%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU684^1 : 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 : n021.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 09:36:23 AM UTC 2026
% Result : Theorem 91.11s 14.41s
% Output : Refutation 91.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 89 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 3811 ( 996 equ; 0 cnn)
% Maximal formula atoms : 203 ( 42 avg)
% Number of connectives : 2528 ( 46 ~; 52 |; 653 &; 922 @)
% ( 3 <=>; 828 =>; 0 <=; 0 <~>)
% Maximal formula depth : 215 ( 19 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 660 ( 655 usr; 212 con; 0-4 aty)
% ( 8 !!; 16 ??; 0 @@+; 0 @@-)
% Number of variables : 281 ( 174 ^; 79 !; 28 ?; 281 :)
% 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_251,type,
sK0: $i > $i > $i ).
thf(func_def_266,type,
sK15: $i > $i ).
thf(func_def_271,type,
sK20: $i > $o ).
thf(func_def_274,type,
sK23: $i > ( $i > $i ) > $i > $i ).
thf(func_def_276,type,
sK25: $i > $i ).
thf(func_def_289,type,
sK38: $i > $o ).
thf(func_def_290,type,
sK39: ( $i > $o ) > $i ).
thf(func_def_295,type,
sK44: $i > $i > $o ).
thf(func_def_304,type,
sK53: $i > $i ).
thf(func_def_305,type,
sK54: ( $i > $i ) > $i > $i > $i ).
thf(func_def_312,type,
sK61: $i > $i > $i ).
thf(func_def_313,type,
sK62: $i > $i ).
thf(func_def_314,type,
sK63: $i > $i > $i ).
thf(func_def_315,type,
sK64: $i > $i > $i ).
thf(func_def_316,type,
sK65: $i > $i > $i ).
thf(func_def_317,type,
sK66: $i > $i > $i > $i ).
thf(func_def_319,type,
sK68: $i > $i ).
thf(func_def_320,type,
sK69: $i > $i ).
thf(func_def_321,type,
sK70: $i > $i ).
thf(func_def_322,type,
sK71: $i > $i ).
thf(func_def_323,type,
sK72: $i > $i ).
thf(func_def_324,type,
sK73: $i > $i > $i > $i ).
thf(func_def_325,type,
sK74: $i > $i > $i > $i ).
thf(func_def_326,type,
sK75: $i > $i > $i ).
thf(func_def_327,type,
sK76: $i > $i ).
thf(func_def_328,type,
sK77: $i > $i ).
thf(func_def_329,type,
sK78: $i > $i ).
thf(func_def_330,type,
sK79: $i > $i ).
thf(func_def_331,type,
sK80: $i > $i ).
thf(func_def_334,type,
sK83: $i > $i > $o ).
thf(func_def_347,type,
sK96: ( $i > $o ) > $i ).
thf(func_def_348,type,
sK97: $i > $o ).
thf(func_def_349,type,
sK98: $i > $i ).
thf(func_def_371,type,
sK120: $i > $o ).
thf(func_def_375,type,
sK124: $i > $o ).
thf(func_def_379,type,
sK128: $i > ( $i > $o ) > $i ).
thf(func_def_380,type,
sK129: $i > $o ).
thf(func_def_386,type,
sK135: $i > $i > $o ).
thf(func_def_393,type,
sK142: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_394,type,
sK143: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_398,type,
sK147: $i > $o ).
thf(func_def_402,type,
sK151: $i > $o ).
thf(func_def_409,type,
sK158: $i > $i ).
thf(func_def_413,type,
sK162: $o > $i > $i > $i ).
thf(func_def_428,type,
sK177: $i > $o ).
thf(func_def_431,type,
sK180: $i > ( $i > $o ) > $i ).
thf(func_def_432,type,
sK181: $i > ( $i > $o ) > $i ).
thf(func_def_433,type,
sK182: $i > $i > $i ).
thf(func_def_445,type,
sK194: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_446,type,
sK195: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_450,type,
sK199: $i > $o ).
thf(func_def_454,type,
sK203: $i > $i > $o ).
thf(func_def_457,type,
sK206: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_458,type,
sK207: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_461,type,
sK210: $i > $o ).
thf(func_def_462,type,
sK211: $i > $o ).
thf(func_def_472,type,
sK221: $i > $o ).
thf(func_def_482,type,
sK231: $i > $o ).
thf(func_def_484,type,
sK233: ( $i > $o ) > $i > $i ).
thf(func_def_486,type,
sK235: $i > $o ).
thf(func_def_488,type,
sK237: ( $i > $o ) > $i > $i ).
thf(func_def_490,type,
sK239: $i > $o ).
thf(func_def_492,type,
sK241: ( $i > $o ) > $i > $i ).
thf(func_def_497,type,
sK246: $i > $i ).
thf(func_def_500,type,
sK249: $i > $i > $i ).
thf(func_def_517,type,
sK266: $i > $i > $i ).
thf(func_def_519,type,
sK268: ( $i > $o ) > $i ).
thf(func_def_520,type,
sK269: ( $i > $o ) > $i ).
thf(func_def_521,type,
sK270: $i > $o ).
thf(func_def_531,type,
sK280: $i > $o ).
thf(func_def_533,type,
sK282: $i > ( $i > $o ) > $i ).
thf(func_def_535,type,
sK284: $i > $i > $o ).
thf(func_def_537,type,
sK286: $i > $i ).
thf(func_def_540,type,
sK289: $i > $i > ( $i > $i ) > $i ).
thf(func_def_544,type,
sK293: $i > $i > $i ).
thf(func_def_545,type,
sK294: $i > $i > $i ).
thf(func_def_548,type,
sK297: $i > $i ).
thf(func_def_549,type,
sK298: $i > $i ).
thf(func_def_560,type,
sK309: $i > $o ).
thf(func_def_564,type,
sK313: $i > $o ).
thf(func_def_583,type,
sK332: $i > $i > $i ).
thf(func_def_589,type,
sK338: $i > $i ).
thf(func_def_605,type,
sK354: $i > $o ).
thf(func_def_607,type,
sK356: $i > ( $i > $o ) > $i ).
thf(func_def_611,type,
sK360: $i > $o ).
thf(func_def_612,type,
sK361: $i > $o ).
thf(func_def_613,type,
sK362: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_614,type,
sK363: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_621,type,
sK370: $i > $i > $o ).
thf(func_def_626,type,
sK375: $i > $o ).
thf(func_def_642,type,
sK391: $i > $o ).
thf(func_def_648,type,
sK397: $i > $o ).
thf(func_def_653,type,
sK402: $i > $o ).
thf(func_def_656,type,
sK405: $i > ( $i > $o ) > $i ).
thf(func_def_676,type,
sK425: ( $i > $o ) > $i ).
thf(func_def_677,type,
sK426: $i > $o ).
thf(func_def_678,type,
sK427: $i > $i ).
thf(func_def_679,type,
sK428: $i > $i > $o ).
thf(func_def_698,type,
sK447: ( $i > $o ) > $i > $i ).
thf(func_def_700,type,
sK449: $i > $o ).
thf(func_def_712,type,
sK461: $i > $i > $i ).
thf(func_def_715,type,
sK464: $i > $i ).
thf(func_def_718,type,
sK467: $i > $o ).
thf(func_def_726,type,
sK475: $i > $o ).
thf(func_def_728,type,
sK477: ( $i > $o ) > $i > $i ).
thf(func_def_729,type,
sK478: ( $i > $o ) > $i > $i ).
thf(func_def_753,type,
sK502: $i > $o ).
thf(func_def_754,type,
sK503: $i > $o ).
thf(func_def_755,type,
sK504: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_756,type,
sK505: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_762,type,
sK511: $i > $i > $i > $i ).
thf(func_def_763,type,
sK512: $i > $i > $i > $i ).
thf(func_def_764,type,
sK513: $i > $o ).
thf(func_def_773,type,
sK522: $i > $i > $o ).
thf(func_def_775,type,
sK524: $i > $i ).
thf(func_def_776,type,
sK525: $i > $i ).
thf(func_def_777,type,
sK526: $i > ( $i > $i > $o ) > $i ).
thf(func_def_778,type,
sK527: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_779,type,
sK528: $i > ( $i > $i > $o ) > $i ).
