbreln1 = $true )
& ( setminusSubset2 = $true )
& ( powersetTE1 = $true )
& ( breln1invI = $true )
& ( in__Cong = $true )
& ( cartprodmempair = $true )
& ( breln1compprop = $true )
& ( singletonsuniq = $true )
& ( descr__Cong = $true )
& ( setminusSubset1 = $true )
& ( complementTcontraSubset = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( dsetconstrER = $true )
& ( setminusT_lem = $true )
& ( cartprodmempair1 = $true )
& ( eqimpsubset2 = $true )
& ( ex1E1 = $true )
& ( kpairiskpair = $true )
& ( subbreln = $true )
& ( kpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( iftrueProp1 = $true )
& ( secondinupair = $true )
& ( lam2lamEq = $true )
& ( beta1 = $true )
& ( woz13rule0 = $true )
& ( setminusLsub = $true )
& ( inIntersectImpInUnion2 = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrI = $true )
& ( eta1 = $true )
& ( symdiffIneg1 = $true )
& ( funcGraphProp1 = $true )
& ( sepInPowerset = $true )
& ( binintersectLsub = $true )
& ( woz13rule4 = $true )
& ( subbreln1 = $true )
& ( woz2Ex = $true )
& ( lamProp = $true )
& ( prop2setI = $true )
& ( setukpairinjL2 = $true )
& ( funcImageSingleton = $true )
& ( binintersectSubset2 = $true )
& ( setukpairinjR2 = $true )
& ( cartprodpairmemER = $true )
& ( ex1E2 = $true )
& ( dpsetconstrI = $true )
& ( eqimpsubset1 = $true )
& ( emptyinunitempty = $true )
& ( nonemptyE1 = $true )
& ( foundationAx = $true )
& ( app = $true )
& ( iftrueorfalse = $true )
& ( prop2setE = $true )
& ( binintersectI = $true )
& ( choice2fnsingleton = $true )
& ( singletoninpowerset = $true )
& ( setunionsingleton = $true )
& ( dpsetconstrERa = $true )
& ( setadjoin__Cong = $true )
& ( uniqinunit = $true )
& ( exuE3u = $true )
& ( demorgan1 = $true )
& ( dpsetconstrEL2 = $true )
& ( setminusELneg = $true )
& ( kfstsingleton = $true )
& ( doubleComplementEq = $true )
& ( iftrue = $true )
& ( symdiffI1 = $true )
& ( notdexE = $true )
& ( binunionTILcontra = $true )
& ( powersetsubset = $true )
& ( demorgan2a1 = $true )
& ( exuEu = $true )
& ( binunionRsub = $true )
& ( iffalse = $true )
& ( quantDeMorgan3 = $true )
& ( ifp = $true )
& ( funcGraphProp4 = $true )
& ( upairsetIL = $true )
& ( nonemptyImpWitness = $true )
& ( setukpairIR = $true )
& ( binintersectRsub = $true )
& ( sepSubset = $true )
& ( notdallE = $true )
& ( woz1_2 = $true )
& ( binintersectSubset5 = $true )
& ( binunionTIRcontra = $true )
& ( funcextLem = $true )
& ( notinsingleton = $true )
& ( subsetI1 = $true )
& ( infuncsetfunc = $true )
& ( upairsetIR = $true )
& ( emptyset__Cong = $true )
& ( omegaIndAx = $true )
& ( doubleComplementSub2 = $true )
& ( apProp = $true )
& ( setadjoinOr = $true )
& ( setukpairinjL = $true )
& ( singletonprop = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( bs114d = $true )
& ( setminusEL = $true )
& ( binintersectEL = $true )
& ( breln1unionE = $true )
& ( demorgan1a = $true )
& ( breln1unionprop = $true )
& ( breln1unionIR = $true )
& ( setadjoinIL = $true )
& ( emptysetsubset = $true )
& ( emptysetE = $true )
& ( woz13rule1 = $true )
& ( breln1unionIL = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( setunionsingleton2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( upairsubunion = $true )
& ( binunionIL = $true )
& ( dpsetconstrER = $true )
& ( dsetconstr__Cong = $true )
& ( breln1invprop = $true )
& ( complementTI1 = $true )
& ( cartprodfstpairEq = $true )
& ( ksndpairEq = $true )
& ( breln1all2 = $true )
& ( prop2set2propI = $true )
& ( contrasubsetT2 = $true )
& ( inPowerset = $true )
& ( quantDeMorgan1 = $true )
& ( breln1unionI = $true )
& ( setunionE2 = $true )
& ( symdiffIneg2 = $true )
& ( subsetE = $true )
& ( subsetE2 = $true )
& ( descrp = $true )
& ( breln1compEex = $true )
& ( woz1_3 = $true )
& ( powersetE = $true )
& ( woz13rule2 = $true )
& ( singletonsubset = $true )
& ( setextAx = $true )
& ( binunionTEcontra = $true )
& ( noeltsimpempty = $true )
& ( ex1I2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42])],[f1291,f1443]) ).
thf(f1443,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
& ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
=> ( ( ( in @ sK41
@ ( image1 @ sK40
@ ^ [Y0: $i] : ( sK42 @ Y0 ) ) )
= $true )
& ! [X3: $i] :
( ( ( sK42 @ X3 )
!= sK41 )
| ( ( in @ X3 @ sK40 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1291,plain,
( ( binunionT_lem = $true )
& ( setadjoinE = $true )
& ( powersetE1 = $true )
& ( eqinunit = $true )
& ( cartprodpairin = $true )
& ( complementT_lem = $true )
& ( cartprodmempaircEq = $true )
& ( notinemptyset = $true )
& ( binintersectSubset1 = $true )
& ( omega0Ax = $true )
& ( setadjoinIR = $true )
& ( eqbreln = $true )
& ( iffalseProp1 = $true )
& ( binintersectSubset3 = $true )
& ( binunionIR = $true )
& ( cartprodfstin = $true )
& ( funcGraphProp2 = $true )
& ( breln1all1 = $true )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( contrasubsetT3 = $true )
& ( ap2apEq2 = $true )
& ( inCongP = $true )
& ( ubforcartprodlem1 = $true )
& ? [X0: $i,X1: $i,X2: $i > $i] :
( ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
& ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( inIntersectImpInUnion = $true )
& ( binintersectT_lem = $true )
& ( demorgan2b = $true )
& ( disjointsetsI1 = $true )
& ( emptyinPowerset = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( breln1compI = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( dpsetconstrSub = $true )
& ( woz13rule3 = $true )
& ( binunionEcases = $true )
& ( singletonsswitch = $true )
& ( complementTE1 = $true )
& ( setunionsingleton1 = $true )
& ( exuI3 = $true )
& ( powersetI1 = $true )
& ( setukpairinjR1 = $true )
& ( demorgan2a2 = $true )
& ( ubforcartprodlem3 = $true )
& ( image1Equiv = $true )
& ( subsetRefl = $true )
& ( symdiffI2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( kfstpairEq = $true )
& ( quantDeMorgan2 = $true )
& ( setminusI = $true )
& ( contraSubsetComplement = $true )
& ( woz2W = $true )
& ( demorgan1b = $true )
& ( notsubsetI = $true )
& ( woz1_5 = $true )
& ( breln1SetBreln1 = $true )
& ( setunionE = $true )
& ( symdiffE = $true )
& ( setadjoinAx = $true )
& ( upairset2IR = $true )
& ( contrasubsetT = $true )
& ( binintersectSubset4 = $true )
& ( exuI2 = $true )
& ( upairset2E = $true )
& ( theprop = $true )
& ( breln1compE = $true )
& ( notequalI2 = $true )
& ( setukpairinjR11 = $true )
& ( exuI1 = $true )
& ( exuE1 = $true )
& ( contrasubsetT1 = $true )
& ( demorgan2b2 = $true )
& ( emptyI = $true )
& ( cartprodpairmemEL = $true )
& ( emptyE1 = $true )
& ( emptysetAx = $true )
& ( setunion__Cong = $true )
& ( brelnall2 = $true )
& ( funcinfuncset = $true )
& ( exu__Cong = $true )
& ( woz1_4 = $true )
& ( powersetAx = $true )
& ( image1Ex1 = $true )
& ( lamp = $true )
& ( powersetTI1 = $true )
& ( setextT = $true )
& ( cartprodsndin = $true )
& ( powersetT_lem = $true )
& ( complementImpComplementIntersect = $true )
& ( binunionLsub = $true )
& ( binintersectER = $true )
& ( singletoninpowunion = $true )
& ( eta2 = $true )
& ( ap2p = $true )
& ( subPowSU = $true )
& ( ex1I = $true )
& ( beta2 = $true )
& ( ifSingleton = $true )
& ( kpairp = $true )
& ( vacuousDall = $true )
& ( binunionE = $true )
& ( subsetI2 = $true )
& ( emptysetimpfalse = $true )
& ( setunionI = $true )
& ( image1Ex = $true )
& ( omega__Cong = $true )
& ( iffalseProp2 = $true )
& ( replAx = $true )
& ( cartprodpairsurjEq = $true )
& ( setadjoinSub = $true )
& ( setOfPairsIsBReln = $true )
& ( iftrueProp2 = $true )
& ( nonemptyI1 = $true )
& ( exuE3e = $true )
& ( subset2powerset = $true )
& ( binunionTE = $true )
& ( wellorderingAx = $true )
& ( upairequniteq = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjL1 = $true )
& ( woz1_1 = $true )
& ( setminusILneg = $true )
& ( subsetTI = $true )
& ( woz2A = $true )
& ( setukpairIL = $true )
& ( setOfPairsIsBReln1 = $true )
& ( setminusER = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setextsub = $true )
& ( setunionAx = $true )
& ( doubleComplementI1 = $true )
& ( complementTnotintersectT = $true )
& ( demorgan2 = $true )
& ( setext = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( breln1unionCommutes = $true )
& ( quantDeMorgan4 = $true )
& ( upairinpowunion = $true )
& ( ksndsingleton = $true )
& ( funcext2 = $true )
& ( lam2p = $true )
& ( binintersectTERcontra = $true )
& ( breln1unionEcases = $true )
& ( subsetTrans = $true )
& ( exuE2 = $true )
& ( doubleComplementE1 = $true )
& ( breln1invE = $true )
& ( setminusERneg = $true )
& ( theeq = $true )
& ( setukpairinjR12 = $true )
& ( demorgan2a = $true )
& ( setbeta = $true )
& ( powerset__Cong = $true )
& ( ap2apEq1 = $true )
& ( woz2B = $true )
& ( ubforcartprodlem2 = $true )
& ( dpsetconstrEL1 = $true )
& ( funcext = $true )
& ( binintersectTELcontra = $true )
& ( setminusIRneg = $true )
& ( doubleComplementSub1 = $true )
& ( funcGraphProp3 = $true )
& ( setukpairinjR = $true )
& ( brelnall1 = $true )
& ( notequalI1 = $true )
& ( nonemptyI = $true )
& ( eqbreln1 = $true )
& ( setminusSubset2 = $true )
& ( powersetTE1 = $true )
& ( breln1invI = $true )
& ( in__Cong = $true )
& ( cartprodmempair = $true )
& ( breln1compprop = $true )
& ( singletonsuniq = $true )
& ( descr__Cong = $true )
& ( setminusSubset1 = $true )
& ( complementTcontraSubset = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( dsetconstrER = $true )
& ( setminusT_lem = $true )
& ( cartprodmempair1 = $true )
& ( eqimpsubset2 = $true )
& ( ex1E1 = $true )
& ( kpairiskpair = $true )
& ( subbreln = $true )
& ( kpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( iftrueProp1 = $true )
& ( secondinupair = $true )
& ( lam2lamEq = $true )
& ( beta1 = $true )
& ( woz13rule0 = $true )
& ( setminusLsub = $true )
& ( inIntersectImpInUnion2 = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrI = $true )
& ( eta1 = $true )
& ( symdiffIneg1 = $true )
& ( funcGraphProp1 = $true )
& ( sepInPowerset = $true )
& ( binintersectLsub = $true )
& ( woz13rule4 = $true )
& ( subbreln1 = $true )
& ( woz2Ex = $true )
& ( lamProp = $true )
& ( prop2setI = $true )
& ( setukpairinjL2 = $true )
& ( funcImageSingleton = $true )
& ( binintersectSubset2 = $true )
& ( setukpairinjR2 = $true )
& ( cartprodpairmemER = $true )
& ( ex1E2 = $true )
& ( dpsetconstrI = $true )
& ( eqimpsubset1 = $true )
& ( emptyinunitempty = $true )
& ( nonemptyE1 = $true )
& ( foundationAx = $true )
& ( app = $true )
& ( iftrueorfalse = $true )
& ( prop2setE = $true )
& ( binintersectI = $true )
& ( choice2fnsingleton = $true )
& ( singletoninpowerset = $true )
& ( setunionsingleton = $true )
& ( dpsetconstrERa = $true )
& ( setadjoin__Cong = $true )
& ( uniqinunit = $true )
& ( exuE3u = $true )
& ( demorgan1 = $true )
& ( dpsetconstrEL2 = $true )
& ( setminusELneg = $true )
& ( kfstsingleton = $true )
& ( doubleComplementEq = $true )
& ( iftrue = $true )
& ( symdiffI1 = $true )
& ( notdexE = $true )
& ( binunionTILcontra = $true )
& ( powersetsubset = $true )
& ( demorgan2a1 = $true )
& ( exuEu = $true )
& ( binunionRsub = $true )
& ( iffalse = $true )
& ( quantDeMorgan3 = $true )
& ( ifp = $true )
& ( funcGraphProp4 = $true )
& ( upairsetIL = $true )
& ( nonemptyImpWitness = $true )
& ( setukpairIR = $true )
& ( binintersectRsub = $true )
& ( sepSubset = $true )
& ( notdallE = $true )
& ( woz1_2 = $true )
& ( binintersectSubset5 = $true )
& ( binunionTIRcontra = $true )
& ( funcextLem = $true )
& ( notinsingleton = $true )
& ( subsetI1 = $true )
& ( infuncsetfunc = $true )
& ( upairsetIR = $true )
& ( emptyset__Cong = $true )
& ( omegaIndAx = $true )
& ( doubleComplementSub2 = $true )
& ( apProp = $true )
& ( setadjoinOr = $true )
& ( setukpairinjL = $true )
& ( singletonprop = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( bs114d = $true )
& ( setminusEL = $true )
& ( binintersectEL = $true )
& ( breln1unionE = $true )
& ( demorgan1a = $true )
& ( breln1unionprop = $true )
& ( breln1unionIR = $true )
& ( setadjoinIL = $true )
& ( emptysetsubset = $true )
& ( emptysetE = $true )
& ( woz13rule1 = $true )
& ( breln1unionIL = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( setunionsingleton2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( upairsubunion = $true )
& ( binunionIL = $true )
& ( dpsetconstrER = $true )
& ( dsetconstr__Cong = $true )
& ( breln1invprop = $true )
& ( complementTI1 = $true )
& ( cartprodfstpairEq = $true )
& ( ksndpairEq = $true )
& ( breln1all2 = $true )
& ( prop2set2propI = $true )
& ( contrasubsetT2 = $true )
& ( inPowerset = $true )
& ( quantDeMorgan1 = $true )
& ( breln1unionI = $true )
& ( setunionE2 = $true )
& ( symdiffIneg2 = $true )
& ( subsetE = $true )
& ( subsetE2 = $true )
& ( descrp = $true )
& ( breln1compEex = $true )
& ( woz1_3 = $true )
& ( powersetE = $true )
& ( woz13rule2 = $true )
& ( singletonsubset = $true )
& ( setextAx = $true )
& ( binunionTEcontra = $true )
& ( noeltsimpempty = $true )
& ( ex1I2 = $true ) ),
inference(flattening,[status(thm)],[f1290]) ).
thf(f1290,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
& ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( image1Equiv = $true )
& ( image1Ex1 = $true )
& ( image1Ex = $true )
& ( woz2B = $true )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1unionEcases = $true )
& ( breln1unionE = $true )
& ( breln1unionI = $true )
& ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ( breln1unionprop = $true )
& ( breln1compEex = $true )
& ( breln1compE = $true )
& ( breln1compI = $true )
& ( breln1compprop = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $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)],[f968]) ).
thf(f968,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 )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
=> ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( X2 @ X3 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f606]) ).
thf(f606,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 )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
=> ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( X2 @ X4 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f605]) ).
thf(f605,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
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ( in @ X1
@ ( image1 @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ? [X4: $i] :
( ( in @ X4 @ X0 )
& ( ( X2 @ X4 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f316]) ).
thf(f316,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
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ! [X3: $i,X1: $i,X12: $i > $i] :
( ( in @ X1
@ ( image1 @ X3
@ ^ [X2: $i] : ( X12 @ X2 ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X3 )
& ( ( X12 @ X2 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f315]) ).
thf(f315,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
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ! [X3: $i,X1: $i,X12: $i > $i] :
( ( in @ X1
@ ( image1 @ X3
@ ^ [X2: $i] : ( X12 @ X2 ) ) )
=> ? [X2: $i] :
( ( in @ X2 @ X3 )
& ( ( X12 @ X2 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c9IygHO5Aa/DTF2THF_16722.p',image1E) ).
thf(f11266,plain,
( ! [X6: $i,X7: $i > $i,X5: $i] :
( ( ( in @ X6 @ ( image1 @ X5 @ X7 ) )
!= $true )
| ( ( X7 @ ( sK516 @ X7 @ X6 @ X5 ) )
= X6 ) )
| ~ spl1056_1360 ),
inference(avatar_component_clause,[status(thm)],[f11265]) ).
thf(f11265,definition,
( spl1056_1360
<=> ! [X6: $i,X5: $i,X7: $i > $i] :
( ( ( in @ X6 @ ( image1 @ X5 @ X7 ) )
!= $true )
| ( ( X7 @ ( sK516 @ X7 @ X6 @ X5 ) )
= X6 ) ) ),
introduced(definition,[new_symbols(naming,[spl1056_1360])],[avatar_definition]) ).
thf(f24516,plain,
( ( ( sK42 @ ( sK516 @ sK42 @ sK41 @ sK40 ) )
!= sK41 )
| ~ spl1056_905 ),
inference(trivial_inequality_removal,[status(thm)],[f24512]) ).
thf(f24512,plain,
( ( ( sK42 @ ( sK516 @ sK42 @ sK41 @ sK40 ) )
!= sK41 )
| ( $true != $true )
| ~ spl1056_905 ),
inference(superposition,[status(thm)],[f3322,f18560]) ).
thf(f18560,plain,
( ( ( in @ ( sK516 @ sK42 @ sK41 @ sK40 ) @ sK40 )
= $true )
| ~ spl1056_905 ),
inference(trivial_inequality_removal,[status(thm)],[f18548]) ).
thf(f18548,plain,
( ( $true != $true )
| ( ( in @ ( sK516 @ sK42 @ sK41 @ sK40 ) @ sK40 )
= $true )
| ~ spl1056_905 ),
inference(superposition,[status(thm)],[f9066,f4831]) ).
thf(f9066,plain,
( ! [X6: $i,X7: $i > $i,X5: $i] :
( ( ( in @ X6 @ ( image1 @ X5 @ X7 ) )
!= $true )
| ( ( in @ ( sK516 @ X7 @ X6 @ X5 ) @ X5 )
= $true ) )
| ~ spl1056_905 ),
inference(avatar_component_clause,[status(thm)],[f9065]) ).
thf(f9065,definition,
( spl1056_905
<=> ! [X6: $i,X5: $i,X7: $i > $i] :
( ( ( in @ X6 @ ( image1 @ X5 @ X7 ) )
!= $true )
| ( ( in @ ( sK516 @ X7 @ X6 @ X5 ) @ X5 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1056_905])],[avatar_definition]) ).
thf(f3322,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK40 )
!= $true )
| ( ( sK42 @ X3 )
!= sK41 ) ),
inference(cnf_transformation,[status(thm)],[f1444]) ).
thf(f12733,plain,
spl1056_265,
inference(avatar_split_clause,[status(thm)],[f3302,f6125]) ).
thf(f6125,definition,
( spl1056_265
<=> ( image1Equiv = $true ) ),
introduced(definition,[new_symbols(naming,[spl1056_265])],[avatar_definition]) ).
thf(f3302,plain,
image1Equiv = $true,
inference(cnf_transformation,[status(thm)],[f1444]) ).
thf(f11267,plain,
( ~ spl1056_265
| spl1056_1360 ),
inference(avatar_split_clause,[status(thm)],[f4834,f11265,f6125]) ).
thf(f4834,plain,
! [X6: $i,X7: $i > $i,X5: $i] :
( ( ( in @ X6 @ ( image1 @ X5 @ X7 ) )
!= $true )
| ( image1Equiv != $true )
| ( ( X7 @ ( sK516 @ X7 @ X6 @ X5 ) )
= X6 ) ),
inference(beta_eta_normalization,[status(thm)],[f4006]) ).
thf(f4006,plain,
! [X6: $i,X7: $i > $i,X5: $i] :
( ( image1Equiv != $true )
| ( ( in @ X6
@ ( image1 @ X5
@ ^ [Y0: $i] : ( X7 @ Y0 ) ) )
!= $true )
| ( ( X7 @ ( sK516 @ X7 @ X6 @ X5 ) )
= X6 ) ),
inference(cnf_transformation,[status(thm)],[f2169]) ).
thf(f2169,plain,
( ( ( image1Equiv = $true )
| ( ( ! [X3: $i] :
( ( sK513
!= ( sK514 @ X3 ) )
| ( $true
!= ( in @ X3 @ sK512 ) ) )
| ( ( in @ sK513
@ ( image1 @ sK512
@ ^ [Y0: $i] : ( sK514 @ Y0 ) ) )
!= $true ) )
& ( ( ( sK513
= ( sK514 @ sK515 ) )
& ( $true
= ( in @ sK515 @ sK512 ) ) )
| ( ( in @ sK513
@ ( image1 @ sK512
@ ^ [Y0: $i] : ( sK514 @ Y0 ) ) )
= $true ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i > $i] :
( ( ( ( in @ X6
@ ( image1 @ X5
@ ^ [Y0: $i] : ( X7 @ Y0 ) ) )
= $true )
| ! [X8: $i] :
( ( ( X7 @ X8 )
!= X6 )
| ( ( in @ X8 @ X5 )
!= $true ) ) )
& ( ( ( ( X7 @ ( sK516 @ X7 @ X6 @ X5 ) )
= X6 )
& ( ( in @ ( sK516 @ X7 @ X6 @ X5 ) @ X5 )
= $true ) )
| ( ( in @ X6
@ ( image1 @ X5
@ ^ [Y0: $i] : ( X7 @ Y0 ) ) )
!= $true ) ) )
| ( image1Equiv != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK512,sK513,sK514,sK515,sK516])],[f2165,f2168,f2167,f2166]) ).
thf(f2166,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ( ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
& ( ? [X4: $i] :
( ( ( X2 @ X4 )
= X1 )
& ( ( in @ X4 @ X0 )
= $true ) )
| ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) )
=> ( ( ! [X3: $i] :
( ( sK513
!= ( sK514 @ X3 ) )
| ( $true
!= ( in @ X3 @ sK512 ) ) )
| ( ( in @ sK513
@ ( image1 @ sK512
@ ^ [Y0: $i] : ( sK514 @ Y0 ) ) )
!= $true ) )
& ( ? [X4: $i] :
( ( sK513
= ( sK514 @ X4 ) )
& ( $true
= ( in @ X4 @ sK512 ) ) )
| ( ( in @ sK513
@ ( image1 @ sK512
@ ^ [Y0: $i] : ( sK514 @ Y0 ) ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2167,plain,
( ? [X4: $i] :
( ( sK513
= ( sK514 @ X4 ) )
& ( $true
= ( in @ X4 @ sK512 ) ) )
=> ( ( sK513
= ( sK514 @ sK515 ) )
& ( $true
= ( in @ sK515 @ sK512 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2168,plain,
! [X5: $i,X6: $i,X7: $i > $i] :
( ? [X9: $i] :
( ( ( X7 @ X9 )
= X6 )
& ( ( in @ X9 @ X5 )
= $true ) )
=> ( ( ( X7 @ ( sK516 @ X7 @ X6 @ X5 ) )
= X6 )
& ( ( in @ ( sK516 @ X7 @ X6 @ X5 ) @ X5 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2165,plain,
( ( ( image1Equiv = $true )
| ? [X0: $i,X1: $i,X2: $i > $i] :
( ( ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
& ( ? [X4: $i] :
( ( ( X2 @ X4 )
= X1 )
& ( ( in @ X4 @ X0 )
= $true ) )
| ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i > $i] :
( ( ( ( in @ X6
@ ( image1 @ X5
@ ^ [Y0: $i] : ( X7 @ Y0 ) ) )
= $true )
| ! [X8: $i] :
( ( ( X7 @ X8 )
!= X6 )
| ( ( in @ X8 @ X5 )
!= $true ) ) )
& ( ? [X9: $i] :
( ( ( X7 @ X9 )
= X6 )
& ( ( in @ X9 @ X5 )
= $true ) )
| ( ( in @ X6
@ ( image1 @ X5
@ ^ [Y0: $i] : ( X7 @ Y0 ) ) )
!= $true ) ) )
| ( image1Equiv != $true ) ) ),
inference(rectify,[status(thm)],[f2164]) ).
thf(f2164,plain,
( ( ( image1Equiv = $true )
| ? [X0: $i,X1: $i,X2: $i > $i] :
( ( ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
& ( ? [X3: $i] :
( ( ( X2 @ X3 )
= X1 )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i > $i] :
( ( ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ! [X3: $i] :
( ( ( X2 @ X3 )
!= X1 )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( ? [X3: $i] :
( ( ( X2 @ X3 )
= X1 )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) ) )
| ( image1Equiv != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f618]) ).
thf(f618,plain,
( ( image1Equiv = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ( ( in @ X1
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
<=> ? [X3: $i] :
( ( ( X2 @ X3 )
= X1 )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f617]) ).
thf(f617,plain,
( image1Equiv
= ( ! [X0: $i,X1: $i,X2: $i > $i] :
( ? [X3: $i] :
( ( ( X2 @ X3 )
= X1 )
& ( in @ X3 @ X0 ) )
<=> ( in @ X1
@ ( image1 @ X0
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f314]) ).
thf(f314,axiom,
( image1Equiv
= ( ! [X3: $i,X1: $i,X12: $i > $i] :
( ? [X2: $i] :
( ( ( X12 @ X2 )
= X1 )
& ( in @ X2 @ X3 ) )
<=> ( in @ X1
@ ( image1 @ X3
@ ^ [X2: $i] : ( X12 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.c9IygHO5Aa/DTF2THF_16722.p',image1Equiv) ).
thf(f9067,plain,
( spl1056_905
| ~ spl1056_265 ),
inference(avatar_split_clause,[status(thm)],[f4895,f6125,f9065]) ).
thf(f4895,plain,
! [X6: $i,X7: $i > $i,X5: $i] :
( ( ( in @ X6 @ ( image1 @ X5 @ X7 ) )
!= $true )
| ( image1Equiv != $true )
| ( ( in @ ( sK516 @ X7 @ X6 @ X5 ) @ X5 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f4005]) ).
thf(f4005,plain,
! [X6: $i,X7: $i > $i,X5: $i] :
( ( ( in @ ( sK516 @ X7 @ X6 @ X5 ) @ X5 )
= $true )
| ( image1Equiv != $true )
| ( ( in @ X6
@ ( image1 @ X5
@ ^ [Y0: $i] : ( X7 @ Y0 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f2169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU796^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n020.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:34:27 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SEU796^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.47 % Domain : Set Theory
% 0.29/0.47 % Problem : More about Functions - Images of Functions
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English : (! A:i.! f:i>i.! x:i.in x (image1 A (^ y:i.f y)) ->
% 0.29/0.47 % (? y:i.in y A & x = f y))
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.47 % Source : [Bro08]
% 0.29/0.47 % Names : ZFC298g [Bro08]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 1.00 v3.7.0
% 0.29/0.47 % Syntax : Number of formulae : 676 ( 314 unt; 361 typ; 314 def)
% 0.29/0.47 % Number of atoms : 1942 ( 453 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 315 ( 6 avg)
% 0.29/0.47 % Number of connectives : 4275 ( 73 ~; 14 |; 52 &;3110 @)
% 0.29/0.47 % ( 17 <=>;1009 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 321 ( 2 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 164 ( 164 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 364 ( 361 usr; 316 con; 0-4 aty)
% 0.29/0.47 % Number of variables : 1113 ( 74 ^; 997 !; 42 ?;1113 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : http://mathgate.info/detsetitem.php?id=419
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(in_type,type,
% 0.29/0.47 in: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(exu_type,type,
% 0.29/0.47 exu: ( $i > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(exu,definition,
% 0.29/0.47 ( exu
% 0.29/0.47 = ( ^ [Xphi: $i > $o] :
% 0.29/0.47 ? [Xx: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setextAx_type,type,
% 0.29/0.47 setextAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setextAx,definition,
% 0.29/0.47 ( setextAx
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 <=> ( in @ Xx @ B ) )
% 0.29/0.47 => ( A = B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset_type,type,
% 0.29/0.47 emptyset: $i ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetAx_type,type,
% 0.29/0.47 emptysetAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetAx,definition,
% 0.29/0.47 ( emptysetAx
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoin_type,type,
% 0.29/0.47 setadjoin: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinAx_type,type,
% 0.29/0.47 setadjoinAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinAx,definition,
% 0.29/0.47 ( setadjoinAx
% 0.29/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.47 <=> ( ( Xy = Xx )
% 0.29/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powerset_type,type,
% 0.29/0.47 powerset: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(powersetAx_type,type,
% 0.29/0.47 powersetAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetAx,definition,
% 0.29/0.47 ( powersetAx
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.47 <=> ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunion_type,type,
% 0.29/0.47 setunion: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(setunionAx_type,type,
% 0.29/0.47 setunionAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionAx,definition,
% 0.29/0.47 ( setunionAx
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.47 <=> ? [B: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omega_type,type,
% 0.29/0.47 omega: $i ).
% 0.29/0.47
% 0.29/0.47 thf(omega0Ax_type,type,
% 0.29/0.47 omega0Ax: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omega0Ax,definition,
% 0.29/0.47 ( omega0Ax
% 0.29/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omegaSAx_type,type,
% 0.29/0.47 omegaSAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omegaSAx,definition,
% 0.29/0.47 ( omegaSAx
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ omega )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omegaIndAx_type,type,
% 0.29/0.47 omegaIndAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omegaIndAx,definition,
% 0.29/0.47 ( omegaIndAx
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( ( in @ emptyset @ A )
% 0.29/0.47 & ! [Xx: $i] :
% 0.29/0.47 ( ( ( in @ Xx @ omega )
% 0.29/0.47 & ( in @ Xx @ A ) )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ omega )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(replAx_type,type,
% 0.29/0.47 replAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(replAx,definition,
% 0.29/0.47 ( replAx
% 0.29/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.47 => ? [B: $i] :
% 0.29/0.47 ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 <=> ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(foundationAx_type,type,
% 0.29/0.47 foundationAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(foundationAx,definition,
% 0.29/0.47 ( foundationAx
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.47 => ? [B: $i] :
% 0.29/0.47 ( ( in @ B @ A )
% 0.29/0.47 & ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(wellorderingAx_type,type,
% 0.29/0.47 wellorderingAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(wellorderingAx,definition,
% 0.29/0.47 ( wellorderingAx
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ? [B: $i] :
% 0.29/0.47 ( ! [C: $i] :
% 0.29/0.47 ( ( in @ C @ B )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ C )
% 0.29/0.47 => ( in @ Xx @ A ) ) )
% 0.29/0.47 & ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( ( in @ Xx @ A )
% 0.29/0.47 & ( in @ Xy @ A ) )
% 0.29/0.47 => ( ! [C: $i] :
% 0.29/0.47 ( ( in @ C @ B )
% 0.29/0.47 => ( ( in @ Xx @ C )
% 0.29/0.47 <=> ( in @ Xy @ C ) ) )
% 0.29/0.47 => ( Xx = Xy ) ) )
% 0.29/0.47 & ! [C: $i,D: $i] :
% 0.29/0.47 ( ( ( in @ C @ B )
% 0.29/0.47 & ( in @ D @ B ) )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ C )
% 0.29/0.47 => ( in @ Xx @ D ) )
% 0.29/0.47 | ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ D )
% 0.29/0.47 => ( in @ Xx @ C ) ) ) )
% 0.29/0.47 & ! [C: $i] :
% 0.29/0.47 ( ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ C )
% 0.29/0.47 => ( in @ Xx @ A ) )
% 0.29/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.47 => ? [D: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ D @ B )
% 0.29/0.47 & ( in @ Xx @ C )
% 0.29/0.47 & ~ ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ D )
% 0.29/0.47 & ( in @ Xy @ C ) )
% 0.29/0.47 & ! [E: $i] :
% 0.29/0.47 ( ( in @ E @ B )
% 0.29/0.47 => ( ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ E )
% 0.29/0.47 => ( in @ Xy @ D ) )
% 0.29/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(descr_type,type,
% 0.29/0.47 descr: ( $i > $o ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(descrp_type,type,
% 0.29/0.47 descrp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(descrp,definition,
% 0.29/0.47 ( descrp
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ( Xphi
% 0.29/0.47 @ ( descr
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr_type,type,
% 0.29/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrI_type,type,
% 0.29/0.47 dsetconstrI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrI,definition,
% 0.29/0.47 ( dsetconstrI
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( in @ Xx
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrEL_type,type,
% 0.29/0.47 dsetconstrEL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrEL,definition,
% 0.29/0.47 ( dsetconstrEL
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrER_type,type,
% 0.29/0.47 dsetconstrER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrER,definition,
% 0.29/0.47 ( dsetconstrER
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE1_type,type,
% 0.29/0.47 exuE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE1,definition,
% 0.29/0.47 ( exuE1
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set_type,type,
% 0.29/0.47 prop2set: $o > $i ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setE_type,type,
% 0.29/0.47 prop2setE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setE,definition,
% 0.29/0.47 ( prop2setE
% 0.29/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.47 => Xphi ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetE_type,type,
% 0.29/0.47 emptysetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetE,definition,
% 0.29/0.47 ( emptysetE
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ emptyset )
% 0.29/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetimpfalse_type,type,
% 0.29/0.47 emptysetimpfalse: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetimpfalse,definition,
% 0.29/0.47 ( emptysetimpfalse
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ emptyset )
% 0.29/0.47 => $false ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notinemptyset_type,type,
% 0.29/0.47 notinemptyset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notinemptyset,definition,
% 0.29/0.47 ( notinemptyset
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE3e_type,type,
% 0.29/0.47 exuE3e: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE3e,definition,
% 0.29/0.47 ( exuE3e
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setext_type,type,
% 0.29/0.47 setext: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setext,definition,
% 0.29/0.47 ( setext
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) )
% 0.29/0.47 => ( A = B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyI_type,type,
% 0.29/0.47 emptyI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyI,definition,
% 0.29/0.47 ( emptyI
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ~ ( in @ Xx @ A )
% 0.29/0.47 => ( A = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(noeltsimpempty_type,type,
% 0.29/0.47 noeltsimpempty: $o ).
% 0.29/0.47
% 0.29/0.47 thf(noeltsimpempty,definition,
% 0.29/0.47 ( noeltsimpempty
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ~ ( in @ Xx @ A )
% 0.29/0.47 => ( A = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setbeta_type,type,
% 0.29/0.47 setbeta: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setbeta,definition,
% 0.29/0.47 ( setbeta
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(nonempty_type,type,
% 0.29/0.47 nonempty: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(nonempty,definition,
% 0.29/0.47 ( nonempty
% 0.29/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyE1_type,type,
% 0.29/0.47 nonemptyE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyE1,definition,
% 0.29/0.47 ( nonemptyE1
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( nonempty @ A )
% 0.29/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyI_type,type,
% 0.29/0.47 nonemptyI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyI,definition,
% 0.29/0.47 ( nonemptyI
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( nonempty
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyI1_type,type,
% 0.29/0.47 nonemptyI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyI1,definition,
% 0.29/0.47 ( nonemptyI1
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinIL_type,type,
% 0.29/0.47 setadjoinIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinIL,definition,
% 0.29/0.47 ( setadjoinIL
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyinunitempty_type,type,
% 0.29/0.47 emptyinunitempty: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyinunitempty,definition,
% 0.29/0.47 ( emptyinunitempty
% 0.29/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinIR_type,type,
% 0.29/0.47 setadjoinIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinIR,definition,
% 0.29/0.47 ( setadjoinIR
% 0.29/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinE_type,type,
% 0.29/0.47 setadjoinE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinE,definition,
% 0.29/0.47 ( setadjoinE
% 0.29/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ( ( Xy = Xx )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => ( ( ( in @ Xy @ A )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinOr_type,type,
% 0.29/0.47 setadjoinOr: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinOr,definition,
% 0.29/0.47 ( setadjoinOr
% 0.29/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.47 => ( ( Xy = Xx )
% 0.29/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setoftrueEq_type,type,
% 0.29/0.47 setoftrueEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setoftrueEq,definition,
% 0.29/0.47 ( setoftrueEq
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : $true )
% 0.29/0.47 = A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI_type,type,
% 0.29/0.47 powersetI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI,definition,
% 0.29/0.47 ( powersetI
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) )
% 0.29/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyinPowerset_type,type,
% 0.29/0.47 emptyinPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyinPowerset,definition,
% 0.29/0.47 ( emptyinPowerset
% 0.29/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyInPowerset_type,type,
% 0.29/0.47 emptyInPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyInPowerset,definition,
% 0.29/0.47 ( emptyInPowerset
% 0.29/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE_type,type,
% 0.29/0.47 powersetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE,definition,
% 0.29/0.47 ( powersetE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionI_type,type,
% 0.29/0.47 setunionI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionI,definition,
% 0.29/0.47 ( setunionI
% 0.29/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( ( in @ B @ A )
% 0.29/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE_type,type,
% 0.29/0.47 setunionE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE,definition,
% 0.29/0.47 ( setunionE
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ! [B: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( ( in @ B @ A )
% 0.29/0.47 => Xphi ) )
% 0.29/0.47 => Xphi ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subPowSU_type,type,
% 0.29/0.47 subPowSU: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subPowSU,definition,
% 0.29/0.47 ( subPowSU
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE2_type,type,
% 0.29/0.47 exuE2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE2,definition,
% 0.29/0.47 ( exuE2
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyImpWitness_type,type,
% 0.29/0.47 nonemptyImpWitness: $o ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyImpWitness,definition,
% 0.29/0.47 ( nonemptyImpWitness
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( nonempty @ A )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & $true ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(uniqinunit_type,type,
% 0.29/0.47 uniqinunit: $o ).
% 0.29/0.47
% 0.29/0.47 thf(uniqinunit,definition,
% 0.29/0.47 ( uniqinunit
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notinsingleton_type,type,
% 0.29/0.47 notinsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notinsingleton,definition,
% 0.29/0.47 ( notinsingleton
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx != Xy )
% 0.29/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqinunit_type,type,
% 0.29/0.47 eqinunit: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqinunit,definition,
% 0.29/0.47 ( eqinunit
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsswitch_type,type,
% 0.29/0.47 singletonsswitch: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsswitch,definition,
% 0.29/0.47 ( singletonsswitch
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetE_type,type,
% 0.29/0.47 upairsetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetE,definition,
% 0.29/0.47 ( upairsetE
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.47 => ( ( Xz = Xx )
% 0.29/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIL_type,type,
% 0.29/0.47 upairsetIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIL,definition,
% 0.29/0.47 ( upairsetIL
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIR_type,type,
% 0.29/0.47 upairsetIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIR,definition,
% 0.29/0.47 ( upairsetIR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyE1_type,type,
% 0.29/0.47 emptyE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyE1,definition,
% 0.29/0.47 ( emptyE1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ( ( ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = emptyset )
% 0.29/0.47 => $false ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(vacuousDall_type,type,
% 0.29/0.47 vacuousDall: $o ).
% 0.29/0.47
% 0.29/0.47 thf(vacuousDall,definition,
% 0.29/0.47 ( vacuousDall
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ emptyset )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan1_type,type,
% 0.29/0.47 quantDeMorgan1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan1,definition,
% 0.29/0.47 ( quantDeMorgan1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan2_type,type,
% 0.29/0.47 quantDeMorgan2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan2,definition,
% 0.29/0.47 ( quantDeMorgan2
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) )
% 0.29/0.47 => ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan3_type,type,
% 0.29/0.47 quantDeMorgan3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan3,definition,
% 0.29/0.47 ( quantDeMorgan3
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan4_type,type,
% 0.29/0.47 quantDeMorgan4: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan4,definition,
% 0.29/0.47 ( quantDeMorgan4
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) )
% 0.29/0.47 => ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setI_type,type,
% 0.29/0.47 prop2setI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setI,definition,
% 0.29/0.47 ( prop2setI
% 0.29/0.47 = ( ! [Xphi: $o] :
% 0.29/0.47 ( Xphi
% 0.29/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(set2prop_type,type,
% 0.29/0.47 set2prop: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set2propI_type,type,
% 0.29/0.47 prop2set2propI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set2propI,definition,
% 0.29/0.47 ( prop2set2propI
% 0.29/0.47 = ( ! [Xphi: $o] :
% 0.29/0.47 ( Xphi
% 0.29/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notdexE_type,type,
% 0.29/0.47 notdexE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notdexE,definition,
% 0.29/0.47 ( notdexE
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notdallE_type,type,
% 0.29/0.47 notdallE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notdallE,definition,
% 0.29/0.47 ( notdallE
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI1_type,type,
% 0.29/0.47 exuI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI1,definition,
% 0.29/0.47 ( exuI1
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI3_type,type,
% 0.29/0.47 exuI3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI3,definition,
% 0.29/0.47 ( exuI3
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI2_type,type,
% 0.29/0.47 exuI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI2,definition,
% 0.29/0.47 ( exuI2
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 <=> ( Xy = Xx ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(inCongP_type,type,
% 0.29/0.47 inCongP: $o ).