thf(func_def_785,type,
sK534: $i > $o ).
thf(func_def_788,type,
sK537: $i > $i > ( $i > $o ) > $i ).
thf(func_def_791,type,
sK540: $i > $i > $i ).
thf(func_def_832,type,
sK581: $i > $o ).
thf(func_def_835,type,
sK584: ( $i > $o ) > $i > $i ).
thf(func_def_837,type,
sK586: $i > $o ).
thf(func_def_839,type,
sK588: $i > ( $i > $o ) > $i ).
thf(func_def_840,type,
sK589: ( $i > $o ) > $i > $i ).
thf(func_def_841,type,
sK590: ( $i > $o ) > $i > $i ).
thf(func_def_842,type,
sK591: ( $i > $o ) > $i ).
thf(func_def_843,type,
sK592: ( $i > $o ) > $i ).
thf(func_def_844,type,
sK593: $i > ( $i > $o ) > $i ).
thf(func_def_845,type,
sK594: ( $i > $o ) > $i > $i ).
thf(func_def_846,type,
sK595: ( $i > $o ) > $i ).
thf(func_def_847,type,
sK596: ( $i > $o ) > $i ).
thf(func_def_848,type,
sK597: ( $i > $o ) > $i ).
thf(func_def_849,type,
sK598: ( $i > $o ) > $i ).
thf(func_def_850,type,
sK599: ( $i > $o ) > $i ).
thf(func_def_851,type,
sK600: ( $i > $o ) > $i ).
thf(func_def_852,type,
sK601: ( $i > $o ) > $i ).
thf(func_def_853,type,
sK602: ( $i > $o ) > $i ).
thf(func_def_854,type,
sK603: ( $i > $o ) > $i > $i ).
thf(func_def_855,type,
sK604: ( $i > $o ) > $i ).
thf(func_def_856,type,
sK605: ( $i > $o ) > $i ).
thf(func_def_857,type,
sK606: ( $i > $o ) > $i ).
thf(func_def_858,type,
sK607: ( $i > $o ) > $i ).
thf(func_def_859,type,
sK608: ( $i > $o ) > $i ).
thf(func_def_860,type,
sK609: ( $i > $o ) > $i ).
thf(func_def_861,type,
sK610: ( $i > $o ) > $i ).
thf(func_def_862,type,
sK611: ( $i > $o ) > $i ).
thf(func_def_863,type,
sK612: ( $i > $o ) > $i > $i ).
thf(func_def_864,type,
sK613: ( $i > $o ) > $i ).
thf(func_def_865,type,
sK614: ( $i > $o ) > $i ).
thf(func_def_866,type,
sK615: ( $i > $o ) > $i ).
thf(func_def_867,type,
sK616: ( $i > $o ) > $i ).
thf(func_def_868,type,
sK617: ( $i > $o ) > $i ).
thf(func_def_869,type,
sK618: ( $i > $o ) > $i ).
thf(func_def_870,type,
sK619: ( $i > $o ) > $i ).
thf(func_def_871,type,
sK620: ( $i > $o ) > $i ).
thf(func_def_872,type,
sK621: ( $i > $o ) > $i ).
thf(func_def_873,type,
sK622: ( $i > $o ) > $i > $i ).
thf(func_def_874,type,
sK623: ( $i > $o ) > $i > $i ).
thf(func_def_875,type,
sK624: ( $i > $o ) > $i > $i ).
thf(func_def_876,type,
sK625: ( $i > $o ) > $i > $i ).
thf(func_def_877,type,
sK626: ( $i > $o ) > $i > $i ).
thf(func_def_878,type,
sK627: ( $i > $o ) > $i ).
thf(func_def_879,type,
sK628: ( $i > $o ) > $i > $i ).
thf(func_def_880,type,
sK629: ( $i > $o ) > $i > $i ).
thf(func_def_881,type,
sK630: ( $i > $o ) > $i > $i ).
thf(func_def_882,type,
sK631: ( $i > $o ) > $i > $i ).
thf(func_def_883,type,
sK632: $i > ( $i > $o ) > $i ).
thf(func_def_884,type,
sK633: $i > ( $i > $o ) > $i ).
thf(func_def_885,type,
sK634: $i > $i ).
thf(func_def_886,type,
sK635: $i > $i ).
thf(func_def_889,type,
sK638: $i > $i ).
thf(func_def_890,type,
sK639: $i > $i ).
thf(func_def_891,type,
sK640: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_892,type,
sK641: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_893,type,
sK642: $i > $i > ( $i > $i ) > $i ).
thf(func_def_894,type,
sK643: $i > $i > ( $i > $i ) > $i ).
thf(func_def_895,type,
sK644: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_896,type,
sK645: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_897,type,
sK646: ( $i > $o ) > $i ).
thf(func_def_898,type,
sK647: ( $i > $o ) > $i ).
thf(func_def_899,type,
sK648: $i > ( $i > $o ) > $i ).
thf(func_def_900,type,
sK649: $i > $i > $i > $i ).
thf(func_def_901,type,
sK650: $i > $i > $i > $i ).
thf(func_def_902,type,
sK651: $i > $i > $i > $i ).
thf(func_def_903,type,
sK652: $i > $i > $i > $i ).
thf(func_def_904,type,
sK653: $i > $i > $i > $i ).
thf(func_def_905,type,
sK654: $i > $i > $i > $i ).
thf(func_def_906,type,
sK655: $i > $i > $i > $i ).
thf(func_def_907,type,
sK656: $i > $i > $i > $i ).
thf(func_def_908,type,
sK657: $i > $i > $i > $i ).
thf(func_def_909,type,
sK658: $i > $i > $i > $i ).
thf(func_def_910,type,
sK659: $i > $i > $i > $i ).
thf(func_def_911,type,
sK660: $i > $i > $i > $i ).
thf(func_def_912,type,
sK661: $i > $i > $i > $i ).
thf(func_def_913,type,
sK662: $i > $i > $i > $i ).
thf(func_def_914,type,
sK663: $i > $i > $i > $i ).
thf(func_def_915,type,
sK664: $i > $i > $i > $i ).
thf(func_def_916,type,
sK665: $i > $i > $i > $i ).
thf(func_def_917,type,
sK666: $i > $i > $i > $i ).
thf(func_def_918,type,
sK667: $i > $i > $i > $i ).
thf(func_def_919,type,
sK668: $i > $i > $i > $i ).
thf(func_def_920,type,
sK669: $i > $i > $i > $i ).
thf(func_def_921,type,
sK670: $i > $i > $i > $i ).
thf(func_def_922,type,
sK671: $i > $i > $i > $i ).
thf(func_def_923,type,
sK672: $i > ( $i > $o ) > $i ).
thf(func_def_924,type,
sK673: $i > ( $i > $o ) > $i ).
thf(func_def_925,type,
sK674: $i > ( $i > $o ) > $i ).
thf(func_def_926,type,
sK675: ( $i > $o ) > $i ).
thf(func_def_927,type,
sK676: ( $i > $o ) > $i ).
thf(func_def_928,type,
sK677: ( $i > $o ) > $i ).
thf(func_def_929,type,
sK678: ( $i > $o ) > $i ).
thf(func_def_930,type,
sK679: $i > $i > $i > $i ).
thf(func_def_931,type,
sK680: $i > $i > $i > $i ).
thf(func_def_932,type,
sK681: $i > $i > $i > $i ).
thf(func_def_933,type,
sK682: $i > $i > $i > $i ).
thf(func_def_934,type,
sK683: $i > $i > $i > $i ).
thf(func_def_935,type,
sK684: $i > ( $i > $o ) > $i ).
thf(func_def_936,type,
sK685: $i > ( $i > $o ) > $i ).
thf(func_def_937,type,
sK686: $i > ( $i > $o ) > $i ).
thf(func_def_938,type,
sK687: $i > ( $i > $o ) > $i ).
thf(func_def_939,type,
sK688: ( $i > $o ) > $i ).
thf(func_def_940,type,
sK689: ( $i > $o ) > $i > $i ).
thf(func_def_941,type,
sK690: ( $i > $o ) > $i > $i ).
thf(func_def_942,type,
sK691: ( $i > $o ) > $i > $i ).
thf(func_def_943,type,
sK692: ( $i > $o ) > $i > $i ).
thf(func_def_944,type,
sK693: ( $i > $o ) > $i > $i ).
thf(func_def_945,type,
sK694: ( $i > $o ) > $i > $i ).
thf(func_def_946,type,
sK695: ( $i > $o ) > $i > $i ).
thf(func_def_947,type,
sK696: ( $i > $o ) > $i > $i ).
thf(func_def_948,type,
sK697: ( $i > $o ) > $i > $i ).
thf(func_def_949,type,
sK698: ( $i > $o ) > $i > $i ).
thf(func_def_950,type,
sK699: ( $i > $o ) > $i ).
thf(func_def_951,type,
sK700: ( $i > $o ) > $i > $i ).
thf(func_def_952,type,
sK701: ( $i > $o ) > $i > $i ).
thf(func_def_953,type,
sK702: ( $i > $o ) > $i > $i ).
thf(func_def_954,type,
sK703: ( $i > $o ) > $i > $i ).
thf(func_def_955,type,
sK704: ( $i > $o ) > $i > $i ).
thf(func_def_956,type,
sK705: ( $i > $o ) > $i > $i ).
thf(func_def_957,type,
sK706: ( $i > $o ) > $i > $i ).
thf(func_def_958,type,
sK707: ( $i > $o ) > $i > $i ).
thf(func_def_959,type,
sK708: ( $i > $o ) > $i ).
thf(func_def_960,type,
sK709: $i > ( $i > $o ) > $i ).
thf(func_def_961,type,
sK710: $i > ( $i > $o ) > $i ).
thf(func_def_962,type,
sK711: $i > ( $i > $o ) > $i ).
thf(func_def_963,type,
sK712: $i > ( $i > $o ) > $i ).
thf(func_def_964,type,
sK713: $i > ( $i > $o ) > $i ).
thf(func_def_965,type,
sK714: $i > ( $i > $o ) > $i ).
thf(func_def_966,type,
sK715: $i > ( $i > $o ) > $i ).
thf(func_def_967,type,
sK716: $i > ( $i > $o ) > $i ).
thf(func_def_968,type,
sK717: ( $i > $o ) > $i ).
thf(func_def_969,type,
sK718: $i > ( $i > $o ) > $i ).
thf(func_def_970,type,
sK719: $i > ( $i > $o ) > $i ).
thf(func_def_971,type,
sK720: $i > ( $i > $o ) > $i ).
thf(func_def_972,type,
sK721: $i > ( $i > $o ) > $i ).
thf(func_def_973,type,
sK722: ( $i > $o ) > $i ).
thf(func_def_974,type,
sK723: $i > ( $i > $o ) > $i ).
thf(func_def_975,type,
sK724: $i > ( $i > $o ) > $i ).
thf(func_def_976,type,
sK725: $i > ( $i > $o ) > $i ).
thf(func_def_977,type,
sK726: $i > ( $i > $o ) > $i ).
thf(func_def_978,type,
sK727: ( $i > $o ) > $i ).
thf(func_def_979,type,
sK728: ( $i > $o ) > $i > $i ).
thf(func_def_980,type,
sK729: ( $i > $o ) > $i > $i ).
thf(func_def_981,type,
sK730: ( $i > $o ) > $i > $i ).
thf(func_def_982,type,
sK731: ( $i > $o ) > $i > $i ).
thf(func_def_983,type,
sK732: ( $i > $o ) > $i > $i ).
thf(func_def_984,type,
sK733: ( $i > $o ) > $i > $i ).
thf(func_def_985,type,
sK734: ( $i > $o ) > $i > $i ).
thf(func_def_986,type,
sK735: ( $i > $o ) > $i > $i ).
thf(func_def_987,type,
sK736: ( $i > $o ) > $i ).
thf(func_def_988,type,
sK737: ( $i > $o ) > $i > $i ).
thf(func_def_989,type,
sK738: ( $i > $o ) > $i > $i ).
thf(func_def_990,type,
sK739: ( $i > $o ) > $i > $i ).
thf(func_def_991,type,
sK740: ( $i > $o ) > $i > $i ).
thf(func_def_992,type,
sK741: ( $i > $o ) > $i > $i ).
thf(func_def_993,type,
sK742: ( $i > $o ) > $i > $i ).
thf(func_def_994,type,
sK743: ( $i > $o ) > $i > $i ).
thf(func_def_995,type,
sK744: ( $i > $o ) > $i > $i ).
thf(func_def_996,type,
sK745: $i > ( $i > $o ) > $i ).
thf(func_def_997,type,
sK746: ( $i > $o ) > $i ).
thf(func_def_998,type,
sK747: ( $i > $o ) > $i ).
thf(func_def_999,type,
sK748: ( $i > $o ) > $i ).
thf(func_def_1000,type,
sK749: ( $i > $o ) > $i ).
thf(func_def_1001,type,
sK750: ( $i > $o ) > $i ).
thf(func_def_1002,type,
sK751: ( $i > $o ) > $i ).
thf(func_def_1003,type,
sK752: ( $i > $o ) > $i ).
thf(func_def_1004,type,
sK753: ( $i > $o ) > $i ).
thf(func_def_1005,type,
sK754: $i > ( $i > $o ) > $i ).
thf(func_def_1006,type,
sK755: ( $i > $o ) > $i ).
thf(func_def_1007,type,
sK756: ( $i > $o ) > $i ).
thf(func_def_1008,type,
sK757: ( $i > $o ) > $i ).
thf(func_def_1009,type,
sK758: ( $i > $o ) > $i ).
thf(func_def_1010,type,
sK759: ( $i > $o ) > $i ).
thf(func_def_1011,type,
sK760: ( $i > $o ) > $i ).
thf(func_def_1012,type,
sK761: ( $i > $o ) > $i ).
thf(func_def_1013,type,
sK762: ( $i > $o ) > $i ).
thf(func_def_1014,type,
sK763: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1015,type,
sK764: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1016,type,
sK765: ( $i > $o ) > $i ).
thf(func_def_1017,type,
sK766: ( $i > $o ) > $i ).
thf(func_def_1018,type,
sK767: ( $i > $o ) > $i ).
thf(func_def_1019,type,
sK768: ( $i > $o ) > $i ).
thf(func_def_1020,type,
sK769: $i > ( $i > $o ) > $i ).
thf(func_def_1021,type,
sK770: $i > ( $i > $o ) > $i ).
thf(func_def_1022,type,
sK771: $i > ( $i > $o ) > $i ).
thf(func_def_1023,type,
sK772: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_1024,type,
sK773: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_1025,type,
sK774: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1026,type,
sK775: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1027,type,
sK776: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_1028,type,
sK777: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_1029,type,
sK778: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_1030,type,
sK779: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_1031,type,
sK780: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1032,type,
sK781: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1033,type,
sK782: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_1034,type,
sK783: ( $i > $i ) > $i > $i > $i > $i ).
thf(func_def_1035,type,
sK784: ( $i > $o ) > $i > $i ).
thf(func_def_1036,type,
sK785: $i > ( $i > $o ) > $i ).
thf(func_def_1037,type,
sK786: $i > ( $i > $o ) > $i ).
thf(func_def_1038,type,
sK787: $i > ( $i > $o ) > $i ).
thf(func_def_1039,type,
sK788: $i > ( $i > $o ) > $i ).
thf(func_def_1040,type,
sK789: $i > ( $i > $o ) > $i ).
thf(func_def_1041,type,
sK790: $i > ( $i > $o ) > $i ).
thf(func_def_1042,type,
sK791: $i > ( $i > $o ) > $i ).
thf(func_def_1043,type,
sK792: $i > ( $i > $o ) > $i ).
thf(func_def_1044,type,
sK793: $i > ( $i > $o ) > $i ).
thf(func_def_1045,type,
sK794: $i > ( $i > $o ) > $i ).
thf(func_def_1046,type,
sK795: $i > ( $i > $o ) > $i ).
thf(func_def_1047,type,
sK796: $i > ( $i > $o ) > $i ).
thf(func_def_1048,type,
sK797: $i > ( $i > $o ) > $i ).
thf(func_def_1049,type,
sK798: $i > ( $i > $o ) > $i ).