% 0.29/0.47
% 0.29/0.47 thf(inCongP,definition,
% 0.29/0.47 ( inCongP
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(in__Cong_type,type,
% 0.29/0.47 in__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(in__Cong,definition,
% 0.29/0.47 ( in__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE3u_type,type,
% 0.29/0.47 exuE3u: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE3u,definition,
% 0.29/0.47 ( exuE3u
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exu__Cong_type,type,
% 0.29/0.47 exu__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exu__Cong,definition,
% 0.29/0.47 ( exu__Cong
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 <=> ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset__Cong_type,type,
% 0.29/0.47 emptyset__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset__Cong,definition,
% 0.29/0.47 ( emptyset__Cong
% 0.29/0.47 = ( emptyset = emptyset ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoin__Cong_type,type,
% 0.29/0.47 setadjoin__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoin__Cong,definition,
% 0.29/0.47 ( setadjoin__Cong
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ! [Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( Xz = Xu )
% 0.29/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powerset__Cong_type,type,
% 0.29/0.47 powerset__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powerset__Cong,definition,
% 0.29/0.47 ( powerset__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( powerset @ A )
% 0.29/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunion__Cong_type,type,
% 0.29/0.47 setunion__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunion__Cong,definition,
% 0.29/0.47 ( setunion__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( setunion @ A )
% 0.29/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omega__Cong_type,type,
% 0.29/0.47 omega__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omega__Cong,definition,
% 0.29/0.47 ( omega__Cong
% 0.29/0.47 = ( omega = omega ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuEu_type,type,
% 0.29/0.47 exuEu: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuEu,definition,
% 0.29/0.47 ( exuEu
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(descr__Cong_type,type,
% 0.29/0.47 descr__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(descr__Cong,definition,
% 0.29/0.47 ( descr__Cong
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.47 => ( ( descr
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = ( descr
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr__Cong_type,type,
% 0.29/0.47 dsetconstr__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr__Cong,definition,
% 0.29/0.47 ( dsetconstr__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.47 => ( ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subset_type,type,
% 0.29/0.47 subset: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(disjoint_type,type,
% 0.29/0.47 disjoint: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(setsmeet_type,type,
% 0.29/0.47 setsmeet: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI1_type,type,
% 0.29/0.47 subsetI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI1,definition,
% 0.29/0.47 ( subsetI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset2_type,type,
% 0.29/0.47 eqimpsubset2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset2,definition,
% 0.29/0.47 ( eqimpsubset2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset1_type,type,
% 0.29/0.47 eqimpsubset1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset1,definition,
% 0.29/0.47 ( eqimpsubset1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI2_type,type,
% 0.29/0.47 subsetI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI2,definition,
% 0.29/0.47 ( subsetI2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetsubset_type,type,
% 0.29/0.47 emptysetsubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetsubset,definition,
% 0.29/0.47 ( emptysetsubset
% 0.29/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE_type,type,
% 0.29/0.47 subsetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE,definition,
% 0.29/0.47 ( subsetE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE2_type,type,
% 0.29/0.47 subsetE2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE2,definition,
% 0.29/0.47 ( subsetE2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notsubsetI_type,type,
% 0.29/0.47 notsubsetI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notsubsetI,definition,
% 0.29/0.47 ( notsubsetI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI1_type,type,
% 0.29/0.47 notequalI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI1,definition,
% 0.29/0.47 ( notequalI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ~ ( subset @ A @ B )
% 0.29/0.47 => ( A != B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI2_type,type,
% 0.29/0.47 notequalI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI2,definition,
% 0.29/0.47 ( notequalI2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ( A != B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetRefl_type,type,
% 0.29/0.47 subsetRefl: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetRefl,definition,
% 0.29/0.47 ( subsetRefl
% 0.29/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetTrans_type,type,
% 0.29/0.47 subsetTrans: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetTrans,definition,
% 0.29/0.47 ( subsetTrans
% 0.29/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( subset @ B @ C )
% 0.29/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub_type,type,
% 0.29/0.47 setadjoinSub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub,definition,
% 0.29/0.47 ( setadjoinSub
% 0.29/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub2_type,type,
% 0.29/0.47 setadjoinSub2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub2,definition,
% 0.29/0.47 ( setadjoinSub2
% 0.29/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subset2powerset_type,type,
% 0.29/0.47 subset2powerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subset2powerset,definition,
% 0.29/0.47 ( subset2powerset
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setextsub_type,type,
% 0.29/0.47 setextsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setextsub,definition,
% 0.29/0.47 ( setextsub
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( subset @ B @ A )
% 0.29/0.47 => ( A = B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetemptysetimpeq_type,type,
% 0.29/0.47 subsetemptysetimpeq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetemptysetimpeq,definition,
% 0.29/0.47 ( subsetemptysetimpeq
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( subset @ A @ emptyset )
% 0.29/0.47 => ( A = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI1_type,type,
% 0.29/0.47 powersetI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI1,definition,
% 0.29/0.47 ( powersetI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ B @ A )
% 0.29/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE1_type,type,
% 0.29/0.47 powersetE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE1,definition,
% 0.29/0.47 ( powersetE1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(inPowerset_type,type,
% 0.29/0.47 inPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(inPowerset,definition,
% 0.29/0.47 ( inPowerset
% 0.29/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetsubset_type,type,
% 0.29/0.47 powersetsubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetsubset,definition,
% 0.29/0.47 ( powersetsubset
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(sepInPowerset_type,type,
% 0.29/0.47 sepInPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(sepInPowerset,definition,
% 0.29/0.47 ( sepInPowerset
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( in
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(sepSubset_type,type,
% 0.29/0.47 sepSubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(sepSubset,definition,
% 0.29/0.47 ( sepSubset
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( subset
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunion_type,type,
% 0.29/0.47 binunion: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIL_type,type,
% 0.29/0.47 binunionIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIL,definition,
% 0.29/0.47 ( binunionIL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2IR_type,type,
% 0.29/0.47 upairset2IR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2IR,definition,
% 0.29/0.47 ( upairset2IR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIR_type,type,
% 0.29/0.47 binunionIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIR,definition,
% 0.29/0.47 ( binunionIR
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionEcases_type,type,
% 0.29/0.47 binunionEcases: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionEcases,definition,
% 0.29/0.47 ( binunionEcases
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.47 => ( ( ( in @ Xx @ A )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => ( ( ( in @ Xx @ B )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionE_type,type,
% 0.29/0.47 binunionE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionE,definition,
% 0.29/0.47 ( binunionE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionLsub_type,type,
% 0.29/0.47 binunionLsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionLsub,definition,
% 0.29/0.47 ( binunionLsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionRsub_type,type,
% 0.29/0.47 binunionRsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionRsub,definition,
% 0.29/0.47 ( binunionRsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersect_type,type,
% 0.29/0.47 binintersect: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectI_type,type,
% 0.29/0.47 binintersectI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectI,definition,
% 0.29/0.47 ( binintersectI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset5_type,type,
% 0.29/0.47 binintersectSubset5: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset5,definition,
% 0.29/0.47 ( binintersectSubset5
% 0.29/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.47 ( ( subset @ C @ A )
% 0.29/0.47 => ( ( subset @ C @ B )
% 0.29/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectEL_type,type,
% 0.29/0.47 binintersectEL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectEL,definition,
% 0.29/0.47 ( binintersectEL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectLsub_type,type,
% 0.29/0.47 binintersectLsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectLsub,definition,
% 0.29/0.47 ( binintersectLsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset2_type,type,
% 0.29/0.47 binintersectSubset2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset2,definition,
% 0.29/0.47 ( binintersectSubset2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( binintersect @ A @ B )
% 0.29/0.47 = A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset3_type,type,
% 0.29/0.47 binintersectSubset3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset3,definition,
% 0.29/0.47 ( binintersectSubset3
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( ( binintersect @ A @ B )
% 0.29/0.47 = B )
% 0.29/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectER_type,type,
% 0.29/0.47 binintersectER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectER,definition,
% 0.29/0.47 ( binintersectER
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(disjointsetsI1_type,type,
% 0.29/0.47 disjointsetsI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(disjointsetsI1,definition,
% 0.29/0.47 ( disjointsetsI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( in @ Xx @ B ) )
% 0.29/0.47 => ( ( binintersect @ A @ B )
% 0.29/0.47 = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectRsub_type,type,
% 0.29/0.47 binintersectRsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectRsub,definition,
% 0.29/0.47 ( binintersectRsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset4_type,type,
% 0.29/0.47 binintersectSubset4: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset4,definition,
% 0.29/0.47 ( binintersectSubset4
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ B @ A )
% 0.29/0.47 => ( ( binintersect @ A @ B )
% 0.29/0.47 = B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset1_type,type,
% 0.29/0.47 binintersectSubset1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset1,definition,
% 0.29/0.47 ( binintersectSubset1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( ( binintersect @ A @ B )
% 0.29/0.47 = A )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(bs114d_type,type,
% 0.29/0.47 bs114d: $o ).
% 0.29/0.47
% 0.29/0.47 thf(bs114d,definition,
% 0.29/0.47 ( bs114d
% 0.29/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(regular_type,type,
% 0.29/0.47 regular: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminus_type,type,
% 0.29/0.47 setminus: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(setminusI_type,type,
% 0.29/0.47 setminusI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusI,definition,
% 0.29/0.47 ( setminusI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusEL_type,type,
% 0.29/0.47 setminusEL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusEL,definition,
% 0.29/0.47 ( setminusEL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusER_type,type,
% 0.29/0.47 setminusER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusER,definition,
% 0.29/0.47 ( setminusER
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusSubset2_type,type,
% 0.29/0.47 setminusSubset2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusSubset2,definition,
% 0.29/0.47 ( setminusSubset2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( setminus @ A @ B )
% 0.29/0.47 = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusERneg_type,type,
% 0.29/0.47 setminusERneg: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusERneg,definition,
% 0.29/0.47 ( setminusERneg
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusELneg_type,type,
% 0.29/0.47 setminusELneg: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusELneg,definition,
% 0.29/0.47 ( setminusELneg
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusILneg_type,type,
% 0.29/0.47 setminusILneg: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusILneg,definition,
% 0.29/0.47 ( setminusILneg
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ A )
% 0.29/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusIRneg_type,type,
% 0.29/0.47 setminusIRneg: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusIRneg,definition,
% 0.29/0.47 ( setminusIRneg
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusLsub_type,type,
% 0.29/0.47 setminusLsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusLsub,definition,
% 0.29/0.47 ( setminusLsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusSubset1_type,type,
% 0.29/0.47 setminusSubset1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusSubset1,definition,
% 0.29/0.47 ( setminusSubset1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( ( setminus @ A @ B )
% 0.29/0.47 = emptyset )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiff_type,type,
% 0.29/0.47 symdiff: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffE_type,type,
% 0.29/0.47 symdiffE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffE,definition,
% 0.29/0.47 ( symdiffE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => Xphi ) )
% 0.29/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => Xphi ) )
% 0.29/0.47 => Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffI1_type,type,
% 0.29/0.47 symdiffI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffI1,definition,
% 0.29/0.47 ( symdiffI1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffI2_type,type,
% 0.29/0.47 symdiffI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffI2,definition,
% 0.29/0.47 ( symdiffI2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffIneg1_type,type,
% 0.29/0.47 symdiffIneg1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffIneg1,definition,
% 0.29/0.47 ( symdiffIneg1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffIneg2_type,type,
% 0.29/0.47 symdiffIneg2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffIneg2,definition,
% 0.29/0.47 ( symdiffIneg2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(iskpair_type,type,
% 0.29/0.47 iskpair: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(secondinupair_type,type,
% 0.29/0.47 secondinupair: $o ).
% 0.29/0.47
% 0.29/0.47 thf(secondinupair,definition,
% 0.29/0.47 ( secondinupair
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairIL_type,type,
% 0.29/0.47 setukpairIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairIL,definition,
% 0.29/0.47 ( setukpairIL
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairIR_type,type,
% 0.29/0.47 setukpairIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairIR,definition,
% 0.29/0.47 ( setukpairIR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kpairiskpair_type,type,
% 0.29/0.47 kpairiskpair: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kpairiskpair,definition,
% 0.29/0.47 ( kpairiskpair
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kpair_type,type,
% 0.29/0.47 kpair: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(kpairp_type,type,
% 0.29/0.47 kpairp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kpairp,definition,
% 0.29/0.47 ( kpairp
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprod_type,type,
% 0.29/0.47 cartprod: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsubset_type,type,
% 0.29/0.47 singletonsubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsubset,definition,
% 0.29/0.47 ( singletonsubset
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletoninpowerset_type,type,
% 0.29/0.47 singletoninpowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletoninpowerset,definition,
% 0.29/0.47 ( singletoninpowerset
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletoninpowunion_type,type,
% 0.29/0.47 singletoninpowunion: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletoninpowunion,definition,
% 0.29/0.47 ( singletoninpowunion
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2E_type,type,
% 0.29/0.47 upairset2E: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2E,definition,
% 0.29/0.47 ( upairset2E
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.47 => ( ( Xz = Xx )
% 0.29/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsubunion_type,type,
% 0.29/0.47 upairsubunion: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsubunion,definition,
% 0.29/0.47 ( upairsubunion
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairinpowunion_type,type,
% 0.29/0.47 upairinpowunion: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairinpowunion,definition,
% 0.29/0.47 ( upairinpowunion
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem1_type,type,
% 0.29/0.47 ubforcartprodlem1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem1,definition,
% 0.29/0.47 ( ubforcartprodlem1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem2_type,type,
% 0.29/0.47 ubforcartprodlem2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem2,definition,
% 0.29/0.47 ( ubforcartprodlem2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem3_type,type,
% 0.29/0.47 ubforcartprodlem3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem3,definition,
% 0.29/0.47 ( ubforcartprodlem3
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairin_type,type,
% 0.29/0.47 cartprodpairin: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairin,definition,
% 0.29/0.47 ( cartprodpairin
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempair1_type,type,
% 0.29/0.47 cartprodmempair1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempair1,definition,
% 0.29/0.47 ( cartprodmempair1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 & ( Xu
% 0.29/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempair_type,type,
% 0.29/0.47 cartprodmempair: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempair,definition,
% 0.29/0.47 ( cartprodmempair
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE2_type,type,
% 0.29/0.47 setunionE2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE2,definition,
% 0.29/0.47 ( setunionE2
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.47 => ? [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton1_type,type,
% 0.29/0.47 setunionsingleton1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton1,definition,
% 0.29/0.47 ( setunionsingleton1
% 0.29/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton2_type,type,
% 0.29/0.47 setunionsingleton2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton2,definition,
% 0.29/0.47 ( setunionsingleton2
% 0.29/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton_type,type,
% 0.29/0.47 setunionsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton,definition,
% 0.29/0.47 ( setunionsingleton
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.29/0.47 = Xx ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singleton_type,type,
% 0.29/0.47 singleton: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonprop_type,type,
% 0.29/0.47 singletonprop: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonprop,definition,
% 0.29/0.47 ( singletonprop
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) )
% 0.29/0.47 => ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ( singleton
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ex1_type,type,
% 0.29/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1E1_type,type,
% 0.29/0.47 ex1E1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1E1,definition,
% 0.29/0.47 ( ex1E1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ( ex1 @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ex1I_type,type,
% 0.29/0.47 ex1I: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1I,definition,
% 0.29/0.47 ( ex1I
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xy = Xx ) ) )
% 0.29/0.47 => ( ex1 @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ex1I2_type,type,
% 0.29/0.47 ex1I2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1I2,definition,
% 0.29/0.47 ( ex1I2
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) )
% 0.29/0.47 => ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ( ex1 @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsuniq_type,type,
% 0.29/0.47 singletonsuniq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsuniq,definition,
% 0.29/0.47 ( singletonsuniq
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.29/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(atmost1p_type,type,
% 0.29/0.47 atmost1p: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(atleast2p_type,type,
% 0.29/0.47 atleast2p: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(atmost2p_type,type,
% 0.29/0.47 atmost2p: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetp_type,type,
% 0.29/0.47 upairsetp: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL1_type,type,
% 0.29/0.47 setukpairinjL1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL1,definition,
% 0.29/0.47 ( setukpairinjL1
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(kfstsingleton_type,type,
% 0.29/0.48 kfstsingleton: $o ).
% 0.29/0.48
% 0.29/0.48 thf(kfstsingleton,definition,
% 0.29/0.48 ( kfstsingleton
% 0.29/0.48 = ( ! [Xu: $i] :
% 0.29/0.48 ( ( iskpair @ Xu )
% 0.29/0.48 => ( singleton
% 0.29/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.48 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(theprop_type,type,
% 0.29/0.48 theprop: $o ).
% 0.29/0.48
% 0.29/0.48 thf(theprop,definition,
% 0.29/0.48 ( theprop
% 0.29/0.48 = ( ! [X: $i] :
% 0.29/0.48 ( ( singleton @ X )
% 0.29/0.48 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(kfst_type,type,
% 0.29/0.48 kfst: $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(kfstpairEq_type,type,
% 0.29/0.48 kfstpairEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(kfstpairEq,definition,
% 0.29/0.48 ( kfstpairEq
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.48 = Xx ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodfstin_type,type,
% 0.29/0.48 cartprodfstin: $o ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodfstin,definition,
% 0.29/0.48 ( cartprodfstin
% 0.29/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.48 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjL2_type,type,
% 0.29/0.48 setukpairinjL2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjL2,definition,
% 0.29/0.48 ( setukpairinjL2
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjL_type,type,
% 0.29/0.48 setukpairinjL: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjL,definition,
% 0.29/0.48 ( setukpairinjL
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.48 = ( kpair @ Xz @ Xu ) )
% 0.29/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR11_type,type,
% 0.29/0.48 setukpairinjR11: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR11,definition,
% 0.29/0.48 ( setukpairinjR11
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( Xx = Xy )
% 0.29/0.48 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR12_type,type,
% 0.29/0.48 setukpairinjR12: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR12,definition,
% 0.29/0.48 ( setukpairinjR12
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( Xx = Xy )
% 0.29/0.48 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.48 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR1_type,type,
% 0.29/0.48 setukpairinjR1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR1,definition,
% 0.29/0.48 ( setukpairinjR1
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.48 => ( ( Xz = Xu )
% 0.29/0.48 => ( Xy = Xu ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(upairequniteq_type,type,
% 0.29/0.48 upairequniteq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(upairequniteq,definition,
% 0.29/0.48 ( upairequniteq
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.48 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.48 = ( setadjoin @ Xz @ emptyset ) )
% 0.29/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR2_type,type,
% 0.29/0.48 setukpairinjR2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR2,definition,
% 0.29/0.48 ( setukpairinjR2
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR_type,type,
% 0.29/0.48 setukpairinjR: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setukpairinjR,definition,
% 0.29/0.48 ( setukpairinjR
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.48 = ( kpair @ Xz @ Xu ) )
% 0.29/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(ksndsingleton_type,type,
% 0.29/0.48 ksndsingleton: $o ).
% 0.29/0.48
% 0.29/0.48 thf(ksndsingleton,definition,
% 0.29/0.48 ( ksndsingleton
% 0.29/0.48 = ( ! [Xu: $i] :
% 0.29/0.48 ( ( iskpair @ Xu )
% 0.29/0.48 => ( singleton
% 0.29/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.48 @ ^ [Xx: $i] :
% 0.29/0.48 ( Xu
% 0.29/0.48 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(ksnd_type,type,
% 0.29/0.48 ksnd: $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(ksndpairEq_type,type,
% 0.29/0.48 ksndpairEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(ksndpairEq,definition,
% 0.29/0.48 ( ksndpairEq
% 0.29/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.48 = Xy ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(kpairsurjEq_type,type,
% 0.29/0.48 kpairsurjEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(kpairsurjEq,definition,
% 0.29/0.48 ( kpairsurjEq
% 0.29/0.48 = ( ! [Xu: $i] :
% 0.29/0.48 ( ( iskpair @ Xu )
% 0.29/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.48 = Xu ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodsndin_type,type,
% 0.29/0.48 cartprodsndin: $o ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodsndin,definition,
% 0.29/0.48 ( cartprodsndin
% 0.29/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.48 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodpairmemEL_type,type,
% 0.29/0.48 cartprodpairmemEL: $o ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodpairmemEL,definition,
% 0.29/0.48 ( cartprodpairmemEL
% 0.29/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodpairmemER_type,type,
% 0.29/0.48 cartprodpairmemER: $o ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodpairmemER,definition,
% 0.29/0.48 ( cartprodpairmemER
% 0.29/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodmempaircEq_type,type,
% 0.29/0.48 cartprodmempaircEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodmempaircEq,definition,
% 0.29/0.48 ( cartprodmempaircEq
% 0.29/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( kpair @ Xx @ Xy )
% 0.29/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodfstpairEq_type,type,
% 0.29/0.48 cartprodfstpairEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodfstpairEq,definition,
% 0.29/0.48 ( cartprodfstpairEq
% 0.29/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.48 = Xx ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodsndpairEq_type,type,
% 0.29/0.48 cartprodsndpairEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodsndpairEq,definition,
% 0.29/0.48 ( cartprodsndpairEq
% 0.29/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.48 = Xy ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodpairsurjEq_type,type,
% 0.29/0.48 cartprodpairsurjEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(cartprodpairsurjEq,definition,
% 0.29/0.48 ( cartprodpairsurjEq
% 0.29/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.48 = Xu ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln_type,type,
% 0.29/0.48 breln: $i > $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstr_type,type,
% 0.29/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrI_type,type,
% 0.29/0.48 dpsetconstrI: $o ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrI,definition,
% 0.29/0.48 ( dpsetconstrI
% 0.29/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( Xphi @ Xx @ Xy )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.48 @ ( dpsetconstr @ A @ B
% 0.29/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrSub_type,type,
% 0.29/0.48 dpsetconstrSub: $o ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrSub,definition,
% 0.29/0.48 ( dpsetconstrSub
% 0.29/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.48 ( subset
% 0.29/0.48 @ ( dpsetconstr @ A @ B
% 0.29/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.29/0.48 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setOfPairsIsBReln_type,type,
% 0.29/0.48 setOfPairsIsBReln: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setOfPairsIsBReln,definition,
% 0.29/0.48 ( setOfPairsIsBReln
% 0.29/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.48 ( breln @ A @ B
% 0.29/0.48 @ ( dpsetconstr @ A @ B
% 0.29/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrERa_type,type,
% 0.29/0.48 dpsetconstrERa: $o ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrERa,definition,
% 0.29/0.48 ( dpsetconstrERa
% 0.29/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.48 @ ( dpsetconstr @ A @ B
% 0.29/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrEL1_type,type,
% 0.29/0.48 dpsetconstrEL1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrEL1,definition,
% 0.29/0.48 ( dpsetconstrEL1
% 0.29/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.48 @ ( dpsetconstr @ A @ B
% 0.29/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrEL2_type,type,
% 0.29/0.48 dpsetconstrEL2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrEL2,definition,
% 0.29/0.48 ( dpsetconstrEL2
% 0.29/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.48 @ ( dpsetconstr @ A @ B
% 0.29/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrER_type,type,
% 0.29/0.48 dpsetconstrER: $o ).
% 0.29/0.48
% 0.29/0.48 thf(dpsetconstrER,definition,
% 0.29/0.48 ( dpsetconstrER
% 0.29/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.48 @ ( dpsetconstr @ A @ B
% 0.29/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(func_type,type,
% 0.29/0.48 func: $i > $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcSet_type,type,
% 0.29/0.48 funcSet: $i > $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(funcImageSingleton_type,type,
% 0.29/0.48 funcImageSingleton: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcImageSingleton,definition,
% 0.29/0.48 ( funcImageSingleton
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( singleton
% 0.29/0.48 @ ( dsetconstr @ B
% 0.29/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(apProp_type,type,
% 0.29/0.48 apProp: $o ).
% 0.29/0.48
% 0.29/0.48 thf(apProp,definition,
% 0.29/0.48 ( apProp
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in
% 0.29/0.48 @ ( setunion
% 0.29/0.48 @ ( dsetconstr @ B
% 0.29/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.29/0.48 @ B ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(ap_type,type,
% 0.29/0.48 ap: $i > $i > $i > $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(app_type,type,
% 0.29/0.48 app: $o ).
% 0.29/0.48
% 0.29/0.48 thf(app,definition,
% 0.29/0.48 ( app
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(infuncsetfunc_type,type,
% 0.29/0.48 infuncsetfunc: $o ).
% 0.29/0.48
% 0.29/0.48 thf(infuncsetfunc,definition,
% 0.29/0.48 ( infuncsetfunc
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.48 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(ap2p_type,type,
% 0.29/0.48 ap2p: $o ).
% 0.29/0.48
% 0.29/0.48 thf(ap2p,definition,
% 0.29/0.48 ( ap2p
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(funcinfuncset_type,type,
% 0.29/0.48 funcinfuncset: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcinfuncset,definition,
% 0.29/0.48 ( funcinfuncset
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(lamProp_type,type,
% 0.29/0.48 lamProp: $o ).
% 0.29/0.48
% 0.29/0.48 thf(lamProp,definition,
% 0.29/0.48 ( lamProp
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.48 => ( func @ A @ B
% 0.29/0.48 @ ( dpsetconstr @ A @ B
% 0.29/0.48 @ ^ [Xx: $i,Xy: $i] :
% 0.29/0.48 ( ( Xf @ Xx )
% 0.29/0.48 = Xy ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(lam_type,type,
% 0.29/0.48 lam: $i > $i > ( $i > $i ) > $i ).
% 0.29/0.48
% 0.29/0.48 thf(lamp_type,type,
% 0.29/0.48 lamp: $o ).
% 0.29/0.48
% 0.29/0.48 thf(lamp,definition,
% 0.29/0.48 ( lamp
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.48 => ( func @ A @ B
% 0.29/0.48 @ ( lam @ A @ B
% 0.29/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(lam2p_type,type,
% 0.29/0.48 lam2p: $o ).
% 0.29/0.48
% 0.29/0.48 thf(lam2p,definition,
% 0.29/0.48 ( lam2p
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.48 => ( in
% 0.29/0.48 @ ( lam @ A @ B
% 0.29/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.48 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(brelnall1_type,type,
% 0.29/0.48 brelnall1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(brelnall1,definition,
% 0.29/0.48 ( brelnall1
% 0.29/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.48 ( ( breln @ A @ B @ R )
% 0.29/0.48 => ! [Xphi: $i > $o] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ R )
% 0.29/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(brelnall2_type,type,
% 0.29/0.48 brelnall2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(brelnall2,definition,
% 0.29/0.48 ( brelnall2
% 0.29/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.48 ( ( breln @ A @ B @ R )
% 0.29/0.48 => ! [Xphi: $i > $o] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ R )
% 0.29/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(ex1E2_type,type,
% 0.29/0.48 ex1E2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(ex1E2,definition,
% 0.29/0.48 ( ex1E2
% 0.29/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.48 ( ( ex1 @ A
% 0.29/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( Xphi @ Xx )
% 0.29/0.48 => ( ( Xphi @ Xy )
% 0.29/0.48 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(funcGraphProp1_type,type,
% 0.29/0.48 funcGraphProp1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcGraphProp1,definition,
% 0.29/0.48 ( funcGraphProp1
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(funcGraphProp3_type,type,
% 0.29/0.48 funcGraphProp3: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcGraphProp3,definition,
% 0.29/0.48 ( funcGraphProp3
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(funcGraphProp2_type,type,
% 0.29/0.48 funcGraphProp2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcGraphProp2,definition,
% 0.29/0.48 ( funcGraphProp2
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.48 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(funcextLem_type,type,
% 0.29/0.48 funcextLem: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcextLem,definition,
% 0.29/0.48 ( funcextLem
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ! [Xg: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xg )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(funcGraphProp4_type,type,
% 0.29/0.48 funcGraphProp4: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcGraphProp4,definition,
% 0.29/0.48 ( funcGraphProp4
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.48 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(subbreln_type,type,
% 0.29/0.48 subbreln: $o ).
% 0.29/0.48
% 0.29/0.48 thf(subbreln,definition,
% 0.29/0.48 ( subbreln
% 0.29/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.48 ( ( breln @ A @ B @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln @ A @ B @ S )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(eqbreln_type,type,
% 0.29/0.48 eqbreln: $o ).
% 0.29/0.48
% 0.29/0.48 thf(eqbreln,definition,
% 0.29/0.48 ( eqbreln
% 0.29/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.48 ( ( breln @ A @ B @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln @ A @ B @ S )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.29/0.48 => ( R = S ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(funcext_type,type,
% 0.29/0.48 funcext: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcext,definition,
% 0.29/0.48 ( funcext
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ! [Xg: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xg )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(funcext2_type,type,
% 0.29/0.48 funcext2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(funcext2,definition,
% 0.29/0.48 ( funcext2
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.48 => ! [Xg: $i] :
% 0.29/0.48 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(ap2apEq1_type,type,
% 0.29/0.48 ap2apEq1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(ap2apEq1,definition,
% 0.29/0.48 ( ap2apEq1
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.48 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(ap2apEq2_type,type,
% 0.29/0.48 ap2apEq2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(ap2apEq2,definition,
% 0.29/0.48 ( ap2apEq2
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.48 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(beta1_type,type,
% 0.29/0.48 beta1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(beta1,definition,
% 0.29/0.48 ( beta1
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( ap @ A @ B
% 0.29/0.48 @ ( lam @ A @ B
% 0.29/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.29/0.48 @ Xx )
% 0.29/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(eta1_type,type,
% 0.29/0.48 eta1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(eta1,definition,
% 0.29/0.48 ( eta1
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( func @ A @ B @ Xf )
% 0.29/0.48 => ( ( lam @ A @ B
% 0.29/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.29/0.48 = Xf ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(lam2lamEq_type,type,
% 0.29/0.48 lam2lamEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(lam2lamEq,definition,
% 0.29/0.48 ( lam2lamEq
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.48 => ( ( lam @ A @ B
% 0.29/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.48 = ( lam @ A @ B
% 0.29/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(beta2_type,type,
% 0.29/0.48 beta2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(beta2,definition,
% 0.29/0.48 ( beta2
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( ap @ A @ B
% 0.29/0.48 @ ( lam @ A @ B
% 0.29/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.29/0.48 @ Xx )
% 0.29/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(eta2_type,type,
% 0.29/0.48 eta2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(eta2,definition,
% 0.29/0.48 ( eta2
% 0.29/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.48 => ( ( lam @ A @ B
% 0.29/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.29/0.48 = Xf ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(iffalseProp1_type,type,
% 0.29/0.48 iffalseProp1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(iffalseProp1,definition,
% 0.29/0.48 ( iffalseProp1
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ~ Xphi
% 0.29/0.48 => ( in @ Xy
% 0.29/0.48 @ ( dsetconstr @ A
% 0.29/0.48 @ ^ [Xz: $i] :
% 0.29/0.48 ( ( Xphi
% 0.29/0.48 & ( Xz = Xx ) )
% 0.29/0.48 | ( ~ Xphi
% 0.29/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(iffalseProp2_type,type,
% 0.29/0.48 iffalseProp2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(iffalseProp2,definition,
% 0.29/0.48 ( iffalseProp2
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ~ Xphi
% 0.29/0.48 => ( ( dsetconstr @ A
% 0.29/0.48 @ ^ [Xz: $i] :
% 0.29/0.48 ( ( Xphi
% 0.29/0.48 & ( Xz = Xx ) )
% 0.29/0.48 | ( ~ Xphi
% 0.29/0.48 & ( Xz = Xy ) ) ) )
% 0.29/0.48 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(iftrueProp1_type,type,
% 0.29/0.48 iftrueProp1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(iftrueProp1,definition,
% 0.29/0.48 ( iftrueProp1
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( Xphi
% 0.29/0.48 => ( in @ Xx
% 0.29/0.48 @ ( dsetconstr @ A
% 0.29/0.48 @ ^ [Xz: $i] :
% 0.29/0.48 ( ( Xphi
% 0.29/0.48 & ( Xz = Xx ) )
% 0.29/0.48 | ( ~ Xphi
% 0.29/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(iftrueProp2_type,type,
% 0.29/0.48 iftrueProp2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(iftrueProp2,definition,
% 0.29/0.48 ( iftrueProp2
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( Xphi
% 0.29/0.48 => ( ( dsetconstr @ A
% 0.29/0.48 @ ^ [Xz: $i] :
% 0.29/0.48 ( ( Xphi
% 0.29/0.48 & ( Xz = Xx ) )
% 0.29/0.48 | ( ~ Xphi
% 0.29/0.48 & ( Xz = Xy ) ) ) )
% 0.29/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(ifSingleton_type,type,
% 0.29/0.48 ifSingleton: $o ).
% 0.29/0.48
% 0.29/0.48 thf(ifSingleton,definition,
% 0.29/0.48 ( ifSingleton
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( singleton
% 0.29/0.48 @ ( dsetconstr @ A
% 0.29/0.48 @ ^ [Xz: $i] :
% 0.29/0.48 ( ( Xphi
% 0.29/0.48 & ( Xz = Xx ) )
% 0.29/0.48 | ( ~ Xphi
% 0.29/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(if_type,type,
% 0.29/0.48 if: $i > $o > $i > $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(ifp_type,type,
% 0.29/0.48 ifp: $o ).
% 0.29/0.48
% 0.29/0.48 thf(ifp,definition,
% 0.29/0.48 ( ifp
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(theeq_type,type,
% 0.29/0.48 theeq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(theeq,definition,
% 0.29/0.48 ( theeq
% 0.29/0.48 = ( ! [X: $i] :
% 0.29/0.48 ( ( singleton @ X )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ X )
% 0.29/0.48 => ( ( setunion @ X )
% 0.29/0.48 = Xx ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(iftrue_type,type,
% 0.29/0.48 iftrue: $o ).
% 0.29/0.48
% 0.29/0.48 thf(iftrue,definition,
% 0.29/0.48 ( iftrue
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( Xphi
% 0.29/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.29/0.48 = Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(iffalse_type,type,
% 0.29/0.48 iffalse: $o ).
% 0.29/0.48
% 0.29/0.48 thf(iffalse,definition,
% 0.29/0.48 ( iffalse
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ~ Xphi
% 0.29/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.29/0.48 = Xy ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(iftrueorfalse_type,type,
% 0.29/0.48 iftrueorfalse: $o ).
% 0.29/0.48
% 0.29/0.48 thf(iftrueorfalse,definition,
% 0.29/0.48 ( iftrueorfalse
% 0.29/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(binintersectT_lem_type,type,
% 0.29/0.48 binintersectT_lem: $o ).
% 0.29/0.48
% 0.29/0.48 thf(binintersectT_lem,definition,
% 0.29/0.48 ( binintersectT_lem
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(binunionT_lem_type,type,
% 0.29/0.48 binunionT_lem: $o ).
% 0.29/0.48
% 0.29/0.48 thf(binunionT_lem,definition,
% 0.29/0.48 ( binunionT_lem
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(powersetT_lem_type,type,
% 0.29/0.48 powersetT_lem: $o ).
% 0.29/0.48
% 0.29/0.48 thf(powersetT_lem,definition,
% 0.29/0.48 ( powersetT_lem
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setminusT_lem_type,type,
% 0.29/0.48 setminusT_lem: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setminusT_lem,definition,
% 0.29/0.48 ( setminusT_lem
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementT_lem_type,type,
% 0.29/0.48 complementT_lem: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementT_lem,definition,
% 0.29/0.48 ( complementT_lem
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setextT_type,type,
% 0.29/0.48 setextT: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setextT,definition,
% 0.29/0.48 ( setextT
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ X )
% 0.29/0.48 => ( in @ Xx @ Y ) ) )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ Y )
% 0.29/0.48 => ( in @ Xx @ X ) ) )
% 0.29/0.48 => ( X = Y ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(subsetTI_type,type,
% 0.29/0.48 subsetTI: $o ).
% 0.29/0.48
% 0.29/0.48 thf(subsetTI,definition,
% 0.29/0.48 ( subsetTI
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ X )
% 0.29/0.48 => ( in @ Xx @ Y ) ) )
% 0.29/0.48 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(powersetTI1_type,type,
% 0.29/0.48 powersetTI1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(powersetTI1,definition,
% 0.29/0.48 ( powersetTI1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ X )
% 0.29/0.48 => ( in @ Xx @ Y ) ) )
% 0.29/0.48 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(powersetTE1_type,type,
% 0.29/0.48 powersetTE1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(powersetTE1,definition,
% 0.29/0.48 ( powersetTE1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ X @ ( powerset @ Y ) )
% 0.29/0.48 => ( ( in @ Xx @ X )
% 0.29/0.48 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementTI1_type,type,
% 0.29/0.48 complementTI1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementTI1,definition,
% 0.29/0.48 ( complementTI1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ X )
% 0.29/0.48 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementTE1_type,type,
% 0.29/0.48 complementTE1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementTE1,definition,
% 0.29/0.48 ( complementTE1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(binintersectTELcontra_type,type,
% 0.29/0.48 binintersectTELcontra: $o ).
% 0.29/0.48
% 0.29/0.48 thf(binintersectTELcontra,definition,
% 0.29/0.48 ( binintersectTELcontra
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ~ ( in @ Xx @ X )
% 0.29/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(binintersectTERcontra_type,type,
% 0.29/0.48 binintersectTERcontra: $o ).
% 0.29/0.48
% 0.29/0.48 thf(binintersectTERcontra,definition,
% 0.29/0.48 ( binintersectTERcontra
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ~ ( in @ Xx @ Y )
% 0.29/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(contrasubsetT_type,type,
% 0.29/0.48 contrasubsetT: $o ).
% 0.29/0.48
% 0.29/0.48 thf(contrasubsetT,definition,
% 0.29/0.48 ( contrasubsetT
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.48 => ( ( in @ Xx @ Y )
% 0.29/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(contrasubsetT1_type,type,
% 0.29/0.48 contrasubsetT1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(contrasubsetT1,definition,
% 0.29/0.48 ( contrasubsetT1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( subset @ X @ Y )
% 0.29/0.48 => ( ~ ( in @ Xx @ Y )
% 0.29/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(contrasubsetT2_type,type,
% 0.29/0.48 contrasubsetT2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(contrasubsetT2,definition,
% 0.29/0.48 ( contrasubsetT2
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ X @ Y )
% 0.29/0.48 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(contrasubsetT3_type,type,
% 0.29/0.48 contrasubsetT3: $o ).
% 0.29/0.48
% 0.29/0.48 thf(contrasubsetT3,definition,
% 0.29/0.48 ( contrasubsetT3
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.29/0.48 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementI1_type,type,
% 0.29/0.48 doubleComplementI1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementI1,definition,
% 0.29/0.48 ( doubleComplementI1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ X )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementE1_type,type,
% 0.29/0.48 doubleComplementE1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementE1,definition,
% 0.29/0.48 ( doubleComplementE1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.29/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementSub1_type,type,
% 0.29/0.48 doubleComplementSub1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementSub1,definition,
% 0.29/0.48 ( doubleComplementSub1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementSub2_type,type,
% 0.29/0.48 doubleComplementSub2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementSub2,definition,
% 0.29/0.48 ( doubleComplementSub2
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementEq_type,type,
% 0.29/0.48 doubleComplementEq: $o ).
% 0.29/0.48
% 0.29/0.48 thf(doubleComplementEq,definition,
% 0.29/0.48 ( doubleComplementEq
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ( X
% 0.29/0.48 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementTnotintersectT_type,type,
% 0.29/0.48 complementTnotintersectT: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementTnotintersectT,definition,
% 0.29/0.48 ( complementTnotintersectT
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementImpComplementIntersect_type,type,
% 0.29/0.48 complementImpComplementIntersect: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementImpComplementIntersect,definition,
% 0.29/0.48 ( complementImpComplementIntersect
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementSubsetComplementIntersect_type,type,
% 0.29/0.48 complementSubsetComplementIntersect: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementSubsetComplementIntersect,definition,
% 0.29/0.48 ( complementSubsetComplementIntersect
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementInPowersetComplementIntersect_type,type,
% 0.29/0.48 complementInPowersetComplementIntersect: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementInPowersetComplementIntersect,definition,
% 0.29/0.48 ( complementInPowersetComplementIntersect
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(contraSubsetComplement_type,type,
% 0.29/0.48 contraSubsetComplement: $o ).
% 0.29/0.48
% 0.29/0.48 thf(contraSubsetComplement,definition,
% 0.29/0.48 ( contraSubsetComplement
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ Y )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementTcontraSubset_type,type,
% 0.29/0.48 complementTcontraSubset: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementTcontraSubset,definition,
% 0.29/0.48 ( complementTcontraSubset
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.48 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(binunionTILcontra_type,type,
% 0.29/0.48 binunionTILcontra: $o ).
% 0.29/0.48
% 0.29/0.48 thf(binunionTILcontra,definition,
% 0.29/0.48 ( binunionTILcontra
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(binunionTIRcontra_type,type,
% 0.29/0.48 binunionTIRcontra: $o ).
% 0.29/0.48
% 0.29/0.48 thf(binunionTIRcontra,definition,
% 0.29/0.48 ( binunionTIRcontra
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.48 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(inIntersectImpInUnion_type,type,
% 0.29/0.48 inIntersectImpInUnion: $o ).
% 0.29/0.48
% 0.29/0.48 thf(inIntersectImpInUnion,definition,
% 0.29/0.48 ( inIntersectImpInUnion
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.48 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(inIntersectImpInUnion2_type,type,
% 0.29/0.48 inIntersectImpInUnion2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(inIntersectImpInUnion2,definition,
% 0.29/0.48 ( inIntersectImpInUnion2
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.48 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(inIntersectImpInIntersectUnions_type,type,
% 0.29/0.48 inIntersectImpInIntersectUnions: $o ).
% 0.29/0.48
% 0.29/0.48 thf(inIntersectImpInIntersectUnions,definition,
% 0.29/0.48 ( inIntersectImpInIntersectUnions
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.48 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(intersectInPowersetIntersectUnions_type,type,
% 0.29/0.48 intersectInPowersetIntersectUnions: $o ).
% 0.29/0.48
% 0.29/0.48 thf(intersectInPowersetIntersectUnions,definition,
% 0.29/0.48 ( intersectInPowersetIntersectUnions
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(inComplementUnionImpNotIn1_type,type,
% 0.29/0.48 inComplementUnionImpNotIn1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(inComplementUnionImpNotIn1,definition,
% 0.29/0.48 ( inComplementUnionImpNotIn1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(inComplementUnionImpInComplement1_type,type,
% 0.29/0.48 inComplementUnionImpInComplement1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(inComplementUnionImpInComplement1,definition,
% 0.29/0.48 ( inComplementUnionImpInComplement1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(binunionTE_type,type,
% 0.29/0.48 binunionTE: $o ).
% 0.29/0.48
% 0.29/0.48 thf(binunionTE,definition,
% 0.29/0.48 ( binunionTE
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xphi: $o,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.48 => ( ( ( in @ Xx @ X )
% 0.29/0.48 => Xphi )
% 0.29/0.48 => ( ( ( in @ Xx @ Y )
% 0.29/0.48 => Xphi )
% 0.29/0.48 => Xphi ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(binunionTEcontra_type,type,
% 0.29/0.48 binunionTEcontra: $o ).
% 0.29/0.48
% 0.29/0.48 thf(binunionTEcontra,definition,
% 0.29/0.48 ( binunionTEcontra
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ~ ( in @ Xx @ X )
% 0.29/0.48 => ( ~ ( in @ Xx @ Y )
% 0.29/0.48 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2a1_type,type,
% 0.29/0.48 demorgan2a1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2a1,definition,
% 0.29/0.48 ( demorgan2a1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(complementUnionInPowersetComplement_type,type,
% 0.29/0.48 complementUnionInPowersetComplement: $o ).
% 0.29/0.48
% 0.29/0.48 thf(complementUnionInPowersetComplement,definition,
% 0.29/0.48 ( complementUnionInPowersetComplement
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2a2_type,type,
% 0.29/0.48 demorgan2a2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2a2,definition,
% 0.29/0.48 ( demorgan2a2
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan1a_type,type,
% 0.29/0.48 demorgan1a: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan1a,definition,
% 0.29/0.48 ( demorgan1a
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.29/0.48 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan1b_type,type,
% 0.29/0.48 demorgan1b: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan1b,definition,
% 0.29/0.48 ( demorgan1b
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan1_type,type,
% 0.29/0.48 demorgan1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan1,definition,
% 0.29/0.48 ( demorgan1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.29/0.48 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2a_type,type,
% 0.29/0.48 demorgan2a: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2a,definition,
% 0.29/0.48 ( demorgan2a
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.48 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2b2_type,type,
% 0.29/0.48 demorgan2b2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2b2,definition,
% 0.29/0.48 ( demorgan2b2
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.48 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2b_type,type,
% 0.29/0.48 demorgan2b: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2b,definition,
% 0.29/0.48 ( demorgan2b
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.29/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2_type,type,
% 0.29/0.48 demorgan2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(demorgan2,definition,
% 0.29/0.48 ( demorgan2
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.29/0.48 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule0_type,type,
% 0.29/0.48 woz13rule0: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule0,definition,
% 0.29/0.48 ( woz13rule0
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.48 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule1_type,type,
% 0.29/0.48 woz13rule1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule1,definition,
% 0.29/0.48 ( woz13rule1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ X @ Z )
% 0.29/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule2_type,type,
% 0.29/0.48 woz13rule2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule2,definition,
% 0.29/0.48 ( woz13rule2
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ Y @ Z )
% 0.29/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule3_type,type,
% 0.29/0.48 woz13rule3: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule3,definition,
% 0.29/0.48 ( woz13rule3
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ X @ Y )
% 0.29/0.48 => ( ( subset @ X @ Z )
% 0.29/0.48 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule4_type,type,
% 0.29/0.48 woz13rule4: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz13rule4,definition,
% 0.29/0.48 ( woz13rule4
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ! [W: $i] :
% 0.29/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ X @ Z )
% 0.29/0.48 => ( ( subset @ Y @ W )
% 0.29/0.48 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_1_type,type,
% 0.29/0.48 woz1_1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_1,definition,
% 0.29/0.48 ( woz1_1
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_2_type,type,
% 0.29/0.48 woz1_2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_2,definition,
% 0.29/0.48 ( woz1_2
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ! [W: $i] :
% 0.29/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.29/0.48 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.29/0.48 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_3_type,type,
% 0.29/0.48 woz1_3: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_3,definition,
% 0.29/0.48 ( woz1_3
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ! [Z: $i] :
% 0.29/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_4_type,type,
% 0.29/0.48 woz1_4: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_4,definition,
% 0.29/0.48 ( woz1_4
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.48 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_5_type,type,
% 0.29/0.48 woz1_5: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz1_5,definition,
% 0.29/0.48 ( woz1_5
% 0.29/0.48 = ( ! [A: $i,X: $i] :
% 0.29/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.48 => ! [Y: $i] :
% 0.29/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1_type,type,
% 0.29/0.48 breln1: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1all2_type,type,
% 0.29/0.48 breln1all2: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1all2,definition,
% 0.29/0.48 ( breln1all2
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [Xphi: $i > $o] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ R )
% 0.29/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1Set_type,type,
% 0.29/0.48 breln1Set: $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(breln1SetBreln1_type,type,
% 0.29/0.48 breln1SetBreln1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1SetBreln1,definition,
% 0.29/0.48 ( breln1SetBreln1
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( in @ R @ ( breln1Set @ A ) )
% 0.29/0.48 => ( breln1 @ A @ R ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(transitive_type,type,
% 0.29/0.48 transitive: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(antisymmetric_type,type,
% 0.29/0.48 antisymmetric: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(reflexive_type,type,
% 0.29/0.48 reflexive: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(refltransitive_type,type,
% 0.29/0.48 refltransitive: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(refllinearorder_type,type,
% 0.29/0.48 refllinearorder: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(reflwellordering_type,type,
% 0.29/0.48 reflwellordering: $i > $i > $o ).
% 0.29/0.48
% 0.29/0.48 thf(choice2fnsingleton_type,type,
% 0.29/0.48 choice2fnsingleton: $o ).