thf(func_def_1050,type,
sK799: ( $i > $o ) > $i > $i ).
thf(func_def_1051,type,
sK800: ( $i > $o ) > $i > $i ).
thf(func_def_1052,type,
sK801: ( $i > $o ) > $i > $i ).
thf(func_def_1053,type,
sK802: ( $i > $o ) > $i > $i ).
thf(func_def_1054,type,
sK803: ( $i > $o ) > $i > $i ).
thf(func_def_1055,type,
sK804: ( $i > $o ) > $i > $i ).
thf(func_def_1056,type,
sK805: ( $i > $o ) > $i > $i ).
thf(func_def_1057,type,
sK806: $i > ( $i > $o ) > $i ).
thf(func_def_1058,type,
sK807: $i > ( $i > $o ) > $i ).
thf(func_def_1059,type,
sK808: $i > ( $i > $o ) > $i ).
thf(func_def_1060,type,
sK809: $i > ( $i > $o ) > $i ).
thf(func_def_1061,type,
sK810: ( $i > $o ) > $i > $i ).
thf(func_def_1062,type,
sK811: $i > ( $i > $o ) > $i ).
thf(func_def_1063,type,
sK812: $i > ( $i > $o ) > $i ).
thf(func_def_1064,type,
sK813: $i > ( $i > $o ) > $i ).
thf(func_def_1065,type,
sK814: $i > ( $i > $o ) > $i ).
thf(func_def_1066,type,
sK815: ( $i > $o ) > $i ).
thf(func_def_1067,type,
sK816: ( $i > $o ) > $i ).
thf(func_def_1068,type,
sK817: $i > $i > $i > $i ).
thf(func_def_1069,type,
sK818: $i > $i > $i > $i ).
thf(func_def_1070,type,
sK819: $i > $i > $i > $i ).
thf(func_def_1071,type,
sK820: $i > $i > $i > $i ).
thf(func_def_1072,type,
sK821: $i > $i > $i > $i ).
thf(func_def_1073,type,
sK822: $i > ( $i > $o ) > $i ).
thf(func_def_1074,type,
sK823: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_1075,type,
sK824: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_1076,type,
sK825: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1077,type,
sK826: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1078,type,
sK827: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_1079,type,
sK828: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_1080,type,
sK829: ( $i > $o ) > $i > $i ).
thf(func_def_1081,type,
sK830: ( $i > $o ) > $i > $i ).
thf(func_def_1082,type,
sK831: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1083,type,
sK832: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1084,type,
sK833: $i > $i > $i > $i ).
thf(func_def_1085,type,
sK834: $i > $i > $i > $i ).
thf(func_def_1086,type,
sK835: $i > $i > $i > $i ).
thf(func_def_1087,type,
sK836: $i > $i > $i > $i ).
thf(func_def_1088,type,
sK837: $i > $i > $i > $i ).
thf(func_def_1089,type,
sK838: $i > $i > $i > $i ).
thf(func_def_1090,type,
sK839: $i > $i ).
thf(func_def_1091,type,
sK840: $i > ( $i > $o ) > $i ).
thf(func_def_1092,type,
sK841: $i > ( $i > $o ) > $i ).
thf(func_def_1093,type,
sK842: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1094,type,
sK843: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1095,type,
sK844: $i > ( $i > $o ) > $i ).
thf(func_def_1096,type,
sK845: $i > ( $i > $o ) > $i ).
thf(func_def_1097,type,
sK846: ( $i > $o ) > $i > $i ).
thf(func_def_1098,type,
sK847: ( $i > $o ) > $i > $i ).
thf(func_def_1099,type,
sK848: $i > ( $i > $o ) > $i ).
thf(func_def_1100,type,
sK849: $i > ( $i > $o ) > $i ).
thf(func_def_1101,type,
sK850: $i > $i ).
thf(func_def_1102,type,
sK851: $i > $i > $i > $i ).
thf(func_def_1103,type,
sK852: $i > $i > $i > $i ).
thf(func_def_1104,type,
sK853: $i > $i > $i > $i ).
thf(func_def_1105,type,
sK854: $i > $i > $i > $i ).
thf(func_def_1106,type,
sK855: $i > $i > $i > $i ).
thf(func_def_1107,type,
sK856: ( $i > $o ) > $i > $i ).
thf(func_def_1108,type,
sK857: $i > ( $i > $o ) > $i ).
thf(func_def_1109,type,
sK858: $i > ( $i > $o ) > $i ).
thf(func_def_1110,type,
sK859: $i > ( $i > $o ) > $i ).
thf(func_def_1111,type,
sK860: $i > ( $i > $o ) > $i ).
thf(func_def_1112,type,
sK861: ( $i > $o ) > $i > $i ).
thf(func_def_1113,type,
sK862: $i > ( $i > $o ) > $i ).
thf(func_def_1114,type,
sK863: $i > ( $i > $o ) > $i ).
thf(func_def_1115,type,
sK864: $i > ( $i > $o ) > $i ).
thf(func_def_1116,type,
sK865: $i > ( $i > $o ) > $i ).
thf(func_def_1117,type,
sK866: $i > ( $i > $o ) > $i ).
thf(func_def_1118,type,
sK867: ( $i > $o ) > $i > $i ).
thf(func_def_1119,type,
sK868: ( $i > $o ) > $i > $i ).
thf(func_def_1120,type,
sK869: ( $i > $o ) > $i > $i ).
thf(func_def_1121,type,
sK870: ( $i > $o ) > $i > $i ).
thf(func_def_1122,type,
sK871: ( $i > $o ) > $i > $i ).
thf(func_def_1123,type,
sK872: ( $i > $o ) > $i > $i ).
thf(func_def_1124,type,
sK873: ( $i > $o ) > $i > $i ).
thf(func_def_1125,type,
sK874: ( $i > $o ) > $i > $i ).
thf(func_def_1126,type,
sK875: $i > ( $i > $o ) > $i ).
thf(func_def_1127,type,
ph876:
!>[X0: $tType] : X0 ).
thf(f14531,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14521]) ).
thf(f14521,plain,
$true = $false,
inference(superposition,[status(thm)],[f3196,f14472]) ).
thf(f14472,plain,
( $false
= ( in @ sK501 @ sK498 ) ),
inference(subsumption_resolution,[status(thm)],[f14471,f14462]) ).
thf(f14462,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK498 ) )
| ( $true
= ( in @ ( kpair @ X0 @ ( sK634 @ X0 ) ) @ sK499 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14461]) ).
thf(f14461,plain,
! [X0: $i] :
( ( $true
= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK499 )
@ ( sK634 @ X0 ) ) )
| ( $false
= ( in @ X0 @ sK498 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f14441]) ).
thf(f14441,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( in @ X0 @ sK498 ) )
| ( $true
= ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ sK499 )
@ ( sK634 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f12671,f6406]) ).
thf(f6406,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK634 @ X1 )
@ ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) ) )
| ( $false
= ( in @ X1 @ sK498 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6405]) ).
thf(f6405,plain,
! [X1: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK634 @ X1 )
@ ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) ) )
| ( $false
= ( in @ X1 @ sK498 ) ) ),
inference(boolean_simplification,[status(thm)],[f6404]) ).
thf(f6404,plain,
! [X1: $i] :
( ( $true
= ( ( ( setadjoin @ ( sK634 @ X1 ) @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) )
& $false ) )
| ( $false
= ( in @ X1 @ sK498 ) )
| ( $true
= ( in @ ( sK634 @ X1 )
@ ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) ) ) ),
inference(cases_simplifying,[status(thm)],[f6400]) ).
thf(f6400,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK498 ) )
| ( $true
= ( ( ( setadjoin @ ( sK634 @ X1 ) @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) )
& ( in @ ( sK634 @ X1 )
@ ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6399]) ).
thf(f6399,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) ) )
@ ( sK634 @ X1 ) ) )
| ( $false
= ( in @ X1 @ sK498 ) ) ),
inference(sigma_clausification,[status(thm)],[f6398]) ).
thf(f6398,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK498 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6397]) ).
thf(f6397,plain,
! [X1: $i] :
( ( $true = $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) ) ) ) )
| ( $false
= ( in @ X1 @ sK498 ) ) ),
inference(boolean_simplification,[status(thm)],[f6394]) ).