% 0.29/0.48
% 0.29/0.48 thf(choice2fnsingleton,definition,
% 0.29/0.48 ( choice2fnsingleton
% 0.29/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ? [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ B )
% 0.29/0.48 & ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.48 => ! [R: $i] :
% 0.29/0.48 ( ( in @ R @ ( breln1Set @ B ) )
% 0.29/0.48 => ( ( reflwellordering @ B @ R )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ( singleton
% 0.29/0.48 @ ( dsetconstr @ B
% 0.29/0.48 @ ^ [Xy: $i] :
% 0.29/0.48 ( ( Xphi @ Xx @ Xy )
% 0.29/0.48 & ! [Xz: $i] :
% 0.29/0.48 ( ( in @ Xz @ B )
% 0.29/0.48 => ( ( Xphi @ Xx @ Xz )
% 0.29/0.48 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(setOfPairsIsBReln1_type,type,
% 0.29/0.48 setOfPairsIsBReln1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(setOfPairsIsBReln1,definition,
% 0.29/0.48 ( setOfPairsIsBReln1
% 0.29/0.48 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.29/0.48 ( breln1 @ A
% 0.29/0.48 @ ( dpsetconstr @ A @ A
% 0.29/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1all1_type,type,
% 0.29/0.48 breln1all1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1all1,definition,
% 0.29/0.48 ( breln1all1
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [Xphi: $i > $o] :
% 0.29/0.48 ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ R )
% 0.29/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(subbreln1_type,type,
% 0.29/0.48 subbreln1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(subbreln1,definition,
% 0.29/0.48 ( subbreln1
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(eqbreln1_type,type,
% 0.29/0.48 eqbreln1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(eqbreln1,definition,
% 0.29/0.48 ( eqbreln1
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.48 => ( ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.29/0.48 => ( R = S ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1invset_type,type,
% 0.29/0.48 breln1invset: $i > $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(breln1invprop_type,type,
% 0.29/0.48 breln1invprop: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1invprop,definition,
% 0.29/0.48 ( breln1invprop
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1invI_type,type,
% 0.29/0.48 breln1invI: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1invI,definition,
% 0.29/0.48 ( breln1invI
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1invE_type,type,
% 0.29/0.48 breln1invE: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1invE,definition,
% 0.29/0.48 ( breln1invE
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compset_type,type,
% 0.29/0.48 breln1compset: $i > $i > $i > $i ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compprop_type,type,
% 0.29/0.48 breln1compprop: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compprop,definition,
% 0.29/0.48 ( breln1compprop
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compI_type,type,
% 0.29/0.48 breln1compI: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compI,definition,
% 0.29/0.48 ( breln1compI
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ! [Xz: $i] :
% 0.29/0.48 ( ( in @ Xz @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.29/0.48 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compE_type,type,
% 0.29/0.48 breln1compE: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compE,definition,
% 0.29/0.48 ( breln1compE
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.29/0.48 => ? [Xz: $i] :
% 0.29/0.48 ( ( in @ Xz @ A )
% 0.29/0.48 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.29/0.48 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compEex_type,type,
% 0.29/0.48 breln1compEex: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1compEex,definition,
% 0.29/0.48 ( breln1compEex
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.29/0.48 => ! [Xphi: $o] :
% 0.29/0.48 ( ! [Xz: $i] :
% 0.29/0.48 ( ( in @ Xz @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.29/0.48 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.29/0.48 => Xphi ) ) )
% 0.29/0.48 => Xphi ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionprop_type,type,
% 0.29/0.48 breln1unionprop: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionprop,definition,
% 0.29/0.48 ( breln1unionprop
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionIL_type,type,
% 0.29/0.48 breln1unionIL: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionIL,definition,
% 0.29/0.48 ( breln1unionIL
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionIR_type,type,
% 0.29/0.48 breln1unionIR: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionIR,definition,
% 0.29/0.48 ( breln1unionIR
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionI_type,type,
% 0.29/0.48 breln1unionI: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionI,definition,
% 0.29/0.48 ( breln1unionI
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.29/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionE_type,type,
% 0.29/0.48 breln1unionE: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionE,definition,
% 0.29/0.48 ( breln1unionE
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionEcases_type,type,
% 0.29/0.48 breln1unionEcases: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionEcases,definition,
% 0.29/0.48 ( breln1unionEcases
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ A )
% 0.29/0.48 => ! [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.29/0.48 => ! [Xphi: $o] :
% 0.29/0.48 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.48 => Xphi )
% 0.29/0.48 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.48 => Xphi )
% 0.29/0.48 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionCommutes_type,type,
% 0.29/0.48 breln1unionCommutes: $o ).
% 0.29/0.48
% 0.29/0.48 thf(breln1unionCommutes,definition,
% 0.29/0.48 ( breln1unionCommutes
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ( ( binunion @ R @ S )
% 0.29/0.48 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz2Ex_type,type,
% 0.29/0.48 woz2Ex: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz2Ex,definition,
% 0.29/0.48 ( woz2Ex
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ( R
% 0.29/0.48 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz2W_type,type,
% 0.29/0.48 woz2W: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz2W,definition,
% 0.29/0.48 ( woz2W
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.29/0.48 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz2A_type,type,
% 0.29/0.48 woz2A: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz2A,definition,
% 0.29/0.48 ( woz2A
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [T: $i] :
% 0.29/0.48 ( ( breln1 @ A @ T )
% 0.29/0.48 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.29/0.48 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(woz2B_type,type,
% 0.29/0.48 woz2B: $o ).
% 0.29/0.48
% 0.29/0.48 thf(woz2B,definition,
% 0.29/0.48 ( woz2B
% 0.29/0.48 = ( ! [A: $i,R: $i] :
% 0.29/0.48 ( ( breln1 @ A @ R )
% 0.29/0.48 => ! [S: $i] :
% 0.29/0.48 ( ( breln1 @ A @ S )
% 0.29/0.48 => ! [T: $i] :
% 0.29/0.48 ( ( breln1 @ A @ T )
% 0.29/0.48 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.29/0.48 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(image1Ex_type,type,
% 0.29/0.48 image1Ex: $o ).
% 0.29/0.48
% 0.29/0.48 thf(image1Ex,definition,
% 0.29/0.48 ( image1Ex
% 0.29/0.48 = ( ! [A: $i,Xf: $i > $i] :
% 0.29/0.48 ? [B: $i] :
% 0.29/0.48 ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ B )
% 0.29/0.48 <=> ? [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 & ( Xx
% 0.29/0.48 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(image1Ex1_type,type,
% 0.29/0.48 image1Ex1: $o ).
% 0.29/0.48
% 0.29/0.48 thf(image1Ex1,definition,
% 0.29/0.48 ( image1Ex1
% 0.29/0.48 = ( ! [A: $i,Xf: $i > $i] :
% 0.29/0.48 ( exu
% 0.29/0.48 @ ^ [B: $i] :
% 0.29/0.48 ! [Xx: $i] :
% 0.29/0.48 ( ( in @ Xx @ B )
% 0.29/0.48 <=> ? [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 & ( Xx
% 0.29/0.48 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(image1_type,type,
% 0.29/0.48 image1: $i > ( $i > $i ) > $i ).
% 0.29/0.48
% 0.29/0.48 thf(image1Equiv_type,type,
% 0.29/0.48 image1Equiv: $o ).
% 0.29/0.48
% 0.29/0.48 thf(image1Equiv,definition,
% 0.29/0.48 ( image1Equiv
% 0.29/0.48 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx
% 0.29/0.48 @ ( image1 @ A
% 0.29/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.29/0.48 <=> ? [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 & ( Xx
% 0.29/0.48 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 thf(image1E,conjecture,
% 0.29/0.48 ( setextAx
% 0.29/0.48 => ( emptysetAx
% 0.29/0.48 => ( setadjoinAx
% 0.29/0.48 => ( powersetAx
% 0.29/0.48 => ( setunionAx
% 0.29/0.48 => ( omega0Ax
% 0.29/0.48 => ( omegaSAx
% 0.29/0.48 => ( omegaIndAx
% 0.29/0.48 => ( replAx
% 0.29/0.48 => ( foundationAx
% 0.29/0.48 => ( wellorderingAx
% 0.29/0.48 => ( descrp
% 0.29/0.48 => ( dsetconstrI
% 0.29/0.48 => ( dsetconstrEL
% 0.29/0.48 => ( dsetconstrER
% 0.29/0.48 => ( exuE1
% 0.29/0.48 => ( prop2setE
% 0.29/0.48 => ( emptysetE
% 0.29/0.48 => ( emptysetimpfalse
% 0.29/0.48 => ( notinemptyset
% 0.29/0.48 => ( exuE3e
% 0.29/0.48 => ( setext
% 0.29/0.48 => ( emptyI
% 0.29/0.48 => ( noeltsimpempty
% 0.29/0.48 => ( setbeta
% 0.29/0.48 => ( nonemptyE1
% 0.29/0.48 => ( nonemptyI
% 0.29/0.48 => ( nonemptyI1
% 0.29/0.48 => ( setadjoinIL
% 0.29/0.48 => ( emptyinunitempty
% 0.29/0.48 => ( setadjoinIR
% 0.29/0.48 => ( setadjoinE
% 0.29/0.48 => ( setadjoinOr
% 0.29/0.48 => ( setoftrueEq
% 0.29/0.48 => ( powersetI
% 0.29/0.48 => ( emptyinPowerset
% 0.29/0.48 => ( emptyInPowerset
% 0.29/0.48 => ( powersetE
% 0.29/0.48 => ( setunionI
% 0.29/0.48 => ( setunionE
% 0.29/0.48 => ( subPowSU
% 0.29/0.48 => ( exuE2
% 0.29/0.48 => ( nonemptyImpWitness
% 0.29/0.48 => ( uniqinunit
% 0.29/0.48 => ( notinsingleton
% 0.29/0.48 => ( eqinunit
% 0.29/0.48 => ( singletonsswitch
% 0.29/0.48 => ( upairsetE
% 0.29/0.48 => ( upairsetIL
% 0.29/0.48 => ( upairsetIR
% 0.29/0.48 => ( emptyE1
% 0.29/0.48 => ( vacuousDall
% 0.29/0.48 => ( quantDeMorgan1
% 0.29/0.48 => ( quantDeMorgan2
% 0.29/0.48 => ( quantDeMorgan3
% 0.29/0.48 => ( quantDeMorgan4
% 0.29/0.48 => ( prop2setI
% 0.29/0.48 => ( prop2set2propI
% 0.29/0.48 => ( notdexE
% 0.29/0.48 => ( notdallE
% 0.29/0.48 => ( exuI1
% 0.29/0.48 => ( exuI3
% 0.29/0.48 => ( exuI2
% 0.29/0.48 => ( inCongP
% 0.29/0.48 => ( in__Cong
% 0.29/0.48 => ( exuE3u
% 0.29/0.48 => ( exu__Cong
% 0.29/0.48 => ( emptyset__Cong
% 0.29/0.48 => ( setadjoin__Cong
% 0.29/0.48 => ( powerset__Cong
% 0.29/0.48 => ( setunion__Cong
% 0.29/0.48 => ( omega__Cong
% 0.29/0.48 => ( exuEu
% 0.29/0.48 => ( descr__Cong
% 0.29/0.48 => ( dsetconstr__Cong
% 0.29/0.48 => ( subsetI1
% 0.29/0.48 => ( eqimpsubset2
% 0.29/0.48 => ( eqimpsubset1
% 0.29/0.48 => ( subsetI2
% 0.29/0.48 => ( emptysetsubset
% 0.29/0.48 => ( subsetE
% 0.29/0.48 => ( subsetE2
% 0.29/0.48 => ( notsubsetI
% 0.29/0.48 => ( notequalI1
% 0.29/0.48 => ( notequalI2
% 0.29/0.48 => ( subsetRefl
% 0.29/0.48 => ( subsetTrans
% 0.29/0.48 => ( setadjoinSub
% 0.29/0.48 => ( setadjoinSub2
% 0.29/0.48 => ( subset2powerset
% 0.29/0.48 => ( setextsub
% 0.29/0.48 => ( subsetemptysetimpeq
% 0.29/0.48 => ( powersetI1
% 0.29/0.48 => ( powersetE1
% 0.29/0.48 => ( inPowerset
% 0.29/0.48 => ( powersetsubset
% 0.29/0.48 => ( sepInPowerset
% 0.29/0.48 => ( sepSubset
% 0.29/0.48 => ( binunionIL
% 0.29/0.48 => ( upairset2IR
% 0.29/0.48 => ( binunionIR
% 0.29/0.48 => ( binunionEcases
% 0.29/0.48 => ( binunionE
% 0.29/0.48 => ( binunionLsub
% 0.29/0.48 => ( binunionRsub
% 0.29/0.48 => ( binintersectI
% 0.29/0.48 => ( binintersectSubset5
% 0.29/0.48 => ( binintersectEL
% 0.29/0.48 => ( binintersectLsub
% 0.29/0.48 => ( binintersectSubset2
% 0.29/0.48 => ( binintersectSubset3
% 0.29/0.48 => ( binintersectER
% 0.29/0.48 => ( disjointsetsI1
% 0.29/0.48 => ( binintersectRsub
% 0.29/0.48 => ( binintersectSubset4
% 0.29/0.48 => ( binintersectSubset1
% 0.29/0.48 => ( bs114d
% 0.29/0.48 => ( setminusI
% 0.29/0.48 => ( setminusEL
% 0.29/0.48 => ( setminusER
% 0.29/0.48 => ( setminusSubset2
% 0.29/0.48 => ( setminusERneg
% 0.29/0.48 => ( setminusELneg
% 0.29/0.48 => ( setminusILneg
% 0.29/0.48 => ( setminusIRneg
% 0.29/0.48 => ( setminusLsub
% 0.29/0.48 => ( setminusSubset1
% 0.29/0.48 => ( symdiffE
% 0.29/0.48 => ( symdiffI1
% 0.29/0.48 => ( symdiffI2
% 0.29/0.48 => ( symdiffIneg1
% 0.29/0.48 => ( symdiffIneg2
% 0.29/0.48 => ( secondinupair
% 0.29/0.48 => ( setukpairIL
% 0.29/0.48 => ( setukpairIR
% 0.29/0.48 => ( kpairiskpair
% 0.29/0.48 => ( kpairp
% 0.29/0.48 => ( singletonsubset
% 0.29/0.48 => ( singletoninpowerset
% 0.29/0.48 => ( singletoninpowunion
% 0.29/0.48 => ( upairset2E
% 0.29/0.48 => ( upairsubunion
% 0.29/0.48 => ( upairinpowunion
% 0.29/0.48 => ( ubforcartprodlem1
% 0.29/0.48 => ( ubforcartprodlem2
% 0.29/0.48 => ( ubforcartprodlem3
% 0.29/0.48 => ( cartprodpairin
% 0.29/0.48 => ( cartprodmempair1
% 0.29/0.48 => ( cartprodmempair
% 0.29/0.48 => ( setunionE2
% 0.29/0.48 => ( setunionsingleton1
% 0.29/0.48 => ( setunionsingleton2
% 0.29/0.48 => ( setunionsingleton
% 0.29/0.48 => ( singletonprop
% 0.29/0.48 => ( ex1E1
% 0.29/0.48 => ( ex1I
% 0.29/0.48 => ( ex1I2
% 0.29/0.48 => ( singletonsuniq
% 0.29/0.48 => ( setukpairinjL1
% 0.29/0.48 => ( kfstsingleton
% 0.29/0.48 => ( theprop
% 0.29/0.48 => ( kfstpairEq
% 0.29/0.48 => ( cartprodfstin
% 0.29/0.48 => ( setukpairinjL2
% 0.29/0.48 => ( setukpairinjL
% 0.29/0.48 => ( setukpairinjR11
% 0.29/0.48 => ( setukpairinjR12
% 0.29/0.48 => ( setukpairinjR1
% 0.29/0.48 => ( upairequniteq
% 0.29/0.48 => ( setukpairinjR2
% 0.29/0.48 => ( setukpairinjR
% 0.29/0.48 => ( ksndsingleton
% 0.29/0.48 => ( ksndpairEq
% 0.29/0.48 => ( kpairsurjEq
% 0.29/0.48 => ( cartprodsndin
% 0.29/0.48 => ( cartprodpairmemEL
% 0.29/0.48 => ( cartprodpairmemER
% 0.29/0.48 => ( cartprodmempaircEq
% 0.29/0.48 => ( cartprodfstpairEq
% 0.29/0.48 => ( cartprodsndpairEq
% 0.29/0.48 => ( cartprodpairsurjEq
% 0.29/0.48 => ( dpsetconstrI
% 0.29/0.48 => ( dpsetconstrSub
% 0.29/0.48 => ( setOfPairsIsBReln
% 0.29/0.48 => ( dpsetconstrERa
% 0.29/0.48 => ( dpsetconstrEL1
% 0.29/0.48 => ( dpsetconstrEL2
% 0.29/0.48 => ( dpsetconstrER
% 0.29/0.48 => ( funcImageSingleton
% 0.29/0.48 => ( apProp
% 0.29/0.48 => ( app
% 0.29/0.48 => ( infuncsetfunc
% 0.29/0.48 => ( ap2p
% 0.29/0.48 => ( funcinfuncset
% 0.29/0.48 => ( lamProp
% 0.29/0.48 => ( lamp
% 0.29/0.48 => ( lam2p
% 0.29/0.48 => ( brelnall1
% 0.29/0.48 => ( brelnall2
% 0.29/0.48 => ( ex1E2
% 0.29/0.48 => ( funcGraphProp1
% 0.29/0.48 => ( funcGraphProp3
% 0.29/0.48 => ( funcGraphProp2
% 0.29/0.48 => ( funcextLem
% 0.29/0.48 => ( funcGraphProp4
% 0.29/0.48 => ( subbreln
% 0.29/0.48 => ( eqbreln
% 0.29/0.48 => ( funcext
% 0.29/0.48 => ( funcext2
% 0.29/0.48 => ( ap2apEq1
% 0.29/0.48 => ( ap2apEq2
% 0.29/0.48 => ( beta1
% 0.29/0.48 => ( eta1
% 0.29/0.48 => ( lam2lamEq
% 0.29/0.48 => ( beta2
% 0.29/0.48 => ( eta2
% 0.29/0.48 => ( iffalseProp1
% 0.29/0.48 => ( iffalseProp2
% 0.29/0.48 => ( iftrueProp1
% 0.29/0.48 => ( iftrueProp2
% 0.29/0.48 => ( ifSingleton
% 0.29/0.48 => ( ifp
% 0.29/0.48 => ( theeq
% 0.29/0.48 => ( iftrue
% 0.29/0.48 => ( iffalse
% 0.29/0.48 => ( iftrueorfalse
% 0.29/0.48 => ( binintersectT_lem
% 0.29/0.48 => ( binunionT_lem
% 0.29/0.48 => ( powersetT_lem
% 0.29/0.48 => ( setminusT_lem
% 0.29/0.48 => ( complementT_lem
% 0.29/0.48 => ( setextT
% 0.29/0.48 => ( subsetTI
% 0.29/0.48 => ( powersetTI1
% 0.29/0.48 => ( powersetTE1
% 0.29/0.48 => ( complementTI1
% 0.29/0.48 => ( complementTE1
% 0.29/0.48 => ( binintersectTELcontra
% 0.29/0.48 => ( binintersectTERcontra
% 0.29/0.48 => ( contrasubsetT
% 0.29/0.48 => ( contrasubsetT1
% 0.29/0.48 => ( contrasubsetT2
% 0.29/0.48 => ( contrasubsetT3
% 0.29/0.48 => ( doubleComplementI1
% 0.29/0.48 => ( doubleComplementE1
% 0.29/0.48 => ( doubleComplementSub1
% 0.29/0.48 => ( doubleComplementSub2
% 0.29/0.48 => ( doubleComplementEq
% 0.29/0.48 => ( complementTnotintersectT
% 0.29/0.48 => ( complementImpComplementIntersect
% 0.29/0.48 => ( complementSubsetComplementIntersect
% 0.29/0.48 => ( complementInPowersetComplementIntersect
% 0.29/0.48 => ( contraSubsetComplement
% 0.29/0.48 => ( complementTcontraSubset
% 0.29/0.48 => ( binunionTILcontra
% 0.29/0.48 => ( binunionTIRcontra
% 0.29/0.48 => ( inIntersectImpInUnion
% 0.29/0.48 => ( inIntersectImpInUnion2
% 0.29/0.48 => ( inIntersectImpInIntersectUnions
% 0.29/0.48 => ( intersectInPowersetIntersectUnions
% 0.29/0.48 => ( inComplementUnionImpNotIn1
% 0.29/0.48 => ( inComplementUnionImpInComplement1
% 0.29/0.48 => ( binunionTE
% 0.29/0.48 => ( binunionTEcontra
% 0.29/0.48 => ( demorgan2a1
% 0.29/0.48 => ( complementUnionInPowersetComplement
% 0.29/0.48 => ( demorgan2a2
% 0.29/0.48 => ( demorgan1a
% 0.29/0.48 => ( demorgan1b
% 0.29/0.48 => ( demorgan1
% 0.29/0.48 => ( demorgan2a
% 0.29/0.48 => ( demorgan2b2
% 0.29/0.48 => ( demorgan2b
% 0.29/0.48 => ( demorgan2
% 0.29/0.48 => ( woz13rule0
% 0.29/0.48 => ( woz13rule1
% 0.29/0.48 => ( woz13rule2
% 0.29/0.48 => ( woz13rule3
% 0.29/0.48 => ( woz13rule4
% 0.29/0.48 => ( woz1_1
% 0.29/0.48 => ( woz1_2
% 0.29/0.48 => ( woz1_3
% 0.29/0.48 => ( woz1_4
% 0.29/0.48 => ( woz1_5
% 0.29/0.48 => ( breln1all2
% 0.29/0.48 => ( breln1SetBreln1
% 0.29/0.48 => ( choice2fnsingleton
% 0.29/0.48 => ( setOfPairsIsBReln1
% 0.29/0.48 => ( breln1all1
% 0.29/0.48 => ( subbreln1
% 0.29/0.48 => ( eqbreln1
% 0.29/0.48 => ( breln1invprop
% 0.29/0.48 => ( breln1invI
% 0.29/0.48 => ( breln1invE
% 0.29/0.48 => ( breln1compprop
% 0.29/0.48 => ( breln1compI
% 0.29/0.48 => ( breln1compE
% 0.29/0.48 => ( breln1compEex
% 0.29/0.48 => ( breln1unionprop
% 0.29/0.48 => ( breln1unionIL
% 0.29/0.48 => ( breln1unionIR
% 0.29/0.48 => ( breln1unionI
% 0.29/0.48 => ( breln1unionE
% 0.29/0.48 => ( breln1unionEcases
% 0.29/0.48 => ( breln1unionCommutes
% 0.29/0.48 => ( woz2Ex
% 0.29/0.48 => ( woz2W
% 0.29/0.48 => ( woz2A
% 0.29/0.48 => ( woz2B
% 0.29/0.48 => ( image1Ex
% 0.29/0.48 => ( image1Ex1
% 0.29/0.48 => ( image1Equiv
% 0.29/0.48 => ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.29/0.48 ( ( in @ Xx
% 0.29/0.48 @ ( image1 @ A
% 0.29/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.29/0.48 => ? [Xy: $i] :
% 0.29/0.48 ( ( in @ Xy @ A )
% 0.29/0.48 & ( Xx
% 0.29/0.48 = ( Xf @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 ------------------------
% 2.95/1.54 ---- Embedded in THF ---
% 2.95/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.95/1.54 %%% Generated on Tue Feb 24 12:34:28 EST 2026
% 2.95/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.95/1.54 %%% Logic specification used:
% 2.95/1.54 %%% thf(spec, logic, $$dhol).
% 2.95/1.54
% 2.95/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.c9IygHO5Aa/DTF2DTF16722.p
% See solution above
% 2.95/1.54 ------------------------
% 2.95/1.57 ---- Cleaned THF ---
% 2.95/1.57 thf(in_type,type,
% 2.95/1.57 in: $i > $i > $o ).
% 2.95/1.57
% 2.95/1.57 thf(exu_type,type,
% 2.95/1.57 exu: ( $i > $o ) > $o ).
% 2.95/1.57
% 2.95/1.57 thf(exu,definition,
% 2.95/1.57 ( exu
% 2.95/1.57 = ( ^ [Xphi: $i > $o] :
% 2.95/1.57 ? [Xx: $i] :
% 2.95/1.57 ( ( Xphi @ Xx )
% 2.95/1.57 & ! [Xy: $i] :
% 2.95/1.57 ( ( Xphi @ Xy )
% 2.95/1.57 => ( Xx = Xy ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setextAx_type,type,
% 2.95/1.57 setextAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setextAx,definition,
% 2.95/1.57 ( setextAx
% 2.95/1.57 = ( ! [A: $i,B: $i] :
% 2.95/1.57 ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 <=> ( in @ Xx @ B ) )
% 2.95/1.57 => ( A = B ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(emptyset_type,type,
% 2.95/1.57 emptyset: $i ).
% 2.95/1.57
% 2.95/1.57 thf(emptysetAx_type,type,
% 2.95/1.57 emptysetAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(emptysetAx,definition,
% 2.95/1.57 ( emptysetAx
% 2.95/1.57 = ( ! [Xx: $i] :
% 2.95/1.57 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoin_type,type,
% 2.95/1.57 setadjoin: $i > $i > $i ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinAx_type,type,
% 2.95/1.57 setadjoinAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinAx,definition,
% 2.95/1.57 ( setadjoinAx
% 2.95/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.95/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.95/1.57 <=> ( ( Xy = Xx )
% 2.95/1.57 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(powerset_type,type,
% 2.95/1.57 powerset: $i > $i ).
% 2.95/1.57
% 2.95/1.57 thf(powersetAx_type,type,
% 2.95/1.57 powersetAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(powersetAx,definition,
% 2.95/1.57 ( powersetAx
% 2.95/1.57 = ( ! [A: $i,B: $i] :
% 2.95/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.95/1.57 <=> ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ B )
% 2.95/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setunion_type,type,
% 2.95/1.57 setunion: $i > $i ).
% 2.95/1.57
% 2.95/1.57 thf(setunionAx_type,type,
% 2.95/1.57 setunionAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setunionAx,definition,
% 2.95/1.57 ( setunionAx
% 2.95/1.57 = ( ! [A: $i,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.95/1.57 <=> ? [B: $i] :
% 2.95/1.57 ( ( in @ Xx @ B )
% 2.95/1.57 & ( in @ B @ A ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(omega_type,type,
% 2.95/1.57 omega: $i ).
% 2.95/1.57
% 2.95/1.57 thf(omega0Ax_type,type,
% 2.95/1.57 omega0Ax: $o ).
% 2.95/1.57
% 2.95/1.57 thf(omega0Ax,definition,
% 2.95/1.57 ( omega0Ax
% 2.95/1.57 = ( in @ emptyset @ omega ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(omegaSAx_type,type,
% 2.95/1.57 omegaSAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(omegaSAx,definition,
% 2.95/1.57 ( omegaSAx
% 2.95/1.57 = ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ omega )
% 2.95/1.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(omegaIndAx_type,type,
% 2.95/1.57 omegaIndAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(omegaIndAx,definition,
% 2.95/1.57 ( omegaIndAx
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ( ( ( in @ emptyset @ A )
% 2.95/1.57 & ! [Xx: $i] :
% 2.95/1.57 ( ( ( in @ Xx @ omega )
% 2.95/1.57 & ( in @ Xx @ A ) )
% 2.95/1.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.95/1.57 => ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ omega )
% 2.95/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(replAx_type,type,
% 2.95/1.57 replAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(replAx,definition,
% 2.95/1.57 ( replAx
% 2.95/1.57 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.95/1.57 ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( exu
% 2.95/1.57 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.95/1.57 => ? [B: $i] :
% 2.95/1.57 ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ B )
% 2.95/1.57 <=> ? [Xy: $i] :
% 2.95/1.57 ( ( in @ Xy @ A )
% 2.95/1.57 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(foundationAx_type,type,
% 2.95/1.57 foundationAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(foundationAx,definition,
% 2.95/1.57 ( foundationAx
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.95/1.57 => ? [B: $i] :
% 2.95/1.57 ( ( in @ B @ A )
% 2.95/1.57 & ~ ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ B )
% 2.95/1.57 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(wellorderingAx_type,type,
% 2.95/1.57 wellorderingAx: $o ).
% 2.95/1.57
% 2.95/1.57 thf(wellorderingAx,definition,
% 2.95/1.57 ( wellorderingAx
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ? [B: $i] :
% 2.95/1.57 ( ! [C: $i] :
% 2.95/1.57 ( ( in @ C @ B )
% 2.95/1.57 => ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ C )
% 2.95/1.57 => ( in @ Xx @ A ) ) )
% 2.95/1.57 & ! [Xx: $i,Xy: $i] :
% 2.95/1.57 ( ( ( in @ Xx @ A )
% 2.95/1.57 & ( in @ Xy @ A ) )
% 2.95/1.57 => ( ! [C: $i] :
% 2.95/1.57 ( ( in @ C @ B )
% 2.95/1.57 => ( ( in @ Xx @ C )
% 2.95/1.57 <=> ( in @ Xy @ C ) ) )
% 2.95/1.57 => ( Xx = Xy ) ) )
% 2.95/1.57 & ! [C: $i,D: $i] :
% 2.95/1.57 ( ( ( in @ C @ B )
% 2.95/1.57 & ( in @ D @ B ) )
% 2.95/1.57 => ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ C )
% 2.95/1.57 => ( in @ Xx @ D ) )
% 2.95/1.57 | ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ D )
% 2.95/1.57 => ( in @ Xx @ C ) ) ) )
% 2.95/1.57 & ! [C: $i] :
% 2.95/1.57 ( ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ C )
% 2.95/1.57 => ( in @ Xx @ A ) )
% 2.95/1.57 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.95/1.57 => ? [D: $i,Xx: $i] :
% 2.95/1.57 ( ( in @ D @ B )
% 2.95/1.57 & ( in @ Xx @ C )
% 2.95/1.57 & ~ ? [Xy: $i] :
% 2.95/1.57 ( ( in @ Xy @ D )
% 2.95/1.57 & ( in @ Xy @ C ) )
% 2.95/1.57 & ! [E: $i] :
% 2.95/1.57 ( ( in @ E @ B )
% 2.95/1.57 => ( ! [Xy: $i] :
% 2.95/1.57 ( ( in @ Xy @ E )
% 2.95/1.57 => ( in @ Xy @ D ) )
% 2.95/1.57 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(descr_type,type,
% 2.95/1.57 descr: ( $i > $o ) > $i ).
% 2.95/1.57
% 2.95/1.57 thf(descrp_type,type,
% 2.95/1.57 descrp: $o ).
% 2.95/1.57
% 2.95/1.57 thf(descrp,definition,
% 2.95/1.57 ( descrp
% 2.95/1.57 = ( ! [Xphi: $i > $o] :
% 2.95/1.57 ( ( exu
% 2.95/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.57 => ( Xphi
% 2.95/1.57 @ ( descr
% 2.95/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(dsetconstr_type,type,
% 2.95/1.57 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.95/1.57
% 2.95/1.57 thf(dsetconstrI_type,type,
% 2.95/1.57 dsetconstrI: $o ).
% 2.95/1.57
% 2.95/1.57 thf(dsetconstrI,definition,
% 2.95/1.57 ( dsetconstrI
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( ( Xphi @ Xx )
% 2.95/1.57 => ( in @ Xx
% 2.95/1.57 @ ( dsetconstr @ A
% 2.95/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(dsetconstrEL_type,type,
% 2.95/1.57 dsetconstrEL: $o ).
% 2.95/1.57
% 2.95/1.57 thf(dsetconstrEL,definition,
% 2.95/1.57 ( dsetconstrEL
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx
% 2.95/1.57 @ ( dsetconstr @ A
% 2.95/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.95/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(dsetconstrER_type,type,
% 2.95/1.57 dsetconstrER: $o ).
% 2.95/1.57
% 2.95/1.57 thf(dsetconstrER,definition,
% 2.95/1.57 ( dsetconstrER
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx
% 2.95/1.57 @ ( dsetconstr @ A
% 2.95/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.95/1.57 => ( Xphi @ Xx ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(exuE1_type,type,
% 2.95/1.57 exuE1: $o ).
% 2.95/1.57
% 2.95/1.57 thf(exuE1,definition,
% 2.95/1.57 ( exuE1
% 2.95/1.57 = ( ! [Xphi: $i > $o] :
% 2.95/1.57 ( ( exu
% 2.95/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.57 => ? [Xx: $i] :
% 2.95/1.57 ( ( Xphi @ Xx )
% 2.95/1.57 & ! [Xy: $i] :
% 2.95/1.57 ( ( Xphi @ Xy )
% 2.95/1.57 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(prop2set_type,type,
% 2.95/1.57 prop2set: $o > $i ).
% 2.95/1.57
% 2.95/1.57 thf(prop2setE_type,type,
% 2.95/1.57 prop2setE: $o ).
% 2.95/1.57
% 2.95/1.57 thf(prop2setE,definition,
% 2.95/1.57 ( prop2setE
% 2.95/1.57 = ( ! [Xphi: $o,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.95/1.57 => Xphi ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(emptysetE_type,type,
% 2.95/1.57 emptysetE: $o ).
% 2.95/1.57
% 2.95/1.57 thf(emptysetE,definition,
% 2.95/1.57 ( emptysetE
% 2.95/1.57 = ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ emptyset )
% 2.95/1.57 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(emptysetimpfalse_type,type,
% 2.95/1.57 emptysetimpfalse: $o ).
% 2.95/1.57
% 2.95/1.57 thf(emptysetimpfalse,definition,
% 2.95/1.57 ( emptysetimpfalse
% 2.95/1.57 = ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ emptyset )
% 2.95/1.57 => $false ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(notinemptyset_type,type,
% 2.95/1.57 notinemptyset: $o ).
% 2.95/1.57
% 2.95/1.57 thf(notinemptyset,definition,
% 2.95/1.57 ( notinemptyset
% 2.95/1.57 = ( ! [Xx: $i] :
% 2.95/1.57 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(exuE3e_type,type,
% 2.95/1.57 exuE3e: $o ).
% 2.95/1.57
% 2.95/1.57 thf(exuE3e,definition,
% 2.95/1.57 ( exuE3e
% 2.95/1.57 = ( ! [Xphi: $i > $o] :
% 2.95/1.57 ( ( exu
% 2.95/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.57 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setext_type,type,
% 2.95/1.57 setext: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setext,definition,
% 2.95/1.57 ( setext
% 2.95/1.57 = ( ! [A: $i,B: $i] :
% 2.95/1.57 ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( in @ Xx @ B ) )
% 2.95/1.57 => ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ B )
% 2.95/1.57 => ( in @ Xx @ A ) )
% 2.95/1.57 => ( A = B ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(emptyI_type,type,
% 2.95/1.57 emptyI: $o ).
% 2.95/1.57
% 2.95/1.57 thf(emptyI,definition,
% 2.95/1.57 ( emptyI
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ( ! [Xx: $i] :
% 2.95/1.57 ~ ( in @ Xx @ A )
% 2.95/1.57 => ( A = emptyset ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(noeltsimpempty_type,type,
% 2.95/1.57 noeltsimpempty: $o ).
% 2.95/1.57
% 2.95/1.57 thf(noeltsimpempty,definition,
% 2.95/1.57 ( noeltsimpempty
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ( ! [Xx: $i] :
% 2.95/1.57 ~ ( in @ Xx @ A )
% 2.95/1.57 => ( A = emptyset ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setbeta_type,type,
% 2.95/1.57 setbeta: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setbeta,definition,
% 2.95/1.57 ( setbeta
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( ( in @ Xx
% 2.95/1.57 @ ( dsetconstr @ A
% 2.95/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.95/1.57 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(nonempty_type,type,
% 2.95/1.57 nonempty: $i > $o ).
% 2.95/1.57
% 2.95/1.57 thf(nonempty,definition,
% 2.95/1.57 ( nonempty
% 2.95/1.57 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(nonemptyE1_type,type,
% 2.95/1.57 nonemptyE1: $o ).
% 2.95/1.57
% 2.95/1.57 thf(nonemptyE1,definition,
% 2.95/1.57 ( nonemptyE1
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ( ( nonempty @ A )
% 2.95/1.57 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(nonemptyI_type,type,
% 2.95/1.57 nonemptyI: $o ).
% 2.95/1.57
% 2.95/1.57 thf(nonemptyI,definition,
% 2.95/1.57 ( nonemptyI
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( ( Xphi @ Xx )
% 2.95/1.57 => ( nonempty
% 2.95/1.57 @ ( dsetconstr @ A
% 2.95/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(nonemptyI1_type,type,
% 2.95/1.57 nonemptyI1: $o ).
% 2.95/1.57
% 2.95/1.57 thf(nonemptyI1,definition,
% 2.95/1.57 ( nonemptyI1
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.95/1.57 => ( nonempty @ A ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinIL_type,type,
% 2.95/1.57 setadjoinIL: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinIL,definition,
% 2.95/1.57 ( setadjoinIL
% 2.95/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(emptyinunitempty_type,type,
% 2.95/1.57 emptyinunitempty: $o ).
% 2.95/1.57
% 2.95/1.57 thf(emptyinunitempty,definition,
% 2.95/1.57 ( emptyinunitempty
% 2.95/1.57 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinIR_type,type,
% 2.95/1.57 setadjoinIR: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinIR,definition,
% 2.95/1.57 ( setadjoinIR
% 2.95/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.95/1.57 ( ( in @ Xy @ A )
% 2.95/1.57 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinE_type,type,
% 2.95/1.57 setadjoinE: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinE,definition,
% 2.95/1.57 ( setadjoinE
% 2.95/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.95/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.95/1.57 => ! [Xphi: $o] :
% 2.95/1.57 ( ( ( Xy = Xx )
% 2.95/1.57 => Xphi )
% 2.95/1.57 => ( ( ( in @ Xy @ A )
% 2.95/1.57 => Xphi )
% 2.95/1.57 => Xphi ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinOr_type,type,
% 2.95/1.57 setadjoinOr: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setadjoinOr,definition,
% 2.95/1.57 ( setadjoinOr
% 2.95/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.95/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.95/1.57 => ( ( Xy = Xx )
% 2.95/1.57 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setoftrueEq_type,type,
% 2.95/1.57 setoftrueEq: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setoftrueEq,definition,
% 2.95/1.57 ( setoftrueEq
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ( ( dsetconstr @ A
% 2.95/1.57 @ ^ [Xx: $i] : $true )
% 2.95/1.57 = A ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(powersetI_type,type,
% 2.95/1.57 powersetI: $o ).
% 2.95/1.57
% 2.95/1.57 thf(powersetI,definition,
% 2.95/1.57 ( powersetI
% 2.95/1.57 = ( ! [A: $i,B: $i] :
% 2.95/1.57 ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ B )
% 2.95/1.57 => ( in @ Xx @ A ) )
% 2.95/1.57 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(emptyinPowerset_type,type,
% 2.95/1.57 emptyinPowerset: $o ).
% 2.95/1.57
% 2.95/1.57 thf(emptyinPowerset,definition,
% 2.95/1.57 ( emptyinPowerset
% 2.95/1.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(emptyInPowerset_type,type,
% 2.95/1.57 emptyInPowerset: $o ).
% 2.95/1.57
% 2.95/1.57 thf(emptyInPowerset,definition,
% 2.95/1.57 ( emptyInPowerset
% 2.95/1.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(powersetE_type,type,
% 2.95/1.57 powersetE: $o ).
% 2.95/1.57
% 2.95/1.57 thf(powersetE,definition,
% 2.95/1.57 ( powersetE
% 2.95/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.95/1.57 => ( ( in @ Xx @ B )
% 2.95/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setunionI_type,type,
% 2.95/1.57 setunionI: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setunionI,definition,
% 2.95/1.57 ( setunionI
% 2.95/1.57 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.95/1.57 ( ( in @ Xx @ B )
% 2.95/1.57 => ( ( in @ B @ A )
% 2.95/1.57 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(setunionE_type,type,
% 2.95/1.57 setunionE: $o ).
% 2.95/1.57
% 2.95/1.57 thf(setunionE,definition,
% 2.95/1.57 ( setunionE
% 2.95/1.57 = ( ! [A: $i,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.95/1.57 => ! [Xphi: $o] :
% 2.95/1.57 ( ! [B: $i] :
% 2.95/1.57 ( ( in @ Xx @ B )
% 2.95/1.57 => ( ( in @ B @ A )
% 2.95/1.57 => Xphi ) )
% 2.95/1.57 => Xphi ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(subPowSU_type,type,
% 2.95/1.57 subPowSU: $o ).
% 2.95/1.57
% 2.95/1.57 thf(subPowSU,definition,
% 2.95/1.57 ( subPowSU
% 2.95/1.57 = ( ! [A: $i,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(exuE2_type,type,
% 2.95/1.57 exuE2: $o ).
% 2.95/1.57
% 2.95/1.57 thf(exuE2,definition,
% 2.95/1.57 ( exuE2
% 2.95/1.57 = ( ! [Xphi: $i > $o] :
% 2.95/1.57 ( ( exu
% 2.95/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.57 => ? [Xx: $i] :
% 2.95/1.57 ! [Xy: $i] :
% 2.95/1.57 ( ( Xphi @ Xy )
% 2.95/1.57 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(nonemptyImpWitness_type,type,
% 2.95/1.57 nonemptyImpWitness: $o ).
% 2.95/1.57
% 2.95/1.57 thf(nonemptyImpWitness,definition,
% 2.95/1.57 ( nonemptyImpWitness
% 2.95/1.57 = ( ! [A: $i] :
% 2.95/1.57 ( ( nonempty @ A )
% 2.95/1.57 => ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 & $true ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(uniqinunit_type,type,
% 2.95/1.57 uniqinunit: $o ).
% 2.95/1.57
% 2.95/1.57 thf(uniqinunit,definition,
% 2.95/1.57 ( uniqinunit
% 2.95/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.95/1.57 => ( Xx = Xy ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(notinsingleton_type,type,
% 2.95/1.57 notinsingleton: $o ).
% 2.95/1.57
% 2.95/1.57 thf(notinsingleton,definition,
% 2.95/1.57 ( notinsingleton
% 2.95/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.57 ( ( Xx != Xy )
% 2.95/1.57 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(eqinunit_type,type,
% 2.95/1.57 eqinunit: $o ).
% 2.95/1.57
% 2.95/1.57 thf(eqinunit,definition,
% 2.95/1.57 ( eqinunit
% 2.95/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.57 ( ( Xx = Xy )
% 2.95/1.57 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(singletonsswitch_type,type,
% 2.95/1.57 singletonsswitch: $o ).
% 2.95/1.57
% 2.95/1.57 thf(singletonsswitch,definition,
% 2.95/1.57 ( singletonsswitch
% 2.95/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.95/1.57 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(upairsetE_type,type,
% 2.95/1.57 upairsetE: $o ).
% 2.95/1.57
% 2.95/1.57 thf(upairsetE,definition,
% 2.95/1.57 ( upairsetE
% 2.95/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.95/1.57 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.95/1.57 => ( ( Xz = Xx )
% 2.95/1.57 | ( Xz = Xy ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(upairsetIL_type,type,
% 2.95/1.57 upairsetIL: $o ).
% 2.95/1.57
% 2.95/1.57 thf(upairsetIL,definition,
% 2.95/1.57 ( upairsetIL
% 2.95/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(upairsetIR_type,type,
% 2.95/1.57 upairsetIR: $o ).
% 2.95/1.57
% 2.95/1.57 thf(upairsetIR,definition,
% 2.95/1.57 ( upairsetIR
% 2.95/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(emptyE1_type,type,
% 2.95/1.57 emptyE1: $o ).
% 2.95/1.57
% 2.95/1.57 thf(emptyE1,definition,
% 2.95/1.57 ( emptyE1
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.57 ( ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 & ( Xphi @ Xx ) )
% 2.95/1.57 => ( ( ( dsetconstr @ A
% 2.95/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.57 = emptyset )
% 2.95/1.57 => $false ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(vacuousDall_type,type,
% 2.95/1.57 vacuousDall: $o ).
% 2.95/1.57
% 2.95/1.57 thf(vacuousDall,definition,
% 2.95/1.57 ( vacuousDall
% 2.95/1.57 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ emptyset )
% 2.95/1.57 => ( Xphi @ Xx ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(quantDeMorgan1_type,type,
% 2.95/1.57 quantDeMorgan1: $o ).
% 2.95/1.57
% 2.95/1.57 thf(quantDeMorgan1,definition,
% 2.95/1.57 ( quantDeMorgan1
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.57 ( ~ ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( Xphi @ Xx ) )
% 2.95/1.57 => ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(quantDeMorgan2_type,type,
% 2.95/1.57 quantDeMorgan2: $o ).
% 2.95/1.57
% 2.95/1.57 thf(quantDeMorgan2,definition,
% 2.95/1.57 ( quantDeMorgan2
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.57 ( ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ~ ( Xphi @ Xx ) )
% 2.95/1.57 => ~ ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(quantDeMorgan3_type,type,
% 2.95/1.57 quantDeMorgan3: $o ).
% 2.95/1.57
% 2.95/1.57 thf(quantDeMorgan3,definition,
% 2.95/1.57 ( quantDeMorgan3
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.57 ( ~ ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 & ( Xphi @ Xx ) )
% 2.95/1.57 => ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(quantDeMorgan4_type,type,
% 2.95/1.57 quantDeMorgan4: $o ).
% 2.95/1.57
% 2.95/1.57 thf(quantDeMorgan4,definition,
% 2.95/1.57 ( quantDeMorgan4
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.57 ( ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 & ~ ( Xphi @ Xx ) )
% 2.95/1.57 => ~ ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(prop2setI_type,type,
% 2.95/1.57 prop2setI: $o ).
% 2.95/1.57
% 2.95/1.57 thf(prop2setI,definition,
% 2.95/1.57 ( prop2setI
% 2.95/1.57 = ( ! [Xphi: $o] :
% 2.95/1.57 ( Xphi
% 2.95/1.57 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(set2prop_type,type,
% 2.95/1.57 set2prop: $i > $o ).
% 2.95/1.57
% 2.95/1.57 thf(prop2set2propI_type,type,
% 2.95/1.57 prop2set2propI: $o ).
% 2.95/1.57
% 2.95/1.57 thf(prop2set2propI,definition,
% 2.95/1.57 ( prop2set2propI
% 2.95/1.57 = ( ! [Xphi: $o] :
% 2.95/1.57 ( Xphi
% 2.95/1.57 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(notdexE_type,type,
% 2.95/1.57 notdexE: $o ).
% 2.95/1.57
% 2.95/1.57 thf(notdexE,definition,
% 2.95/1.57 ( notdexE
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.57 ( ~ ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 & ( Xphi @ Xx ) )
% 2.95/1.57 => ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(notdallE_type,type,
% 2.95/1.57 notdallE: $o ).
% 2.95/1.57
% 2.95/1.57 thf(notdallE,definition,
% 2.95/1.57 ( notdallE
% 2.95/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.57 ( ~ ! [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 => ( Xphi @ Xx ) )
% 2.95/1.57 => ? [Xx: $i] :
% 2.95/1.57 ( ( in @ Xx @ A )
% 2.95/1.57 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.57
% 2.95/1.57 thf(exuI1_type,type,
% 2.95/1.58 exuI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(exuI1,definition,
% 2.95/1.58 ( exuI1
% 2.95/1.58 = ( ! [Xphi: $i > $o] :
% 2.95/1.58 ( ? [Xx: $i] :
% 2.95/1.58 ( ( Xphi @ Xx )
% 2.95/1.58 & ! [Xy: $i] :
% 2.95/1.58 ( ( Xphi @ Xy )
% 2.95/1.58 => ( Xx = Xy ) ) )
% 2.95/1.58 => ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(exuI3_type,type,
% 2.95/1.58 exuI3: $o ).
% 2.95/1.58
% 2.95/1.58 thf(exuI3,definition,
% 2.95/1.58 ( exuI3
% 2.95/1.58 = ( ! [Xphi: $i > $o] :
% 2.95/1.58 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.95/1.58 => ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xphi @ Xx )
% 2.95/1.58 => ( ( Xphi @ Xy )
% 2.95/1.58 => ( Xx = Xy ) ) )
% 2.95/1.58 => ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(exuI2_type,type,
% 2.95/1.58 exuI2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(exuI2,definition,
% 2.95/1.58 ( exuI2
% 2.95/1.58 = ( ! [Xphi: $i > $o] :
% 2.95/1.58 ( ? [Xx: $i] :
% 2.95/1.58 ! [Xy: $i] :
% 2.95/1.58 ( ( Xphi @ Xy )
% 2.95/1.58 <=> ( Xy = Xx ) )
% 2.95/1.58 => ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(inCongP_type,type,
% 2.95/1.58 inCongP: $o ).
% 2.95/1.58
% 2.95/1.58 thf(inCongP,definition,
% 2.95/1.58 ( inCongP
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( A = B )
% 2.95/1.58 => ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xx = Xy )
% 2.95/1.58 => ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(in__Cong_type,type,
% 2.95/1.58 in__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(in__Cong,definition,
% 2.95/1.58 ( in__Cong
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( A = B )
% 2.95/1.58 => ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xx = Xy )
% 2.95/1.58 => ( ( in @ Xx @ A )
% 2.95/1.58 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(exuE3u_type,type,
% 2.95/1.58 exuE3u: $o ).
% 2.95/1.58
% 2.95/1.58 thf(exuE3u,definition,
% 2.95/1.58 ( exuE3u
% 2.95/1.58 = ( ! [Xphi: $i > $o] :
% 2.95/1.58 ( ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 => ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xphi @ Xx )
% 2.95/1.58 => ( ( Xphi @ Xy )
% 2.95/1.58 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(exu__Cong_type,type,
% 2.95/1.58 exu__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(exu__Cong,definition,
% 2.95/1.58 ( exu__Cong
% 2.95/1.58 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xx = Xy )
% 2.95/1.58 => ( ( Xphi @ Xx )
% 2.95/1.58 <=> ( Xpsi @ Xy ) ) )
% 2.95/1.58 => ( ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 <=> ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(emptyset__Cong_type,type,
% 2.95/1.58 emptyset__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(emptyset__Cong,definition,
% 2.95/1.58 ( emptyset__Cong
% 2.95/1.58 = ( emptyset = emptyset ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setadjoin__Cong_type,type,
% 2.95/1.58 setadjoin__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setadjoin__Cong,definition,
% 2.95/1.58 ( setadjoin__Cong
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xx = Xy )
% 2.95/1.58 => ! [Xz: $i,Xu: $i] :
% 2.95/1.58 ( ( Xz = Xu )
% 2.95/1.58 => ( ( setadjoin @ Xx @ Xz )
% 2.95/1.58 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(powerset__Cong_type,type,
% 2.95/1.58 powerset__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(powerset__Cong,definition,
% 2.95/1.58 ( powerset__Cong
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( A = B )
% 2.95/1.58 => ( ( powerset @ A )
% 2.95/1.58 = ( powerset @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setunion__Cong_type,type,
% 2.95/1.58 setunion__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setunion__Cong,definition,
% 2.95/1.58 ( setunion__Cong
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( A = B )
% 2.95/1.58 => ( ( setunion @ A )
% 2.95/1.58 = ( setunion @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(omega__Cong_type,type,
% 2.95/1.58 omega__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(omega__Cong,definition,
% 2.95/1.58 ( omega__Cong
% 2.95/1.58 = ( omega = omega ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(exuEu_type,type,
% 2.95/1.58 exuEu: $o ).
% 2.95/1.58
% 2.95/1.58 thf(exuEu,definition,
% 2.95/1.58 ( exuEu
% 2.95/1.58 = ( ! [Xphi: $i > $o] :
% 2.95/1.58 ( ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 => ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xphi @ Xx )
% 2.95/1.58 => ( ( Xphi @ Xy )
% 2.95/1.58 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(descr__Cong_type,type,
% 2.95/1.58 descr__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(descr__Cong,definition,
% 2.95/1.58 ( descr__Cong
% 2.95/1.58 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xx = Xy )
% 2.95/1.58 => ( ( Xphi @ Xx )
% 2.95/1.58 <=> ( Xpsi @ Xy ) ) )
% 2.95/1.58 => ( ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 => ( ( exu
% 2.95/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.95/1.58 => ( ( descr
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 = ( descr
% 2.95/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(dsetconstr__Cong_type,type,
% 2.95/1.58 dsetconstr__Cong: $o ).
% 2.95/1.58
% 2.95/1.58 thf(dsetconstr__Cong,definition,
% 2.95/1.58 ( dsetconstr__Cong
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( A = B )
% 2.95/1.58 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( Xx = Xy )
% 2.95/1.58 => ( ( Xphi @ Xx )
% 2.95/1.58 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.95/1.58 => ( ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 = ( dsetconstr @ B
% 2.95/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subset_type,type,
% 2.95/1.58 subset: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(disjoint_type,type,
% 2.95/1.58 disjoint: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(setsmeet_type,type,
% 2.95/1.58 setsmeet: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetI1_type,type,
% 2.95/1.58 subsetI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetI1,definition,
% 2.95/1.58 ( subsetI1
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ Xx @ B ) )
% 2.95/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(eqimpsubset2_type,type,
% 2.95/1.58 eqimpsubset2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(eqimpsubset2,definition,
% 2.95/1.58 ( eqimpsubset2
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( A = B )
% 2.95/1.58 => ( subset @ B @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(eqimpsubset1_type,type,
% 2.95/1.58 eqimpsubset1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(eqimpsubset1,definition,
% 2.95/1.58 ( eqimpsubset1
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( A = B )
% 2.95/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subsetI2_type,type,
% 2.95/1.58 subsetI2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetI2,definition,
% 2.95/1.58 ( subsetI2
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ Xx @ B ) )
% 2.95/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(emptysetsubset_type,type,
% 2.95/1.58 emptysetsubset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(emptysetsubset,definition,
% 2.95/1.58 ( emptysetsubset
% 2.95/1.58 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subsetE_type,type,
% 2.95/1.58 subsetE: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetE,definition,
% 2.95/1.58 ( subsetE
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subsetE2_type,type,
% 2.95/1.58 subsetE2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetE2,definition,
% 2.95/1.58 ( subsetE2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( ~ ( in @ Xx @ B )
% 2.95/1.58 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(notsubsetI_type,type,
% 2.95/1.58 notsubsetI: $o ).
% 2.95/1.58
% 2.95/1.58 thf(notsubsetI,definition,
% 2.95/1.58 ( notsubsetI
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ B )
% 2.95/1.58 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(notequalI1_type,type,
% 2.95/1.58 notequalI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(notequalI1,definition,
% 2.95/1.58 ( notequalI1
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ~ ( subset @ A @ B )
% 2.95/1.58 => ( A != B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(notequalI2_type,type,
% 2.95/1.58 notequalI2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(notequalI2,definition,
% 2.95/1.58 ( notequalI2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ B )
% 2.95/1.58 => ( A != B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subsetRefl_type,type,
% 2.95/1.58 subsetRefl: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetRefl,definition,
% 2.95/1.58 ( subsetRefl
% 2.95/1.58 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subsetTrans_type,type,
% 2.95/1.58 subsetTrans: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetTrans,definition,
% 2.95/1.58 ( subsetTrans
% 2.95/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( ( subset @ B @ C )
% 2.95/1.58 => ( subset @ A @ C ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setadjoinSub_type,type,
% 2.95/1.58 setadjoinSub: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setadjoinSub,definition,
% 2.95/1.58 ( setadjoinSub
% 2.95/1.58 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setadjoinSub2_type,type,
% 2.95/1.58 setadjoinSub2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setadjoinSub2,definition,
% 2.95/1.58 ( setadjoinSub2
% 2.95/1.58 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subset2powerset_type,type,
% 2.95/1.58 subset2powerset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subset2powerset,definition,
% 2.95/1.58 ( subset2powerset
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setextsub_type,type,
% 2.95/1.58 setextsub: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setextsub,definition,
% 2.95/1.58 ( setextsub
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( ( subset @ B @ A )
% 2.95/1.58 => ( A = B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subsetemptysetimpeq_type,type,
% 2.95/1.58 subsetemptysetimpeq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetemptysetimpeq,definition,
% 2.95/1.58 ( subsetemptysetimpeq
% 2.95/1.58 = ( ! [A: $i] :
% 2.95/1.58 ( ( subset @ A @ emptyset )
% 2.95/1.58 => ( A = emptyset ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(powersetI1_type,type,
% 2.95/1.58 powersetI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(powersetI1,definition,
% 2.95/1.58 ( powersetI1
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( subset @ B @ A )
% 2.95/1.58 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(powersetE1_type,type,
% 2.95/1.58 powersetE1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(powersetE1,definition,
% 2.95/1.58 ( powersetE1
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( in @ B @ ( powerset @ A ) )
% 2.95/1.58 => ( subset @ B @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(inPowerset_type,type,
% 2.95/1.58 inPowerset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(inPowerset,definition,
% 2.95/1.58 ( inPowerset
% 2.95/1.58 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(powersetsubset_type,type,
% 2.95/1.58 powersetsubset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(powersetsubset,definition,
% 2.95/1.58 ( powersetsubset
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(sepInPowerset_type,type,
% 2.95/1.58 sepInPowerset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(sepInPowerset,definition,
% 2.95/1.58 ( sepInPowerset
% 2.95/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.58 ( in
% 2.95/1.58 @ ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 @ ( powerset @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(sepSubset_type,type,
% 2.95/1.58 sepSubset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(sepSubset,definition,
% 2.95/1.58 ( sepSubset
% 2.95/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.58 ( subset
% 2.95/1.58 @ ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 @ A ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunion_type,type,
% 2.95/1.58 binunion: $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(binunionIL_type,type,
% 2.95/1.58 binunionIL: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionIL,definition,
% 2.95/1.58 ( binunionIL
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(upairset2IR_type,type,
% 2.95/1.58 upairset2IR: $o ).
% 2.95/1.58
% 2.95/1.58 thf(upairset2IR,definition,
% 2.95/1.58 ( upairset2IR
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionIR_type,type,
% 2.95/1.58 binunionIR: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionIR,definition,
% 2.95/1.58 ( binunionIR
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ B )
% 2.95/1.58 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionEcases_type,type,
% 2.95/1.58 binunionEcases: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionEcases,definition,
% 2.95/1.58 ( binunionEcases
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.95/1.58 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.95/1.58 => ( ( ( in @ Xx @ A )
% 2.95/1.58 => Xphi )
% 2.95/1.58 => ( ( ( in @ Xx @ B )
% 2.95/1.58 => Xphi )
% 2.95/1.58 => Xphi ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionE_type,type,
% 2.95/1.58 binunionE: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionE,definition,
% 2.95/1.58 ( binunionE
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.95/1.58 => ( ( in @ Xx @ A )
% 2.95/1.58 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionLsub_type,type,
% 2.95/1.58 binunionLsub: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionLsub,definition,
% 2.95/1.58 ( binunionLsub
% 2.95/1.58 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionRsub_type,type,
% 2.95/1.58 binunionRsub: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionRsub,definition,
% 2.95/1.58 ( binunionRsub
% 2.95/1.58 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersect_type,type,
% 2.95/1.58 binintersect: $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectI_type,type,
% 2.95/1.58 binintersectI: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectI,definition,
% 2.95/1.58 ( binintersectI
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ B )
% 2.95/1.58 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset5_type,type,
% 2.95/1.58 binintersectSubset5: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset5,definition,
% 2.95/1.58 ( binintersectSubset5
% 2.95/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 2.95/1.58 ( ( subset @ C @ A )
% 2.95/1.58 => ( ( subset @ C @ B )
% 2.95/1.58 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectEL_type,type,
% 2.95/1.58 binintersectEL: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectEL,definition,
% 2.95/1.58 ( binintersectEL
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.95/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectLsub_type,type,
% 2.95/1.58 binintersectLsub: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectLsub,definition,
% 2.95/1.58 ( binintersectLsub
% 2.95/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset2_type,type,
% 2.95/1.58 binintersectSubset2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset2,definition,
% 2.95/1.58 ( binintersectSubset2
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( ( binintersect @ A @ B )
% 2.95/1.58 = A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset3_type,type,
% 2.95/1.58 binintersectSubset3: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset3,definition,
% 2.95/1.58 ( binintersectSubset3
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( ( binintersect @ A @ B )
% 2.95/1.58 = B )
% 2.95/1.58 => ( subset @ B @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectER_type,type,
% 2.95/1.58 binintersectER: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectER,definition,
% 2.95/1.58 ( binintersectER
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.95/1.58 => ( in @ Xx @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(disjointsetsI1_type,type,
% 2.95/1.58 disjointsetsI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(disjointsetsI1,definition,
% 2.95/1.58 ( disjointsetsI1
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ~ ? [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 & ( in @ Xx @ B ) )
% 2.95/1.58 => ( ( binintersect @ A @ B )
% 2.95/1.58 = emptyset ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectRsub_type,type,
% 2.95/1.58 binintersectRsub: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectRsub,definition,
% 2.95/1.58 ( binintersectRsub
% 2.95/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset4_type,type,
% 2.95/1.58 binintersectSubset4: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset4,definition,
% 2.95/1.58 ( binintersectSubset4
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( subset @ B @ A )
% 2.95/1.58 => ( ( binintersect @ A @ B )
% 2.95/1.58 = B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset1_type,type,
% 2.95/1.58 binintersectSubset1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectSubset1,definition,
% 2.95/1.58 ( binintersectSubset1
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( ( binintersect @ A @ B )
% 2.95/1.58 = A )
% 2.95/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(bs114d_type,type,
% 2.95/1.58 bs114d: $o ).
% 2.95/1.58
% 2.95/1.58 thf(bs114d,definition,
% 2.95/1.58 ( bs114d
% 2.95/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 2.95/1.58 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.95/1.58 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(regular_type,type,
% 2.95/1.58 regular: $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminus_type,type,
% 2.95/1.58 setminus: $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(setminusI_type,type,
% 2.95/1.58 setminusI: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusI,definition,
% 2.95/1.58 ( setminusI
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ B )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusEL_type,type,
% 2.95/1.58 setminusEL: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusEL,definition,
% 2.95/1.58 ( setminusEL
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.95/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusER_type,type,
% 2.95/1.58 setminusER: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusER,definition,
% 2.95/1.58 ( setminusER
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.95/1.58 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusSubset2_type,type,
% 2.95/1.58 setminusSubset2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusSubset2,definition,
% 2.95/1.58 ( setminusSubset2
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( subset @ A @ B )
% 2.95/1.58 => ( ( setminus @ A @ B )
% 2.95/1.58 = emptyset ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusERneg_type,type,
% 2.95/1.58 setminusERneg: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusERneg,definition,
% 2.95/1.58 ( setminusERneg
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.95/1.58 => ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusELneg_type,type,
% 2.95/1.58 setminusELneg: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusELneg,definition,
% 2.95/1.58 ( setminusELneg
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.95/1.58 => ( ~ ( in @ Xx @ B )
% 2.95/1.58 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusILneg_type,type,
% 2.95/1.58 setminusILneg: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusILneg,definition,
% 2.95/1.58 ( setminusILneg
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ~ ( in @ Xx @ A )
% 2.95/1.58 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusIRneg_type,type,
% 2.95/1.58 setminusIRneg: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusIRneg,definition,
% 2.95/1.58 ( setminusIRneg
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ B )
% 2.95/1.58 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusLsub_type,type,
% 2.95/1.58 setminusLsub: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusLsub,definition,
% 2.95/1.58 ( setminusLsub
% 2.95/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusSubset1_type,type,
% 2.95/1.58 setminusSubset1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusSubset1,definition,
% 2.95/1.58 ( setminusSubset1
% 2.95/1.58 = ( ! [A: $i,B: $i] :
% 2.95/1.58 ( ( ( setminus @ A @ B )
% 2.95/1.58 = emptyset )
% 2.95/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(symdiff_type,type,
% 2.95/1.58 symdiff: $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffE_type,type,
% 2.95/1.58 symdiffE: $o ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffE,definition,
% 2.95/1.58 ( symdiffE
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.95/1.58 => ! [Xphi: $o] :
% 2.95/1.58 ( ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ B )
% 2.95/1.58 => Xphi ) )
% 2.95/1.58 => ( ( ~ ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ B )
% 2.95/1.58 => Xphi ) )
% 2.95/1.58 => Xphi ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffI1_type,type,
% 2.95/1.58 symdiffI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffI1,definition,
% 2.95/1.58 ( symdiffI1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ B )
% 2.95/1.58 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffI2_type,type,
% 2.95/1.58 symdiffI2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffI2,definition,
% 2.95/1.58 ( symdiffI2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ~ ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ B )
% 2.95/1.58 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffIneg1_type,type,
% 2.95/1.58 symdiffIneg1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffIneg1,definition,
% 2.95/1.58 ( symdiffIneg1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ B )
% 2.95/1.58 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffIneg2_type,type,
% 2.95/1.58 symdiffIneg2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(symdiffIneg2,definition,
% 2.95/1.58 ( symdiffIneg2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ~ ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ B )
% 2.95/1.58 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(iskpair_type,type,
% 2.95/1.58 iskpair: $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(secondinupair_type,type,
% 2.95/1.58 secondinupair: $o ).
% 2.95/1.58
% 2.95/1.58 thf(secondinupair,definition,
% 2.95/1.58 ( secondinupair
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairIL_type,type,
% 2.95/1.58 setukpairIL: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairIL,definition,
% 2.95/1.58 ( setukpairIL
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairIR_type,type,
% 2.95/1.58 setukpairIR: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairIR,definition,
% 2.95/1.58 ( setukpairIR
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(kpairiskpair_type,type,
% 2.95/1.58 kpairiskpair: $o ).
% 2.95/1.58
% 2.95/1.58 thf(kpairiskpair,definition,
% 2.95/1.58 ( kpairiskpair
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(kpair_type,type,
% 2.95/1.58 kpair: $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(kpairp_type,type,
% 2.95/1.58 kpairp: $o ).
% 2.95/1.58
% 2.95/1.58 thf(kpairp,definition,
% 2.95/1.58 ( kpairp
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprod_type,type,
% 2.95/1.58 cartprod: $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(singletonsubset_type,type,
% 2.95/1.58 singletonsubset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(singletonsubset,definition,
% 2.95/1.58 ( singletonsubset
% 2.95/1.58 = ( ! [A: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(singletoninpowerset_type,type,
% 2.95/1.58 singletoninpowerset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(singletoninpowerset,definition,
% 2.95/1.58 ( singletoninpowerset
% 2.95/1.58 = ( ! [A: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(singletoninpowunion_type,type,
% 2.95/1.58 singletoninpowunion: $o ).
% 2.95/1.58
% 2.95/1.58 thf(singletoninpowunion,definition,
% 2.95/1.58 ( singletoninpowunion
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(upairset2E_type,type,
% 2.95/1.58 upairset2E: $o ).
% 2.95/1.58
% 2.95/1.58 thf(upairset2E,definition,
% 2.95/1.58 ( upairset2E
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.95/1.58 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.95/1.58 => ( ( Xz = Xx )
% 2.95/1.58 | ( Xz = Xy ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(upairsubunion_type,type,
% 2.95/1.58 upairsubunion: $o ).
% 2.95/1.58
% 2.95/1.58 thf(upairsubunion,definition,
% 2.95/1.58 ( upairsubunion
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(upairinpowunion_type,type,
% 2.95/1.58 upairinpowunion: $o ).
% 2.95/1.58
% 2.95/1.58 thf(upairinpowunion,definition,
% 2.95/1.58 ( upairinpowunion
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ubforcartprodlem1_type,type,
% 2.95/1.58 ubforcartprodlem1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ubforcartprodlem1,definition,
% 2.95/1.58 ( ubforcartprodlem1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ubforcartprodlem2_type,type,
% 2.95/1.58 ubforcartprodlem2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ubforcartprodlem2,definition,
% 2.95/1.58 ( ubforcartprodlem2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ubforcartprodlem3_type,type,
% 2.95/1.58 ubforcartprodlem3: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ubforcartprodlem3,definition,
% 2.95/1.58 ( ubforcartprodlem3
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodpairin_type,type,
% 2.95/1.58 cartprodpairin: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodpairin,definition,
% 2.95/1.58 ( cartprodpairin
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodmempair1_type,type,
% 2.95/1.58 cartprodmempair1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodmempair1,definition,
% 2.95/1.58 ( cartprodmempair1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.95/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.95/1.58 => ? [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 & ? [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 & ( Xu
% 2.95/1.58 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodmempair_type,type,
% 2.95/1.58 cartprodmempair: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodmempair,definition,
% 2.95/1.58 ( cartprodmempair
% 2.95/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.95/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.95/1.58 => ( iskpair @ Xu ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setunionE2_type,type,
% 2.95/1.58 setunionE2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setunionE2,definition,
% 2.95/1.58 ( setunionE2
% 2.95/1.58 = ( ! [A: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ ( setunion @ A ) )
% 2.95/1.58 => ? [X: $i] :
% 2.95/1.58 ( ( in @ X @ A )
% 2.95/1.58 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setunionsingleton1_type,type,
% 2.95/1.58 setunionsingleton1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setunionsingleton1,definition,
% 2.95/1.58 ( setunionsingleton1
% 2.95/1.58 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setunionsingleton2_type,type,
% 2.95/1.58 setunionsingleton2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setunionsingleton2,definition,
% 2.95/1.58 ( setunionsingleton2
% 2.95/1.58 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setunionsingleton_type,type,
% 2.95/1.58 setunionsingleton: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setunionsingleton,definition,
% 2.95/1.58 ( setunionsingleton
% 2.95/1.58 = ( ! [Xx: $i] :
% 2.95/1.58 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.95/1.58 = Xx ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(singleton_type,type,
% 2.95/1.58 singleton: $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(singletonprop_type,type,
% 2.95/1.58 singletonprop: $o ).
% 2.95/1.58
% 2.95/1.58 thf(singletonprop,definition,
% 2.95/1.58 ( singletonprop
% 2.95/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( Xphi @ Xx )
% 2.95/1.58 => ( ( Xphi @ Xy )
% 2.95/1.58 => ( Xx = Xy ) ) ) ) )
% 2.95/1.58 => ( ? [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 & ( Xphi @ Xx ) )
% 2.95/1.58 => ( singleton
% 2.95/1.58 @ ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ex1_type,type,
% 2.95/1.58 ex1: $i > ( $i > $o ) > $o ).
% 2.95/1.58
% 2.95/1.58 thf(ex1E1_type,type,
% 2.95/1.58 ex1E1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ex1E1,definition,
% 2.95/1.58 ( ex1E1
% 2.95/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.58 ( ( ex1 @ A
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 => ? [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ex1I_type,type,
% 2.95/1.58 ex1I: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ex1I,definition,
% 2.95/1.58 ( ex1I
% 2.95/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( Xphi @ Xx )
% 2.95/1.58 => ( ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( Xphi @ Xy )
% 2.95/1.58 => ( Xy = Xx ) ) )
% 2.95/1.58 => ( ex1 @ A
% 2.95/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ex1I2_type,type,
% 2.95/1.58 ex1I2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ex1I2,definition,
% 2.95/1.58 ( ex1I2
% 2.95/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( Xphi @ Xx )
% 2.95/1.58 => ( ( Xphi @ Xy )
% 2.95/1.58 => ( Xx = Xy ) ) ) ) )
% 2.95/1.58 => ( ? [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 & ( Xphi @ Xx ) )
% 2.95/1.58 => ( ex1 @ A
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(singletonsuniq_type,type,
% 2.95/1.58 singletonsuniq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(singletonsuniq,definition,
% 2.95/1.58 ( singletonsuniq
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( ( setadjoin @ Xx @ emptyset )
% 2.95/1.58 = ( setadjoin @ Xy @ emptyset ) )
% 2.95/1.58 => ( Xx = Xy ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(atmost1p_type,type,
% 2.95/1.58 atmost1p: $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(atleast2p_type,type,
% 2.95/1.58 atleast2p: $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(atmost2p_type,type,
% 2.95/1.58 atmost2p: $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(upairsetp_type,type,
% 2.95/1.58 upairsetp: $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjL1_type,type,
% 2.95/1.58 setukpairinjL1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjL1,definition,
% 2.95/1.58 ( setukpairinjL1
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.95/1.58 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.95/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(kfstsingleton_type,type,
% 2.95/1.58 kfstsingleton: $o ).
% 2.95/1.58
% 2.95/1.58 thf(kfstsingleton,definition,
% 2.95/1.58 ( kfstsingleton
% 2.95/1.58 = ( ! [Xu: $i] :
% 2.95/1.58 ( ( iskpair @ Xu )
% 2.95/1.58 => ( singleton
% 2.95/1.58 @ ( dsetconstr @ ( setunion @ Xu )
% 2.95/1.58 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(theprop_type,type,
% 2.95/1.58 theprop: $o ).
% 2.95/1.58
% 2.95/1.58 thf(theprop,definition,
% 2.95/1.58 ( theprop
% 2.95/1.58 = ( ! [X: $i] :
% 2.95/1.58 ( ( singleton @ X )
% 2.95/1.58 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(kfst_type,type,
% 2.95/1.58 kfst: $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(kfstpairEq_type,type,
% 2.95/1.58 kfstpairEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(kfstpairEq,definition,
% 2.95/1.58 ( kfstpairEq
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.95/1.58 = Xx ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodfstin_type,type,
% 2.95/1.58 cartprodfstin: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodfstin,definition,
% 2.95/1.58 ( cartprodfstin
% 2.95/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.95/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.95/1.58 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjL2_type,type,
% 2.95/1.58 setukpairinjL2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjL2,definition,
% 2.95/1.58 ( setukpairinjL2
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.95/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.95/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.95/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjL_type,type,
% 2.95/1.58 setukpairinjL: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjL,definition,
% 2.95/1.58 ( setukpairinjL
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.95/1.58 ( ( ( kpair @ Xx @ Xy )
% 2.95/1.58 = ( kpair @ Xz @ Xu ) )
% 2.95/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR11_type,type,
% 2.95/1.58 setukpairinjR11: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR11,definition,
% 2.95/1.58 ( setukpairinjR11
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xx = Xy )
% 2.95/1.58 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.95/1.58 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR12_type,type,
% 2.95/1.58 setukpairinjR12: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR12,definition,
% 2.95/1.58 ( setukpairinjR12
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xx = Xy )
% 2.95/1.58 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.95/1.58 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR1_type,type,
% 2.95/1.58 setukpairinjR1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR1,definition,
% 2.95/1.58 ( setukpairinjR1
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.95/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.95/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.95/1.58 => ( ( Xz = Xu )
% 2.95/1.58 => ( Xy = Xu ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(upairequniteq_type,type,
% 2.95/1.58 upairequniteq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(upairequniteq,definition,
% 2.95/1.58 ( upairequniteq
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.95/1.58 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.95/1.58 = ( setadjoin @ Xz @ emptyset ) )
% 2.95/1.58 => ( Xx = Xy ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR2_type,type,
% 2.95/1.58 setukpairinjR2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR2,definition,
% 2.95/1.58 ( setukpairinjR2
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.95/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.95/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.95/1.58 => ( Xy = Xu ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR_type,type,
% 2.95/1.58 setukpairinjR: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setukpairinjR,definition,
% 2.95/1.58 ( setukpairinjR
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.95/1.58 ( ( ( kpair @ Xx @ Xy )
% 2.95/1.58 = ( kpair @ Xz @ Xu ) )
% 2.95/1.58 => ( Xy = Xu ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ksndsingleton_type,type,
% 2.95/1.58 ksndsingleton: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ksndsingleton,definition,
% 2.95/1.58 ( ksndsingleton
% 2.95/1.58 = ( ! [Xu: $i] :
% 2.95/1.58 ( ( iskpair @ Xu )
% 2.95/1.58 => ( singleton
% 2.95/1.58 @ ( dsetconstr @ ( setunion @ Xu )
% 2.95/1.58 @ ^ [Xx: $i] :
% 2.95/1.58 ( Xu
% 2.95/1.58 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ksnd_type,type,
% 2.95/1.58 ksnd: $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(ksndpairEq_type,type,
% 2.95/1.58 ksndpairEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ksndpairEq,definition,
% 2.95/1.58 ( ksndpairEq
% 2.95/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.95/1.58 = Xy ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(kpairsurjEq_type,type,
% 2.95/1.58 kpairsurjEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(kpairsurjEq,definition,
% 2.95/1.58 ( kpairsurjEq
% 2.95/1.58 = ( ! [Xu: $i] :
% 2.95/1.58 ( ( iskpair @ Xu )
% 2.95/1.58 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.95/1.58 = Xu ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodsndin_type,type,
% 2.95/1.58 cartprodsndin: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodsndin,definition,
% 2.95/1.58 ( cartprodsndin
% 2.95/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.95/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.95/1.58 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodpairmemEL_type,type,
% 2.95/1.58 cartprodpairmemEL: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodpairmemEL,definition,
% 2.95/1.58 ( cartprodpairmemEL
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.95/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodpairmemER_type,type,
% 2.95/1.58 cartprodpairmemER: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodpairmemER,definition,
% 2.95/1.58 ( cartprodpairmemER
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.95/1.58 => ( in @ Xy @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodmempaircEq_type,type,
% 2.95/1.58 cartprodmempaircEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodmempaircEq,definition,
% 2.95/1.58 ( cartprodmempaircEq
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( kpair @ Xx @ Xy )
% 2.95/1.58 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodfstpairEq_type,type,
% 2.95/1.58 cartprodfstpairEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodfstpairEq,definition,
% 2.95/1.58 ( cartprodfstpairEq
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.95/1.58 = Xx ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodsndpairEq_type,type,
% 2.95/1.58 cartprodsndpairEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodsndpairEq,definition,
% 2.95/1.58 ( cartprodsndpairEq
% 2.95/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.95/1.58 = Xy ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodpairsurjEq_type,type,
% 2.95/1.58 cartprodpairsurjEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(cartprodpairsurjEq,definition,
% 2.95/1.58 ( cartprodpairsurjEq
% 2.95/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.95/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.95/1.58 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.95/1.58 = Xu ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln_type,type,
% 2.95/1.58 breln: $i > $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstr_type,type,
% 2.95/1.58 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrI_type,type,
% 2.95/1.58 dpsetconstrI: $o ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrI,definition,
% 2.95/1.58 ( dpsetconstrI
% 2.95/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( Xphi @ Xx @ Xy )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy )
% 2.95/1.58 @ ( dpsetconstr @ A @ B
% 2.95/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrSub_type,type,
% 2.95/1.58 dpsetconstrSub: $o ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrSub,definition,
% 2.95/1.58 ( dpsetconstrSub
% 2.95/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.95/1.58 ( subset
% 2.95/1.58 @ ( dpsetconstr @ A @ B
% 2.95/1.58 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.95/1.58 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setOfPairsIsBReln_type,type,
% 2.95/1.58 setOfPairsIsBReln: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setOfPairsIsBReln,definition,
% 2.95/1.58 ( setOfPairsIsBReln
% 2.95/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.95/1.58 ( breln @ A @ B
% 2.95/1.58 @ ( dpsetconstr @ A @ B
% 2.95/1.58 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrERa_type,type,
% 2.95/1.58 dpsetconstrERa: $o ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrERa,definition,
% 2.95/1.58 ( dpsetconstrERa
% 2.95/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.95/1.58 @ ( dpsetconstr @ A @ B
% 2.95/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.95/1.58 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrEL1_type,type,
% 2.95/1.58 dpsetconstrEL1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrEL1,definition,
% 2.95/1.58 ( dpsetconstrEL1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 2.95/1.58 @ ( dpsetconstr @ A @ B
% 2.95/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.95/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrEL2_type,type,
% 2.95/1.58 dpsetconstrEL2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrEL2,definition,
% 2.95/1.58 ( dpsetconstrEL2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 2.95/1.58 @ ( dpsetconstr @ A @ B
% 2.95/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.95/1.58 => ( in @ Xy @ B ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrER_type,type,
% 2.95/1.58 dpsetconstrER: $o ).
% 2.95/1.58
% 2.95/1.58 thf(dpsetconstrER,definition,
% 2.95/1.58 ( dpsetconstrER
% 2.95/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 2.95/1.58 @ ( dpsetconstr @ A @ B
% 2.95/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.95/1.58 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(func_type,type,
% 2.95/1.58 func: $i > $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcSet_type,type,
% 2.95/1.58 funcSet: $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(funcImageSingleton_type,type,
% 2.95/1.58 funcImageSingleton: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcImageSingleton,definition,
% 2.95/1.58 ( funcImageSingleton
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( singleton
% 2.95/1.58 @ ( dsetconstr @ B
% 2.95/1.58 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(apProp_type,type,
% 2.95/1.58 apProp: $o ).
% 2.95/1.58
% 2.95/1.58 thf(apProp,definition,
% 2.95/1.58 ( apProp
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in
% 2.95/1.58 @ ( setunion
% 2.95/1.58 @ ( dsetconstr @ B
% 2.95/1.58 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.95/1.58 @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ap_type,type,
% 2.95/1.58 ap: $i > $i > $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(app_type,type,
% 2.95/1.58 app: $o ).
% 2.95/1.58
% 2.95/1.58 thf(app,definition,
% 2.95/1.58 ( app
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(infuncsetfunc_type,type,
% 2.95/1.58 infuncsetfunc: $o ).
% 2.95/1.58
% 2.95/1.58 thf(infuncsetfunc,definition,
% 2.95/1.58 ( infuncsetfunc
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.95/1.58 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ap2p_type,type,
% 2.95/1.58 ap2p: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ap2p,definition,
% 2.95/1.58 ( ap2p
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(funcinfuncset_type,type,
% 2.95/1.58 funcinfuncset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcinfuncset,definition,
% 2.95/1.58 ( funcinfuncset
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(lamProp_type,type,
% 2.95/1.58 lamProp: $o ).
% 2.95/1.58
% 2.95/1.58 thf(lamProp,definition,
% 2.95/1.58 ( lamProp
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.95/1.58 => ( func @ A @ B
% 2.95/1.58 @ ( dpsetconstr @ A @ B
% 2.95/1.58 @ ^ [Xx: $i,Xy: $i] :
% 2.95/1.58 ( ( Xf @ Xx )
% 2.95/1.58 = Xy ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(lam_type,type,
% 2.95/1.58 lam: $i > $i > ( $i > $i ) > $i ).
% 2.95/1.58
% 2.95/1.58 thf(lamp_type,type,
% 2.95/1.58 lamp: $o ).
% 2.95/1.58
% 2.95/1.58 thf(lamp,definition,
% 2.95/1.58 ( lamp
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.95/1.58 => ( func @ A @ B
% 2.95/1.58 @ ( lam @ A @ B
% 2.95/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(lam2p_type,type,
% 2.95/1.58 lam2p: $o ).
% 2.95/1.58
% 2.95/1.58 thf(lam2p,definition,
% 2.95/1.58 ( lam2p
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.95/1.58 => ( in
% 2.95/1.58 @ ( lam @ A @ B
% 2.95/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.95/1.58 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(brelnall1_type,type,
% 2.95/1.58 brelnall1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(brelnall1,definition,
% 2.95/1.58 ( brelnall1
% 2.95/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 2.95/1.58 ( ( breln @ A @ B @ R )
% 2.95/1.58 => ! [Xphi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ R )
% 2.95/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(brelnall2_type,type,
% 2.95/1.58 brelnall2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(brelnall2,definition,
% 2.95/1.58 ( brelnall2
% 2.95/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 2.95/1.58 ( ( breln @ A @ B @ R )
% 2.95/1.58 => ! [Xphi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ R )
% 2.95/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ex1E2_type,type,
% 2.95/1.58 ex1E2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ex1E2,definition,
% 2.95/1.58 ( ex1E2
% 2.95/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.95/1.58 ( ( ex1 @ A
% 2.95/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( Xphi @ Xx )
% 2.95/1.58 => ( ( Xphi @ Xy )
% 2.95/1.58 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(funcGraphProp1_type,type,
% 2.95/1.58 funcGraphProp1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcGraphProp1,definition,
% 2.95/1.58 ( funcGraphProp1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(funcGraphProp3_type,type,
% 2.95/1.58 funcGraphProp3: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcGraphProp3,definition,
% 2.95/1.58 ( funcGraphProp3
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(funcGraphProp2_type,type,
% 2.95/1.58 funcGraphProp2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcGraphProp2,definition,
% 2.95/1.58 ( funcGraphProp2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.95/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.95/1.58 = Xy ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(funcextLem_type,type,
% 2.95/1.58 funcextLem: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcextLem,definition,
% 2.95/1.58 ( funcextLem
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ! [Xg: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xg )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.95/1.58 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(funcGraphProp4_type,type,
% 2.95/1.58 funcGraphProp4: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcGraphProp4,definition,
% 2.95/1.58 ( funcGraphProp4
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.95/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.95/1.58 = Xy ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subbreln_type,type,
% 2.95/1.58 subbreln: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subbreln,definition,
% 2.95/1.58 ( subbreln
% 2.95/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 2.95/1.58 ( ( breln @ A @ B @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln @ A @ B @ S )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.95/1.58 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(eqbreln_type,type,
% 2.95/1.58 eqbreln: $o ).
% 2.95/1.58
% 2.95/1.58 thf(eqbreln,definition,
% 2.95/1.58 ( eqbreln
% 2.95/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 2.95/1.58 ( ( breln @ A @ B @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln @ A @ B @ S )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.95/1.58 => ( R = S ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(funcext_type,type,
% 2.95/1.58 funcext: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcext,definition,
% 2.95/1.58 ( funcext
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ! [Xg: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xg )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.95/1.58 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.95/1.58 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(funcext2_type,type,
% 2.95/1.58 funcext2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(funcext2,definition,
% 2.95/1.58 ( funcext2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.95/1.58 => ! [Xg: $i] :
% 2.95/1.58 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.95/1.58 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.95/1.58 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ap2apEq1_type,type,
% 2.95/1.58 ap2apEq1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ap2apEq1,definition,
% 2.95/1.58 ( ap2apEq1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.95/1.58 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ap2apEq2_type,type,
% 2.95/1.58 ap2apEq2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ap2apEq2,definition,
% 2.95/1.58 ( ap2apEq2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.95/1.58 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(beta1_type,type,
% 2.95/1.58 beta1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(beta1,definition,
% 2.95/1.58 ( beta1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( ap @ A @ B
% 2.95/1.58 @ ( lam @ A @ B
% 2.95/1.58 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.95/1.58 @ Xx )
% 2.95/1.58 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(eta1_type,type,
% 2.95/1.58 eta1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(eta1,definition,
% 2.95/1.58 ( eta1
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( func @ A @ B @ Xf )
% 2.95/1.58 => ( ( lam @ A @ B
% 2.95/1.58 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.95/1.58 = Xf ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(lam2lamEq_type,type,
% 2.95/1.58 lam2lamEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(lam2lamEq,definition,
% 2.95/1.58 ( lam2lamEq
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.95/1.58 => ( ( lam @ A @ B
% 2.95/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.95/1.58 = ( lam @ A @ B
% 2.95/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(beta2_type,type,
% 2.95/1.58 beta2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(beta2,definition,
% 2.95/1.58 ( beta2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( ap @ A @ B
% 2.95/1.58 @ ( lam @ A @ B
% 2.95/1.58 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.95/1.58 @ Xx )
% 2.95/1.58 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(eta2_type,type,
% 2.95/1.58 eta2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(eta2,definition,
% 2.95/1.58 ( eta2
% 2.95/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.95/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.95/1.58 => ( ( lam @ A @ B
% 2.95/1.58 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.95/1.58 = Xf ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(iffalseProp1_type,type,
% 2.95/1.58 iffalseProp1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(iffalseProp1,definition,
% 2.95/1.58 ( iffalseProp1
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ~ Xphi
% 2.95/1.58 => ( in @ Xy
% 2.95/1.58 @ ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xz: $i] :
% 2.95/1.58 ( ( Xphi
% 2.95/1.58 & ( Xz = Xx ) )
% 2.95/1.58 | ( ~ Xphi
% 2.95/1.58 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(iffalseProp2_type,type,
% 2.95/1.58 iffalseProp2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(iffalseProp2,definition,
% 2.95/1.58 ( iffalseProp2
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ~ Xphi
% 2.95/1.58 => ( ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xz: $i] :
% 2.95/1.58 ( ( Xphi
% 2.95/1.58 & ( Xz = Xx ) )
% 2.95/1.58 | ( ~ Xphi
% 2.95/1.58 & ( Xz = Xy ) ) ) )
% 2.95/1.58 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(iftrueProp1_type,type,
% 2.95/1.58 iftrueProp1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(iftrueProp1,definition,
% 2.95/1.58 ( iftrueProp1
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( Xphi
% 2.95/1.58 => ( in @ Xx
% 2.95/1.58 @ ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xz: $i] :
% 2.95/1.58 ( ( Xphi
% 2.95/1.58 & ( Xz = Xx ) )
% 2.95/1.58 | ( ~ Xphi
% 2.95/1.58 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(iftrueProp2_type,type,
% 2.95/1.58 iftrueProp2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(iftrueProp2,definition,
% 2.95/1.58 ( iftrueProp2
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( Xphi
% 2.95/1.58 => ( ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xz: $i] :
% 2.95/1.58 ( ( Xphi
% 2.95/1.58 & ( Xz = Xx ) )
% 2.95/1.58 | ( ~ Xphi
% 2.95/1.58 & ( Xz = Xy ) ) ) )
% 2.95/1.58 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(ifSingleton_type,type,
% 2.95/1.58 ifSingleton: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ifSingleton,definition,
% 2.95/1.58 ( ifSingleton
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( singleton
% 2.95/1.58 @ ( dsetconstr @ A
% 2.95/1.58 @ ^ [Xz: $i] :
% 2.95/1.58 ( ( Xphi
% 2.95/1.58 & ( Xz = Xx ) )
% 2.95/1.58 | ( ~ Xphi
% 2.95/1.58 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(if_type,type,
% 2.95/1.58 if: $i > $o > $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(ifp_type,type,
% 2.95/1.58 ifp: $o ).
% 2.95/1.58
% 2.95/1.58 thf(ifp,definition,
% 2.95/1.58 ( ifp
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(theeq_type,type,
% 2.95/1.58 theeq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(theeq,definition,
% 2.95/1.58 ( theeq
% 2.95/1.58 = ( ! [X: $i] :
% 2.95/1.58 ( ( singleton @ X )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ X )
% 2.95/1.58 => ( ( setunion @ X )
% 2.95/1.58 = Xx ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(iftrue_type,type,
% 2.95/1.58 iftrue: $o ).
% 2.95/1.58
% 2.95/1.58 thf(iftrue,definition,
% 2.95/1.58 ( iftrue
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( Xphi
% 2.95/1.58 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.95/1.58 = Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(iffalse_type,type,
% 2.95/1.58 iffalse: $o ).
% 2.95/1.58
% 2.95/1.58 thf(iffalse,definition,
% 2.95/1.58 ( iffalse
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ~ Xphi
% 2.95/1.58 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.95/1.58 = Xy ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(iftrueorfalse_type,type,
% 2.95/1.58 iftrueorfalse: $o ).
% 2.95/1.58
% 2.95/1.58 thf(iftrueorfalse,definition,
% 2.95/1.58 ( iftrueorfalse
% 2.95/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectT_lem_type,type,
% 2.95/1.58 binintersectT_lem: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectT_lem,definition,
% 2.95/1.58 ( binintersectT_lem
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionT_lem_type,type,
% 2.95/1.58 binunionT_lem: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionT_lem,definition,
% 2.95/1.58 ( binunionT_lem
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(powersetT_lem_type,type,
% 2.95/1.58 powersetT_lem: $o ).