thf(f6394,plain,
! [X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) ) ) ) )
| ( $true = ( ~ $true ) )
| ( $false
= ( in @ X1 @ sK498 ) ) ),
inference(cases_simplifying,[status(thm)],[f6393]) ).
thf(f6393,plain,
! [X1: $i] :
( ( $true
= ( ~ ( in @ X1 @ sK498 ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f6392]) ).
thf(f6392,plain,
! [X1: $i] :
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) ) ) ) )
| ( $true
= ( ( in @ X1 @ sK498 )
=> $false ) ) ),
inference(cases_simplifying,[status(thm)],[f6388]) ).
thf(f6388,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK498 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) )
& ( in @ Y0
@ ( dsetconstr @ sK500
@ ^ [Y1: $i] : ( in @ ( kpair @ X1 @ Y1 ) @ sK499 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6387]) ).
thf(f6387,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK498 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f6386]) ).
thf(f6386,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK498 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6385]) ).
thf(f6385,plain,
( ( $true = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK498 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f6384]) ).
thf(f6384,plain,
( ( $true
= ( ( subset @ sK499 @ ( cartprod @ sK498 @ sK500 ) )
& $false ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK498 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) ) ) ) ) ) ) ),
inference(cases_simplifying,[status(thm)],[f6380]) ).
thf(f6380,plain,
( $true
= ( ( subset @ sK499 @ ( cartprod @ sK498 @ sK500 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK498 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK500
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK499 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4797]) ).
thf(f4797,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) )
@ sK498
@ sK500
@ sK499 ) ),
inference(definition_unfolding,[status(thm)],[f3198,f3451]) ).
thf(f3451,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f2765,f1835,f3450]) ).
thf(f3450,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f2992,f2964]) ).
thf(f2964,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f411]) ).
thf(f411,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f410]) ).
thf(f410,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) )
= singleton ),
inference(rectify,[status(thm)],[f156]) ).
thf(f156,axiom,
( ( ^ [X3: $i] :
? [X1: $i] :
( ( in @ X1 @ X3 )
& ( ( setadjoin @ X1 @ emptyset )
= X3 ) ) )
= singleton ),
file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',singleton) ).
thf(f2992,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f515]) ).
thf(f515,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f514]) ).
thf(f514,plain,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
inference(rectify,[status(thm)],[f158]) ).
thf(f158,axiom,
( ( ^ [X3: $i,X0: $i > $o] :
( singleton
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',ex1) ).
thf(f1835,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f465]) ).
thf(f465,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f464]) ).
thf(f464,plain,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f186]) ).
thf(f186,axiom,
( breln
= ( ^ [X3: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',breln) ).
thf(f2765,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f569]) ).
thf(f569,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f568]) ).
thf(f568,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f194]) ).
thf(f194,axiom,
( func
= ( ^ [X3: $i,X4: $i,X12: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( in @ ( kpair @ X1 @ X2 ) @ X12 ) ) )
& ( breln @ X3 @ X4 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',func) ).
thf(f3198,plain,
( $true
= ( func @ sK498 @ sK500 @ sK499 ) ),
inference(cnf_transformation,[status(thm)],[f1655]) ).
thf(f1655,plain,
( ( quantDeMorgan4 = $true )
& ( subsetTrans = $true )
& ( omegaIndAx = $true )
& ( setextsub = $true )
& ( omega__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( subsetemptysetimpeq = $true )
& ( notequalI1 = $true )
& ( inCongP = $true )
& ( powersetI1 = $true )
& ( binintersectER = $true )
& ( dpsetconstrSub = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem2 = $true )
& ( kpairp = $true )
& ( binunionRsub = $true )
& ( ubforcartprodlem1 = $true )
& ( singletonsswitch = $true )
& ( replAx = $true )
& ( binunionE = $true )
& ( upairsetE = $true )
& ( exu__Cong = $true )
& ( binintersectSubset3 = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( setukpairinjL1 = $true )
& ( emptysetimpfalse = $true )
& ( eqimpsubset1 = $true )
& ( setukpairIL = $true )
& ( cartprodmempair1 = $true )
& ( subsetI2 = $true )
& ( notequalI2 = $true )
& ( theprop = $true )
& ( emptysetAx = $true )
& ( prop2setE = $true )
& ( binintersectSubset5 = $true )
& ( notsubsetI = $true )
& ( notdexE = $true )
& ( ex1I = $true )
& ( symdiffIneg1 = $true )
& ( singletonprop = $true )
& ( symdiffIneg2 = $true )
& ( quantDeMorgan3 = $true )
& ( cartprodfstin = $true )
& ( binintersectSubset2 = $true )
& ( subsetE = $true )
& ( upairequniteq = $true )
& ( setadjoinAx = $true )
& ( setminusELneg = $true )
& ( setadjoin__Cong = $true )
& ( wellorderingAx = $true )
& ( kfstpairEq = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( inPowerset = $true )
& ( binintersectEL = $true )
& ( exuE3e = $true )
& ( upairsetIR = $true )
& ( setextAx = $true )
& ( funcImageSingleton = $true )
& ( binintersectRsub = $true )
& ( emptyinPowerset = $true )
& ( setunionsingleton = $true )
& ( infuncsetfunc = $true )
& ( setukpairinjR2 = $true )
& ( cartprodfstpairEq = $true )
& ( binunionIL = $true )
& ( setunionI = $true )
& ( setadjoinIR = $true )
& ( cartprodsndpairEq = $true )
& ( powersetsubset = $true )
& ( symdiffI2 = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset1 = $true )
& ( emptyinunitempty = $true )
& ( setunionsingleton1 = $true )
& ( cartprodmempair = $true )
& ( setminusILneg = $true )
& ( setbeta = $true )
& ( powersetI = $true )
& ( upairsetIL = $true )
& ( cartprodpairin = $true )
& ( setunionAx = $true )
& ( lam2p = $true )
& ( setukpairinjR = $true )
& ( setOfPairsIsBReln = $true )
& ( setunion__Cong = $true )
& ( setadjoinE = $true )
& ( apProp = $true )
& ( descr__Cong = $true )
& ( emptysetsubset = $true )
& ( binunionEcases = $true )
& ( ksndpairEq = $true )
& ( brelnall1 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan2 = $true )
& ( emptyE1 = $true )
& ( cartprodpairmemER = $true )
& ( symdiffI1 = $true )
& ( exuE1 = $true )
& ( binunionLsub = $true )
& ( symdiffE = $true )
& ( secondinupair = $true )
& ( ex1E2 = $true )
& ( bs114d = $true )
& ( upairset2E = $true )
& ( brelnall2 = $true )
& ( powersetE = $true )
& ( setminusER = $true )
& ( notdallE = $true )
& ( setadjoinSub2 = $true )
& ( cartprodsndin = $true )
& ( eqinunit = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinOr = $true )
& ( setminusERneg = $true )
& ( dsetconstr__Cong = $true )
& ( binintersectI = $true )
& ( in__Cong = $true )
& ( disjointsetsI1 = $true )
& ( upairsubunion = $true )
& ( exuE2 = $true )
& ( setminusI = $true )
& ( noeltsimpempty = $true )
& ( setukpairinjR11 = $true )
& ( emptyI = $true )
& ( setminusIRneg = $true )
& ( setoftrueEq = $true )
& ( ksndsingleton = $true )
& ( sepInPowerset = $true )
& ( setadjoinIL = $true )
& ( dpsetconstrEL1 = $true )
& ( singletoninpowunion = $true )
& ( subsetI1 = $true )
& ( cartprodpairsurjEq = $true )
& ( $true
= ( func @ sK498 @ sK500 @ sK499 ) )
& ( $true
!= ( in @ ( kpair @ sK501 @ ( ap @ sK498 @ sK500 @ sK499 @ sK501 ) ) @ sK499 ) )
& ( $true
= ( in @ sK501 @ sK498 ) )
& ( cartprodpairmemEL = $true )
& ( setminusSubset2 = $true )
& ( exuEu = $true )
& ( kfstsingleton = $true )
& ( dsetconstrER = $true )
& ( singletoninpowerset = $true )
& ( funcinfuncset = $true )
& ( binintersectSubset1 = $true )
& ( vacuousDall = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL2 = $true )
& ( nonemptyE1 = $true )
& ( binunionIR = $true )
& ( powersetE1 = $true )
& ( dpsetconstrI = $true )
& ( notinsingleton = $true )
& ( prop2set2propI = $true )
& ( ex1I2 = $true )
& ( exuI2 = $true )
& ( setukpairinjL = $true )
& ( singletonsuniq = $true )
& ( lamProp = $true )
& ( binintersectSubset4 = $true )
& ( exuI3 = $true )
& ( setadjoinSub = $true )
& ( singletonsubset = $true )
& ( subPowSU = $true )
& ( app = $true )
& ( setminusLsub = $true )
& ( dpsetconstrERa = $true )
& ( subset2powerset = $true )
& ( dsetconstrEL = $true )
& ( sepSubset = $true )
& ( nonemptyI1 = $true )
& ( kpairsurjEq = $true )
& ( lamp = $true )
& ( setext = $true )
& ( setukpairIR = $true )
& ( ubforcartprodlem3 = $true )
& ( notinemptyset = $true )
& ( exuE3u = $true )
& ( setukpairinjR1 = $true )
& ( ex1E1 = $true )
& ( eqimpsubset2 = $true )
& ( setukpairinjL2 = $true )
& ( powerset__Cong = $true )
& ( setukpairinjR12 = $true )
& ( subsetRefl = $true )
& ( kpairiskpair = $true )
& ( emptyset__Cong = $true )
& ( dpsetconstrER = $true )
& ( setunionsingleton2 = $true )
& ( ap2p = $true )
& ( binintersectLsub = $true )
& ( upairset2IR = $true )
& ( upairinpowunion = $true )
& ( foundationAx = $true )
& ( nonemptyI = $true )
& ( omega0Ax = $true )
& ( setunionE2 = $true )
& ( setunionE = $true )
& ( uniqinunit = $true )
& ( emptysetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK498,sK499,sK500,sK501])],[f771,f1654,f1653]) ).
thf(f1653,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
=> ( ( $true
= ( func @ sK498 @ sK500 @ sK499 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ sK498 @ sK500 @ sK499 @ X3 ) ) @ sK499 ) )
& ( $true
= ( in @ X3 @ sK498 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1654,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ sK498 @ sK500 @ sK499 @ X3 ) ) @ sK499 ) )
& ( $true
= ( in @ X3 @ sK498 ) ) )
=> ( ( $true
!= ( in @ ( kpair @ sK501 @ ( ap @ sK498 @ sK500 @ sK499 @ sK501 ) ) @ sK499 ) )
& ( $true
= ( in @ sK501 @ sK498 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f771,plain,
( ( quantDeMorgan4 = $true )
& ( subsetTrans = $true )
& ( omegaIndAx = $true )
& ( setextsub = $true )
& ( omega__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( subsetemptysetimpeq = $true )
& ( notequalI1 = $true )
& ( inCongP = $true )
& ( powersetI1 = $true )
& ( binintersectER = $true )
& ( dpsetconstrSub = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem2 = $true )
& ( kpairp = $true )
& ( binunionRsub = $true )
& ( ubforcartprodlem1 = $true )
& ( singletonsswitch = $true )
& ( replAx = $true )
& ( binunionE = $true )
& ( upairsetE = $true )
& ( exu__Cong = $true )
& ( binintersectSubset3 = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( setukpairinjL1 = $true )
& ( emptysetimpfalse = $true )
& ( eqimpsubset1 = $true )
& ( setukpairIL = $true )
& ( cartprodmempair1 = $true )
& ( subsetI2 = $true )
& ( notequalI2 = $true )
& ( theprop = $true )
& ( emptysetAx = $true )
& ( prop2setE = $true )
& ( binintersectSubset5 = $true )
& ( notsubsetI = $true )
& ( notdexE = $true )
& ( ex1I = $true )
& ( symdiffIneg1 = $true )
& ( singletonprop = $true )
& ( symdiffIneg2 = $true )
& ( quantDeMorgan3 = $true )
& ( cartprodfstin = $true )
& ( binintersectSubset2 = $true )
& ( subsetE = $true )
& ( upairequniteq = $true )
& ( setadjoinAx = $true )
& ( setminusELneg = $true )
& ( setadjoin__Cong = $true )
& ( wellorderingAx = $true )
& ( kfstpairEq = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( inPowerset = $true )
& ( binintersectEL = $true )
& ( exuE3e = $true )
& ( upairsetIR = $true )
& ( setextAx = $true )
& ( funcImageSingleton = $true )
& ( binintersectRsub = $true )
& ( emptyinPowerset = $true )
& ( setunionsingleton = $true )
& ( infuncsetfunc = $true )
& ( setukpairinjR2 = $true )
& ( cartprodfstpairEq = $true )
& ( binunionIL = $true )
& ( setunionI = $true )
& ( setadjoinIR = $true )
& ( cartprodsndpairEq = $true )
& ( powersetsubset = $true )
& ( symdiffI2 = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset1 = $true )
& ( emptyinunitempty = $true )
& ( setunionsingleton1 = $true )
& ( cartprodmempair = $true )
& ( setminusILneg = $true )
& ( setbeta = $true )
& ( powersetI = $true )
& ( upairsetIL = $true )
& ( cartprodpairin = $true )
& ( setunionAx = $true )
& ( lam2p = $true )
& ( setukpairinjR = $true )
& ( setOfPairsIsBReln = $true )
& ( setunion__Cong = $true )
& ( setadjoinE = $true )
& ( apProp = $true )
& ( descr__Cong = $true )
& ( emptysetsubset = $true )
& ( binunionEcases = $true )
& ( ksndpairEq = $true )
& ( brelnall1 = $true )
& ( powersetAx = $true )
& ( quantDeMorgan2 = $true )
& ( emptyE1 = $true )
& ( cartprodpairmemER = $true )
& ( symdiffI1 = $true )
& ( exuE1 = $true )
& ( binunionLsub = $true )
& ( symdiffE = $true )
& ( secondinupair = $true )
& ( ex1E2 = $true )
& ( bs114d = $true )
& ( upairset2E = $true )
& ( brelnall2 = $true )
& ( powersetE = $true )
& ( setminusER = $true )
& ( notdallE = $true )
& ( setadjoinSub2 = $true )
& ( cartprodsndin = $true )
& ( eqinunit = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinOr = $true )
& ( setminusERneg = $true )
& ( dsetconstr__Cong = $true )
& ( binintersectI = $true )
& ( in__Cong = $true )
& ( disjointsetsI1 = $true )
& ( upairsubunion = $true )
& ( exuE2 = $true )
& ( setminusI = $true )
& ( noeltsimpempty = $true )
& ( setukpairinjR11 = $true )
& ( emptyI = $true )
& ( setminusIRneg = $true )
& ( setoftrueEq = $true )
& ( ksndsingleton = $true )
& ( sepInPowerset = $true )
& ( setadjoinIL = $true )
& ( dpsetconstrEL1 = $true )
& ( singletoninpowunion = $true )
& ( subsetI1 = $true )
& ( cartprodpairsurjEq = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
& ( cartprodpairmemEL = $true )
& ( setminusSubset2 = $true )
& ( exuEu = $true )
& ( kfstsingleton = $true )
& ( dsetconstrER = $true )
& ( singletoninpowerset = $true )
& ( funcinfuncset = $true )
& ( binintersectSubset1 = $true )
& ( vacuousDall = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL2 = $true )
& ( nonemptyE1 = $true )
& ( binunionIR = $true )
& ( powersetE1 = $true )
& ( dpsetconstrI = $true )
& ( notinsingleton = $true )
& ( prop2set2propI = $true )
& ( ex1I2 = $true )
& ( exuI2 = $true )
& ( setukpairinjL = $true )
& ( singletonsuniq = $true )
& ( lamProp = $true )
& ( binintersectSubset4 = $true )
& ( exuI3 = $true )
& ( setadjoinSub = $true )
& ( singletonsubset = $true )
& ( subPowSU = $true )
& ( app = $true )
& ( setminusLsub = $true )
& ( dpsetconstrERa = $true )
& ( subset2powerset = $true )
& ( dsetconstrEL = $true )
& ( sepSubset = $true )
& ( nonemptyI1 = $true )
& ( kpairsurjEq = $true )
& ( lamp = $true )
& ( setext = $true )
& ( setukpairIR = $true )
& ( ubforcartprodlem3 = $true )
& ( notinemptyset = $true )
& ( exuE3u = $true )
& ( setukpairinjR1 = $true )
& ( ex1E1 = $true )
& ( eqimpsubset2 = $true )
& ( setukpairinjL2 = $true )
& ( powerset__Cong = $true )
& ( setukpairinjR12 = $true )
& ( subsetRefl = $true )
& ( kpairiskpair = $true )
& ( emptyset__Cong = $true )
& ( dpsetconstrER = $true )
& ( setunionsingleton2 = $true )
& ( ap2p = $true )
& ( binintersectLsub = $true )
& ( upairset2IR = $true )
& ( upairinpowunion = $true )
& ( foundationAx = $true )
& ( nonemptyI = $true )
& ( omega0Ax = $true )
& ( setunionE2 = $true )
& ( setunionE = $true )
& ( uniqinunit = $true )
& ( emptysetE = $true ) ),
inference(flattening,[status(thm)],[f770]) ).