% 2.95/1.58
% 2.95/1.58 thf(powersetT_lem,definition,
% 2.95/1.58 ( powersetT_lem
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setminusT_lem_type,type,
% 2.95/1.58 setminusT_lem: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setminusT_lem,definition,
% 2.95/1.58 ( setminusT_lem
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementT_lem_type,type,
% 2.95/1.58 complementT_lem: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementT_lem,definition,
% 2.95/1.58 ( complementT_lem
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setextT_type,type,
% 2.95/1.58 setextT: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setextT,definition,
% 2.95/1.58 ( setextT
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ X )
% 2.95/1.58 => ( in @ Xx @ Y ) ) )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ Y )
% 2.95/1.58 => ( in @ Xx @ X ) ) )
% 2.95/1.58 => ( X = Y ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subsetTI_type,type,
% 2.95/1.58 subsetTI: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subsetTI,definition,
% 2.95/1.58 ( subsetTI
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ X )
% 2.95/1.58 => ( in @ Xx @ Y ) ) )
% 2.95/1.58 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(powersetTI1_type,type,
% 2.95/1.58 powersetTI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(powersetTI1,definition,
% 2.95/1.58 ( powersetTI1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ X )
% 2.95/1.58 => ( in @ Xx @ Y ) ) )
% 2.95/1.58 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(powersetTE1_type,type,
% 2.95/1.58 powersetTE1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(powersetTE1,definition,
% 2.95/1.58 ( powersetTE1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ X @ ( powerset @ Y ) )
% 2.95/1.58 => ( ( in @ Xx @ X )
% 2.95/1.58 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementTI1_type,type,
% 2.95/1.58 complementTI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementTI1,definition,
% 2.95/1.58 ( complementTI1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ X )
% 2.95/1.58 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementTE1_type,type,
% 2.95/1.58 complementTE1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementTE1,definition,
% 2.95/1.58 ( complementTE1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.95/1.58 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectTELcontra_type,type,
% 2.95/1.58 binintersectTELcontra: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectTELcontra,definition,
% 2.95/1.58 ( binintersectTELcontra
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ X )
% 2.95/1.58 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectTERcontra_type,type,
% 2.95/1.58 binintersectTERcontra: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binintersectTERcontra,definition,
% 2.95/1.58 ( binintersectTERcontra
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ Y )
% 2.95/1.58 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(contrasubsetT_type,type,
% 2.95/1.58 contrasubsetT: $o ).
% 2.95/1.58
% 2.95/1.58 thf(contrasubsetT,definition,
% 2.95/1.58 ( contrasubsetT
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.95/1.58 => ( ( in @ Xx @ Y )
% 2.95/1.58 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(contrasubsetT1_type,type,
% 2.95/1.58 contrasubsetT1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(contrasubsetT1,definition,
% 2.95/1.58 ( contrasubsetT1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( subset @ X @ Y )
% 2.95/1.58 => ( ~ ( in @ Xx @ Y )
% 2.95/1.58 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(contrasubsetT2_type,type,
% 2.95/1.58 contrasubsetT2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(contrasubsetT2,definition,
% 2.95/1.58 ( contrasubsetT2
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ X @ Y )
% 2.95/1.58 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(contrasubsetT3_type,type,
% 2.95/1.58 contrasubsetT3: $o ).
% 2.95/1.58
% 2.95/1.58 thf(contrasubsetT3,definition,
% 2.95/1.58 ( contrasubsetT3
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.95/1.58 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementI1_type,type,
% 2.95/1.58 doubleComplementI1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementI1,definition,
% 2.95/1.58 ( doubleComplementI1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ X )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementE1_type,type,
% 2.95/1.58 doubleComplementE1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementE1,definition,
% 2.95/1.58 ( doubleComplementE1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.95/1.58 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementSub1_type,type,
% 2.95/1.58 doubleComplementSub1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementSub1,definition,
% 2.95/1.58 ( doubleComplementSub1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementSub2_type,type,
% 2.95/1.58 doubleComplementSub2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementSub2,definition,
% 2.95/1.58 ( doubleComplementSub2
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementEq_type,type,
% 2.95/1.58 doubleComplementEq: $o ).
% 2.95/1.58
% 2.95/1.58 thf(doubleComplementEq,definition,
% 2.95/1.58 ( doubleComplementEq
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ( X
% 2.95/1.58 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementTnotintersectT_type,type,
% 2.95/1.58 complementTnotintersectT: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementTnotintersectT,definition,
% 2.95/1.58 ( complementTnotintersectT
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.95/1.58 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementImpComplementIntersect_type,type,
% 2.95/1.58 complementImpComplementIntersect: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementImpComplementIntersect,definition,
% 2.95/1.58 ( complementImpComplementIntersect
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementSubsetComplementIntersect_type,type,
% 2.95/1.58 complementSubsetComplementIntersect: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementSubsetComplementIntersect,definition,
% 2.95/1.58 ( complementSubsetComplementIntersect
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementInPowersetComplementIntersect_type,type,
% 2.95/1.58 complementInPowersetComplementIntersect: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementInPowersetComplementIntersect,definition,
% 2.95/1.58 ( complementInPowersetComplementIntersect
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(contraSubsetComplement_type,type,
% 2.95/1.58 contraSubsetComplement: $o ).
% 2.95/1.58
% 2.95/1.58 thf(contraSubsetComplement,definition,
% 2.95/1.58 ( contraSubsetComplement
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ Y )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementTcontraSubset_type,type,
% 2.95/1.58 complementTcontraSubset: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementTcontraSubset,definition,
% 2.95/1.58 ( complementTcontraSubset
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.95/1.58 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionTILcontra_type,type,
% 2.95/1.58 binunionTILcontra: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionTILcontra,definition,
% 2.95/1.58 ( binunionTILcontra
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.95/1.58 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionTIRcontra_type,type,
% 2.95/1.58 binunionTIRcontra: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionTIRcontra,definition,
% 2.95/1.58 ( binunionTIRcontra
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.95/1.58 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(inIntersectImpInUnion_type,type,
% 2.95/1.58 inIntersectImpInUnion: $o ).
% 2.95/1.58
% 2.95/1.58 thf(inIntersectImpInUnion,definition,
% 2.95/1.58 ( inIntersectImpInUnion
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.95/1.58 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(inIntersectImpInUnion2_type,type,
% 2.95/1.58 inIntersectImpInUnion2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(inIntersectImpInUnion2,definition,
% 2.95/1.58 ( inIntersectImpInUnion2
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.95/1.58 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(inIntersectImpInIntersectUnions_type,type,
% 2.95/1.58 inIntersectImpInIntersectUnions: $o ).
% 2.95/1.58
% 2.95/1.58 thf(inIntersectImpInIntersectUnions,definition,
% 2.95/1.58 ( inIntersectImpInIntersectUnions
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.95/1.58 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(intersectInPowersetIntersectUnions_type,type,
% 2.95/1.58 intersectInPowersetIntersectUnions: $o ).
% 2.95/1.58
% 2.95/1.58 thf(intersectInPowersetIntersectUnions,definition,
% 2.95/1.58 ( intersectInPowersetIntersectUnions
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(inComplementUnionImpNotIn1_type,type,
% 2.95/1.58 inComplementUnionImpNotIn1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(inComplementUnionImpNotIn1,definition,
% 2.95/1.58 ( inComplementUnionImpNotIn1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.95/1.58 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(inComplementUnionImpInComplement1_type,type,
% 2.95/1.58 inComplementUnionImpInComplement1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(inComplementUnionImpInComplement1,definition,
% 2.95/1.58 ( inComplementUnionImpInComplement1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionTE_type,type,
% 2.95/1.58 binunionTE: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionTE,definition,
% 2.95/1.58 ( binunionTE
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xphi: $o,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.95/1.58 => ( ( ( in @ Xx @ X )
% 2.95/1.58 => Xphi )
% 2.95/1.58 => ( ( ( in @ Xx @ Y )
% 2.95/1.58 => Xphi )
% 2.95/1.58 => Xphi ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(binunionTEcontra_type,type,
% 2.95/1.58 binunionTEcontra: $o ).
% 2.95/1.58
% 2.95/1.58 thf(binunionTEcontra,definition,
% 2.95/1.58 ( binunionTEcontra
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ~ ( in @ Xx @ X )
% 2.95/1.58 => ( ~ ( in @ Xx @ Y )
% 2.95/1.58 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2a1_type,type,
% 2.95/1.58 demorgan2a1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2a1,definition,
% 2.95/1.58 ( demorgan2a1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(complementUnionInPowersetComplement_type,type,
% 2.95/1.58 complementUnionInPowersetComplement: $o ).
% 2.95/1.58
% 2.95/1.58 thf(complementUnionInPowersetComplement,definition,
% 2.95/1.58 ( complementUnionInPowersetComplement
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2a2_type,type,
% 2.95/1.58 demorgan2a2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2a2,definition,
% 2.95/1.58 ( demorgan2a2
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan1a_type,type,
% 2.95/1.58 demorgan1a: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan1a,definition,
% 2.95/1.58 ( demorgan1a
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 2.95/1.58 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan1b_type,type,
% 2.95/1.58 demorgan1b: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan1b,definition,
% 2.95/1.58 ( demorgan1b
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan1_type,type,
% 2.95/1.58 demorgan1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan1,definition,
% 2.95/1.58 ( demorgan1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 2.95/1.58 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2a_type,type,
% 2.95/1.58 demorgan2a: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2a,definition,
% 2.95/1.58 ( demorgan2a
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.95/1.58 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2b2_type,type,
% 2.95/1.58 demorgan2b2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2b2,definition,
% 2.95/1.58 ( demorgan2b2
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.95/1.58 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2b_type,type,
% 2.95/1.58 demorgan2b: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2b,definition,
% 2.95/1.58 ( demorgan2b
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.95/1.58 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2_type,type,
% 2.95/1.58 demorgan2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(demorgan2,definition,
% 2.95/1.58 ( demorgan2
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 2.95/1.58 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule0_type,type,
% 2.95/1.58 woz13rule0: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule0,definition,
% 2.95/1.58 ( woz13rule0
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.95/1.58 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule1_type,type,
% 2.95/1.58 woz13rule1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule1,definition,
% 2.95/1.58 ( woz13rule1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ X @ Z )
% 2.95/1.58 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule2_type,type,
% 2.95/1.58 woz13rule2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule2,definition,
% 2.95/1.58 ( woz13rule2
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ Y @ Z )
% 2.95/1.58 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule3_type,type,
% 2.95/1.58 woz13rule3: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule3,definition,
% 2.95/1.58 ( woz13rule3
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ X @ Y )
% 2.95/1.58 => ( ( subset @ X @ Z )
% 2.95/1.58 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule4_type,type,
% 2.95/1.58 woz13rule4: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz13rule4,definition,
% 2.95/1.58 ( woz13rule4
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ! [W: $i] :
% 2.95/1.58 ( ( in @ W @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ X @ Z )
% 2.95/1.58 => ( ( subset @ Y @ W )
% 2.95/1.58 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_1_type,type,
% 2.95/1.58 woz1_1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_1,definition,
% 2.95/1.58 ( woz1_1
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_2_type,type,
% 2.95/1.58 woz1_2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_2,definition,
% 2.95/1.58 ( woz1_2
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ! [W: $i] :
% 2.95/1.58 ( ( in @ W @ ( powerset @ A ) )
% 2.95/1.58 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 2.95/1.58 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_3_type,type,
% 2.95/1.58 woz1_3: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_3,definition,
% 2.95/1.58 ( woz1_3
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ! [Z: $i] :
% 2.95/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_4_type,type,
% 2.95/1.58 woz1_4: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_4,definition,
% 2.95/1.58 ( woz1_4
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.95/1.58 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_5_type,type,
% 2.95/1.58 woz1_5: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz1_5,definition,
% 2.95/1.58 ( woz1_5
% 2.95/1.58 = ( ! [A: $i,X: $i] :
% 2.95/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.95/1.58 => ! [Y: $i] :
% 2.95/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.95/1.58 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1_type,type,
% 2.95/1.58 breln1: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1all2_type,type,
% 2.95/1.58 breln1all2: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1all2,definition,
% 2.95/1.58 ( breln1all2
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [Xphi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ R )
% 2.95/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1Set_type,type,
% 2.95/1.58 breln1Set: $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(breln1SetBreln1_type,type,
% 2.95/1.58 breln1SetBreln1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1SetBreln1,definition,
% 2.95/1.58 ( breln1SetBreln1
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( in @ R @ ( breln1Set @ A ) )
% 2.95/1.58 => ( breln1 @ A @ R ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(transitive_type,type,
% 2.95/1.58 transitive: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(antisymmetric_type,type,
% 2.95/1.58 antisymmetric: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(reflexive_type,type,
% 2.95/1.58 reflexive: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(refltransitive_type,type,
% 2.95/1.58 refltransitive: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(refllinearorder_type,type,
% 2.95/1.58 refllinearorder: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(reflwellordering_type,type,
% 2.95/1.58 reflwellordering: $i > $i > $o ).
% 2.95/1.58
% 2.95/1.58 thf(choice2fnsingleton_type,type,
% 2.95/1.58 choice2fnsingleton: $o ).
% 2.95/1.58
% 2.95/1.58 thf(choice2fnsingleton,definition,
% 2.95/1.58 ( choice2fnsingleton
% 2.95/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ? [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ B )
% 2.95/1.58 & ( Xphi @ Xx @ Xy ) ) )
% 2.95/1.58 => ! [R: $i] :
% 2.95/1.58 ( ( in @ R @ ( breln1Set @ B ) )
% 2.95/1.58 => ( ( reflwellordering @ B @ R )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ( singleton
% 2.95/1.58 @ ( dsetconstr @ B
% 2.95/1.58 @ ^ [Xy: $i] :
% 2.95/1.58 ( ( Xphi @ Xx @ Xy )
% 2.95/1.58 & ! [Xz: $i] :
% 2.95/1.58 ( ( in @ Xz @ B )
% 2.95/1.58 => ( ( Xphi @ Xx @ Xz )
% 2.95/1.58 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(setOfPairsIsBReln1_type,type,
% 2.95/1.58 setOfPairsIsBReln1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(setOfPairsIsBReln1,definition,
% 2.95/1.58 ( setOfPairsIsBReln1
% 2.95/1.58 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 2.95/1.58 ( breln1 @ A
% 2.95/1.58 @ ( dpsetconstr @ A @ A
% 2.95/1.58 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1all1_type,type,
% 2.95/1.58 breln1all1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1all1,definition,
% 2.95/1.58 ( breln1all1
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [Xphi: $i > $o] :
% 2.95/1.58 ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ R )
% 2.95/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(subbreln1_type,type,
% 2.95/1.58 subbreln1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(subbreln1,definition,
% 2.95/1.58 ( subbreln1
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.95/1.58 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(eqbreln1_type,type,
% 2.95/1.58 eqbreln1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(eqbreln1,definition,
% 2.95/1.58 ( eqbreln1
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.95/1.58 => ( ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.95/1.58 => ( R = S ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1invset_type,type,
% 2.95/1.58 breln1invset: $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(breln1invprop_type,type,
% 2.95/1.58 breln1invprop: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1invprop,definition,
% 2.95/1.58 ( breln1invprop
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1invI_type,type,
% 2.95/1.58 breln1invI: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1invI,definition,
% 2.95/1.58 ( breln1invI
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1invE_type,type,
% 2.95/1.58 breln1invE: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1invE,definition,
% 2.95/1.58 ( breln1invE
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compset_type,type,
% 2.95/1.58 breln1compset: $i > $i > $i > $i ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compprop_type,type,
% 2.95/1.58 breln1compprop: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compprop,definition,
% 2.95/1.58 ( breln1compprop
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compI_type,type,
% 2.95/1.58 breln1compI: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compI,definition,
% 2.95/1.58 ( breln1compI
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ! [Xz: $i] :
% 2.95/1.58 ( ( in @ Xz @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.95/1.58 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compE_type,type,
% 2.95/1.58 breln1compE: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compE,definition,
% 2.95/1.58 ( breln1compE
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 2.95/1.58 => ? [Xz: $i] :
% 2.95/1.58 ( ( in @ Xz @ A )
% 2.95/1.58 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.95/1.58 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compEex_type,type,
% 2.95/1.58 breln1compEex: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1compEex,definition,
% 2.95/1.58 ( breln1compEex
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 2.95/1.58 => ! [Xphi: $o] :
% 2.95/1.58 ( ! [Xz: $i] :
% 2.95/1.58 ( ( in @ Xz @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.95/1.58 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 2.95/1.58 => Xphi ) ) )
% 2.95/1.58 => Xphi ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionprop_type,type,
% 2.95/1.58 breln1unionprop: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionprop,definition,
% 2.95/1.58 ( breln1unionprop
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionIL_type,type,
% 2.95/1.58 breln1unionIL: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionIL,definition,
% 2.95/1.58 ( breln1unionIL
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionIR_type,type,
% 2.95/1.58 breln1unionIR: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionIR,definition,
% 2.95/1.58 ( breln1unionIR
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionI_type,type,
% 2.95/1.58 breln1unionI: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionI,definition,
% 2.95/1.58 ( breln1unionI
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 2.95/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionE_type,type,
% 2.95/1.58 breln1unionE: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionE,definition,
% 2.95/1.58 ( breln1unionE
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionEcases_type,type,
% 2.95/1.58 breln1unionEcases: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionEcases,definition,
% 2.95/1.58 ( breln1unionEcases
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ A )
% 2.95/1.58 => ! [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 2.95/1.58 => ! [Xphi: $o] :
% 2.95/1.58 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.95/1.58 => Xphi )
% 2.95/1.58 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.95/1.58 => Xphi )
% 2.95/1.58 => Xphi ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionCommutes_type,type,
% 2.95/1.58 breln1unionCommutes: $o ).
% 2.95/1.58
% 2.95/1.58 thf(breln1unionCommutes,definition,
% 2.95/1.58 ( breln1unionCommutes
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ( ( binunion @ R @ S )
% 2.95/1.58 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz2Ex_type,type,
% 2.95/1.58 woz2Ex: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz2Ex,definition,
% 2.95/1.58 ( woz2Ex
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ( R
% 2.95/1.58 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz2W_type,type,
% 2.95/1.58 woz2W: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz2W,definition,
% 2.95/1.58 ( woz2W
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 2.95/1.58 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz2A_type,type,
% 2.95/1.58 woz2A: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz2A,definition,
% 2.95/1.58 ( woz2A
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [T: $i] :
% 2.95/1.58 ( ( breln1 @ A @ T )
% 2.95/1.58 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 2.95/1.58 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(woz2B_type,type,
% 2.95/1.58 woz2B: $o ).
% 2.95/1.58
% 2.95/1.58 thf(woz2B,definition,
% 2.95/1.58 ( woz2B
% 2.95/1.58 = ( ! [A: $i,R: $i] :
% 2.95/1.58 ( ( breln1 @ A @ R )
% 2.95/1.58 => ! [S: $i] :
% 2.95/1.58 ( ( breln1 @ A @ S )
% 2.95/1.58 => ! [T: $i] :
% 2.95/1.58 ( ( breln1 @ A @ T )
% 2.95/1.58 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 2.95/1.58 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(image1Ex_type,type,
% 2.95/1.58 image1Ex: $o ).
% 2.95/1.58
% 2.95/1.58 thf(image1Ex,definition,
% 2.95/1.58 ( image1Ex
% 2.95/1.58 = ( ! [A: $i,Xf: $i > $i] :
% 2.95/1.58 ? [B: $i] :
% 2.95/1.58 ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ B )
% 2.95/1.58 <=> ? [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 & ( Xx
% 2.95/1.58 = ( Xf @ Xy ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(image1Ex1_type,type,
% 2.95/1.58 image1Ex1: $o ).
% 2.95/1.58
% 2.95/1.58 thf(image1Ex1,definition,
% 2.95/1.58 ( image1Ex1
% 2.95/1.58 = ( ! [A: $i,Xf: $i > $i] :
% 2.95/1.58 ( exu
% 2.95/1.58 @ ^ [B: $i] :
% 2.95/1.58 ! [Xx: $i] :
% 2.95/1.58 ( ( in @ Xx @ B )
% 2.95/1.58 <=> ? [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 & ( Xx
% 2.95/1.58 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(image1_type,type,
% 2.95/1.58 image1: $i > ( $i > $i ) > $i ).
% 2.95/1.58
% 2.95/1.58 thf(image1Equiv_type,type,
% 2.95/1.58 image1Equiv: $o ).
% 2.95/1.58
% 2.95/1.58 thf(image1Equiv,definition,
% 2.95/1.58 ( image1Equiv
% 2.95/1.58 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx
% 2.95/1.58 @ ( image1 @ A
% 2.95/1.58 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 2.95/1.58 <=> ? [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 & ( Xx
% 2.95/1.58 = ( Xf @ Xy ) ) ) ) ) ) ).
% 2.95/1.58
% 2.95/1.58 thf(image1E,conjecture,
% 2.95/1.58 ( setextAx
% 2.95/1.58 => ( emptysetAx
% 2.95/1.58 => ( setadjoinAx
% 2.95/1.58 => ( powersetAx
% 2.95/1.58 => ( setunionAx
% 2.95/1.58 => ( omega0Ax
% 2.95/1.58 => ( omegaSAx
% 2.95/1.58 => ( omegaIndAx
% 2.95/1.58 => ( replAx
% 2.95/1.58 => ( foundationAx
% 2.95/1.58 => ( wellorderingAx
% 2.95/1.58 => ( descrp
% 2.95/1.58 => ( dsetconstrI
% 2.95/1.58 => ( dsetconstrEL
% 2.95/1.58 => ( dsetconstrER
% 2.95/1.58 => ( exuE1
% 2.95/1.58 => ( prop2setE
% 2.95/1.58 => ( emptysetE
% 2.95/1.58 => ( emptysetimpfalse
% 2.95/1.58 => ( notinemptyset
% 2.95/1.58 => ( exuE3e
% 2.95/1.58 => ( setext
% 2.95/1.58 => ( emptyI
% 2.95/1.58 => ( noeltsimpempty
% 2.95/1.58 => ( setbeta
% 2.95/1.58 => ( nonemptyE1
% 2.95/1.58 => ( nonemptyI
% 2.95/1.58 => ( nonemptyI1
% 2.95/1.58 => ( setadjoinIL
% 2.95/1.58 => ( emptyinunitempty
% 2.95/1.58 => ( setadjoinIR
% 2.95/1.58 => ( setadjoinE
% 2.95/1.58 => ( setadjoinOr
% 2.95/1.58 => ( setoftrueEq
% 2.95/1.58 => ( powersetI
% 2.95/1.58 => ( emptyinPowerset
% 2.95/1.58 => ( emptyInPowerset
% 2.95/1.58 => ( powersetE
% 2.95/1.58 => ( setunionI
% 2.95/1.58 => ( setunionE
% 2.95/1.58 => ( subPowSU
% 2.95/1.58 => ( exuE2
% 2.95/1.58 => ( nonemptyImpWitness
% 2.95/1.58 => ( uniqinunit
% 2.95/1.58 => ( notinsingleton
% 2.95/1.58 => ( eqinunit
% 2.95/1.58 => ( singletonsswitch
% 2.95/1.58 => ( upairsetE
% 2.95/1.58 => ( upairsetIL
% 2.95/1.58 => ( upairsetIR
% 2.95/1.58 => ( emptyE1
% 2.95/1.58 => ( vacuousDall
% 2.95/1.58 => ( quantDeMorgan1
% 2.95/1.58 => ( quantDeMorgan2
% 2.95/1.58 => ( quantDeMorgan3
% 2.95/1.58 => ( quantDeMorgan4
% 2.95/1.58 => ( prop2setI
% 2.95/1.58 => ( prop2set2propI
% 2.95/1.58 => ( notdexE
% 2.95/1.58 => ( notdallE
% 2.95/1.58 => ( exuI1
% 2.95/1.58 => ( exuI3
% 2.95/1.58 => ( exuI2
% 2.95/1.58 => ( inCongP
% 2.95/1.58 => ( in__Cong
% 2.95/1.58 => ( exuE3u
% 2.95/1.58 => ( exu__Cong
% 2.95/1.58 => ( emptyset__Cong
% 2.95/1.58 => ( setadjoin__Cong
% 2.95/1.58 => ( powerset__Cong
% 2.95/1.58 => ( setunion__Cong
% 2.95/1.58 => ( omega__Cong
% 2.95/1.58 => ( exuEu
% 2.95/1.58 => ( descr__Cong
% 2.95/1.58 => ( dsetconstr__Cong
% 2.95/1.58 => ( subsetI1
% 2.95/1.58 => ( eqimpsubset2
% 2.95/1.58 => ( eqimpsubset1
% 2.95/1.58 => ( subsetI2
% 2.95/1.58 => ( emptysetsubset
% 2.95/1.58 => ( subsetE
% 2.95/1.58 => ( subsetE2
% 2.95/1.58 => ( notsubsetI
% 2.95/1.58 => ( notequalI1
% 2.95/1.58 => ( notequalI2
% 2.95/1.58 => ( subsetRefl
% 2.95/1.58 => ( subsetTrans
% 2.95/1.58 => ( setadjoinSub
% 2.95/1.58 => ( setadjoinSub2
% 2.95/1.58 => ( subset2powerset
% 2.95/1.58 => ( setextsub
% 2.95/1.58 => ( subsetemptysetimpeq
% 2.95/1.58 => ( powersetI1
% 2.95/1.58 => ( powersetE1
% 2.95/1.58 => ( inPowerset
% 2.95/1.58 => ( powersetsubset
% 2.95/1.58 => ( sepInPowerset
% 2.95/1.58 => ( sepSubset
% 2.95/1.58 => ( binunionIL
% 2.95/1.58 => ( upairset2IR
% 2.95/1.58 => ( binunionIR
% 2.95/1.58 => ( binunionEcases
% 2.95/1.58 => ( binunionE
% 2.95/1.58 => ( binunionLsub
% 2.95/1.58 => ( binunionRsub
% 2.95/1.58 => ( binintersectI
% 2.95/1.58 => ( binintersectSubset5
% 2.95/1.58 => ( binintersectEL
% 2.95/1.58 => ( binintersectLsub
% 2.95/1.58 => ( binintersectSubset2
% 2.95/1.58 => ( binintersectSubset3
% 2.95/1.58 => ( binintersectER
% 2.95/1.58 => ( disjointsetsI1
% 2.95/1.58 => ( binintersectRsub
% 2.95/1.58 => ( binintersectSubset4
% 2.95/1.58 => ( binintersectSubset1
% 2.95/1.58 => ( bs114d
% 2.95/1.58 => ( setminusI
% 2.95/1.58 => ( setminusEL
% 2.95/1.58 => ( setminusER
% 2.95/1.58 => ( setminusSubset2
% 2.95/1.58 => ( setminusERneg
% 2.95/1.58 => ( setminusELneg
% 2.95/1.58 => ( setminusILneg
% 2.95/1.58 => ( setminusIRneg
% 2.95/1.58 => ( setminusLsub
% 2.95/1.58 => ( setminusSubset1
% 2.95/1.58 => ( symdiffE
% 2.95/1.58 => ( symdiffI1
% 2.95/1.58 => ( symdiffI2
% 2.95/1.58 => ( symdiffIneg1
% 2.95/1.58 => ( symdiffIneg2
% 2.95/1.58 => ( secondinupair
% 2.95/1.58 => ( setukpairIL
% 2.95/1.58 => ( setukpairIR
% 2.95/1.58 => ( kpairiskpair
% 2.95/1.58 => ( kpairp
% 2.95/1.58 => ( singletonsubset
% 2.95/1.58 => ( singletoninpowerset
% 2.95/1.58 => ( singletoninpowunion
% 2.95/1.58 => ( upairset2E
% 2.95/1.58 => ( upairsubunion
% 2.95/1.58 => ( upairinpowunion
% 2.95/1.58 => ( ubforcartprodlem1
% 2.95/1.58 => ( ubforcartprodlem2
% 2.95/1.58 => ( ubforcartprodlem3
% 2.95/1.58 => ( cartprodpairin
% 2.95/1.58 => ( cartprodmempair1
% 2.95/1.58 => ( cartprodmempair
% 2.95/1.58 => ( setunionE2
% 2.95/1.58 => ( setunionsingleton1
% 2.95/1.58 => ( setunionsingleton2
% 2.95/1.58 => ( setunionsingleton
% 2.95/1.58 => ( singletonprop
% 2.95/1.58 => ( ex1E1
% 2.95/1.58 => ( ex1I
% 2.95/1.58 => ( ex1I2
% 2.95/1.58 => ( singletonsuniq
% 2.95/1.58 => ( setukpairinjL1
% 2.95/1.58 => ( kfstsingleton
% 2.95/1.58 => ( theprop
% 2.95/1.58 => ( kfstpairEq
% 2.95/1.58 => ( cartprodfstin
% 2.95/1.58 => ( setukpairinjL2
% 2.95/1.58 => ( setukpairinjL
% 2.95/1.58 => ( setukpairinjR11
% 2.95/1.58 => ( setukpairinjR12
% 2.95/1.58 => ( setukpairinjR1
% 2.95/1.58 => ( upairequniteq
% 2.95/1.58 => ( setukpairinjR2
% 2.95/1.58 => ( setukpairinjR
% 2.95/1.58 => ( ksndsingleton
% 2.95/1.58 => ( ksndpairEq
% 2.95/1.58 => ( kpairsurjEq
% 2.95/1.58 => ( cartprodsndin
% 2.95/1.58 => ( cartprodpairmemEL
% 2.95/1.58 => ( cartprodpairmemER
% 2.95/1.58 => ( cartprodmempaircEq
% 2.95/1.58 => ( cartprodfstpairEq
% 2.95/1.58 => ( cartprodsndpairEq
% 2.95/1.58 => ( cartprodpairsurjEq
% 2.95/1.58 => ( dpsetconstrI
% 2.95/1.58 => ( dpsetconstrSub
% 2.95/1.58 => ( setOfPairsIsBReln
% 2.95/1.58 => ( dpsetconstrERa
% 2.95/1.58 => ( dpsetconstrEL1
% 2.95/1.58 => ( dpsetconstrEL2
% 2.95/1.58 => ( dpsetconstrER
% 2.95/1.58 => ( funcImageSingleton
% 2.95/1.58 => ( apProp
% 2.95/1.58 => ( app
% 2.95/1.58 => ( infuncsetfunc
% 2.95/1.58 => ( ap2p
% 2.95/1.58 => ( funcinfuncset
% 2.95/1.58 => ( lamProp
% 2.95/1.58 => ( lamp
% 2.95/1.58 => ( lam2p
% 2.95/1.58 => ( brelnall1
% 2.95/1.58 => ( brelnall2
% 2.95/1.58 => ( ex1E2
% 2.95/1.58 => ( funcGraphProp1
% 2.95/1.58 => ( funcGraphProp3
% 2.95/1.58 => ( funcGraphProp2
% 2.95/1.58 => ( funcextLem
% 2.95/1.58 => ( funcGraphProp4
% 2.95/1.58 => ( subbreln
% 2.95/1.58 => ( eqbreln
% 2.95/1.58 => ( funcext
% 2.95/1.58 => ( funcext2
% 2.95/1.58 => ( ap2apEq1
% 2.95/1.58 => ( ap2apEq2
% 2.95/1.58 => ( beta1
% 2.95/1.58 => ( eta1
% 2.95/1.58 => ( lam2lamEq
% 2.95/1.58 => ( beta2
% 2.95/1.58 => ( eta2
% 2.95/1.58 => ( iffalseProp1
% 2.95/1.58 => ( iffalseProp2
% 2.95/1.58 => ( iftrueProp1
% 2.95/1.58 => ( iftrueProp2
% 2.95/1.58 => ( ifSingleton
% 2.95/1.58 => ( ifp
% 2.95/1.58 => ( theeq
% 2.95/1.58 => ( iftrue
% 2.95/1.58 => ( iffalse
% 2.95/1.58 => ( iftrueorfalse
% 2.95/1.58 => ( binintersectT_lem
% 2.95/1.58 => ( binunionT_lem
% 2.95/1.58 => ( powersetT_lem
% 2.95/1.58 => ( setminusT_lem
% 2.95/1.58 => ( complementT_lem
% 2.95/1.58 => ( setextT
% 2.95/1.58 => ( subsetTI
% 2.95/1.58 => ( powersetTI1
% 2.95/1.58 => ( powersetTE1
% 2.95/1.58 => ( complementTI1
% 2.95/1.58 => ( complementTE1
% 2.95/1.58 => ( binintersectTELcontra
% 2.95/1.58 => ( binintersectTERcontra
% 2.95/1.58 => ( contrasubsetT
% 2.95/1.58 => ( contrasubsetT1
% 2.95/1.58 => ( contrasubsetT2
% 2.95/1.58 => ( contrasubsetT3
% 2.95/1.58 => ( doubleComplementI1
% 2.95/1.58 => ( doubleComplementE1
% 2.95/1.58 => ( doubleComplementSub1
% 2.95/1.58 => ( doubleComplementSub2
% 2.95/1.58 => ( doubleComplementEq
% 2.95/1.58 => ( complementTnotintersectT
% 2.95/1.58 => ( complementImpComplementIntersect
% 2.95/1.58 => ( complementSubsetComplementIntersect
% 2.95/1.58 => ( complementInPowersetComplementIntersect
% 2.95/1.58 => ( contraSubsetComplement
% 2.95/1.58 => ( complementTcontraSubset
% 2.95/1.58 => ( binunionTILcontra
% 2.95/1.58 => ( binunionTIRcontra
% 2.95/1.58 => ( inIntersectImpInUnion
% 2.95/1.58 => ( inIntersectImpInUnion2
% 2.95/1.58 => ( inIntersectImpInIntersectUnions
% 2.95/1.58 => ( intersectInPowersetIntersectUnions
% 2.95/1.58 => ( inComplementUnionImpNotIn1
% 2.95/1.58 => ( inComplementUnionImpInComplement1
% 2.95/1.58 => ( binunionTE
% 2.95/1.58 => ( binunionTEcontra
% 2.95/1.58 => ( demorgan2a1
% 2.95/1.58 => ( complementUnionInPowersetComplement
% 2.95/1.58 => ( demorgan2a2
% 2.95/1.58 => ( demorgan1a
% 2.95/1.58 => ( demorgan1b
% 2.95/1.58 => ( demorgan1
% 2.95/1.58 => ( demorgan2a
% 2.95/1.58 => ( demorgan2b2
% 2.95/1.58 => ( demorgan2b
% 2.95/1.58 => ( demorgan2
% 2.95/1.58 => ( woz13rule0
% 2.95/1.58 => ( woz13rule1
% 2.95/1.58 => ( woz13rule2
% 2.95/1.58 => ( woz13rule3
% 2.95/1.58 => ( woz13rule4
% 2.95/1.58 => ( woz1_1
% 2.95/1.58 => ( woz1_2
% 2.95/1.58 => ( woz1_3
% 2.95/1.58 => ( woz1_4
% 2.95/1.58 => ( woz1_5
% 2.95/1.58 => ( breln1all2
% 2.95/1.58 => ( breln1SetBreln1
% 2.95/1.58 => ( choice2fnsingleton
% 2.95/1.58 => ( setOfPairsIsBReln1
% 2.95/1.58 => ( breln1all1
% 2.95/1.58 => ( subbreln1
% 2.95/1.58 => ( eqbreln1
% 2.95/1.58 => ( breln1invprop
% 2.95/1.58 => ( breln1invI
% 2.95/1.58 => ( breln1invE
% 2.95/1.58 => ( breln1compprop
% 2.95/1.58 => ( breln1compI
% 2.95/1.58 => ( breln1compE
% 2.95/1.58 => ( breln1compEex
% 2.95/1.58 => ( breln1unionprop
% 2.95/1.58 => ( breln1unionIL
% 2.95/1.58 => ( breln1unionIR
% 2.95/1.58 => ( breln1unionI
% 2.95/1.58 => ( breln1unionE
% 2.95/1.58 => ( breln1unionEcases
% 2.95/1.58 => ( breln1unionCommutes
% 2.95/1.58 => ( woz2Ex
% 2.95/1.58 => ( woz2W
% 2.95/1.58 => ( woz2A
% 2.95/1.58 => ( woz2B
% 2.95/1.58 => ( image1Ex
% 2.95/1.58 => ( image1Ex1
% 2.95/1.58 => ( image1Equiv
% 2.95/1.58 => ! [A: $i,Xf: $i > $i,Xx: $i] :
% 2.95/1.58 ( ( in @ Xx
% 2.95/1.58 @ ( image1 @ A
% 2.95/1.58 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 2.95/1.58 => ? [Xy: $i] :
% 2.95/1.58 ( ( in @ Xy @ A )
% 2.95/1.58 & ( Xx
% 2.95/1.58 = ( Xf @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.95/1.58 ------------------------
% 3.07/1.62 % (17001)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_16722 for (2999ds/4Mi)
% 3.07/1.62 % (17002)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_16722 for (2999ds/27Mi)
% 3.07/1.62 % (17003)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/2Mi)
% 3.07/1.62 % (17001)Instruction limit reached!
% 3.07/1.62 % (17001)------------------------------
% 3.07/1.62 % (17001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.62 % (17001)Termination reason: Unknown
% 3.07/1.62 % (17001)Termination phase: shuffling
% 3.07/1.62
% 3.07/1.62 % (17001)Memory used [KB]: 1663
% 3.07/1.62 % (17001)Time elapsed: 0.003 s
% 3.07/1.62 % (17001)Instructions burned: 5 (million)
% 3.07/1.62 % (17001)------------------------------
% 3.07/1.62 % (17001)------------------------------
% 3.07/1.62 % (17003)Instruction limit reached!
% 3.07/1.62 % (17003)------------------------------
% 3.07/1.62 % (17003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.62 % (17003)Termination reason: Unknown
% 3.07/1.62 % (17003)Termination phase: shuffling
% 3.07/1.62
% 3.07/1.62 % (17003)Memory used [KB]: 1663
% 3.07/1.62 % (17003)Time elapsed: 0.002 s
% 3.07/1.62 % (17003)Instructions burned: 2 (million)
% 3.07/1.62 % (17003)------------------------------
% 3.07/1.62 % (17003)------------------------------
% 3.07/1.63 % (17000)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/183Mi)
% 3.07/1.63 % (17004)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_16722 for (2999ds/2Mi)
% 3.07/1.63 % (17006)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/18Mi)
% 3.07/1.63 % (17005)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_16722 for (2999ds/275Mi)
% 3.07/1.63 % (17002)Instruction limit reached!
% 3.07/1.63 % (17002)------------------------------
% 3.07/1.63 % (17002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.63 % (17002)Termination reason: Unknown
% 3.07/1.63 % (17002)Termination phase: shuffling
% 3.07/1.63
% 3.07/1.63 % (17002)Memory used [KB]: 2174
% 3.07/1.63 % (17002)Time elapsed: 0.010 s
% 3.07/1.63 % (17002)Instructions burned: 29 (million)
% 3.07/1.63 % (17002)------------------------------
% 3.07/1.63 % (17002)------------------------------
% 3.07/1.63 % (17004)Instruction limit reached!
% 3.07/1.63 % (17004)------------------------------
% 3.07/1.63 % (17004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.63 % (17004)Termination reason: Unknown
% 3.07/1.63 % (17004)Termination phase: shuffling
% 3.07/1.63
% 3.07/1.63 % (17004)Memory used [KB]: 1663
% 3.07/1.63 % (17004)Time elapsed: 0.003 s
% 3.07/1.63 % (17004)Instructions burned: 2 (million)
% 3.07/1.63 % (17004)------------------------------
% 3.07/1.63 % (17004)------------------------------
% 3.07/1.63 % (17007)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/3Mi)
% 3.07/1.63 % (17008)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_16722 for (2999ds/37Mi)
% 3.07/1.63 % (17007)Instruction limit reached!
% 3.07/1.63 % (17007)------------------------------
% 3.07/1.63 % (17007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.63 % (17007)Termination reason: Unknown
% 3.07/1.63 % (17007)Termination phase: shuffling
% 3.07/1.63
% 3.07/1.63 % (17007)Memory used [KB]: 1663
% 3.07/1.63 % (17007)Time elapsed: 0.003 s
% 3.07/1.63 % (17007)Instructions burned: 6 (million)
% 3.07/1.63 % (17007)------------------------------
% 3.07/1.63 % (17007)------------------------------
% 3.07/1.64 % (17006)Instruction limit reached!
% 3.07/1.64 % (17006)------------------------------
% 3.07/1.64 % (17006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (17006)Termination reason: Unknown
% 3.07/1.64 % (17006)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (17006)Memory used [KB]: 1918
% 3.07/1.64 % (17006)Time elapsed: 0.013 s
% 3.07/1.64 % (17006)Instructions burned: 19 (million)
% 3.07/1.64 % (17006)------------------------------
% 3.07/1.64 % (17006)------------------------------
% 3.07/1.64 % (17009)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_16722 for (2999ds/15Mi)
% 3.07/1.64 % (17011)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_16722 for (2999ds/1041Mi)
% 3.07/1.64 % (17008)Instruction limit reached!
% 3.07/1.64 % (17008)------------------------------
% 3.07/1.64 % (17008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (17008)Termination reason: Unknown
% 3.07/1.64 % (17008)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (17008)Memory used [KB]: 2302
% 3.07/1.64 % (17008)Time elapsed: 0.012 s
% 3.07/1.64 % (17008)Instructions burned: 38 (million)
% 3.07/1.64 % (17008)------------------------------
% 3.07/1.64 % (17008)------------------------------
% 3.07/1.64 % (17009)Instruction limit reached!
% 3.07/1.64 % (17009)------------------------------
% 3.07/1.64 % (17009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (17009)Termination reason: Unknown
% 3.07/1.64 % (17009)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (17009)Memory used [KB]: 1918
% 3.07/1.64 % (17009)Time elapsed: 0.007 s
% 3.07/1.64 % (17009)Instructions burned: 17 (million)
% 3.07/1.64 % (17009)------------------------------
% 3.07/1.64 % (17009)------------------------------
% 3.07/1.65 % (17010)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_16722 for (2999ds/3Mi)
% 3.07/1.65 % (17010)Instruction limit reached!
% 3.07/1.65 % (17010)------------------------------
% 3.07/1.65 % (17010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.65 % (17010)Termination reason: Unknown
% 3.07/1.65 % (17010)Termination phase: shuffling
% 3.07/1.65
% 3.07/1.65 % (17010)Memory used [KB]: 1663
% 3.07/1.65 % (17010)Time elapsed: 0.004 s
% 3.07/1.65 % (17010)Instructions burned: 3 (million)
% 3.07/1.65 % (17010)------------------------------
% 3.07/1.65 % (17010)------------------------------
% 3.07/1.65 % (17013)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/16Mi)
% 3.07/1.66 % (17014)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_16722 for (2999ds/3Mi)
% 3.07/1.66 % (17014)Instruction limit reached!
% 3.07/1.66 % (17014)------------------------------
% 3.07/1.66 % (17014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (17014)Termination reason: Unknown
% 3.07/1.66 % (17014)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (17014)Memory used [KB]: 1663
% 3.07/1.66 % (17014)Time elapsed: 0.002 s
% 3.07/1.66 % (17014)Instructions burned: 3 (million)
% 3.07/1.66 % (17014)------------------------------
% 3.07/1.66 % (17014)------------------------------
% 3.07/1.66 % (17012)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/7Mi)
% 3.07/1.66 % (17013)Instruction limit reached!
% 3.07/1.66 % (17013)------------------------------
% 3.07/1.66 % (17013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (17013)Termination reason: Unknown
% 3.07/1.66 % (17013)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (17013)Memory used [KB]: 2046
% 3.07/1.66 % (17013)Time elapsed: 0.006 s
% 3.07/1.66 % (17013)Instructions burned: 17 (million)
% 3.07/1.66 % (17013)------------------------------
% 3.07/1.66 % (17013)------------------------------
% 3.07/1.66 % (17012)Instruction limit reached!
% 3.07/1.66 % (17012)------------------------------
% 3.07/1.66 % (17012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (17012)Termination reason: Unknown
% 3.07/1.66 % (17012)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (17012)Memory used [KB]: 1663
% 3.07/1.66 % (17012)Time elapsed: 0.006 s
% 3.07/1.66 % (17012)Instructions burned: 7 (million)
% 3.07/1.66 % (17012)------------------------------
% 3.07/1.66 % (17012)------------------------------
% 3.07/1.67 % (17015)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_16722 for (2999ds/3Mi)
% 3.07/1.67 % (17016)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/7Mi)
% 3.07/1.67 % (17017)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/3Mi)
% 3.07/1.67 % (17015)Instruction limit reached!
% 3.07/1.67 % (17015)------------------------------
% 3.07/1.67 % (17015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (17015)Termination reason: Unknown
% 3.07/1.67 % (17015)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (17015)Memory used [KB]: 1663
% 3.07/1.67 % (17015)Time elapsed: 0.004 s
% 3.07/1.67 % (17015)Instructions burned: 3 (million)
% 3.07/1.67 % (17015)------------------------------
% 3.07/1.67 % (17015)------------------------------
% 3.07/1.67 % (17016)Instruction limit reached!
% 3.07/1.67 % (17016)------------------------------
% 3.07/1.67 % (17016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (17016)Termination reason: Unknown
% 3.07/1.67 % (17016)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (17016)Memory used [KB]: 1663
% 3.07/1.67 % (17016)Time elapsed: 0.004 s
% 3.07/1.67 % (17016)Instructions burned: 9 (million)
% 3.07/1.67 % (17016)------------------------------
% 3.07/1.67 % (17016)------------------------------
% 3.07/1.67 % (17017)Instruction limit reached!
% 3.07/1.67 % (17017)------------------------------
% 3.07/1.67 % (17017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (17017)Termination reason: Unknown
% 3.07/1.67 % (17017)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (17017)Memory used [KB]: 1663
% 3.07/1.67 % (17017)Time elapsed: 0.002 s
% 3.07/1.67 % (17017)Instructions burned: 4 (million)
% 3.07/1.67 % (17017)------------------------------
% 3.07/1.67 % (17017)------------------------------
% 3.07/1.68 % (17018)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/4Mi)
% 3.07/1.68 % (17021)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/6Mi)
% 3.07/1.68 % (17018)Instruction limit reached!