thf(f770,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
& ( 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)],[f565]) ).
thf(f565,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f564]) ).
thf(f564,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( kpair @ X3 @ ( ap @ X0 @ X2 @ X1 @ X3 ) ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f210]) ).
thf(f210,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
=> ! [X3: $i,X13: $i,X4: $i] :
( ( func @ X3 @ X4 @ X13 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( kpair @ X1 @ ( ap @ X3 @ X4 @ X13 @ X1 ) ) @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f209]) ).
thf(f209,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
=> ! [X3: $i,X13: $i,X4: $i] :
( ( func @ X3 @ X4 @ X13 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( kpair @ X1 @ ( ap @ X3 @ X4 @ X13 @ X1 ) ) @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',funcGraphProp1) ).
thf(f12671,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X2 @ ( dsetconstr @ X1 @ X0 ) ) )
| ( ( X0 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f12670]) ).
thf(f12670,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( ( X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4313]) ).
thf(f4313,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f2643,f3191]) ).
thf(f3191,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f1655]) ).
thf(f2643,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f1054]) ).
thf(f1054,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( $true
!= ( sK120 @ sK122 ) )
& ( $true
= ( in @ sK122
@ ( dsetconstr @ sK121
@ ^ [Y0: $i] : ( sK120 @ Y0 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK120,sK121,sK122])],[f1052,f1053]) ).
thf(f1053,plain,
( ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( X3 @ X5 ) )
& ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true ) )
=> ( ( $true
!= ( sK120 @ sK122 ) )
& ( $true
= ( in @ sK122
@ ( dsetconstr @ sK121
@ ^ [Y0: $i] : ( sK120 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1052,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( X3 @ X5 ) )
& ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1051]) ).
thf(f1051,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
!= $true )
& ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f773]) ).
thf(f773,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f262]) ).
thf(f262,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( ( X0 @ X2 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f261]) ).
thf(f261,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X0: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',dsetconstrER) ).
thf(f14471,plain,
( ( $true
!= ( in @ ( kpair @ sK501 @ ( sK634 @ sK501 ) ) @ sK499 ) )
| ( $false
= ( in @ sK501 @ sK498 ) ) ),
inference(forward_demodulation,[status(thm)],[f14464,f5149]) ).
thf(f5149,plain,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(trivial_inequality_removal,[status(thm)],[f4297]) ).
thf(f4297,plain,
! [X1: $i] :
( ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f2624,f3272]) ).
thf(f3272,plain,
setunionsingleton = $true,
inference(cnf_transformation,[status(thm)],[f1655]) ).
thf(f2624,plain,
! [X1: $i] :
( ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( setunionsingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f1038]) ).
thf(f1038,plain,
( ( ( setunionsingleton = $true )
| ( sK110
!= ( setunion @ ( setadjoin @ sK110 @ emptyset ) ) ) )
& ( ! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( setunionsingleton != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110])],[f1036,f1037]) ).
thf(f1037,plain,
( ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 )
=> ( sK110
!= ( setunion @ ( setadjoin @ sK110 @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1036,plain,
( ( ( setunionsingleton = $true )
| ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 ) )
& ( ! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 )
| ( setunionsingleton != $true ) ) ),
inference(rectify,[status(thm)],[f1035]) ).
thf(f1035,plain,
( ( ( setunionsingleton = $true )
| ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 ) )
& ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f591]) ).
thf(f591,plain,
( ( setunionsingleton = $true )
<=> ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f590]) ).
thf(f590,plain,
( setunionsingleton
= ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ),
inference(rectify,[status(thm)],[f155]) ).
thf(f155,axiom,
( setunionsingleton
= ( ! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',setunionsingleton) ).
thf(f14464,plain,
( ( $true
!= ( in @ ( kpair @ sK501 @ ( setunion @ ( setadjoin @ ( sK634 @ sK501 ) @ emptyset ) ) ) @ sK499 ) )
| ( $false
= ( in @ sK501 @ sK498 ) ) ),
inference(superposition,[status(thm)],[f5104,f6411]) ).
thf(f6411,plain,
! [X1: $i] :
( ( ( setadjoin @ ( sK634 @ X1 ) @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) )
| ( $false
= ( in @ X1 @ sK498 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f6410]) ).
thf(f6410,plain,
! [X1: $i] :
( ( $true
= ( ( setadjoin @ ( sK634 @ X1 ) @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) ) )
| ( $false
= ( in @ X1 @ sK498 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6409]) ).
thf(f6409,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ sK498 ) )
| ( $true = $false )
| ( $true
= ( ( setadjoin @ ( sK634 @ X1 ) @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f6402]) ).
thf(f6402,plain,
! [X1: $i] :
( ( $true
= ( ( setadjoin @ ( sK634 @ X1 ) @ emptyset )
= ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) ) )
| ( $true
= ( $false
& ( in @ ( sK634 @ X1 )
@ ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ X1 @ Y0 ) @ sK499 ) ) ) ) )
| ( $false
= ( in @ X1 @ sK498 ) ) ),
inference(cases_simplifying,[status(thm)],[f6400]) ).
thf(f5104,plain,
( $true
!= ( in
@ ( kpair @ sK501
@ ( setunion
@ ( dsetconstr @ sK500
@ ^ [Y0: $i] : ( in @ ( kpair @ sK501 @ Y0 ) @ sK499 ) ) ) )
@ sK499 ) ),
inference(beta_eta_normalization,[status(thm)],[f4798]) ).
thf(f4798,plain,
( $true
!= ( in
@ ( kpair @ sK501
@ ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) )
@ sK498
@ sK500
@ sK499
@ sK501 ) )
@ sK499 ) ),
inference(definition_unfolding,[status(thm)],[f3197,f3098]) ).
thf(f3098,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
thf(f221,plain,
( ap
= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f220]) ).
thf(f220,plain,
( ap
= ( ^ [X0: $i,X1: $i,X2: $i,X3: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f197]) ).
thf(f197,axiom,
( ap
= ( ^ [X3: $i,X4: $i,X13: $i,X1: $i] :
( setunion
@ ( dsetconstr @ X4
@ ^ [X2: $i] : ( in @ ( kpair @ X1 @ X2 ) @ X13 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',ap) ).
thf(f3197,plain,
( $true
!= ( in @ ( kpair @ sK501 @ ( ap @ sK498 @ sK500 @ sK499 @ sK501 ) ) @ sK499 ) ),
inference(cnf_transformation,[status(thm)],[f1655]) ).
thf(f3196,plain,
( $true
= ( in @ sK501 @ sK498 ) ),
inference(cnf_transformation,[status(thm)],[f1655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU684^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n021.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:30:38 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SEU684^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.39 % Domain : Set Theory
% 0.18/0.39 % Problem : Functions - Extensionality and Beta Reduction
% 0.18/0.39 % Version : Especial.