% 3.07/1.68 % (17018)------------------------------
% 3.07/1.68 % (17018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (17018)Termination reason: Unknown
% 3.07/1.68 % (17018)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (17018)Memory used [KB]: 1663
% 3.07/1.68 % (17018)Time elapsed: 0.005 s
% 3.07/1.68 % (17018)Instructions burned: 5 (million)
% 3.07/1.68 % (17018)------------------------------
% 3.07/1.68 % (17018)------------------------------
% 3.07/1.68 % (17021)Instruction limit reached!
% 3.07/1.68 % (17021)------------------------------
% 3.07/1.68 % (17021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (17021)Termination reason: Unknown
% 3.07/1.68 % (17021)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (17021)Memory used [KB]: 1663
% 3.07/1.68 % (17021)Time elapsed: 0.003 s
% 3.07/1.68 % (17021)Instructions burned: 6 (million)
% 3.07/1.68 % (17021)------------------------------
% 3.07/1.68 % (17021)------------------------------
% 3.07/1.68 % (17019)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/18Mi)
% 3.07/1.69 % (17020)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/710Mi)
% 3.07/1.69 % (17019)Instruction limit reached!
% 3.07/1.69 % (17019)------------------------------
% 3.07/1.69 % (17019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (17019)Termination reason: Unknown
% 3.07/1.69 % (17019)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (17019)Memory used [KB]: 2046
% 3.07/1.69 % (17019)Time elapsed: 0.008 s
% 3.07/1.69 % (17019)Instructions burned: 21 (million)
% 3.07/1.69 % (17019)------------------------------
% 3.07/1.69 % (17019)------------------------------
% 3.07/1.69 % (17000)Instruction limit reached!
% 3.07/1.69 % (17000)------------------------------
% 3.07/1.69 % (17000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (17000)Termination reason: Unknown
% 3.07/1.69 % (17000)Termination phase: Property scanning
% 3.07/1.69
% 3.07/1.69 % (17000)Memory used [KB]: 3070
% 3.07/1.69 % (17000)Time elapsed: 0.063 s
% 3.07/1.69 % (17000)Instructions burned: 184 (million)
% 3.07/1.69 % (17000)------------------------------
% 3.07/1.69 % (17000)------------------------------
% 3.07/1.69 % (17022)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_16722 for (2999ds/902Mi)
% 3.07/1.70 % (17025)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_16722 for (2999ds/6Mi)
% 3.07/1.70 % (17024)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16722 for (2999ds/5Mi)
% 3.07/1.70 % (17023)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_16722 for (2999ds/21Mi)
% 3.07/1.70 % (17024)Instruction limit reached!
% 3.07/1.70 % (17024)------------------------------
% 3.07/1.70 % (17024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.70 % (17024)Termination reason: Unknown
% 3.07/1.70 % (17024)Termination phase: shuffling
% 3.07/1.70
% 3.07/1.70 % (17024)Memory used [KB]: 1663
% 3.07/1.70 % (17024)Time elapsed: 0.003 s
% 3.07/1.70 % (17024)Instructions burned: 7 (million)
% 3.07/1.70 % (17024)------------------------------
% 3.07/1.70 % (17024)------------------------------
% 3.07/1.70 % (17025)Instruction limit reached!
% 3.07/1.70 % (17025)------------------------------
% 3.07/1.70 % (17025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.70 % (17025)Termination reason: Unknown
% 3.07/1.70 % (17025)Termination phase: shuffling
% 3.07/1.70
% 3.07/1.70 % (17025)Memory used [KB]: 1663
% 3.07/1.70 % (17025)Time elapsed: 0.004 s
% 3.07/1.70 % (17025)Instructions burned: 9 (million)
% 3.07/1.70 % (17025)------------------------------
% 3.07/1.70 % (17025)------------------------------
% 3.07/1.71 % (17027)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_16722 for (2998ds/779Mi)
% 3.07/1.71 % (17023)Instruction limit reached!
% 3.07/1.71 % (17023)------------------------------
% 3.07/1.71 % (17023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.71 % (17023)Termination reason: Unknown
% 3.07/1.71 % (17023)Termination phase: shuffling
% 3.07/1.71
% 3.07/1.71 % (17023)Memory used [KB]: 1918
% 3.07/1.71 % (17023)Time elapsed: 0.013 s
% 3.07/1.71 % (17023)Instructions burned: 22 (million)
% 3.07/1.71 % (17023)------------------------------
% 3.07/1.71 % (17023)------------------------------
% 3.07/1.71 % (17026)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16722 for (2998ds/377Mi)
% 3.07/1.73 % (17028)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_16722 for (2998ds/19Mi)
% 3.07/1.74 % (17028)Instruction limit reached!
% 3.07/1.74 % (17028)------------------------------
% 3.07/1.74 % (17028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.74 % (17028)Termination reason: Unknown
% 3.07/1.74 % (17028)Termination phase: shuffling
% 3.07/1.74
% 3.07/1.74 % (17028)Memory used [KB]: 1918
% 3.07/1.74 % (17028)Time elapsed: 0.012 s
% 3.07/1.74 % (17028)Instructions burned: 20 (million)
% 3.07/1.74 % (17028)------------------------------
% 3.07/1.74 % (17028)------------------------------
% 3.07/1.75 % (17029)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16722 for (2998ds/879Mi)
% 3.07/1.76 % (17005)Instruction limit reached!
% 3.07/1.76 % (17005)------------------------------
% 3.07/1.76 % (17005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.76 % (17005)Termination reason: Unknown
% 3.07/1.76 % (17005)Termination phase: Saturation
% 3.07/1.76
% 3.07/1.76 % (17005)Memory used [KB]: 6012
% 3.07/1.76 % (17005)Time elapsed: 0.136 s
% 3.07/1.76 % (17005)Instructions burned: 277 (million)
% 3.07/1.76 % (17005)------------------------------
% 3.07/1.76 % (17005)------------------------------
% 3.07/1.77 % (17030)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16722 for (2998ds/17Mi)
% 3.07/1.78 % (17030)Instruction limit reached!
% 3.07/1.78 % (17030)------------------------------
% 3.07/1.78 % (17030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.78 % (17030)Termination reason: Unknown
% 3.07/1.78 % (17030)Termination phase: shuffling
% 3.07/1.78
% 3.07/1.78 % (17030)Memory used [KB]: 1918
% 3.07/1.78 % (17030)Time elapsed: 0.006 s
% 3.07/1.78 % (17030)Instructions burned: 17 (million)
% 3.07/1.78 % (17030)------------------------------
% 3.07/1.78 % (17030)------------------------------
% 3.07/1.79 % (17031)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16722 for (2998ds/3Mi)
% 3.07/1.79 % (17031)Instruction limit reached!
% 3.07/1.79 % (17031)------------------------------
% 3.07/1.79 % (17031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.79 % (17031)Termination reason: Unknown
% 3.07/1.79 % (17031)Termination phase: shuffling
% 3.07/1.79
% 3.07/1.79 % (17031)Memory used [KB]: 1663
% 3.07/1.79 % (17031)Time elapsed: 0.002 s
% 3.07/1.79 % (17031)Instructions burned: 3 (million)
% 3.07/1.79 % (17031)------------------------------
% 3.07/1.79 % (17031)------------------------------
% 3.07/1.80 % (17032)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16722 for (2998ds/30Mi)
% 3.07/1.81 % (17032)Instruction limit reached!
% 3.07/1.81 % (17032)------------------------------
% 3.07/1.81 % (17032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.81 % (17032)Termination reason: Unknown
% 3.07/1.81 % (17032)Termination phase: shuffling
% 3.07/1.81
% 3.07/1.81 % (17032)Memory used [KB]: 2302
% 3.07/1.81 % (17032)Time elapsed: 0.010 s
% 3.07/1.81 % (17032)Instructions burned: 31 (million)
% 3.07/1.81 % (17032)------------------------------
% 3.07/1.81 % (17032)------------------------------
% 3.07/1.82 % (17026)Instruction limit reached!
% 3.07/1.82 % (17026)------------------------------
% 3.07/1.82 % (17026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.82 % (17026)Termination reason: Unknown
% 3.07/1.82 % (17026)Termination phase: Saturation
% 3.07/1.82
% 3.07/1.82 % (17026)Memory used [KB]: 9338
% 3.07/1.82 % (17026)Time elapsed: 0.108 s
% 3.07/1.82 % (17026)Instructions burned: 378 (million)
% 3.07/1.82 % (17026)------------------------------
% 3.07/1.82 % (17026)------------------------------
% 3.07/1.82 % (17033)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16722 for (2997ds/127Mi)
% 3.07/1.83 % (17034)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16722 for (2997ds/100Mi)
% 3.07/1.85 % (17033)Instruction limit reached!
% 3.07/1.85 % (17033)------------------------------
% 3.07/1.85 % (17033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.85 % (17033)Termination reason: Unknown
% 3.07/1.85 % (17033)Termination phase: Property scanning
% 3.07/1.85
% 3.07/1.85 % (17033)Memory used [KB]: 2942
% 3.07/1.85 % (17033)Time elapsed: 0.037 s
% 3.07/1.85 % (17033)Instructions burned: 127 (million)
% 3.07/1.85 % (17033)------------------------------
% 3.07/1.85 % (17033)------------------------------
% 3.07/1.86 % (17034)Instruction limit reached!
% 3.07/1.86 % (17034)------------------------------
% 3.07/1.86 % (17034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.86 % (17034)Termination reason: Unknown
% 3.07/1.86 % (17034)Termination phase: Property scanning
% 3.07/1.86
% 3.07/1.86 % (17034)Memory used [KB]: 2942
% 3.07/1.86 % (17034)Time elapsed: 0.029 s
% 3.07/1.86 % (17034)Instructions burned: 100 (million)
% 3.07/1.86 % (17034)------------------------------
% 3.07/1.86 % (17034)------------------------------
% 3.07/1.86 % (17035)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_16722 for (2997ds/3Mi)
% 3.07/1.87 % (17035)Instruction limit reached!
% 3.07/1.87 % (17035)------------------------------
% 3.07/1.87 % (17035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.87 % (17035)Termination reason: Unknown
% 3.07/1.87 % (17035)Termination phase: shuffling
% 3.07/1.87
% 3.07/1.87 % (17035)Memory used [KB]: 1663
% 3.07/1.87 % (17035)Time elapsed: 0.002 s
% 3.07/1.87 % (17035)Instructions burned: 3 (million)
% 3.07/1.87 % (17035)------------------------------
% 3.07/1.87 % (17035)------------------------------
% 3.07/1.87 % (17036)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_16722 for (2997ds/20Mi)
% 3.07/1.87 % (17036)Instruction limit reached!
% 3.07/1.87 % (17036)------------------------------
% 3.07/1.87 % (17036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.87 % (17036)Termination reason: Unknown
% 3.07/1.87 % (17036)Termination phase: shuffling
% 3.07/1.87
% 3.07/1.87 % (17036)Memory used [KB]: 1918
% 3.07/1.87 % (17036)Time elapsed: 0.008 s
% 3.07/1.87 % (17036)Instructions burned: 20 (million)
% 3.07/1.87 % (17036)------------------------------
% 3.07/1.87 % (17036)------------------------------
% 3.07/1.88 % (17037)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_16722 for (2997ds/86Mi)
% 3.07/1.88 % (17038)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_16722 for (2997ds/107Mi)
% 3.07/1.90 % (17037)Instruction limit reached!
% 3.07/1.90 % (17037)------------------------------
% 3.07/1.90 % (17037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.90 % (17037)Termination reason: Unknown
% 3.07/1.90 % (17037)Termination phase: Property scanning
% 3.07/1.90
% 3.07/1.90 % (17037)Memory used [KB]: 2814
% 3.07/1.90 % (17037)Time elapsed: 0.026 s
% 3.07/1.90 % (17037)Instructions burned: 89 (million)
% 3.07/1.90 % (17037)------------------------------
% 3.07/1.90 % (17037)------------------------------
% 3.07/1.90 % (17027)Instruction limit reached!
% 3.07/1.90 % (17027)------------------------------
% 3.07/1.90 % (17027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.90 % (17027)Termination reason: Unknown
% 3.07/1.90 % (17027)Termination phase: Saturation
% 3.07/1.90
% 3.07/1.90 % (17027)Memory used [KB]: 7931
% 3.07/1.90 % (17027)Time elapsed: 0.193 s
% 3.07/1.90 % (17027)Instructions burned: 782 (million)
% 3.07/1.90 % (17027)------------------------------
% 3.07/1.90 % (17027)------------------------------
% 3.07/1.90 % (17011)Instruction limit reached!
% 3.07/1.90 % (17011)------------------------------
% 3.07/1.90 % (17011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.90 % (17011)Termination reason: Unknown
% 3.07/1.90 % (17011)Termination phase: Saturation
% 3.07/1.90
% 3.07/1.90 % (17011)Memory used [KB]: 17910
% 3.07/1.90 % (17011)Time elapsed: 0.263 s
% 3.07/1.90 % (17011)Instructions burned: 1042 (million)
% 3.07/1.90 % (17011)------------------------------
% 3.07/1.90 % (17011)------------------------------
% 3.07/1.91 % (17039)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_16722 for (2996ds/39Mi)
% 3.07/1.91 % (17040)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_16722 for (2996ds/448Mi)
% 3.07/1.91 % (17041)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_16722 for (2996ds/46Mi)
% 3.07/1.91 % (17038)Instruction limit reached!
% 3.07/1.91 % (17038)------------------------------
% 3.07/1.91 % (17038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.91 % (17038)Termination reason: Unknown
% 3.07/1.91 % (17038)Termination phase: SInE selection
% 3.07/1.91
% 3.07/1.91 % (17038)Memory used [KB]: 2814
% 3.07/1.91 % (17038)Time elapsed: 0.031 s
% 3.07/1.91 % (17038)Instructions burned: 108 (million)
% 3.07/1.91 % (17038)------------------------------
% 3.07/1.91 % (17038)------------------------------
% 3.07/1.92 % (17039)Instruction limit reached!
% 3.07/1.92 % (17039)------------------------------
% 3.07/1.92 % (17039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.92 % (17039)Termination reason: Unknown
% 3.07/1.92 % (17039)Termination phase: shuffling
% 3.07/1.92
% 3.07/1.92 % (17039)Memory used [KB]: 2430
% 3.07/1.92 % (17039)Time elapsed: 0.013 s
% 3.07/1.92 % (17039)Instructions burned: 41 (million)
% 3.07/1.92 % (17039)------------------------------
% 3.07/1.92 % (17039)------------------------------
% 3.07/1.92 % (17020)Instruction limit reached!
% 3.07/1.92 % (17020)------------------------------
% 3.07/1.92 % (17020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.92 % (17020)Termination reason: Unknown
% 3.07/1.92 % (17020)Termination phase: Saturation
% 3.07/1.92
% 3.07/1.92 % (17020)Memory used [KB]: 11769
% 3.07/1.92 % (17020)Time elapsed: 0.239 s
% 3.07/1.92 % (17020)Instructions burned: 713 (million)
% 3.07/1.92 % (17020)------------------------------
% 3.07/1.92 % (17020)------------------------------
% 3.07/1.93 % (17042)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_16722 for (2996ds/98Mi)
% 3.07/1.93 % (17041)Instruction limit reached!
% 3.07/1.93 % (17041)------------------------------
% 3.07/1.93 % (17041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.93 % (17041)Termination reason: Unknown
% 3.07/1.93 % (17041)Termination phase: shuffling
% 3.07/1.93
% 3.07/1.93 % (17041)Memory used [KB]: 2558
% 3.07/1.93 % (17041)Time elapsed: 0.014 s
% 3.07/1.93 % (17041)Instructions burned: 46 (million)
% 3.07/1.93 % (17041)------------------------------
% 3.07/1.93 % (17041)------------------------------
% 3.07/1.93 % (17043)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_16722 for (2996ds/507Mi)
% 3.07/1.93 % (17044)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_16722 for (2996ds/149Mi)
% 3.07/1.94 % (17045)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_16722 for (2996ds/39Mi)
% 3.07/1.95 % (17045)Instruction limit reached!
% 3.07/1.95 % (17045)------------------------------
% 3.07/1.95 % (17045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.95 % (17045)Termination reason: Unknown
% 3.07/1.95 % (17045)Termination phase: shuffling
% 3.07/1.95
% 3.07/1.95 % (17045)Memory used [KB]: 2430
% 3.07/1.95 % (17045)Time elapsed: 0.012 s
% 3.07/1.95 % (17045)Instructions burned: 40 (million)
% 3.07/1.95 % (17045)------------------------------
% 3.07/1.95 % (17045)------------------------------
% 3.07/1.95 % (17042)Instruction limit reached!
% 3.07/1.95 % (17042)------------------------------
% 3.07/1.95 % (17042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.95 % (17042)Termination reason: Unknown
% 3.07/1.95 % (17042)Termination phase: Property scanning
% 3.07/1.95
% 3.07/1.95 % (17042)Memory used [KB]: 2686
% 3.07/1.95 % (17042)Time elapsed: 0.028 s
% 3.07/1.95 % (17042)Instructions burned: 98 (million)
% 3.07/1.95 % (17042)------------------------------
% 3.07/1.95 % (17042)------------------------------
% 3.07/1.96 % (17046)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_16722 for (2996ds/6Mi)
% 3.07/1.96 % (17046)Instruction limit reached!
% 3.07/1.96 % (17046)------------------------------
% 3.07/1.96 % (17046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.96 % (17046)Termination reason: Unknown
% 3.07/1.96 % (17046)Termination phase: shuffling
% 3.07/1.96
% 3.07/1.96 % (17046)Memory used [KB]: 1663
% 3.07/1.96 % (17046)Time elapsed: 0.003 s
% 3.07/1.96 % (17046)Instructions burned: 7 (million)
% 3.07/1.96 % (17046)------------------------------
% 3.07/1.96 % (17046)------------------------------
% 3.07/1.96 % (17022)Instruction limit reached!
% 3.07/1.96 % (17022)------------------------------
% 3.07/1.96 % (17022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.96 % (17022)Termination reason: Unknown
% 3.07/1.96 % (17022)Termination phase: Saturation
% 3.07/1.96
% 3.07/1.96 % (17022)Memory used [KB]: 13176
% 3.07/1.96 % (17022)Time elapsed: 0.272 s
% 3.07/1.96 % (17022)Instructions burned: 902 (million)
% 3.07/1.96 % (17022)------------------------------
% 3.07/1.96 % (17022)------------------------------
% 3.07/1.97 % (17048)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_16722 for (2996ds/47Mi)
% 3.07/1.97 % (17047)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_16722 for (2996ds/1087Mi)
% 3.07/1.97 % (17044)Instruction limit reached!
% 3.07/1.97 % (17044)------------------------------
% 3.07/1.97 % (17044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.97 % (17044)Termination reason: Unknown
% 3.07/1.97 % (17044)Termination phase: Function definition elimination
% 3.07/1.97
% 3.07/1.97 % (17044)Memory used [KB]: 2942
% 3.07/1.97 % (17044)Time elapsed: 0.039 s
% 3.07/1.97 % (17044)Instructions burned: 149 (million)
% 3.07/1.97 % (17044)------------------------------
% 3.07/1.97 % (17044)------------------------------
% 3.07/1.97 % (17049)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_16722 for (2996ds/44Mi)
% 3.07/1.98 % (17048)Instruction limit reached!
% 3.07/1.98 % (17048)------------------------------
% 3.07/1.98 % (17048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.98 % (17048)Termination reason: Unknown
% 3.07/1.98 % (17048)Termination phase: shuffling
% 3.07/1.98
% 3.07/1.98 % (17048)Memory used [KB]: 2430
% 3.07/1.98 % (17048)Time elapsed: 0.014 s
% 3.07/1.98 % (17048)Instructions burned: 48 (million)
% 3.07/1.98 % (17048)------------------------------
% 3.07/1.98 % (17048)------------------------------
% 3.07/1.98 % (17050)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_16722 for (2996ds/432Mi)
% 3.07/1.98 % (17049)Instruction limit reached!
% 3.07/1.98 % (17049)------------------------------
% 3.07/1.98 % (17049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.98 % (17049)Termination reason: Unknown
% 3.07/1.98 % (17049)Termination phase: shuffling
% 3.07/1.98
% 3.07/1.98 % (17049)Memory used [KB]: 2430
% 3.07/1.98 % (17049)Time elapsed: 0.013 s
% 3.07/1.98 % (17049)Instructions burned: 45 (million)
% 3.07/1.98 % (17049)------------------------------
% 3.07/1.98 % (17049)------------------------------
% 3.07/1.99 % (17051)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_16722 for (2996ds/62Mi)
% 3.07/1.99 % (17052)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_16722 for (2996ds/31Mi)
% 3.07/2.00 % (17052)Instruction limit reached!
% 3.07/2.00 % (17052)------------------------------
% 3.07/2.00 % (17052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/2.00 % (17052)Termination reason: Unknown
% 3.07/2.00 % (17052)Termination phase: shuffling
% 3.07/2.00
% 3.07/2.00 % (17052)Memory used [KB]: 2174
% 3.07/2.00 % (17052)Time elapsed: 0.010 s
% 3.07/2.00 % (17052)Instructions burned: 31 (million)
% 3.07/2.00 % (17052)------------------------------
% 3.07/2.00 % (17052)------------------------------
% 3.07/2.01 % (17051)Instruction limit reached!
% 3.07/2.01 % (17051)------------------------------
% 3.07/2.01 % (17051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/2.01 % (17051)Termination reason: Unknown
% 3.07/2.01 % (17051)Termination phase: Property scanning
% 3.07/2.01
% 3.07/2.01 % (17051)Memory used [KB]: 2686
% 3.07/2.01 % (17051)Time elapsed: 0.018 s
% 3.07/2.01 % (17051)Instructions burned: 63 (million)
% 3.07/2.01 % (17051)------------------------------
% 3.07/2.01 % (17051)------------------------------
% 3.07/2.01 % (17053)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_16722 for (2995ds/96Mi)
% 5.83/2.02 % (17054)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_16722 for (2995ds/453Mi)
% 5.83/2.02 % (17040)Instruction limit reached!
% 5.83/2.02 % (17040)------------------------------
% 5.83/2.02 % (17040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.02 % (17040)Termination reason: Unknown
% 5.83/2.02 % (17040)Termination phase: Saturation
% 5.83/2.02
% 5.83/2.02 % (17040)Memory used [KB]: 7803
% 5.83/2.02 % (17040)Time elapsed: 0.111 s
% 5.83/2.02 % (17040)Instructions burned: 449 (million)
% 5.83/2.02 % (17040)------------------------------
% 5.83/2.02 % (17040)------------------------------
% 5.83/2.02 % (17029)Instruction limit reached!
% 5.83/2.02 % (17029)------------------------------
% 5.83/2.02 % (17029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.02 % (17029)Termination reason: Unknown
% 5.83/2.02 % (17029)Termination phase: Saturation
% 5.83/2.02
% 5.83/2.02 % (17029)Memory used [KB]: 10618
% 5.83/2.02 % (17029)Time elapsed: 0.277 s
% 5.83/2.02 % (17029)Instructions burned: 879 (million)
% 5.83/2.02 % (17029)------------------------------
% 5.83/2.02 % (17029)------------------------------
% 5.83/2.03 % (17055)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_16722 for (2995ds/71Mi)
% 5.83/2.03 % (17056)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_16722 for (2995ds/83Mi)
% 5.83/2.04 % (17053)Instruction limit reached!
% 5.83/2.04 % (17053)------------------------------
% 5.83/2.04 % (17053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.04 % (17053)Termination reason: Unknown
% 5.83/2.04 % (17053)Termination phase: Property scanning
% 5.83/2.04
% 5.83/2.04 % (17053)Memory used [KB]: 2686
% 5.83/2.04 % (17053)Time elapsed: 0.026 s
% 5.83/2.04 % (17053)Instructions burned: 96 (million)
% 5.83/2.04 % (17053)------------------------------
% 5.83/2.04 % (17053)------------------------------
% 5.83/2.05 % (17057)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_16722 for (2995ds/11Mi)
% 5.83/2.05 % (17057)Instruction limit reached!
% 5.83/2.05 % (17057)------------------------------
% 5.83/2.05 % (17057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.05 % (17057)Termination reason: Unknown
% 5.83/2.05 % (17057)Termination phase: shuffling
% 5.83/2.05
% 5.83/2.05 % (17057)Memory used [KB]: 1791
% 5.83/2.05 % (17057)Time elapsed: 0.005 s
% 5.83/2.05 % (17057)Instructions burned: 12 (million)
% 5.83/2.05 % (17057)------------------------------
% 5.83/2.05 % (17057)------------------------------
% 5.83/2.05 % (17055)Instruction limit reached!
% 5.83/2.05 % (17055)------------------------------
% 5.83/2.05 % (17055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.05 % (17055)Termination reason: Unknown
% 5.83/2.05 % (17055)Termination phase: Property scanning
% 5.83/2.05
% 5.83/2.05 % (17055)Memory used [KB]: 2686
% 5.83/2.05 % (17055)Time elapsed: 0.021 s
% 5.83/2.05 % (17055)Instructions burned: 73 (million)
% 5.83/2.05 % (17055)------------------------------
% 5.83/2.05 % (17055)------------------------------
% 5.83/2.06 % (17056)Instruction limit reached!
% 5.83/2.06 % (17056)------------------------------
% 5.83/2.06 % (17056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.06 % (17056)Termination reason: Unknown
% 5.83/2.06 % (17056)Termination phase: Property scanning
% 5.83/2.06
% 5.83/2.06 % (17056)Memory used [KB]: 2686
% 5.83/2.06 % (17056)Time elapsed: 0.024 s
% 5.83/2.06 % (17056)Instructions burned: 84 (million)
% 5.83/2.06 % (17056)------------------------------
% 5.83/2.06 % (17056)------------------------------
% 5.83/2.06 % (17058)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_16722 for (2995ds/41Mi)
% 5.83/2.06 % (17059)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16722 for (2995ds/6Mi)
% 5.83/2.06 % (17059)Instruction limit reached!
% 5.83/2.06 % (17059)------------------------------
% 5.83/2.06 % (17059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.06 % (17059)Termination reason: Unknown
% 5.83/2.06 % (17059)Termination phase: shuffling
% 5.83/2.06
% 5.83/2.06 % (17059)Memory used [KB]: 1663
% 5.83/2.06 % (17059)Time elapsed: 0.004 s
% 5.83/2.06 % (17059)Instructions burned: 9 (million)
% 5.83/2.06 % (17059)------------------------------
% 5.83/2.06 % (17059)------------------------------
% 5.83/2.07 % (17060)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_16722 for (2995ds/150Mi)
% 5.83/2.07 % (17058)Instruction limit reached!
% 5.83/2.07 % (17058)------------------------------
% 5.83/2.07 % (17058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.07 % (17058)Termination reason: Unknown
% 5.83/2.07 % (17058)Termination phase: shuffling
% 5.83/2.07
% 5.83/2.07 % (17058)Memory used [KB]: 2430
% 5.83/2.07 % (17058)Time elapsed: 0.013 s
% 5.83/2.07 % (17058)Instructions burned: 43 (million)
% 5.83/2.07 % (17058)------------------------------
% 5.83/2.07 % (17058)------------------------------
% 5.83/2.07 % (17061)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_16722 for (2995ds/343Mi)
% 5.83/2.08 % (17062)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_16722 for (2995ds/109Mi)
% 5.83/2.09 % (17043)Instruction limit reached!
% 5.83/2.09 % (17043)------------------------------
% 5.83/2.09 % (17043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.09 % (17043)Termination reason: Unknown
% 5.83/2.09 % (17043)Termination phase: Saturation
% 5.83/2.09
% 5.83/2.09 % (17043)Memory used [KB]: 8315
% 5.83/2.09 % (17043)Time elapsed: 0.155 s
% 5.83/2.09 % (17043)Instructions burned: 508 (million)
% 5.83/2.09 % (17043)------------------------------
% 5.83/2.09 % (17043)------------------------------
% 5.83/2.09 % (17050)Instruction limit reached!
% 5.83/2.09 % (17050)------------------------------
% 5.83/2.09 % (17050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.09 % (17050)Termination reason: Unknown
% 5.83/2.09 % (17050)Termination phase: Saturation
% 5.83/2.09
% 5.83/2.09 % (17050)Memory used [KB]: 3198
% 5.83/2.09 % (17050)Time elapsed: 0.109 s
% 5.83/2.09 % (17050)Instructions burned: 435 (million)
% 5.83/2.09 % (17050)------------------------------
% 5.83/2.09 % (17050)------------------------------
% 5.83/2.10 % (17063)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_16722 for (2995ds/253Mi)
% 5.83/2.10 % (17064)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_16722 for (2994ds/140Mi)
% 5.83/2.11 % (17062)Instruction limit reached!
% 5.83/2.11 % (17062)------------------------------
% 5.83/2.11 % (17062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.11 % (17062)Termination reason: Unknown
% 5.83/2.11 % (17062)Termination phase: SInE selection
% 5.83/2.11
% 5.83/2.11 % (17062)Memory used [KB]: 2814
% 5.83/2.11 % (17062)Time elapsed: 0.030 s
% 5.83/2.11 % (17062)Instructions burned: 110 (million)
% 5.83/2.11 % (17062)------------------------------
% 5.83/2.11 % (17062)------------------------------
% 5.83/2.11 % (17060)Instruction limit reached!
% 5.83/2.11 % (17060)------------------------------
% 5.83/2.11 % (17060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.11 % (17060)Termination reason: Unknown
% 5.83/2.11 % (17060)Termination phase: Clausification
% 5.83/2.11
% 5.83/2.11 % (17060)Memory used [KB]: 5245
% 5.83/2.11 % (17060)Time elapsed: 0.046 s
% 5.83/2.11 % (17060)Instructions burned: 150 (million)
% 5.83/2.11 % (17060)------------------------------
% 5.83/2.11 % (17060)------------------------------
% 6.38/2.12 % (17065)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_16722 for (2994ds/614Mi)
% 6.38/2.12 % (17066)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_16722 for (2994ds/202Mi)
% 6.38/2.13 % (17054)Instruction limit reached!
% 6.38/2.13 % (17054)------------------------------
% 6.38/2.13 % (17054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.13 % (17054)Termination reason: Unknown
% 6.38/2.13 % (17054)Termination phase: Saturation
% 6.38/2.13
% 6.38/2.13 % (17054)Memory used [KB]: 7803
% 6.38/2.13 % (17054)Time elapsed: 0.114 s
% 6.38/2.13 % (17054)Instructions burned: 454 (million)
% 6.38/2.13 % (17054)------------------------------
% 6.38/2.13 % (17054)------------------------------
% 6.38/2.14 % (17064)Instruction limit reached!
% 6.38/2.14 % (17064)------------------------------
% 6.38/2.14 % (17064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.14 % (17064)Termination reason: Unknown
% 6.38/2.14 % (17064)Termination phase: Property scanning
% 6.38/2.14
% 6.38/2.14 % (17064)Memory used [KB]: 2942
% 6.38/2.14 % (17064)Time elapsed: 0.038 s
% 6.38/2.14 % (17064)Instructions burned: 141 (million)
% 6.38/2.14 % (17064)------------------------------
% 6.38/2.14 % (17064)------------------------------
% 6.38/2.14 % (17067)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_16722 for (2994ds/339Mi)
% 6.38/2.15 % (17068)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_16722 for (2994ds/283Mi)
% 6.38/2.16 % (17061)Instruction limit reached!
% 6.38/2.16 % (17061)------------------------------
% 6.38/2.16 % (17061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.16 % (17061)Termination reason: Unknown
% 6.38/2.16 % (17061)Termination phase: Saturation
% 6.38/2.16
% 6.38/2.16 % (17061)Memory used [KB]: 8315
% 6.38/2.16 % (17061)Time elapsed: 0.089 s
% 6.38/2.16 % (17061)Instructions burned: 345 (million)
% 6.38/2.16 % (17061)------------------------------
% 6.38/2.16 % (17061)------------------------------
% 6.38/2.17 % (17063)Instruction limit reached!
% 6.38/2.17 % (17063)------------------------------
% 6.38/2.17 % (17063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.17 % (17063)Termination reason: Unknown
% 6.38/2.17 % (17063)Termination phase: Property scanning
% 6.38/2.17
% 6.38/2.17 % (17063)Memory used [KB]: 5884
% 6.38/2.17 % (17063)Time elapsed: 0.072 s
% 6.38/2.17 % (17063)Instructions burned: 254 (million)
% 6.38/2.17 % (17063)------------------------------
% 6.38/2.17 % (17063)------------------------------
% 6.38/2.17 % (17069)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_16722 for (2994ds/134Mi)
% 6.38/2.18 % (17070)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_16722 for (2994ds/298Mi)
% 6.38/2.18 % (17066)Instruction limit reached!
% 6.38/2.18 % (17066)------------------------------
% 6.38/2.18 % (17066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.18 % (17066)Termination reason: Unknown
% 6.38/2.18 % (17066)Termination phase: Property scanning
% 6.38/2.18
% 6.38/2.18 % (17066)Memory used [KB]: 5628
% 6.38/2.18 % (17066)Time elapsed: 0.059 s
% 6.38/2.18 % (17066)Instructions burned: 204 (million)
% 6.38/2.18 % (17066)------------------------------
% 6.38/2.18 % (17066)------------------------------
% 6.38/2.19 % (17071)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_16722 for (2994ds/192Mi)
% 6.88/2.21 % (17069)Instruction limit reached!
% 6.88/2.21 % (17069)------------------------------
% 6.88/2.21 % (17069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.21 % (17069)Termination reason: Unknown
% 6.88/2.21 % (17069)Termination phase: Property scanning
% 6.88/2.21
% 6.88/2.21 % (17069)Memory used [KB]: 2942
% 6.88/2.21 % (17069)Time elapsed: 0.036 s
% 6.88/2.21 % (17069)Instructions burned: 134 (million)
% 6.88/2.21 % (17069)------------------------------
% 6.88/2.21 % (17069)------------------------------
% 6.88/2.22 % (17072)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_16722 for (2993ds/258Mi)
% 6.88/2.22 % (17068)Instruction limit reached!
% 6.88/2.22 % (17068)------------------------------
% 6.88/2.22 % (17068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.22 % (17068)Termination reason: Unknown
% 6.88/2.22 % (17068)Termination phase: Saturation
% 6.88/2.22
% 6.88/2.22 % (17068)Memory used [KB]: 7675
% 6.88/2.22 % (17068)Time elapsed: 0.072 s
% 6.88/2.22 % (17068)Instructions burned: 286 (million)
% 6.88/2.22 % (17068)------------------------------
% 6.88/2.22 % (17068)------------------------------
% 6.88/2.23 % (17073)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_16722 for (2993ds/90Mi)
% 6.88/2.23 % (17067)Instruction limit reached!
% 6.88/2.23 % (17067)------------------------------
% 6.88/2.23 % (17067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.23 % (17067)Termination reason: Unknown
% 6.88/2.23 % (17067)Termination phase: Saturation
% 6.88/2.23
% 6.88/2.23 % (17067)Memory used [KB]: 8187
% 6.88/2.23 % (17067)Time elapsed: 0.091 s
% 6.88/2.23 % (17067)Instructions burned: 340 (million)
% 6.88/2.23 % (17067)------------------------------
% 6.88/2.23 % (17067)------------------------------
% 6.88/2.24 % (17071)Instruction limit reached!
% 6.88/2.24 % (17071)------------------------------
% 6.88/2.24 % (17071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.24 % (17071)Termination reason: Unknown
% 6.88/2.24 % (17071)Termination phase: Saturation
% 6.88/2.24
% 6.88/2.24 % (17071)Memory used [KB]: 7547
% 6.88/2.24 % (17071)Time elapsed: 0.050 s
% 6.88/2.24 % (17071)Instructions burned: 193 (million)
% 6.88/2.24 % (17071)------------------------------
% 6.88/2.24 % (17071)------------------------------
% 6.88/2.24 % (17074)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_16722 for (2993ds/231Mi)
% 6.88/2.25 % (17075)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_16722 for (2993ds/458Mi)
% 6.88/2.25 % (17073)Instruction limit reached!
% 6.88/2.25 % (17073)------------------------------
% 6.88/2.25 % (17073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.25 % (17073)Termination reason: Unknown
% 6.88/2.25 % (17073)Termination phase: Property scanning
% 6.88/2.25
% 6.88/2.25 % (17073)Memory used [KB]: 2686
% 6.88/2.25 % (17073)Time elapsed: 0.026 s
% 6.88/2.25 % (17073)Instructions burned: 91 (million)
% 6.88/2.25 % (17073)------------------------------
% 6.88/2.25 % (17073)------------------------------
% 6.88/2.25 % (17070)Instruction limit reached!
% 6.88/2.25 % (17070)------------------------------
% 6.88/2.25 % (17070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.25 % (17070)Termination reason: Unknown
% 6.88/2.25 % (17070)Termination phase: Saturation
% 6.88/2.25
% 6.88/2.25 % (17070)Memory used [KB]: 7675
% 6.88/2.25 % (17070)Time elapsed: 0.076 s
% 6.88/2.25 % (17070)Instructions burned: 298 (million)
% 6.88/2.25 % (17070)------------------------------
% 6.88/2.25 % (17070)------------------------------
% 6.88/2.26 % (17076)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_16722 for (2993ds/31Mi)
% 6.88/2.26 % (17077)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_16722 for (2993ds/297Mi)
% 6.88/2.27 % (17076)Instruction limit reached!
% 6.88/2.27 % (17076)------------------------------
% 6.88/2.27 % (17076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.27 % (17076)Termination reason: Unknown
% 6.88/2.27 % (17076)Termination phase: shuffling
% 6.88/2.27
% 6.88/2.27 % (17076)Memory used [KB]: 2302
% 6.88/2.27 % (17076)Time elapsed: 0.010 s
% 6.88/2.27 % (17076)Instructions burned: 33 (million)
% 6.88/2.27 % (17076)------------------------------
% 6.88/2.27 % (17076)------------------------------
% 6.88/2.28 % (17078)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_16722 for (2993ds/987Mi)
% 6.88/2.28 % (17072)Instruction limit reached!
% 6.88/2.28 % (17072)------------------------------
% 6.88/2.28 % (17072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.28 % (17072)Termination reason: Unknown
% 6.88/2.28 % (17072)Termination phase: Saturation
% 6.88/2.28
% 6.88/2.28 % (17072)Memory used [KB]: 7931
% 6.88/2.28 % (17072)Time elapsed: 0.068 s
% 6.88/2.28 % (17072)Instructions burned: 261 (million)
% 6.88/2.28 % (17072)------------------------------
% 6.88/2.28 % (17072)------------------------------
% 6.88/2.29 % (17079)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_16722 for (2993ds/182Mi)
% 6.88/2.29 % (17065)Instruction limit reached!
% 6.88/2.29 % (17065)------------------------------
% 6.88/2.29 % (17065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.29 % (17065)Termination reason: Unknown
% 6.88/2.29 % (17065)Termination phase: Saturation
% 6.88/2.29
% 6.88/2.29 % (17065)Memory used [KB]: 10234
% 6.88/2.29 % (17065)Time elapsed: 0.175 s
% 6.88/2.29 % (17065)Instructions burned: 615 (million)
% 6.88/2.29 % (17065)------------------------------
% 6.88/2.29 % (17065)------------------------------
% 7.67/2.30 % (17074)Instruction limit reached!
% 7.67/2.30 % (17074)------------------------------
% 7.67/2.30 % (17074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.30 % (17074)Termination reason: Unknown
% 7.67/2.30 % (17074)Termination phase: Property scanning
% 7.67/2.30
% 7.67/2.30 % (17074)Memory used [KB]: 3965
% 7.67/2.30 % (17074)Time elapsed: 0.062 s
% 7.67/2.30 % (17074)Instructions burned: 234 (million)
% 7.67/2.30 % (17074)------------------------------
% 7.67/2.30 % (17074)------------------------------
% 7.67/2.30 % (17080)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_16722 for (2992ds/182Mi)
% 7.67/2.31 % (17081)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_16722 for (2992ds/154Mi)
% 7.67/2.34 % (17077)Instruction limit reached!
% 7.67/2.34 % (17077)------------------------------
% 7.67/2.34 % (17077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.34 % (17077)Termination reason: Unknown
% 7.67/2.34 % (17077)Termination phase: Saturation
% 7.67/2.34
% 7.67/2.34 % (17077)Memory used [KB]: 7675
% 7.67/2.34 % (17077)Time elapsed: 0.075 s
% 7.67/2.34 % (17077)Instructions burned: 299 (million)
% 7.67/2.34 % (17077)------------------------------
% 7.67/2.34 % (17077)------------------------------
% 7.67/2.34 % (17079)Instruction limit reached!
% 7.67/2.34 % (17079)------------------------------
% 7.67/2.34 % (17079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.34 % (17079)Termination reason: Unknown
% 7.67/2.34 % (17079)Termination phase: Property scanning
% 7.67/2.34
% 7.67/2.34 % (17079)Memory used [KB]: 3070
% 7.67/2.34 % (17079)Time elapsed: 0.048 s
% 7.67/2.34 % (17079)Instructions burned: 186 (million)
% 7.67/2.34 % (17079)------------------------------
% 7.67/2.34 % (17079)------------------------------
% 7.67/2.35 % (17082)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_16722 for (2992ds/79Mi)
% 7.67/2.35 % (17081)Instruction limit reached!
% 7.67/2.35 % (17081)------------------------------
% 7.67/2.35 % (17081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.35 % (17081)Termination reason: Unknown
% 7.67/2.35 % (17081)Termination phase: Function definition elimination
% 7.67/2.35
% 7.67/2.35 % (17081)Memory used [KB]: 3198
% 7.67/2.35 % (17081)Time elapsed: 0.040 s
% 7.67/2.35 % (17081)Instructions burned: 157 (million)
% 7.67/2.35 % (17081)------------------------------
% 7.67/2.35 % (17081)------------------------------
% 7.67/2.35 % (17083)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_16722 for (2992ds/216Mi)
% 7.67/2.36 % (17080)Instruction limit reached!
% 7.67/2.36 % (17080)------------------------------
% 7.67/2.36 % (17080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.36 % (17080)Termination reason: Unknown
% 7.67/2.36 % (17080)Termination phase: Property scanning
% 7.67/2.36
% 7.67/2.36 % (17080)Memory used [KB]: 5628
% 7.67/2.36 % (17080)Time elapsed: 0.053 s
% 7.67/2.36 % (17080)Instructions burned: 182 (million)
% 7.67/2.36 % (17080)------------------------------
% 7.67/2.36 % (17080)------------------------------
% 7.67/2.36 % (17047)Instruction limit reached!
% 7.67/2.36 % (17047)------------------------------
% 7.67/2.36 % (17047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.36 % (17047)Termination reason: Unknown
% 7.67/2.36 % (17047)Termination phase: Saturation
% 7.67/2.36
% 7.67/2.36 % (17047)Memory used [KB]: 13176
% 7.67/2.36 % (17047)Time elapsed: 0.390 s
% 7.67/2.36 % (17047)Instructions burned: 1088 (million)
% 7.67/2.36 % (17047)------------------------------
% 7.67/2.36 % (17047)------------------------------
% 7.67/2.36 % (17084)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_16722 for (2992ds/114Mi)
% 7.67/2.37 % (17085)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_16722 for (2992ds/922Mi)
% 7.67/2.37 % (17082)Instruction limit reached!
% 7.67/2.37 % (17082)------------------------------
% 7.67/2.37 % (17082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.37 % (17082)Termination reason: Unknown
% 7.67/2.37 % (17082)Termination phase: Property scanning
% 7.67/2.37
% 7.67/2.37 % (17082)Memory used [KB]: 2686
% 7.67/2.37 % (17082)Time elapsed: 0.022 s
% 7.67/2.37 % (17082)Instructions burned: 79 (million)
% 7.67/2.37 % (17082)------------------------------
% 7.67/2.37 % (17082)------------------------------
% 7.67/2.37 % (17075)Instruction limit reached!
% 7.67/2.37 % (17075)------------------------------
% 7.67/2.37 % (17075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.37 % (17075)Termination reason: Unknown
% 7.67/2.37 % (17075)Termination phase: Saturation
% 7.67/2.37
% 7.67/2.37 % (17075)Memory used [KB]: 9722
% 7.67/2.37 % (17075)Time elapsed: 0.121 s
% 7.67/2.37 % (17075)Instructions burned: 458 (million)
% 7.67/2.37 % (17075)------------------------------
% 7.67/2.37 % (17075)------------------------------
% 7.67/2.37 % (17086)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_16722 for (2992ds/182Mi)
% 7.67/2.38 % (17087)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_16722 for (2992ds/164Mi)
% 7.67/2.38 % (17088)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_16722 for (2992ds/50Mi)
% 7.67/2.39 % (17084)Instruction limit reached!
% 7.67/2.39 % (17084)------------------------------
% 7.67/2.39 % (17084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.39 % (17084)Termination reason: Unknown
% 7.67/2.39 % (17084)Termination phase: Property scanning
% 7.67/2.39
% 7.67/2.39 % (17084)Memory used [KB]: 2942
% 7.67/2.39 % (17084)Time elapsed: 0.031 s
% 7.67/2.39 % (17084)Instructions burned: 116 (million)
% 7.67/2.39 % (17084)------------------------------
% 7.67/2.39 % (17084)------------------------------
% 7.67/2.39 % (17088)Instruction limit reached!
% 7.67/2.39 % (17088)------------------------------
% 7.67/2.39 % (17088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.39 % (17088)Termination reason: Unknown
% 7.67/2.39 % (17088)Termination phase: shuffling
% 7.67/2.39
% 7.67/2.39 % (17088)Memory used [KB]: 2558
% 7.67/2.39 % (17088)Time elapsed: 0.015 s
% 7.67/2.39 % (17088)Instructions burned: 52 (million)
% 7.67/2.39 % (17088)------------------------------
% 7.67/2.39 % (17088)------------------------------
% 8.30/2.40 % (17089)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_16722 for (2992ds/368Mi)
% 8.30/2.40 % (17090)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_16722 for (2992ds/1021Mi)
% 8.30/2.40 % (17083)Instruction limit reached!
% 8.30/2.40 % (17083)------------------------------
% 8.30/2.40 % (17083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.40 % (17083)Termination reason: Unknown
% 8.30/2.40 % (17083)Termination phase: Property scanning
% 8.30/2.40
% 8.30/2.40 % (17083)Memory used [KB]: 3198
% 8.30/2.40 % (17083)Time elapsed: 0.054 s
% 8.30/2.40 % (17083)Instructions burned: 218 (million)
% 8.30/2.40 % (17083)------------------------------
% 8.30/2.40 % (17083)------------------------------
% 8.30/2.41 % (17091)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_16722 for (2991ds/267Mi)
% 8.30/2.41 % (17086)Instruction limit reached!
% 8.30/2.41 % (17086)------------------------------
% 8.30/2.41 % (17086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.41 % (17086)Termination reason: Unknown
% 8.30/2.41 % (17086)Termination phase: Property scanning
% 8.30/2.41
% 8.30/2.41 % (17086)Memory used [KB]: 3198
% 8.30/2.41 % (17086)Time elapsed: 0.047 s
% 8.30/2.41 % (17086)Instructions burned: 186 (million)
% 8.30/2.41 % (17086)------------------------------
% 8.30/2.41 % (17086)------------------------------
% 8.30/2.42 % (17087)Instruction limit reached!
% 8.30/2.42 % (17087)------------------------------
% 8.30/2.42 % (17087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.42 % (17087)Termination reason: Unknown
% 8.30/2.42 % (17087)Termination phase: Property scanning
% 8.30/2.42
% 8.30/2.42 % (17087)Memory used [KB]: 2942
% 8.30/2.42 % (17087)Time elapsed: 0.042 s
% 8.30/2.42 % (17087)Instructions burned: 165 (million)
% 8.30/2.42 % (17087)------------------------------
% 8.30/2.42 % (17087)------------------------------
% 8.30/2.42 % (17092)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_16722 for (2991ds/204Mi)
% 8.30/2.43 % (17093)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_16722 for (2991ds/26Mi)
% 8.30/2.43 % (17093)Instruction limit reached!
% 8.30/2.43 % (17093)------------------------------
% 8.30/2.43 % (17093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.43 % (17093)Termination reason: Unknown
% 8.30/2.43 % (17093)Termination phase: shuffling
% 8.30/2.43
% 8.30/2.43 % (17093)Memory used [KB]: 2046
% 8.30/2.43 % (17093)Time elapsed: 0.008 s
% 8.30/2.43 % (17093)Instructions burned: 26 (million)
% 8.30/2.43 % (17093)------------------------------
% 8.30/2.43 % (17093)------------------------------
% 8.30/2.44 % (17094)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_16722 for (2991ds/53Mi)
% 8.30/2.46 % (17094)Instruction limit reached!
% 8.30/2.46 % (17094)------------------------------
% 8.30/2.46 % (17094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.46 % (17094)Termination reason: Unknown
% 8.30/2.46 % (17094)Termination phase: shuffling
% 8.30/2.46
% 8.30/2.46 % (17094)Memory used [KB]: 2686
% 8.30/2.46 % (17094)Time elapsed: 0.016 s
% 8.30/2.46 % (17094)Instructions burned: 56 (million)
% 8.30/2.46 % (17094)------------------------------
% 8.30/2.46 % (17094)------------------------------
% 8.30/2.47 % (17095)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_16722 for (2991ds/4436Mi)
% 8.30/2.47 % (17092)Instruction limit reached!
% 8.30/2.47 % (17092)------------------------------
% 8.30/2.47 % (17092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.47 % (17092)Termination reason: Unknown
% 8.30/2.47 % (17092)Termination phase: Property scanning
% 8.30/2.47
% 8.30/2.47 % (17092)Memory used [KB]: 3070
% 8.30/2.47 % (17092)Time elapsed: 0.052 s
% 8.30/2.47 % (17092)Instructions burned: 207 (million)
% 8.30/2.47 % (17092)------------------------------
% 8.30/2.47 % (17092)------------------------------
% 8.30/2.48 % (17091)Instruction limit reached!
% 8.30/2.48 % (17091)------------------------------
% 8.30/2.48 % (17091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.48 % (17091)Termination reason: Unknown
% 8.30/2.48 % (17091)Termination phase: Saturation
% 8.30/2.48
% 8.30/2.48 % (17091)Memory used [KB]: 7675
% 8.30/2.48 % (17091)Time elapsed: 0.067 s
% 8.30/2.48 % (17091)Instructions burned: 267 (million)
% 8.30/2.48 % (17091)------------------------------
% 8.30/2.48 % (17091)------------------------------
% 8.30/2.48 % (17096)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_16722 for (2991ds/1539Mi)
% 8.30/2.49 % (17097)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_16722 for (2991ds/408Mi)
% 8.30/2.49 % (17089)Instruction limit reached!
% 8.30/2.49 % (17089)------------------------------
% 8.30/2.49 % (17089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.49 % (17089)Termination reason: Unknown
% 8.30/2.49 % (17089)Termination phase: Saturation
% 8.30/2.49
% 8.30/2.49 % (17089)Memory used [KB]: 8827
% 8.30/2.49 % (17089)Time elapsed: 0.097 s
% 8.30/2.49 % (17089)Instructions burned: 368 (million)
% 8.30/2.49 % (17089)------------------------------
% 8.30/2.49 % (17089)------------------------------
% 8.74/2.50 % (17098)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_16722 for (2991ds/5205Mi)
% 8.74/2.53 % (17078)Instruction limit reached!
% 8.74/2.53 % (17078)------------------------------
% 8.74/2.53 % (17078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.74/2.53 % (17078)Termination reason: Unknown
% 8.74/2.53 % (17078)Termination phase: Saturation
% 8.74/2.53
% 8.74/2.53 % (17078)Memory used [KB]: 13944
% 8.74/2.53 % (17078)Time elapsed: 0.249 s
% 8.74/2.53 % (17078)Instructions burned: 988 (million)
% 8.74/2.53 % (17078)------------------------------
% 8.74/2.53 % (17078)------------------------------
% 8.74/2.54 % (17099)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_16722 for (2990ds/1913Mi)
% 9.02/2.60 % (17097)Instruction limit reached!
% 9.02/2.60 % (17097)------------------------------
% 9.02/2.60 % (17097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.60 % (17097)Termination reason: Unknown
% 9.02/2.60 % (17097)Termination phase: Saturation
% 9.02/2.60
% 9.02/2.60 % (17097)Memory used [KB]: 11769
% 9.02/2.60 % (17097)Time elapsed: 0.119 s
% 9.02/2.60 % (17097)Instructions burned: 409 (million)
% 9.02/2.60 % (17097)------------------------------
% 9.02/2.60 % (17097)------------------------------
% 9.02/2.62 % (17100)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_16722 for (2989ds/4350Mi)
% 9.02/2.65 % (17085)Instruction limit reached!
% 9.02/2.65 % (17085)------------------------------
% 9.02/2.65 % (17085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.65 % (17085)Termination reason: Unknown
% 9.02/2.65 % (17085)Termination phase: Saturation
% 9.02/2.65
% 9.02/2.65 % (17085)Memory used [KB]: 12920
% 9.02/2.65 % (17085)Time elapsed: 0.283 s
% 9.02/2.65 % (17085)Instructions burned: 922 (million)
% 9.02/2.65 % (17085)------------------------------
% 9.02/2.65 % (17085)------------------------------
% 9.02/2.66 % (17101)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_16722 for (2989ds/68Mi)
% 9.02/2.68 % (17101)Instruction limit reached!
% 9.02/2.68 % (17101)------------------------------
% 9.02/2.68 % (17101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.68 % (17101)Termination reason: Unknown
% 9.02/2.68 % (17101)Termination phase: Property scanning
% 9.02/2.68
% 9.02/2.68 % (17101)Memory used [KB]: 2686
% 9.02/2.68 % (17101)Time elapsed: 0.020 s
% 9.02/2.68 % (17101)Instructions burned: 69 (million)
% 9.02/2.68 % (17101)------------------------------
% 9.02/2.68 % (17101)------------------------------
% 9.02/2.69 % (17102)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_16722 for (2989ds/358Mi)
% 9.46/2.71 % (17090)Instruction limit reached!
% 9.46/2.71 % (17090)------------------------------
% 9.46/2.71 % (17090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.71 % (17090)Termination reason: Unknown
% 9.46/2.71 % (17090)Termination phase: Saturation
% 9.46/2.71
% 9.46/2.71 % (17090)Memory used [KB]: 13048
% 9.46/2.71 % (17090)Time elapsed: 0.314 s
% 9.46/2.71 % (17090)Instructions burned: 1023 (million)
% 9.46/2.71 % (17090)------------------------------
% 9.46/2.71 % (17090)------------------------------
% 9.46/2.72 % (17103)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_16722 for (2988ds/31Mi)
% 9.46/2.73 % (17103)Instruction limit reached!
% 9.46/2.73 % (17103)------------------------------
% 9.46/2.73 % (17103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.73 % (17103)Termination reason: Unknown
% 9.46/2.73 % (17103)Termination phase: shuffling
% 9.46/2.73
% 9.46/2.73 % (17103)Memory used [KB]: 2174
% 9.46/2.73 % (17103)Time elapsed: 0.010 s
% 9.46/2.73 % (17103)Instructions burned: 32 (million)
% 9.46/2.73 % (17103)------------------------------
% 9.46/2.73 % (17103)------------------------------
% 9.46/2.74 % (17104)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_16722 for (2988ds/279Mi)
% 9.46/2.78 % (17102)Instruction limit reached!
% 9.46/2.78 % (17102)------------------------------
% 9.46/2.78 % (17102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.78 % (17102)Termination reason: Unknown
% 9.46/2.78 % (17102)Termination phase: Saturation
% 9.46/2.78
% 9.46/2.78 % (17102)Memory used [KB]: 8443
% 9.46/2.78 % (17102)Time elapsed: 0.092 s
% 9.46/2.78 % (17102)Instructions burned: 360 (million)
% 9.46/2.78 % (17102)------------------------------
% 9.46/2.78 % (17102)------------------------------
% 9.46/2.79 % (17105)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_16722 for (2988ds/258Mi)
% 9.91/2.81 % (17104)Instruction limit reached!
% 9.91/2.81 % (17104)------------------------------
% 9.91/2.81 % (17104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.81 % (17104)Termination reason: Unknown
% 9.91/2.81 % (17104)Termination phase: Saturation
% 9.91/2.81
% 9.91/2.81 % (17104)Memory used [KB]: 7675
% 9.91/2.81 % (17104)Time elapsed: 0.071 s
% 9.91/2.81 % (17104)Instructions burned: 281 (million)
% 9.91/2.81 % (17104)------------------------------
% 9.91/2.81 % (17104)------------------------------
% 9.91/2.82 % (17106)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_16722 for (2987ds/26Mi)
% 9.91/2.83 % (17106)Instruction limit reached!
% 9.91/2.83 % (17106)------------------------------
% 9.91/2.83 % (17106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.83 % (17106)Termination reason: Unknown
% 9.91/2.83 % (17106)Termination phase: shuffling
% 9.91/2.83
% 9.91/2.83 % (17106)Memory used [KB]: 2046
% 9.91/2.83 % (17106)Time elapsed: 0.008 s
% 9.91/2.83 % (17106)Instructions burned: 26 (million)
% 9.91/2.83 % (17106)------------------------------
% 9.91/2.83 % (17106)------------------------------
% 9.91/2.84 % (17107)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_16722 for (2987ds/995Mi)
% 9.91/2.85 % (17105)Instruction limit reached!
% 9.91/2.85 % (17105)------------------------------
% 9.91/2.85 % (17105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.85 % (17105)Termination reason: Unknown
% 9.91/2.85 % (17105)Termination phase: Saturation
% 9.91/2.85
% 9.91/2.85 % (17105)Memory used [KB]: 8315
% 9.91/2.85 % (17105)Time elapsed: 0.069 s
% 9.91/2.85 % (17105)Instructions burned: 259 (million)
% 9.91/2.85 % (17105)------------------------------
% 9.91/2.85 % (17105)------------------------------
% 9.91/2.86 % (17108)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_16722 for (2987ds/373Mi)
% 10.07/2.95 % (17096)Instruction limit reached!
% 10.07/2.95 % (17096)------------------------------
% 10.07/2.95 % (17096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.07/2.95 % (17096)Termination reason: Unknown
% 10.07/2.95 % (17096)Termination phase: Saturation
% 10.07/2.95
% 10.07/2.95 % (17096)Memory used [KB]: 11001
% 10.07/2.95 % (17096)Time elapsed: 0.466 s
% 10.07/2.95 % (17096)Instructions burned: 1539 (million)
% 10.07/2.95 % (17096)------------------------------
% 10.07/2.95 % (17096)------------------------------
% 10.07/2.96 % (17109)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_16722 for (2986ds/253Mi)
% 10.07/2.96 % (17108)Instruction limit reached!
% 10.07/2.96 % (17108)------------------------------
% 10.07/2.96 % (17108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.07/2.96 % (17108)Termination reason: Unknown
% 10.07/2.96 % (17108)Termination phase: Saturation
% 10.07/2.96
% 10.07/2.96 % (17108)Memory used [KB]: 9466
% 10.07/2.96 % (17108)Time elapsed: 0.098 s
% 10.07/2.96 % (17108)Instructions burned: 374 (million)
% 10.07/2.96 % (17108)------------------------------
% 10.07/2.96 % (17108)------------------------------
% 10.07/2.97 % (17110)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_16722 for (2986ds/832Mi)
% 10.07/3.02 % (17109)Instruction limit reached!
% 10.07/3.02 % (17109)------------------------------
% 10.07/3.02 % (17109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.07/3.02 % (17109)Termination reason: Unknown
% 10.07/3.02 % (17109)Termination phase: Saturation
% 10.07/3.02
% 10.07/3.02 % (17109)Memory used [KB]: 7675
% 10.07/3.02 % (17109)Time elapsed: 0.064 s
% 10.07/3.02 % (17109)Instructions burned: 255 (million)
% 10.07/3.02 % (17109)------------------------------
% 10.07/3.02 % (17109)------------------------------
% 12.92/3.03 % (17111)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_16722 for (2985ds/668Mi)
% 12.92/3.09 % (17107)Instruction limit reached!
% 12.92/3.09 % (17107)------------------------------
% 12.92/3.09 % (17107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.92/3.09 % (17107)Termination reason: Unknown
% 12.92/3.09 % (17107)Termination phase: Saturation
% 12.92/3.09
% 12.92/3.09 % (17107)Memory used [KB]: 16886
% 12.92/3.09 % (17107)Time elapsed: 0.248 s
% 12.92/3.09 % (17107)Instructions burned: 995 (million)
% 12.92/3.09 % (17107)------------------------------
% 12.92/3.09 % (17107)------------------------------
% 12.92/3.10 % (17112)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_16722 for (2985ds/40Mi)
% 12.92/3.10 % (17099)Instruction limit reached!
% 12.92/3.10 % (17099)------------------------------
% 12.92/3.10 % (17099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.92/3.10 % (17099)Termination reason: Unknown
% 12.92/3.10 % (17099)Termination phase: Saturation
% 12.92/3.10
% 12.92/3.10 % (17099)Memory used [KB]: 6396
% 12.92/3.10 % (17099)Time elapsed: 0.565 s
% 12.92/3.10 % (17099)Instructions burned: 1914 (million)
% 12.92/3.10 % (17099)------------------------------
% 12.92/3.10 % (17099)------------------------------
% 12.92/3.11 % (17112)Instruction limit reached!
% 12.92/3.11 % (17112)------------------------------
% 12.92/3.11 % (17112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.92/3.11 % (17112)Termination reason: Unknown
% 12.92/3.11 % (17112)Termination phase: shuffling
% 12.92/3.11
% 12.92/3.11 % (17112)Memory used [KB]: 2430
% 12.92/3.11 % (17112)Time elapsed: 0.013 s
% 12.92/3.11 % (17112)Instructions burned: 41 (million)
% 12.92/3.11 % (17112)------------------------------
% 12.92/3.11 % (17112)------------------------------
% 12.92/3.11 % (17113)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_16722 for (2984ds/294Mi)
% 12.92/3.12 % (17114)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_16722 for (2984ds/187Mi)
% 13.52/3.16 % (17114)Instruction limit reached!
% 13.52/3.16 % (17114)------------------------------
% 13.52/3.16 % (17114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.16 % (17114)Termination reason: Unknown
% 13.52/3.16 % (17114)Termination phase: Property scanning
% 13.52/3.16
% 13.52/3.16 % (17114)Memory used [KB]: 3070
% 13.52/3.16 % (17114)Time elapsed: 0.048 s
% 13.52/3.16 % (17114)Instructions burned: 189 (million)
% 13.52/3.16 % (17114)------------------------------
% 13.52/3.16 % (17114)------------------------------
% 13.52/3.17 % (17115)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_16722 for (2984ds/371Mi)
% 13.52/3.18 % (17113)Instruction limit reached!
% 13.52/3.18 % (17113)------------------------------
% 13.52/3.18 % (17113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.18 % (17113)Termination reason: Unknown
% 13.52/3.18 % (17113)Termination phase: Saturation
% 13.52/3.18
% 13.52/3.18 % (17113)Memory used [KB]: 7675
% 13.52/3.18 % (17113)Time elapsed: 0.074 s
% 13.52/3.18 % (17113)Instructions burned: 296 (million)
% 13.52/3.18 % (17113)------------------------------
% 13.52/3.18 % (17113)------------------------------
% 13.52/3.19 % (17116)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_16722 for (2983ds/1827Mi)
% 13.95/3.20 % (17111)Instruction limit reached!
% 13.95/3.20 % (17111)------------------------------
% 13.95/3.20 % (17111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/3.20 % (17111)Termination reason: Unknown
% 13.95/3.20 % (17111)Termination phase: Saturation
% 13.95/3.20
% 13.95/3.20 % (17111)Memory used [KB]: 12792
% 13.95/3.20 % (17111)Time elapsed: 0.167 s
% 13.95/3.20 % (17111)Instructions burned: 671 (million)
% 13.95/3.20 % (17111)------------------------------
% 13.95/3.20 % (17111)------------------------------
% 13.95/3.21 % (17117)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_16722 for (2983ds/70Mi)
% 13.95/3.22 % (17110)Instruction limit reached!
% 13.95/3.22 % (17110)------------------------------
% 13.95/3.22 % (17110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/3.22 % (17110)Termination reason: Unknown
% 13.95/3.22 % (17110)Termination phase: Saturation
% 13.95/3.22
% 13.95/3.22 % (17110)Memory used [KB]: 13176
% 13.95/3.22 % (17110)Time elapsed: 0.250 s
% 13.95/3.22 % (17110)Instructions burned: 832 (million)
% 13.95/3.22 % (17110)------------------------------
% 13.95/3.22 % (17110)------------------------------
% 13.95/3.23 % (17117)Instruction limit reached!
% 13.95/3.23 % (17117)------------------------------
% 13.95/3.23 % (17117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/3.23 % (17117)Termination reason: Unknown
% 13.95/3.23 % (17117)Termination phase: Property scanning
% 13.95/3.23
% 13.95/3.23 % (17117)Memory used [KB]: 2686
% 13.95/3.23 % (17117)Time elapsed: 0.020 s
% 13.95/3.23 % (17117)Instructions burned: 72 (million)
% 13.95/3.23 % (17117)------------------------------
% 13.95/3.23 % (17117)------------------------------
% 13.95/3.23 % (17118)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_16722 for (2983ds/316Mi)
% 13.95/3.24 % (17119)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_16722 for (2983ds/932Mi)
% 13.95/3.27 % (17115)Instruction limit reached!
% 13.95/3.27 % (17115)------------------------------
% 13.95/3.27 % (17115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.95/3.27 % (17115)Termination reason: Unknown
% 13.95/3.27 % (17115)Termination phase: Saturation
% 13.95/3.27
% 13.95/3.27 % (17115)Memory used [KB]: 8827
% 13.95/3.27 % (17115)Time elapsed: 0.098 s
% 13.95/3.27 % (17115)Instructions burned: 374 (million)
% 13.95/3.27 % (17115)------------------------------
% 13.95/3.27 % (17115)------------------------------
% 13.95/3.28 % (17120)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_16722 for (2983ds/4714Mi)
% 14.61/3.31 % (17118)Instruction limit reached!
% 14.61/3.31 % (17118)------------------------------
% 14.61/3.31 % (17118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.61/3.31 % (17118)Termination reason: Unknown
% 14.61/3.31 % (17118)Termination phase: Saturation
% 14.61/3.31
% 14.61/3.31 % (17118)Memory used [KB]: 7675
% 14.61/3.31 % (17118)Time elapsed: 0.080 s
% 14.61/3.31 % (17118)Instructions burned: 317 (million)
% 14.61/3.31 % (17118)------------------------------
% 14.61/3.31 % (17118)------------------------------
% 14.61/3.32 % (17121)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_16722 for (2982ds/8250Mi)
% 15.00/3.47 % (17119)Instruction limit reached!
% 15.00/3.47 % (17119)------------------------------
% 15.00/3.47 % (17119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.00/3.47 % (17119)Termination reason: Unknown
% 15.00/3.47 % (17119)Termination phase: Saturation
% 15.00/3.47
% 15.00/3.47 % (17119)Memory used [KB]: 14072
% 15.00/3.47 % (17119)Time elapsed: 0.240 s
% 15.00/3.47 % (17119)Instructions burned: 933 (million)
% 15.00/3.47 % (17119)------------------------------
% 15.00/3.47 % (17119)------------------------------
% 15.00/3.49 % (17122)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_16722 for (2981ds/770Mi)
% 15.85/3.69 % (17116)Instruction limit reached!
% 15.85/3.69 % (17116)------------------------------
% 15.85/3.69 % (17116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.85/3.69 % (17116)Termination reason: Unknown
% 15.85/3.69 % (17116)Termination phase: Saturation
% 15.85/3.69
% 15.85/3.69 % (17116)Memory used [KB]: 21748
% 15.85/3.69 % (17116)Time elapsed: 0.502 s
% 15.85/3.69 % (17116)Instructions burned: 1829 (million)
% 15.85/3.69 % (17116)------------------------------
% 15.85/3.69 % (17116)------------------------------
% 15.85/3.69 % (17122)Instruction limit reached!
% 15.85/3.69 % (17122)------------------------------
% 15.85/3.69 % (17122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.85/3.69 % (17122)Termination reason: Unknown
% 15.85/3.69 % (17122)Termination phase: Saturation
% 15.85/3.69
% 15.85/3.69 % (17122)Memory used [KB]: 7931
% 15.85/3.69 % (17122)Time elapsed: 0.211 s
% 15.85/3.69 % (17122)Instructions burned: 772 (million)
% 15.85/3.69 % (17122)------------------------------
% 15.85/3.69 % (17122)------------------------------
% 16.88/3.71 % (17123)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_16722 for (2978ds/794Mi)
% 16.88/3.71 % (17124)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_16722 for (2978ds/464Mi)
% 17.19/3.81 % (17098)Instruction limit reached!
% 17.19/3.81 % (17098)------------------------------
% 17.19/3.81 % (17098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.19/3.81 % (17098)Termination reason: Unknown
% 17.19/3.81 % (17098)Termination phase: Saturation
% 17.19/3.81
% 17.19/3.81 % (17098)Memory used [KB]: 18805
% 17.19/3.81 % (17098)Time elapsed: 1.308 s
% 17.19/3.81 % (17098)Instructions burned: 5207 (million)
% 17.19/3.81 % (17098)------------------------------
% 17.19/3.81 % (17098)------------------------------
% 17.19/3.82 % (17125)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_16722 for (2977ds/1376Mi)
% 17.19/3.83 % (17124)Instruction limit reached!
% 17.19/3.83 % (17124)------------------------------
% 17.19/3.83 % (17124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.19/3.83 % (17124)Termination reason: Unknown
% 17.19/3.83 % (17124)Termination phase: Saturation
% 17.19/3.83
% 17.19/3.83 % (17124)Memory used [KB]: 9722
% 17.19/3.83 % (17124)Time elapsed: 0.124 s
% 17.19/3.83 % (17124)Instructions burned: 467 (million)
% 17.19/3.83 % (17124)------------------------------
% 17.19/3.83 % (17124)------------------------------
% 17.19/3.84 % (17126)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_16722 for (2977ds/906Mi)
% 17.19/3.87 % (17095)Instruction limit reached!
% 17.19/3.87 % (17095)------------------------------
% 17.19/3.87 % (17095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.19/3.87 % (17095)Termination reason: Unknown
% 17.19/3.87 % (17095)Termination phase: Saturation
% 17.19/3.87
% 17.19/3.87 % (17095)Memory used [KB]: 15735
% 17.19/3.87 % (17095)Time elapsed: 1.398 s
% 17.19/3.87 % (17095)Instructions burned: 4437 (million)
% 17.19/3.87 % (17095)------------------------------
% 17.19/3.87 % (17095)------------------------------
% 17.19/3.88 % (17127)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_16722 for (2977ds/434Mi)
% 17.53/3.93 % (17123)Instruction limit reached!
% 17.53/3.93 % (17123)------------------------------
% 17.53/3.93 % (17123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.53/3.93 % (17123)Termination reason: Unknown
% 17.53/3.93 % (17123)Termination phase: Saturation
% 17.53/3.93
% 17.53/3.93 % (17123)Memory used [KB]: 6396
% 17.53/3.93 % (17123)Time elapsed: 0.229 s
% 17.53/3.93 % (17123)Instructions burned: 795 (million)
% 17.53/3.93 % (17123)------------------------------
% 17.53/3.93 % (17123)------------------------------
% 17.53/3.94 % (17128)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_16722 for (2976ds/865Mi)
% 17.53/3.95 % (17100)Instruction limit reached!
% 17.53/3.95 % (17100)------------------------------
% 17.53/3.95 % (17100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.53/3.95 % (17100)Termination reason: Unknown
% 17.53/3.95 % (17100)Termination phase: Saturation
% 17.53/3.95
% 17.53/3.95 % (17100)Memory used [KB]: 14200
% 17.53/3.95 % (17100)Time elapsed: 1.359 s
% 17.53/3.95 % (17100)Instructions burned: 4350 (million)
% 17.53/3.95 % (17100)------------------------------
% 17.53/3.95 % (17100)------------------------------
% 17.53/3.96 % (17129)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_16722 for (2976ds/593Mi)
% 17.53/4.00 % (17127)Instruction limit reached!
% 17.53/4.00 % (17127)------------------------------
% 17.53/4.00 % (17127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.53/4.00 % (17127)Termination reason: Unknown
% 17.53/4.00 % (17127)Termination phase: Saturation
% 17.53/4.00
% 17.53/4.00 % (17127)Memory used [KB]: 11769
% 17.53/4.00 % (17127)Time elapsed: 0.127 s
% 17.53/4.00 % (17127)Instructions burned: 436 (million)
% 17.53/4.00 % (17127)------------------------------
% 17.53/4.00 % (17127)------------------------------
% 17.53/4.01 % (17130)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_16722 for (2975ds/443Mi)
% 19.94/4.11 % (17126)Instruction limit reached!
% 19.94/4.11 % (17126)------------------------------
% 19.94/4.11 % (17126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.94/4.11 % (17126)Termination reason: Unknown
% 19.94/4.11 % (17126)Termination phase: Saturation
% 19.94/4.11
% 19.94/4.11 % (17126)Memory used [KB]: 11513
% 19.94/4.11 % (17126)Time elapsed: 0.272 s
% 19.94/4.11 % (17126)Instructions burned: 906 (million)
% 19.94/4.11 % (17126)------------------------------
% 19.94/4.11 % (17126)------------------------------
% 19.94/4.11 % (17129)Instruction limit reached!
% 19.94/4.11 % (17129)------------------------------
% 19.94/4.11 % (17129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.94/4.11 % (17129)Termination reason: Unknown
% 19.94/4.11 % (17129)Termination phase: Saturation
% 19.94/4.11
% 19.94/4.11 % (17129)Memory used [KB]: 7803
% 19.94/4.11 % (17129)Time elapsed: 0.150 s
% 19.94/4.11 % (17129)Instructions burned: 596 (million)
% 19.94/4.11 % (17129)------------------------------
% 19.94/4.11 % (17129)------------------------------
% 19.94/4.12 % (17131)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_16722 for (2974ds/594Mi)
% 19.94/4.12 % (17132)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_16722 for (2974ds/327Mi)
% 20.57/4.13 % (17130)Instruction limit reached!
% 20.57/4.13 % (17130)------------------------------
% 20.57/4.13 % (17130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.13 % (17130)Termination reason: Unknown
% 20.57/4.13 % (17130)Termination phase: Saturation
% 20.57/4.13
% 20.57/4.13 % (17130)Memory used [KB]: 9594
% 20.57/4.13 % (17130)Time elapsed: 0.115 s
% 20.57/4.13 % (17130)Instructions burned: 444 (million)
% 20.57/4.13 % (17130)------------------------------
% 20.57/4.13 % (17130)------------------------------
% 20.57/4.14 % (17133)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_16722 for (2974ds/5411Mi)
% 20.57/4.17 % (17125)Instruction limit reached!
% 20.57/4.17 % (17125)------------------------------
% 20.57/4.17 % (17125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.17 % (17125)Termination reason: Unknown
% 20.57/4.17 % (17125)Termination phase: Saturation
% 20.57/4.17
% 20.57/4.17 % (17125)Memory used [KB]: 10106
% 20.57/4.17 % (17125)Time elapsed: 0.346 s
% 20.57/4.17 % (17125)Instructions burned: 1379 (million)
% 20.57/4.17 % (17125)------------------------------
% 20.57/4.17 % (17125)------------------------------
% 20.57/4.18 % (17134)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_16722 for (2974ds/1762Mi)
% 20.57/4.19 % (17128)Instruction limit reached!
% 20.57/4.19 % (17128)------------------------------
% 20.57/4.19 % (17128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.19 % (17128)Termination reason: Unknown
% 20.57/4.19 % (17128)Termination phase: Saturation
% 20.57/4.19
% 20.57/4.19 % (17128)Memory used [KB]: 10234
% 20.57/4.19 % (17128)Time elapsed: 0.248 s
% 20.57/4.19 % (17128)Instructions burned: 868 (million)
% 20.57/4.19 % (17128)------------------------------
% 20.57/4.19 % (17128)------------------------------
% 20.94/4.20 % (17135)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_16722 for (2974ds/96Mi)
% 20.94/4.21 % (17132)Instruction limit reached!
% 20.94/4.21 % (17132)------------------------------
% 20.94/4.21 % (17132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.21 % (17132)Termination reason: Unknown
% 20.94/4.21 % (17132)Termination phase: Saturation
% 20.94/4.21
% 20.94/4.21 % (17132)Memory used [KB]: 11385
% 20.94/4.21 % (17132)Time elapsed: 0.094 s
% 20.94/4.21 % (17132)Instructions burned: 329 (million)
% 20.94/4.21 % (17132)------------------------------
% 20.94/4.21 % (17132)------------------------------
% 20.94/4.22 % (17136)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_16722 for (2973ds/503Mi)
% 20.94/4.22 % (17135)Instruction limit reached!
% 20.94/4.22 % (17135)------------------------------
% 20.94/4.22 % (17135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.22 % (17135)Termination reason: Unknown
% 20.94/4.22 % (17135)Termination phase: Property scanning
% 20.94/4.22
% 20.94/4.22 % (17135)Memory used [KB]: 2814
% 20.94/4.22 % (17135)Time elapsed: 0.026 s
% 20.94/4.22 % (17135)Instructions burned: 97 (million)
% 20.94/4.22 % (17135)------------------------------
% 20.94/4.22 % (17135)------------------------------
% 20.94/4.23 % (17137)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_16722 for (2973ds/90Mi)
% 20.94/4.26 % (17137)Instruction limit reached!
% 20.94/4.26 % (17137)------------------------------
% 20.94/4.26 % (17137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.26 % (17137)Termination reason: Unknown
% 20.94/4.26 % (17137)Termination phase: Property scanning
% 20.94/4.26
% 20.94/4.26 % (17137)Memory used [KB]: 2686
% 20.94/4.26 % (17137)Time elapsed: 0.025 s
% 20.94/4.26 % (17137)Instructions burned: 92 (million)
% 20.94/4.26 % (17137)------------------------------
% 20.94/4.26 % (17137)------------------------------
% 20.94/4.27 % (17138)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_16722 for (2973ds/593Mi)
% 20.94/4.28 % (17131)Instruction limit reached!
% 20.94/4.28 % (17131)------------------------------
% 20.94/4.28 % (17131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.28 % (17131)Termination reason: Unknown
% 20.94/4.28 % (17131)Termination phase: Saturation
% 20.94/4.28
% 20.94/4.28 % (17131)Memory used [KB]: 10106
% 20.94/4.28 % (17131)Time elapsed: 0.165 s
% 20.94/4.28 % (17131)Instructions burned: 594 (million)
% 20.94/4.28 % (17131)------------------------------
% 20.94/4.28 % (17131)------------------------------
% 20.94/4.29 % (17139)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_16722 for (2973ds/1512Mi)
% 21.50/4.36 % (17136)Instruction limit reached!
% 21.50/4.36 % (17136)------------------------------
% 21.50/4.36 % (17136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.50/4.36 % (17136)Termination reason: Unknown
% 21.50/4.36 % (17136)Termination phase: Saturation
% 21.50/4.36
% 21.50/4.36 % (17136)Memory used [KB]: 9978
% 21.50/4.36 % (17136)Time elapsed: 0.135 s
% 21.50/4.36 % (17136)Instructions burned: 505 (million)
% 21.50/4.36 % (17136)------------------------------
% 21.50/4.36 % (17136)------------------------------
% 21.50/4.37 % (17140)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_16722 for (2972ds/569Mi)
% 21.84/4.43 % (17138)Instruction limit reached!
% 21.84/4.43 % (17138)------------------------------
% 21.84/4.43 % (17138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.84/4.43 % (17138)Termination reason: Unknown
% 21.84/4.43 % (17138)Termination phase: Saturation
% 21.84/4.43
% 21.84/4.43 % (17138)Memory used [KB]: 10362
% 21.84/4.43 % (17138)Time elapsed: 0.165 s
% 21.84/4.43 % (17138)Instructions burned: 595 (million)
% 21.84/4.43 % (17138)------------------------------
% 21.84/4.43 % (17138)------------------------------
% 21.84/4.44 % (17141)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_16722 for (2971ds/501Mi)
% 21.84/4.46 % (17120)Instruction limit reached!
% 21.84/4.46 % (17120)------------------------------
% 21.84/4.46 % (17120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.84/4.46 % (17120)Termination reason: Unknown
% 21.84/4.46 % (17120)Termination phase: Saturation
% 21.84/4.46
% 21.84/4.46 % (17120)Memory used [KB]: 7931
% 21.84/4.46 % (17120)Time elapsed: 1.185 s
% 21.84/4.46 % (17120)Instructions burned: 4714 (million)
% 21.84/4.46 % (17120)------------------------------
% 21.84/4.46 % (17120)------------------------------
% 21.84/4.47 % (17142)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_16722 for (2971ds/562Mi)
% 22.20/4.51 % (17140)Instruction limit reached!
% 22.20/4.51 % (17140)------------------------------
% 22.20/4.51 % (17140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.51 % (17140)Termination reason: Unknown
% 22.20/4.51 % (17140)Termination phase: Saturation
% 22.20/4.51
% 22.20/4.51 % (17140)Memory used [KB]: 7803
% 22.20/4.51 % (17140)Time elapsed: 0.140 s
% 22.20/4.51 % (17140)Instructions burned: 569 (million)
% 22.20/4.51 % (17140)------------------------------
% 22.20/4.51 % (17140)------------------------------
% 22.20/4.52 % (17143)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_16722 for (2970ds/406Mi)
% 22.20/4.59 % (17141)Instruction limit reached!
% 22.20/4.59 % (17141)------------------------------
% 22.20/4.59 % (17141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.59 % (17141)Termination reason: Unknown
% 22.20/4.59 % (17141)Termination phase: Saturation
% 22.20/4.59
% 22.20/4.59 % (17141)Memory used [KB]: 11001
% 22.20/4.59 % (17141)Time elapsed: 0.151 s
% 22.20/4.59 % (17141)Instructions burned: 503 (million)
% 22.20/4.59 % (17141)------------------------------
% 22.20/4.59 % (17141)------------------------------
% 22.59/4.60 % (17144)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_16722 for (2970ds/582Mi)
% 22.59/4.61 % (17134)Instruction limit reached!
% 22.59/4.61 % (17134)------------------------------
% 22.59/4.61 % (17134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.59/4.61 % (17134)Termination reason: Unknown
% 22.59/4.61 % (17134)Termination phase: Saturation
% 22.59/4.61
% 22.59/4.61 % (17134)Memory used [KB]: 21108
% 22.59/4.61 % (17134)Time elapsed: 0.432 s
% 22.59/4.61 % (17134)Instructions burned: 1764 (million)
% 22.59/4.61 % (17134)------------------------------
% 22.59/4.61 % (17134)------------------------------
% 22.59/4.62 % (17145)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_16722 for (2969ds/456Mi)
% 22.59/4.62 % (17143)Instruction limit reached!
% 22.59/4.62 % (17143)------------------------------
% 22.59/4.62 % (17143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.59/4.62 % (17143)Termination reason: Unknown
% 22.59/4.62 % (17143)Termination phase: Saturation
% 22.59/4.62
% 22.59/4.62 % (17143)Memory used [KB]: 7931
% 22.59/4.62 % (17143)Time elapsed: 0.109 s
% 22.59/4.62 % (17143)Instructions burned: 406 (million)
% 22.59/4.62 % (17143)------------------------------
% 22.59/4.62 % (17143)------------------------------
% 22.59/4.63 % (17146)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_16722 for (2969ds/393Mi)
% 22.59/4.63 % (17142)Instruction limit reached!
% 22.59/4.63 % (17142)------------------------------
% 22.59/4.63 % (17142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.59/4.63 % (17142)Termination reason: Unknown
% 22.59/4.63 % (17142)Termination phase: Saturation
% 22.59/4.63
% 22.59/4.63 % (17142)Memory used [KB]: 9466
% 22.59/4.63 % (17142)Time elapsed: 0.161 s
% 22.59/4.63 % (17142)Instructions burned: 562 (million)
% 22.59/4.63 % (17142)------------------------------
% 22.59/4.63 % (17142)------------------------------
% 22.59/4.64 % (17147)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_16722 for (2969ds/1335Mi)
% 23.42/4.71 % (17121)First to succeed.
% 23.42/4.72 % (17121)Refutation found. Thanks to Tanya!
% 23.42/4.72 % SZS status Theorem for DTF2THF_16722
% 23.42/4.72 % SZS output start Proof for DTF2THF_16722
% 23.42/4.72 thf(func_def_0, type, in: $i > $i > $o).
% 23.42/4.72 thf(func_def_1, type, exu: ($i > $o) > $o).
% 23.42/4.72 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 23.42/4.72 thf(func_def_8, type, powerset: $i > $i).
% 23.42/4.72 thf(func_def_10, type, setunion: $i > $i).
% 23.42/4.72 thf(func_def_19, type, descr: ($i > $o) > $i).
% 23.42/4.72 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_26, type, prop2set: $o > $i).
% 23.42/4.72 thf(func_def_36, type, nonempty: $i > $o).
% 23.42/4.72 thf(func_def_69, type, set2prop: $i > $o).
% 23.42/4.72 thf(func_def_88, type, subset: $i > $i > $o).
% 23.42/4.72 thf(func_def_89, type, disjoint: $i > $i > $o).
% 23.42/4.72 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 23.42/4.72 thf(func_def_114, type, binunion: $i > $i > $i).
% 23.42/4.72 thf(func_def_122, type, binintersect: $i > $i > $i).
% 23.42/4.72 thf(func_def_135, type, regular: $i > $o).
% 23.42/4.72 thf(func_def_136, type, setminus: $i > $i > $i).
% 23.42/4.72 thf(func_def_147, type, symdiff: $i > $i > $i).
% 23.42/4.72 thf(func_def_153, type, iskpair: $i > $o).
% 23.42/4.72 thf(func_def_158, type, kpair: $i > $i > $i).
% 23.42/4.72 thf(func_def_160, type, cartprod: $i > $i > $i).
% 23.42/4.72 thf(func_def_177, type, singleton: $i > $o).
% 23.42/4.72 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 23.42/4.72 thf(func_def_184, type, atmost1p: $i > $o).
% 23.42/4.72 thf(func_def_185, type, atleast2p: $i > $o).
% 23.42/4.72 thf(func_def_186, type, atmost2p: $i > $o).
% 23.42/4.72 thf(func_def_187, type, upairsetp: $i > $o).
% 23.42/4.72 thf(func_def_191, type, kfst: $i > $i).
% 23.42/4.72 thf(func_def_203, type, ksnd: $i > $i).
% 23.42/4.72 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 23.42/4.72 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 23.42/4.72 thf(func_def_222, type, func: $i > $i > $i > $o).
% 23.42/4.72 thf(func_def_223, type, funcSet: $i > $i > $i).
% 23.42/4.72 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 23.42/4.72 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 23.42/4.72 thf(func_def_323, type, breln1: $i > $i > $o).
% 23.42/4.72 thf(func_def_325, type, breln1Set: $i > $i).
% 23.42/4.72 thf(func_def_327, type, transitive: $i > $i > $o).
% 23.42/4.72 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 23.42/4.72 thf(func_def_329, type, reflexive: $i > $i > $o).
% 23.42/4.72 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 23.42/4.72 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 23.42/4.72 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 23.42/4.72 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 23.42/4.72 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_360, type, image1: $i > ($i > $i) > $i).
% 23.42/4.72 thf(func_def_376, type, sP0: $i > $i > $i > $o).
% 23.42/4.72 thf(func_def_378, type, sP2: $i > $i > $o).
% 23.42/4.72 thf(func_def_379, type, sP3: $i > $o).
% 23.42/4.72 thf(func_def_380, type, sP4: $i > $i > $o).
% 23.42/4.72 thf(func_def_381, type, sP5: $i > $i > $o).
% 23.42/4.72 thf(func_def_382, type, sP6: $i > $i > $i > $i > $o).
% 23.42/4.72 thf(func_def_388, type, sP12: $i > $i > $i > $o).
% 23.42/4.72 thf(func_def_393, type, sP17: $i > $o > $i > $i > $o).
% 23.42/4.72 thf(func_def_396, type, sK20: $i > $o).
% 23.42/4.72 thf(func_def_398, type, sK22: ($i > $o) > $i > $i > $i).
% 23.42/4.72 thf(func_def_399, type, sK23: ($i > $o) > $i > $i > $i).
% 23.42/4.72 thf(func_def_400, type, sK24: $i > $o).
% 23.42/4.72 thf(func_def_403, type, sK27: $i > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_404, type, sK28: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_405, type, sK29: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_418, type, sK42: $i > $i).
% 23.42/4.72 thf(func_def_419, type, sK43: $i > $i).
% 23.42/4.72 thf(func_def_421, type, sK45: $i > $o).
% 23.42/4.72 thf(func_def_422, type, sK46: $i > $i).
% 23.42/4.72 thf(func_def_423, type, sK47: ($i > $o) > $i).
% 23.42/4.72 thf(func_def_433, type, sK57: $i > $i > $i).
% 23.42/4.72 thf(func_def_465, type, sK89: ($i > $o) > $i > $i > $i).
% 23.42/4.72 thf(func_def_466, type, sK90: ($i > $o) > $i > $i > $i).
% 23.42/4.72 thf(func_def_469, type, sK93: $i > $o).
% 23.42/4.72 thf(func_def_495, type, sK119: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_499, type, sK123: $o > $i > $i > $i).
% 23.42/4.72 thf(func_def_523, type, sK147: $i > $o).
% 23.42/4.72 thf(func_def_525, type, sK149: ($i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_564, type, sK188: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_579, type, sK203: $i > $o).
% 23.42/4.72 thf(func_def_602, type, sK226: $i > $o).
% 23.42/4.72 thf(func_def_603, type, sK227: $i > $o).
% 23.42/4.72 thf(func_def_604, type, sK228: ($i > $o) > ($i > $o) > $i > $i > $i).
% 23.42/4.72 thf(func_def_605, type, sK229: ($i > $o) > ($i > $o) > $i > $i > $i).
% 23.42/4.72 thf(func_def_618, type, sK242: $i > $o).
% 23.42/4.72 thf(func_def_619, type, sK243: ($i > $o) > $i > $i > $i).
% 23.42/4.72 thf(func_def_622, type, sK246: $i > $o).
% 23.42/4.72 thf(func_def_627, type, sK251: $i > $i > $i).
% 23.42/4.72 thf(func_def_628, type, sK252: $i > $i > $i).
% 23.42/4.72 thf(func_def_629, type, sK253: $i > $i > $i).
% 23.42/4.72 thf(func_def_630, type, sK254: $i > $i > $i).
% 23.42/4.72 thf(func_def_631, type, sK255: $i > $i > $i).
% 23.42/4.72 thf(func_def_632, type, sK256: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_633, type, sK257: $i > $i).
% 23.42/4.72 thf(func_def_634, type, sK258: $i > $i).
% 23.42/4.72 thf(func_def_635, type, sK259: $i > $i).
% 23.42/4.72 thf(func_def_636, type, sK260: $i > $i).
% 23.42/4.72 thf(func_def_637, type, sK261: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_638, type, sK262: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_639, type, sK263: $i > $i > $i).
% 23.42/4.72 thf(func_def_640, type, sK264: $i > $i > $i).
% 23.42/4.72 thf(func_def_641, type, sK265: $i > $i > $i).
% 23.42/4.72 thf(func_def_642, type, sK266: $i > $i).
% 23.42/4.72 thf(func_def_644, type, sK268: $i > $i).
% 23.42/4.72 thf(func_def_645, type, sK269: $i > $i).
% 23.42/4.72 thf(func_def_646, type, sK270: ($i > $i) > $i > $i > $i).
% 23.42/4.72 thf(func_def_649, type, sK273: $i > $i).
% 23.42/4.72 thf(func_def_666, type, sK290: $i > $o).
% 23.42/4.72 thf(func_def_677, type, sK301: $i > $i > $o).
% 23.42/4.72 thf(func_def_682, type, sK306: $i > $i > $o).
% 23.42/4.72 thf(func_def_698, type, sK322: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_699, type, sK323: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_700, type, sK324: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_701, type, sK325: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_708, type, sK332: $i > $o).
% 23.42/4.72 thf(func_def_737, type, sK361: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_756, type, sK380: $o > $i > $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_761, type, sK385: $i > $o).
% 23.42/4.72 thf(func_def_764, type, sK388: $i > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_765, type, sK389: $i > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_774, type, sK398: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_775, type, sK399: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_794, type, sK418: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_796, type, sK420: $i > $i).
% 23.42/4.72 thf(func_def_800, type, sK424: $i > $i > $o).
% 23.42/4.72 thf(func_def_801, type, sK425: $i > $i).
% 23.42/4.72 thf(func_def_804, type, sK428: ($i > $i > $o) > $i > $i > $i).
% 23.42/4.72 thf(func_def_822, type, sK446: $i > $i).
% 23.42/4.72 thf(func_def_825, type, sK449: $i > $i > ($i > $i) > $i).
% 23.42/4.72 thf(func_def_835, type, sK459: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_836, type, sK460: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_853, type, sK477: $i > $i).
% 23.42/4.72 thf(func_def_855, type, sK479: $i > $i).
% 23.42/4.72 thf(func_def_856, type, sK480: $i > $i).
% 23.42/4.72 thf(func_def_857, type, sK481: $i > ($i > $i) > $i).
% 23.42/4.72 thf(func_def_858, type, sK482: $i > $i > ($i > $i) > $i).
% 23.42/4.72 thf(func_def_863, type, sK487: $i > $i > $i).
% 23.42/4.72 thf(func_def_864, type, sK488: $i > $i > $i).
% 23.42/4.72 thf(func_def_870, type, sK494: $i > $i > $i).
% 23.42/4.72 thf(func_def_885, type, sK509: ($i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_887, type, sK511: $i > $o).
% 23.42/4.72 thf(func_def_890, type, sK514: $i > $i).
% 23.42/4.72 thf(func_def_892, type, sK516: ($i > $i) > $i > $i > $i).
% 23.42/4.72 thf(func_def_894, type, sK518: $i > $i > $o).
% 23.42/4.72 thf(func_def_895, type, sK519: $i > $i).
% 23.42/4.72 thf(func_def_896, type, sK520: $i > $i).
% 23.42/4.72 thf(func_def_897, type, sK521: ($i > $i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_898, type, sK522: $i > ($i > $i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_899, type, sK523: ($i > $i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_904, type, sK528: $i > $i > $i).
% 23.42/4.72 thf(func_def_921, type, sK545: $i > $i > $o).
% 23.42/4.72 thf(func_def_925, type, sK549: $i > $i > $o).
% 23.42/4.72 thf(func_def_956, type, sK580: ($i > $o) > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_957, type, sK581: ($i > $o) > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_958, type, sK582: $i > $o).
% 23.42/4.72 thf(func_def_959, type, sK583: $i > $o).
% 23.42/4.72 thf(func_def_971, type, sK595: $i > $i > $i).
% 23.42/4.72 thf(func_def_987, type, sK611: $i > $i).
% 23.42/4.72 thf(func_def_999, type, sK623: $i > $o).
% 23.42/4.72 thf(func_def_1001, type, sK625: ($i > $o) > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1002, type, sK626: ($i > $o) > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1015, type, sK639: $i > $i > $i).
% 23.42/4.72 thf(func_def_1017, type, sK641: $i > $o).
% 23.42/4.72 thf(func_def_1021, type, sK645: $i > $i > $o).
% 23.42/4.72 thf(func_def_1026, type, sK650: ($i > $o) > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1027, type, sK651: ($i > $o) > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1031, type, sK655: $i > $o).
% 23.42/4.72 thf(func_def_1043, type, sK667: $i > $i > $i).
% 23.42/4.72 thf(func_def_1049, type, sK673: $i > $o).
% 23.42/4.72 thf(func_def_1057, type, sK681: $i > $i).
% 23.42/4.72 thf(func_def_1059, type, sK683: ($i > $i) > $i > $i > $i).
% 23.42/4.72 thf(func_def_1064, type, sK688: $i > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_1065, type, sK689: $i > $o).
% 23.42/4.72 thf(func_def_1076, type, sK700: $i > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_1077, type, sK701: $i > $o).
% 23.42/4.72 thf(func_def_1079, type, sK703: $i > $o).
% 23.42/4.72 thf(func_def_1080, type, sK704: $i > $i).
% 23.42/4.72 thf(func_def_1081, type, sK705: ($i > $o) > $i).
% 23.42/4.72 thf(func_def_1099, type, sK723: $i > $o).
% 23.42/4.72 thf(func_def_1101, type, sK725: $i > $o).
% 23.42/4.72 thf(func_def_1125, type, sK749: $i > $i).
% 23.42/4.72 thf(func_def_1127, type, sK751: ($i > $i) > $i > $i > $i).
% 23.42/4.72 thf(func_def_1137, type, sK761: ($i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_1139, type, sK763: $i > $o).
% 23.42/4.72 thf(func_def_1142, type, sK766: $i > $o).
% 23.42/4.72 thf(func_def_1144, type, sK768: $i > $i > $i).
% 23.42/4.72 thf(func_def_1154, type, sK778: $i > $i).
% 23.42/4.72 thf(func_def_1159, type, sK783: ($i > $o) > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_1160, type, sK784: ($i > $o) > ($i > $o) > $i).
% 23.42/4.72 thf(func_def_1161, type, sK785: $i > $o).
% 23.42/4.72 thf(func_def_1162, type, sK786: $i > $o).
% 23.42/4.72 thf(func_def_1182, type, sK806: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1183, type, sK807: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1184, type, sK808: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1185, type, sK809: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1192, type, sK816: $i > $i > $o).
% 23.42/4.72 thf(func_def_1197, type, sK821: ($i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_1199, type, sK823: $i > $o).
% 23.42/4.72 thf(func_def_1201, type, sK825: $i > $i > $o).
% 23.42/4.72 thf(func_def_1219, type, sK843: $i > $o).
% 23.42/4.72 thf(func_def_1220, type, sK844: ($i > $o) > $i).
% 23.42/4.72 thf(func_def_1221, type, sK845: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1222, type, sK846: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1240, type, sK864: $i > $o).
% 23.42/4.72 thf(func_def_1242, type, sK866: ($i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_1248, type, sK872: $i > $o).
% 23.42/4.72 thf(func_def_1252, type, sK876: $i > $i).
% 23.42/4.72 thf(func_def_1254, type, sK878: $i > $i).
% 23.42/4.72 thf(func_def_1263, type, sK887: $i > $i).
% 23.42/4.72 thf(func_def_1264, type, sK888: $i > $o).
% 23.42/4.72 thf(func_def_1285, type, sK909: $i > $i > $o).
% 23.42/4.72 thf(func_def_1298, type, sK922: ($i > $i) > $i > $i > $i).
% 23.42/4.72 thf(func_def_1301, type, sK925: $i > $i).
% 23.42/4.72 thf(func_def_1314, type, sK938: $i > $o).
% 23.42/4.72 thf(func_def_1316, type, sK940: ($i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_1317, type, sK941: ($i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_1338, type, sK962: $i > $i > $i).
% 23.42/4.72 thf(func_def_1342, type, sK966: $i > $o).
% 23.42/4.72 thf(func_def_1349, type, sK973: $i > $o).
% 23.42/4.72 thf(func_def_1351, type, sK975: ($i > $o) > $i > $i).
% 23.42/4.72 thf(func_def_1359, type, sK983: $i > $o).
% 23.42/4.72 thf(func_def_1361, type, sK985: ($i > $o) > $i).
% 23.42/4.72 thf(func_def_1362, type, sK986: ($i > $o) > $i).
% 23.42/4.72 thf(func_def_1371, type, sK995: $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1374, type, sK998: $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1379, type, sK1003: $i > $i).
% 23.42/4.72 thf(func_def_1389, type, sK1013: $i > $i > $i > $i > $i > $i).
% 23.42/4.72 thf(func_def_1390, type, sK1014: $i > $i).
% 23.42/4.72 thf(func_def_1415, type, sK1039: $i > $o).
% 23.42/4.72 thf(func_def_1433, type, ph1057: !>[X0: $tType]:(X0)).
% 23.42/4.72 thf(func_def_1434, type, sK1058: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1435, type, sK1059: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1436, type, sK1060: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1437, type, sK1061: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1438, type, sK1062: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1439, type, sK1063: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1440, type, sK1064: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1441, type, sK1065: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1442, type, sK1066: $i > $i > ($i > $i) > $i).
% 23.42/4.72 thf(func_def_1443, type, sK1067: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1444, type, sK1068: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1445, type, sK1069: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1446, type, sK1070: $i > $i > ($i > $i) > $i).
% 23.42/4.72 thf(func_def_1447, type, sK1071: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(func_def_1448, type, sK1072: $i > ($i > $i) > $i > $i).
% 23.42/4.72 thf(f24522,plain,(
% 23.42/4.72 $false),
% 23.42/4.72 inference(avatar_sat_refutation,[status(thm)],[f9067,f11267,f12733,f24521])).
% 23.42/4.72 thf(f24521,plain,(
% 23.42/4.72 ~spl1056_905 | ~spl1056_1360),
% 23.42/4.72 inference(avatar_contradiction_clause,[status(thm)],[f24520])).
% 23.42/4.72 thf(f24520,plain,(
% 23.42/4.72 $false | (~spl1056_905 | ~spl1056_1360)),
% 23.42/4.72 inference(subsumption_resolution,[status(thm)],[f24516,f18305])).
% 23.42/4.72 thf(f18305,plain,(
% 23.42/4.72 ((sK42 @ (sK516 @ sK42 @ sK41 @ sK40)) = sK41) | ~spl1056_1360),
% 23.42/4.72 inference(trivial_inequality_removal,[status(thm)],[f18266])).
% 23.42/4.72 thf(f18266,plain,(
% 23.42/4.72 ($true != $true) | ((sK42 @ (sK516 @ sK42 @ sK41 @ sK40)) = sK41) | ~spl1056_1360),
% 23.42/4.72 inference(superposition,[status(thm)],[f11266,f4831])).
% 23.42/4.72 thf(f4831,plain,(
% 23.42/4.72 ($true = (in @ sK41 @ (image1 @ sK40 @ sK42)))),
% 23.42/4.72 inference(beta_eta_normalization,[status(thm)],[f3323])).
% 23.42/4.72 thf(f3323,plain,(
% 23.42/4.72 ((in @ sK41 @ (image1 @ sK40 @ (^[Y0 : $i]: (sK42 @ Y0)))) = $true)),
% 23.42/4.72 inference(cnf_transformation,[status(thm)],[f1444])).
% 23.42/4.72 thf(f1444,plain,(
% 23.42/4.72 (binunionT_lem = $true) & (setadjoinE = $true) & (powersetE1 = $true) & (eqinunit = $true) & (cartprodpairin = $true) & (complementT_lem = $true) & (cartprodmempaircEq = $true) & (notinemptyset = $true) & (binintersectSubset1 = $true) & (omega0Ax = $true) & (setadjoinIR = $true) & (eqbreln = $true) & (iffalseProp1 = $true) & (binintersectSubset3 = $true) & (binunionIR = $true) & (cartprodfstin = $true) & (funcGraphProp2 = $true) & (breln1all1 = $true) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (contrasubsetT3 = $true) & (ap2apEq2 = $true) & (inCongP = $true) & (ubforcartprodlem1 = $true) & (((in @ sK41 @ (image1 @ sK40 @ (^[Y0 : $i]: (sK42 @ Y0)))) = $true) & ! [X3 : $i] : (((sK42 @ X3) != sK41) | ((in @ X3 @ sK40) != $true))) & (inIntersectImpInUnion = $true) & (binintersectT_lem = $true) & (demorgan2b = $true) & (disjointsetsI1 = $true) & (emptyinPowerset = $true) & (complementInPowersetComplementIntersect = $true) & (breln1compI = $true) & (intersectInPowersetIntersectUnions = $true) & (dpsetconstrSub = $true) & (woz13rule3 = $true) & (binunionEcases = $true) & (singletonsswitch = $true) & (complementTE1 = $true) & (setunionsingleton1 = $true) & (exuI3 = $true) & (powersetI1 = $true) & (setukpairinjR1 = $true) & (demorgan2a2 = $true) & (ubforcartprodlem3 = $true) & (image1Equiv = $true) & (subsetRefl = $true) & (symdiffI2 = $true) & (complementUnionInPowersetComplement = $true) & (kfstpairEq = $true) & (quantDeMorgan2 = $true) & (setminusI = $true) & (contraSubsetComplement = $true) & (woz2W = $true) & (demorgan1b = $true) & (notsubsetI = $true) & (woz1_5 = $true) & (breln1SetBreln1 = $true) & (setunionE = $true) & (symdiffE = $true) & (setadjoinAx = $true) & (upairset2IR = $true) & (contrasubsetT = $true) & (binintersectSubset4 = $true) & (exuI2 = $true) & (upairset2E = $true) & (theprop = $true) & (breln1compE = $true) & (notequalI2 = $true) & (setukpairinjR11 = $true) & (exuI1 = $true) & (exuE1 = $true) & (contrasubsetT1 = $true) & (demorgan2b2 = $true) & (emptyI = $true) & (cartprodpairmemEL = $true) & (emptyE1 = $true) & (emptysetAx = $true) & (setunion__Cong = $true) & (brelnall2 = $true) & (funcinfuncset = $true) & (exu__Cong = $true) & (woz1_4 = $true) & (powersetAx = $true) & (image1Ex1 = $true) & (lamp = $true) & (powersetTI1 = $true) & (setextT = $true) & (cartprodsndin = $true) & (powersetT_lem = $true) & (complementImpComplementIntersect = $true) & (binunionLsub = $true) & (binintersectER = $true) & (singletoninpowunion = $true) & (eta2 = $true) & (ap2p = $true) & (subPowSU = $true) & (ex1I = $true) & (beta2 = $true) & (ifSingleton = $true) & (kpairp = $true) & (vacuousDall = $true) & (binunionE = $true) & (subsetI2 = $true) & (emptysetimpfalse = $true) & (setunionI = $true) & (image1Ex = $true) & (omega__Cong = $true) & (iffalseProp2 = $true) & (replAx = $true) & (cartprodpairsurjEq = $true) & (setadjoinSub = $true) & (setOfPairsIsBReln = $true) & (iftrueProp2 = $true) & (nonemptyI1 = $true) & (exuE3e = $true) & (subset2powerset = $true) & (binunionTE = $true) & (wellorderingAx = $true) & (upairequniteq = $true) & (emptyInPowerset = $true) & (setukpairinjL1 = $true) & (woz1_1 = $true) & (setminusILneg = $true) & (subsetTI = $true) & (woz2A = $true) & (setukpairIL = $true) & (setOfPairsIsBReln1 = $true) & (setminusER = $true) & (inComplementUnionImpNotIn1 = $true) & (setextsub = $true) & (setunionAx = $true) & (doubleComplementI1 = $true) & (complementTnotintersectT = $true) & (demorgan2 = $true) & (setext = $true) & (inIntersectImpInIntersectUnions = $true) & (breln1unionCommutes = $true) & (quantDeMorgan4 = $true) & (upairinpowunion = $true) & (ksndsingleton = $true) & (funcext2 = $true) & (lam2p = $true) & (binintersectTERcontra = $true) & (breln1unionEcases = $true) & (subsetTrans = $true) & (exuE2 = $true) & (doubleComplementE1 = $true) & (breln1invE = $true) & (setminusERneg = $true) & (theeq = $true) & (setukpairinjR12 = $true) & (demorgan2a = $true) & (setbeta = $true) & (powerset__Cong = $true) & (ap2apEq1 = $true) & (woz2B = $true) & (ubforcartprodlem2 = $true) & (dpsetconstrEL1 = $true) & (funcext = $true) & (binintersectTELcontra = $true) & (setminusIRneg = $true) & (doubleComplementSub1 = $true) & (funcGraphProp3 = $true) & (setukpairinjR = $true) & (brelnall1 = $true) & (notequalI1 = $true) & (nonemptyI = $true) & (eqbreln1 = $true) & (setminusSubset2 = $true) & (powersetTE1 = $true) & (breln1invI = $true) & (in__Cong = $true) & (cartprodmempair = $true) & (breln1compprop = $true) & (singletonsuniq = $true) & (descr__Cong = $true) & (setminusSubset1 = $true) & (complementTcontraSubset = $true) & (upairsetE = $true) & (omegaSAx = $true) & (dsetconstrER = $true) & (setminusT_lem = $true) & (cartprodmempair1 = $true) & (eqimpsubset2 = $true) & (ex1E1 = $true) & (kpairiskpair = $true) & (subbreln = $true) & (kpairsurjEq = $true) & (cartprodsndpairEq = $true) & (iftrueProp1 = $true) & (secondinupair = $true) & (lam2lamEq = $true) & (beta1 = $true) & (woz13rule0 = $true) & (setminusLsub = $true) & (inIntersectImpInUnion2 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrI = $true) & (eta1 = $true) & (symdiffIneg1 = $true) & (funcGraphProp1 = $true) & (sepInPowerset = $true) & (binintersectLsub = $true) & (woz13rule4 = $true) & (subbreln1 = $true) & (woz2Ex = $true) & (lamProp = $true) & (prop2setI = $true) & (setukpairinjL2 = $true) & (funcImageSingleton = $true) & (binintersectSubset2 = $true) & (setukpairinjR2 = $true) & (cartprodpairmemER = $true) & (ex1E2 = $true) & (dpsetconstrI = $true) & (eqimpsubset1 = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (foundationAx = $true) & (app = $true) & (iftrueorfalse = $true) & (prop2setE = $true) & (binintersectI = $true) & (choice2fnsingleton = $true) & (singletoninpowerset = $true) & (setunionsingleton = $true) & (dpsetconstrERa = $true) & (setadjoin__Cong = $true) & (uniqinunit = $true) & (exuE3u = $true) & (demorgan1 = $true) & (dpsetconstrEL2 = $true) & (setminusELneg = $true) & (kfstsingleton = $true) & (doubleComplementEq = $true) & (iftrue = $true) & (symdiffI1 = $true) & (notdexE = $true) & (binunionTILcontra = $true) & (powersetsubset = $true) & (demorgan2a1 = $true) & (exuEu = $true) & (binunionRsub = $true) & (iffalse = $true) & (quantDeMorgan3 = $true) & (ifp = $true) & (funcGraphProp4 = $true) & (upairsetIL = $true) & (nonemptyImpWitness = $true) & (setukpairIR = $true) & (binintersectRsub = $true) & (sepSubset = $true) & (notdallE = $true) & (woz1_2 = $true) & (binintersectSubset5 = $true) & (binunionTIRcontra = $true) & (funcextLem = $true) & (notinsingleton = $true) & (subsetI1 = $true) & (infuncsetfunc = $true) & (upairsetIR = $true) & (emptyset__Cong = $true) & (omegaIndAx = $true) & (doubleComplementSub2 = $true) & (apProp = $true) & (setadjoinOr = $true) & (setukpairinjL = $true) & (singletonprop = $true) & (inComplementUnionImpInComplement1 = $true) & (bs114d = $true) & (setminusEL = $true) & (binintersectEL = $true) & (breln1unionE = $true) & (demorgan1a = $true) & (breln1unionprop = $true) & (breln1unionIR = $true) & (setadjoinIL = $true) & (emptysetsubset = $true) & (emptysetE = $true) & (woz13rule1 = $true) & (breln1unionIL = $true) & (powersetI = $true) & (dsetconstrEL = $true) & (setunionsingleton2 = $true) & (complementSubsetComplementIntersect = $true) & (upairsubunion = $true) & (binunionIL = $true) & (dpsetconstrER = $true) & (dsetconstr__Cong = $true) & (breln1invprop = $true) & (complementTI1 = $true) & (cartprodfstpairEq = $true) & (ksndpairEq = $true) & (breln1all2 = $true) & (prop2set2propI = $true) & (contrasubsetT2 = $true) & (inPowerset = $true) & (quantDeMorgan1 = $true) & (breln1unionI = $true) & (setunionE2 = $true) & (symdiffIneg2 = $true) & (subsetE = $true) & (subsetE2 = $true) & (descrp = $true) & (breln1compEex = $true) & (woz1_3 = $true) & (powersetE = $true) & (woz13rule2 = $true) & (singletonsubset = $true) & (setextAx = $true) & (binunionTEcontra = $true) & (noeltsimpempty = $true) & (ex1I2 = $true)),
% 23.42/4.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42])],[f1291,f1443])).
% 23.42/4.72 thf(f1443,plain,(
% 23.42/4.72 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) & ! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true))) => (((in @ sK41 @ (image1 @ sK40 @ (^[Y0 : $i]: (sK42 @ Y0)))) = $true) & ! [X3 : $i] : (((sK42 @ X3) != sK41) | ((in @ X3 @ sK40) != $true)))),
% 23.42/4.72 introduced(definition,[],[choice_axiom])).
% 23.42/4.72 thf(f1291,plain,(
% 23.42/4.72 (binunionT_lem = $true) & (setadjoinE = $true) & (powersetE1 = $true) & (eqinunit = $true) & (cartprodpairin = $true) & (complementT_lem = $true) & (cartprodmempaircEq = $true) & (notinemptyset = $true) & (binintersectSubset1 = $true) & (omega0Ax = $true) & (setadjoinIR = $true) & (eqbreln = $true) & (iffalseProp1 = $true) & (binintersectSubset3 = $true) & (binunionIR = $true) & (cartprodfstin = $true) & (funcGraphProp2 = $true) & (breln1all1 = $true) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (contrasubsetT3 = $true) & (ap2apEq2 = $true) & (inCongP = $true) & (ubforcartprodlem1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i > $i] : (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) & ! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true))) & (inIntersectImpInUnion = $true) & (binintersectT_lem = $true) & (demorgan2b = $true) & (disjointsetsI1 = $true) & (emptyinPowerset = $true) & (complementInPowersetComplementIntersect = $true) & (breln1compI = $true) & (intersectInPowersetIntersectUnions = $true) & (dpsetconstrSub = $true) & (woz13rule3 = $true) & (binunionEcases = $true) & (singletonsswitch = $true) & (complementTE1 = $true) & (setunionsingleton1 = $true) & (exuI3 = $true) & (powersetI1 = $true) & (setukpairinjR1 = $true) & (demorgan2a2 = $true) & (ubforcartprodlem3 = $true) & (image1Equiv = $true) & (subsetRefl = $true) & (symdiffI2 = $true) & (complementUnionInPowersetComplement = $true) & (kfstpairEq = $true) & (quantDeMorgan2 = $true) & (setminusI = $true) & (contraSubsetComplement = $true) & (woz2W = $true) & (demorgan1b = $true) & (notsubsetI = $true) & (woz1_5 = $true) & (breln1SetBreln1 = $true) & (setunionE = $true) & (symdiffE = $true) & (setadjoinAx = $true) & (upairset2IR = $true) & (contrasubsetT = $true) & (binintersectSubset4 = $true) & (exuI2 = $true) & (upairset2E = $true) & (theprop = $true) & (breln1compE = $true) & (notequalI2 = $true) & (setukpairinjR11 = $true) & (exuI1 = $true) & (exuE1 = $true) & (contrasubsetT1 = $true) & (demorgan2b2 = $true) & (emptyI = $true) & (cartprodpairmemEL = $true) & (emptyE1 = $true) & (emptysetAx = $true) & (setunion__Cong = $true) & (brelnall2 = $true) & (funcinfuncset = $true) & (exu__Cong = $true) & (woz1_4 = $true) & (powersetAx = $true) & (image1Ex1 = $true) & (lamp = $true) & (powersetTI1 = $true) & (setextT = $true) & (cartprodsndin = $true) & (powersetT_lem = $true) & (complementImpComplementIntersect = $true) & (binunionLsub = $true) & (binintersectER = $true) & (singletoninpowunion = $true) & (eta2 = $true) & (ap2p = $true) & (subPowSU = $true) & (ex1I = $true) & (beta2 = $true) & (ifSingleton = $true) & (kpairp = $true) & (vacuousDall = $true) & (binunionE = $true) & (subsetI2 = $true) & (emptysetimpfalse = $true) & (setunionI = $true) & (image1Ex = $true) & (omega__Cong = $true) & (iffalseProp2 = $true) & (replAx = $true) & (cartprodpairsurjEq = $true) & (setadjoinSub = $true) & (setOfPairsIsBReln = $true) & (iftrueProp2 = $true) & (nonemptyI1 = $true) & (exuE3e = $true) & (subset2powerset = $true) & (binunionTE = $true) & (wellorderingAx = $true) & (upairequniteq = $true) & (emptyInPowerset = $true) & (setukpairinjL1 = $true) & (woz1_1 = $true) & (setminusILneg = $true) & (subsetTI = $true) & (woz2A = $true) & (setukpairIL = $true) & (setOfPairsIsBReln1 = $true) & (setminusER = $true) & (inComplementUnionImpNotIn1 = $true) & (setextsub = $true) & (setunionAx = $true) & (doubleComplementI1 = $true) & (complementTnotintersectT = $true) & (demorgan2 = $true) & (setext = $true) & (inIntersectImpInIntersectUnions = $true) & (breln1unionCommutes = $true) & (quantDeMorgan4 = $true) & (upairinpowunion = $true) & (ksndsingleton = $true) & (funcext2 = $true) & (lam2p = $true) & (binintersectTERcontra = $true) & (breln1unionEcases = $true) & (subsetTrans = $true) & (exuE2 = $true) & (doubleComplementE1 = $true) & (breln1invE = $true) & (setminusERneg = $true) & (theeq = $true) & (setukpairinjR12 = $true) & (demorgan2a = $true) & (setbeta = $true) & (powerset__Cong = $true) & (ap2apEq1 = $true) & (woz2B = $true) & (ubforcartprodlem2 = $true) & (dpsetconstrEL1 = $true) & (funcext = $true) & (binintersectTELcontra = $true) & (setminusIRneg = $true) & (doubleComplementSub1 = $true) & (funcGraphProp3 = $true) & (setukpairinjR = $true) & (brelnall1 = $true) & (notequalI1 = $true) & (nonemptyI = $true) & (eqbreln1 = $true) & (setminusSubset2 = $true) & (powersetTE1 = $true) & (breln1invI = $true) & (in__Cong = $true) & (cartprodmempair = $true) & (breln1compprop = $true) & (singletonsuniq = $true) & (descr__Cong = $true) & (setminusSubset1 = $true) & (complementTcontraSubset = $true) & (upairsetE = $true) & (omegaSAx = $true) & (dsetconstrER = $true) & (setminusT_lem = $true) & (cartprodmempair1 = $true) & (eqimpsubset2 = $true) & (ex1E1 = $true) & (kpairiskpair = $true) & (subbreln = $true) & (kpairsurjEq = $true) & (cartprodsndpairEq = $true) & (iftrueProp1 = $true) & (secondinupair = $true) & (lam2lamEq = $true) & (beta1 = $true) & (woz13rule0 = $true) & (setminusLsub = $true) & (inIntersectImpInUnion2 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrI = $true) & (eta1 = $true) & (symdiffIneg1 = $true) & (funcGraphProp1 = $true) & (sepInPowerset = $true) & (binintersectLsub = $true) & (woz13rule4 = $true) & (subbreln1 = $true) & (woz2Ex = $true) & (lamProp = $true) & (prop2setI = $true) & (setukpairinjL2 = $true) & (funcImageSingleton = $true) & (binintersectSubset2 = $true) & (setukpairinjR2 = $true) & (cartprodpairmemER = $true) & (ex1E2 = $true) & (dpsetconstrI = $true) & (eqimpsubset1 = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (foundationAx = $true) & (app = $true) & (iftrueorfalse = $true) & (prop2setE = $true) & (binintersectI = $true) & (choice2fnsingleton = $true) & (singletoninpowerset = $true) & (setunionsingleton = $true) & (dpsetconstrERa = $true) & (setadjoin__Cong = $true) & (uniqinunit = $true) & (exuE3u = $true) & (demorgan1 = $true) & (dpsetconstrEL2 = $true) & (setminusELneg = $true) & (kfstsingleton = $true) & (doubleComplementEq = $true) & (iftrue = $true) & (symdiffI1 = $true) & (notdexE = $true) & (binunionTILcontra = $true) & (powersetsubset = $true) & (demorgan2a1 = $true) & (exuEu = $true) & (binunionRsub = $true) & (iffalse = $true) & (quantDeMorgan3 = $true) & (ifp = $true) & (funcGraphProp4 = $true) & (upairsetIL = $true) & (nonemptyImpWitness = $true) & (setukpairIR = $true) & (binintersectRsub = $true) & (sepSubset = $true) & (notdallE = $true) & (woz1_2 = $true) & (binintersectSubset5 = $true) & (binunionTIRcontra = $true) & (funcextLem = $true) & (notinsingleton = $true) & (subsetI1 = $true) & (infuncsetfunc = $true) & (upairsetIR = $true) & (emptyset__Cong = $true) & (omegaIndAx = $true) & (doubleComplementSub2 = $true) & (apProp = $true) & (setadjoinOr = $true) & (setukpairinjL = $true) & (singletonprop = $true) & (inComplementUnionImpInComplement1 = $true) & (bs114d = $true) & (setminusEL = $true) & (binintersectEL = $true) & (breln1unionE = $true) & (demorgan1a = $true) & (breln1unionprop = $true) & (breln1unionIR = $true) & (setadjoinIL = $true) & (emptysetsubset = $true) & (emptysetE = $true) & (woz13rule1 = $true) & (breln1unionIL = $true) & (powersetI = $true) & (dsetconstrEL = $true) & (setunionsingleton2 = $true) & (complementSubsetComplementIntersect = $true) & (upairsubunion = $true) & (binunionIL = $true) & (dpsetconstrER = $true) & (dsetconstr__Cong = $true) & (breln1invprop = $true) & (complementTI1 = $true) & (cartprodfstpairEq = $true) & (ksndpairEq = $true) & (breln1all2 = $true) & (prop2set2propI = $true) & (contrasubsetT2 = $true) & (inPowerset = $true) & (quantDeMorgan1 = $true) & (breln1unionI = $true) & (setunionE2 = $true) & (symdiffIneg2 = $true) & (subsetE = $true) & (subsetE2 = $true) & (descrp = $true) & (breln1compEex = $true) & (woz1_3 = $true) & (powersetE = $true) & (woz13rule2 = $true) & (singletonsubset = $true) & (setextAx = $true) & (binunionTEcontra = $true) & (noeltsimpempty = $true) & (ex1I2 = $true)),
% 23.42/4.72 inference(flattening,[status(thm)],[f1290])).
% 23.42/4.72 thf(f1290,plain,(
% 23.42/4.72 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i > $i] : (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) & ! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true))) & (image1Equiv = $true)) & (image1Ex1 = $true)) & (image1Ex = $true)) & (woz2B = $true)) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1unionEcases = $true)) & (breln1unionE = $true)) & (breln1unionI = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)) & (breln1unionprop = $true)) & (breln1compEex = $true)) & (breln1compE = $true)) & (breln1compI = $true)) & (breln1compprop = $true)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $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)),
% 23.42/4.72 inference(ennf_transformation,[status(thm)],[f968])).
% 23.42/4.72 thf(f968,plain,(
% 23.42/4.72 ~((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) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) => ? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((X2 @ X3) = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 23.42/4.72 inference(rectify,[status(thm)],[f606])).
% 23.42/4.72 thf(f606,plain,(
% 23.42/4.72 ~((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) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) => ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ((X2 @ X4) = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 23.42/4.72 inference(fool_elimination,[status(thm)],[f605])).
% 23.42/4.72 thf(f605,plain,(
% 23.42/4.72 ~(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 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => ! [X0 : $i,X1 : $i,X2 : $i > $i] : ((in @ X1 @ (image1 @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => ? [X4 : $i] : ((in @ X4 @ X0) & ((X2 @ X4) = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 23.42/4.72 inference(rectify,[status(thm)],[f316])).
% 23.42/4.72 thf(f316,negated_conjecture,(
% 23.42/4.72 ~(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 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => ! [X3 : $i,X1 : $i,X12 : $i > $i] : ((in @ X1 @ (image1 @ X3 @ (^[X2 : $i] : (X12 @ X2)))) => ? [X2 : $i] : ((in @ X2 @ X3) & ((X12 @ X2) = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 23.42/4.72 inference(negated_conjecture,[status(cth)],[f315])).
% 23.42/4.72 thf(f315,conjecture,(
% 23.42/4.72 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 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => ! [X3 : $i,X1 : $i,X12 : $i > $i] : ((in @ X1 @ (image1 @ X3 @ (^[X2 : $i] : (X12 @ X2)))) => ? [X2 : $i] : ((in @ X2 @ X3) & ((X12 @ X2) = X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 23.42/4.72 file('/export/starexec/sandbox/tmp/tmp.c9IygHO5Aa/DTF2THF_16722.p',image1E)).
% 23.42/4.72 thf(f11266,plain,(
% 23.42/4.72 ( ! [X6 : $i,X7 : $i > $i,X5 : $i] : (((in @ X6 @ (image1 @ X5 @ X7)) != $true) | ((X7 @ (sK516 @ X7 @ X6 @ X5)) = X6)) ) | ~spl1056_1360),
% 23.42/4.72 inference(avatar_component_clause,[status(thm)],[f11265])).
% 23.42/4.72 thf(f11265,definition,(
% 23.42/4.72 spl1056_1360 <=> ! [X6 : $i,X5 : $i,X7 : $i > $i] : (((in @ X6 @ (image1 @ X5 @ X7)) != $true) | ((X7 @ (sK516 @ X7 @ X6 @ X5)) = X6))),
% 23.42/4.72 introduced(definition,[new_symbols(naming,[spl1056_1360])],[avatar_definition])).
% 23.42/4.72 thf(f24516,plain,(
% 23.42/4.72 ((sK42 @ (sK516 @ sK42 @ sK41 @ sK40)) != sK41) | ~spl1056_905),
% 23.42/4.72 inference(trivial_inequality_removal,[status(thm)],[f24512])).
% 23.42/4.72 thf(f24512,plain,(
% 23.42/4.72 ((sK42 @ (sK516 @ sK42 @ sK41 @ sK40)) != sK41) | ($true != $true) | ~spl1056_905),
% 23.42/4.72 inference(superposition,[status(thm)],[f3322,f18560])).
% 23.42/4.72 thf(f18560,plain,(
% 23.42/4.72 ((in @ (sK516 @ sK42 @ sK41 @ sK40) @ sK40) = $true) | ~spl1056_905),
% 23.42/4.72 inference(trivial_inequality_removal,[status(thm)],[f18548])).
% 23.42/4.72 thf(f18548,plain,(
% 23.42/4.72 ($true != $true) | ((in @ (sK516 @ sK42 @ sK41 @ sK40) @ sK40) = $true) | ~spl1056_905),
% 23.42/4.72 inference(superposition,[status(thm)],[f9066,f4831])).
% 23.42/4.72 thf(f9066,plain,(
% 23.42/4.72 ( ! [X6 : $i,X7 : $i > $i,X5 : $i] : (((in @ X6 @ (image1 @ X5 @ X7)) != $true) | ((in @ (sK516 @ X7 @ X6 @ X5) @ X5) = $true)) ) | ~spl1056_905),
% 23.42/4.72 inference(avatar_component_clause,[status(thm)],[f9065])).
% 23.42/4.72 thf(f9065,definition,(
% 23.42/4.72 spl1056_905 <=> ! [X6 : $i,X5 : $i,X7 : $i > $i] : (((in @ X6 @ (image1 @ X5 @ X7)) != $true) | ((in @ (sK516 @ X7 @ X6 @ X5) @ X5) = $true))),
% 23.42/4.72 introduced(definition,[new_symbols(naming,[spl1056_905])],[avatar_definition])).
% 23.42/4.72 thf(f3322,plain,(
% 23.42/4.72 ( ! [X3 : $i] : (((in @ X3 @ sK40) != $true) | ((sK42 @ X3) != sK41)) )),
% 23.42/4.72 inference(cnf_transformation,[status(thm)],[f1444])).
% 23.42/4.72 thf(f12733,plain,(
% 23.42/4.72 spl1056_265),
% 23.42/4.72 inference(avatar_split_clause,[status(thm)],[f3302,f6125])).
% 23.42/4.72 thf(f6125,definition,(
% 23.42/4.72 spl1056_265 <=> (image1Equiv = $true)),
% 23.42/4.72 introduced(definition,[new_symbols(naming,[spl1056_265])],[avatar_definition])).
% 23.42/4.72 thf(f3302,plain,(
% 23.42/4.72 (image1Equiv = $true)),
% 23.42/4.72 inference(cnf_transformation,[status(thm)],[f1444])).
% 23.42/4.72 thf(f11267,plain,(
% 23.42/4.72 ~spl1056_265 | spl1056_1360),
% 23.42/4.72 inference(avatar_split_clause,[status(thm)],[f4834,f11265,f6125])).
% 23.42/4.72 thf(f4834,plain,(
% 23.42/4.72 ( ! [X6 : $i,X7 : $i > $i,X5 : $i] : (((in @ X6 @ (image1 @ X5 @ X7)) != $true) | (image1Equiv != $true) | ((X7 @ (sK516 @ X7 @ X6 @ X5)) = X6)) )),
% 23.42/4.72 inference(beta_eta_normalization,[status(thm)],[f4006])).
% 23.42/4.72 thf(f4006,plain,(
% 23.42/4.72 ( ! [X6 : $i,X7 : $i > $i,X5 : $i] : ((image1Equiv != $true) | ((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0)))) != $true) | ((X7 @ (sK516 @ X7 @ X6 @ X5)) = X6)) )),
% 23.42/4.72 inference(cnf_transformation,[status(thm)],[f2169])).
% 23.42/4.72 thf(f2169,plain,(
% 23.42/4.72 ((image1Equiv = $true) | ((! [X3 : $i] : ((sK513 != (sK514 @ X3)) | ($true != (in @ X3 @ sK512))) | ((in @ sK513 @ (image1 @ sK512 @ (^[Y0 : $i]: (sK514 @ Y0)))) != $true)) & (((sK513 = (sK514 @ sK515)) & ($true = (in @ sK515 @ sK512))) | ((in @ sK513 @ (image1 @ sK512 @ (^[Y0 : $i]: (sK514 @ Y0)))) = $true)))) & (! [X5 : $i,X6 : $i,X7 : $i > $i] : ((((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0)))) = $true) | ! [X8 : $i] : (((X7 @ X8) != X6) | ((in @ X8 @ X5) != $true))) & ((((X7 @ (sK516 @ X7 @ X6 @ X5)) = X6) & ((in @ (sK516 @ X7 @ X6 @ X5) @ X5) = $true)) | ((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0)))) != $true))) | (image1Equiv != $true))),
% 23.42/4.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK512,sK513,sK514,sK515,sK516])],[f2165,f2168,f2167,f2166])).
% 23.42/4.72 thf(f2166,plain,(
% 23.42/4.72 ? [X0 : $i,X1 : $i,X2 : $i > $i] : ((! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true)) | ((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) & (? [X4 : $i] : (((X2 @ X4) = X1) & ((in @ X4 @ X0) = $true)) | ((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true))) => ((! [X3 : $i] : ((sK513 != (sK514 @ X3)) | ($true != (in @ X3 @ sK512))) | ((in @ sK513 @ (image1 @ sK512 @ (^[Y0 : $i]: (sK514 @ Y0)))) != $true)) & (? [X4 : $i] : ((sK513 = (sK514 @ X4)) & ($true = (in @ X4 @ sK512))) | ((in @ sK513 @ (image1 @ sK512 @ (^[Y0 : $i]: (sK514 @ Y0)))) = $true)))),
% 23.42/4.72 introduced(definition,[],[choice_axiom])).
% 23.42/4.72 thf(f2167,plain,(
% 23.42/4.72 ? [X4 : $i] : ((sK513 = (sK514 @ X4)) & ($true = (in @ X4 @ sK512))) => ((sK513 = (sK514 @ sK515)) & ($true = (in @ sK515 @ sK512)))),
% 23.42/4.72 introduced(definition,[],[choice_axiom])).
% 23.42/4.72 thf(f2168,plain,(
% 23.42/4.72 ! [X5 : $i,X6 : $i,X7 : $i > $i] : (? [X9 : $i] : (((X7 @ X9) = X6) & ((in @ X9 @ X5) = $true)) => (((X7 @ (sK516 @ X7 @ X6 @ X5)) = X6) & ((in @ (sK516 @ X7 @ X6 @ X5) @ X5) = $true)))),
% 23.42/4.72 introduced(definition,[],[choice_axiom])).
% 23.42/4.72 thf(f2165,plain,(
% 23.42/4.72 ((image1Equiv = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $i] : ((! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true)) | ((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) & (? [X4 : $i] : (((X2 @ X4) = X1) & ((in @ X4 @ X0) = $true)) | ((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)))) & (! [X5 : $i,X6 : $i,X7 : $i > $i] : ((((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0)))) = $true) | ! [X8 : $i] : (((X7 @ X8) != X6) | ((in @ X8 @ X5) != $true))) & (? [X9 : $i] : (((X7 @ X9) = X6) & ((in @ X9 @ X5) = $true)) | ((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0)))) != $true))) | (image1Equiv != $true))),
% 23.42/4.72 inference(rectify,[status(thm)],[f2164])).
% 23.42/4.72 thf(f2164,plain,(
% 23.42/4.72 ((image1Equiv = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $i] : ((! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true)) | ((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) & (? [X3 : $i] : (((X2 @ X3) = X1) & ((in @ X3 @ X0) = $true)) | ((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)))) & (! [X0 : $i,X1 : $i,X2 : $i > $i] : ((((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ! [X3 : $i] : (((X2 @ X3) != X1) | ((in @ X3 @ X0) != $true))) & (? [X3 : $i] : (((X2 @ X3) = X1) & ((in @ X3 @ X0) = $true)) | ((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true))) | (image1Equiv != $true))),
% 23.42/4.72 inference(nnf_transformation,[status(thm)],[f618])).
% 23.42/4.72 thf(f618,plain,(
% 23.42/4.72 (image1Equiv = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $i] : (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) <=> ? [X3 : $i] : (((X2 @ X3) = X1) & ((in @ X3 @ X0) = $true)))),
% 23.42/4.72 inference(fool_elimination,[status(thm)],[f617])).
% 23.42/4.72 thf(f617,plain,(
% 23.42/4.72 (image1Equiv = ! [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X3 : $i] : (((X2 @ X3) = X1) & (in @ X3 @ X0)) <=> (in @ X1 @ (image1 @ X0 @ (^[X4 : $i] : (X2 @ X4))))))),
% 23.42/4.72 inference(rectify,[status(thm)],[f314])).
% 23.42/4.72 thf(f314,axiom,(
% 23.42/4.72 (image1Equiv = ! [X3 : $i,X1 : $i,X12 : $i > $i] : (? [X2 : $i] : (((X12 @ X2) = X1) & (in @ X2 @ X3)) <=> (in @ X1 @ (image1 @ X3 @ (^[X2 : $i] : (X12 @ X2))))))),
% 23.42/4.72 file('/export/starexec/sandbox/tmp/tmp.c9IygHO5Aa/DTF2THF_16722.p',image1Equiv)).
% 23.42/4.72 thf(f9067,plain,(
% 23.42/4.72 spl1056_905 | ~spl1056_265),
% 23.42/4.72 inference(avatar_split_clause,[status(thm)],[f4895,f6125,f9065])).
% 23.42/4.72 thf(f4895,plain,(
% 23.42/4.72 ( ! [X6 : $i,X7 : $i > $i,X5 : $i] : (((in @ X6 @ (image1 @ X5 @ X7)) != $true) | (image1Equiv != $true) | ((in @ (sK516 @ X7 @ X6 @ X5) @ X5) = $true)) )),
% 23.42/4.72 inference(beta_eta_normalization,[status(thm)],[f4005])).
% 23.42/4.72 thf(f4005,plain,(
% 23.42/4.72 ( ! [X6 : $i,X7 : $i > $i,X5 : $i] : (((in @ (sK516 @ X7 @ X6 @ X5) @ X5) = $true) | (image1Equiv != $true) | ((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0)))) != $true)) )),
% 23.42/4.72 inference(cnf_transformation,[status(thm)],[f2169])).
% 23.42/4.72 % SZS output end Proof for DTF2THF_16722
% 23.42/4.72 % (17121)------------------------------
% 23.42/4.72 % (17121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.42/4.72 % (17121)Termination reason: Refutation
% 23.42/4.72
% 23.42/4.72 % (17121)Memory used [KB]: 23666
% 23.42/4.72 % (17121)Time elapsed: 1.401 s
% 23.42/4.72 % (17121)Instructions burned: 4390 (million)
% 23.42/4.72 % (17121)------------------------------
% 23.42/4.72 % (17121)------------------------------
% 23.42/4.72 % (16999)Success in time 3.123 s
%------------------------------------------------------------------------------