% 0.18/0.39 % English : (! A:i.! B:i.! f:i.func A B f -> (! x:i.in x A ->
% 0.18/0.39 % in (kpair x (ap A B f x)) f))
% 0.18/0.39
% 0.18/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.39 % Source : [Bro08]
% 0.18/0.39 % Names : ZFC186g [Bro08]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.80 v8.2.0, 0.77 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 1.00 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 1.00 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.18/0.39 % Syntax : Number of formulae : 446 ( 208 unt; 237 typ; 208 def)
% 0.18/0.39 % Number of atoms : 1110 ( 304 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 203 ( 5 avg)
% 0.18/0.39 % Number of connectives : 2046 ( 47 ~; 7 |; 36 &;1444 @)
% 0.18/0.39 % ( 14 <=>; 498 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 214 ( 2 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 240 ( 237 usr; 204 con; 0-4 aty)
% 0.18/0.39 % Number of variables : 667 ( 78 ^; 553 !; 36 ?; 667 :)
% 0.18/0.39 % SPC : TH0_THM_EQU_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : http://mathgate.info/detsetitem.php?id=241
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(in_type,type,
% 0.18/0.39 in: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(exu_type,type,
% 0.18/0.39 exu: ( $i > $o ) > $o ).
% 0.18/0.39
% 0.18/0.39 thf(exu,definition,
% 0.18/0.39 ( exu
% 0.18/0.39 = ( ^ [Xphi: $i > $o] :
% 0.18/0.39 ? [Xx: $i] :
% 0.18/0.39 ( ( Xphi @ Xx )
% 0.18/0.39 & ! [Xy: $i] :
% 0.18/0.39 ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setextAx_type,type,
% 0.18/0.39 setextAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setextAx,definition,
% 0.18/0.39 ( setextAx
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 <=> ( in @ Xx @ B ) )
% 0.18/0.39 => ( A = B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptyset_type,type,
% 0.18/0.39 emptyset: $i ).
% 0.18/0.39
% 0.18/0.39 thf(emptysetAx_type,type,
% 0.18/0.39 emptysetAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptysetAx,definition,
% 0.18/0.39 ( emptysetAx
% 0.18/0.39 = ( ! [Xx: $i] :
% 0.18/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoin_type,type,
% 0.18/0.39 setadjoin: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinAx_type,type,
% 0.18/0.39 setadjoinAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinAx,definition,
% 0.18/0.39 ( setadjoinAx
% 0.18/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.39 <=> ( ( Xy = Xx )
% 0.18/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(powerset_type,type,
% 0.18/0.39 powerset: $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(powersetAx_type,type,
% 0.18/0.39 powersetAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(powersetAx,definition,
% 0.18/0.39 ( powersetAx
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.39 <=> ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setunion_type,type,
% 0.18/0.39 setunion: $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(setunionAx_type,type,
% 0.18/0.39 setunionAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setunionAx,definition,
% 0.18/0.39 ( setunionAx
% 0.18/0.39 = ( ! [A: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.39 <=> ? [B: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(omega_type,type,
% 0.18/0.39 omega: $i ).
% 0.18/0.39
% 0.18/0.39 thf(omega0Ax_type,type,
% 0.18/0.39 omega0Ax: $o ).
% 0.18/0.39
% 0.18/0.39 thf(omega0Ax,definition,
% 0.18/0.39 ( omega0Ax
% 0.18/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(omegaSAx_type,type,
% 0.18/0.39 omegaSAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(omegaSAx,definition,
% 0.18/0.39 ( omegaSAx
% 0.18/0.39 = ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ omega )
% 0.18/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(omegaIndAx_type,type,
% 0.18/0.39 omegaIndAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(omegaIndAx,definition,
% 0.18/0.39 ( omegaIndAx
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ( ( in @ emptyset @ A )
% 0.18/0.39 & ! [Xx: $i] :
% 0.18/0.39 ( ( ( in @ Xx @ omega )
% 0.18/0.39 & ( in @ Xx @ A ) )
% 0.18/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ omega )
% 0.18/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(replAx_type,type,
% 0.18/0.39 replAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(replAx,definition,
% 0.18/0.39 ( replAx
% 0.18/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( exu
% 0.18/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.18/0.39 => ? [B: $i] :
% 0.18/0.39 ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 <=> ? [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ A )
% 0.18/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(foundationAx_type,type,
% 0.18/0.39 foundationAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(foundationAx,definition,
% 0.18/0.39 ( foundationAx
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.39 => ? [B: $i] :
% 0.18/0.39 ( ( in @ B @ A )
% 0.18/0.39 & ~ ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(wellorderingAx_type,type,
% 0.18/0.39 wellorderingAx: $o ).
% 0.18/0.39
% 0.18/0.39 thf(wellorderingAx,definition,
% 0.18/0.39 ( wellorderingAx
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ? [B: $i] :
% 0.18/0.39 ( ! [C: $i] :
% 0.18/0.39 ( ( in @ C @ B )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ C )
% 0.18/0.39 => ( in @ Xx @ A ) ) )
% 0.18/0.39 & ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( ( in @ Xx @ A )
% 0.18/0.39 & ( in @ Xy @ A ) )
% 0.18/0.39 => ( ! [C: $i] :
% 0.18/0.39 ( ( in @ C @ B )
% 0.18/0.39 => ( ( in @ Xx @ C )
% 0.18/0.39 <=> ( in @ Xy @ C ) ) )
% 0.18/0.39 => ( Xx = Xy ) ) )
% 0.18/0.39 & ! [C: $i,D: $i] :
% 0.18/0.39 ( ( ( in @ C @ B )
% 0.18/0.39 & ( in @ D @ B ) )
% 0.18/0.39 => ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ C )
% 0.18/0.39 => ( in @ Xx @ D ) )
% 0.18/0.39 | ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ D )
% 0.18/0.39 => ( in @ Xx @ C ) ) ) )
% 0.18/0.39 & ! [C: $i] :
% 0.18/0.39 ( ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ C )
% 0.18/0.39 => ( in @ Xx @ A ) )
% 0.18/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.18/0.39 => ? [D: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ D @ B )
% 0.18/0.39 & ( in @ Xx @ C )
% 0.18/0.39 & ~ ? [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ D )
% 0.18/0.39 & ( in @ Xy @ C ) )
% 0.18/0.39 & ! [E: $i] :
% 0.18/0.39 ( ( in @ E @ B )
% 0.18/0.39 => ( ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ E )
% 0.18/0.39 => ( in @ Xy @ D ) )
% 0.18/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(descr_type,type,
% 0.18/0.39 descr: ( $i > $o ) > $i ).
% 0.18/0.39
% 0.18/0.39 thf(descrp_type,type,
% 0.18/0.39 descrp: $o ).
% 0.18/0.39
% 0.18/0.39 thf(descrp,definition,
% 0.18/0.39 ( descrp
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ( Xphi
% 0.18/0.39 @ ( descr
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstr_type,type,
% 0.18/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstrI_type,type,
% 0.18/0.39 dsetconstrI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstrI,definition,
% 0.18/0.39 ( dsetconstrI
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 => ( in @ Xx
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstrEL_type,type,
% 0.18/0.39 dsetconstrEL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstrEL,definition,
% 0.18/0.39 ( dsetconstrEL
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstrER_type,type,
% 0.18/0.39 dsetconstrER: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstrER,definition,
% 0.18/0.39 ( dsetconstrER
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exuE1_type,type,
% 0.18/0.39 exuE1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exuE1,definition,
% 0.18/0.39 ( exuE1
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ? [Xx: $i] :
% 0.18/0.39 ( ( Xphi @ Xx )
% 0.18/0.39 & ! [Xy: $i] :
% 0.18/0.39 ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(prop2set_type,type,
% 0.18/0.39 prop2set: $o > $i ).
% 0.18/0.39
% 0.18/0.39 thf(prop2setE_type,type,
% 0.18/0.39 prop2setE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(prop2setE,definition,
% 0.18/0.39 ( prop2setE
% 0.18/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.18/0.39 => Xphi ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptysetE_type,type,
% 0.18/0.39 emptysetE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptysetE,definition,
% 0.18/0.39 ( emptysetE
% 0.18/0.39 = ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ emptyset )
% 0.18/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptysetimpfalse_type,type,
% 0.18/0.39 emptysetimpfalse: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptysetimpfalse,definition,
% 0.18/0.39 ( emptysetimpfalse
% 0.18/0.39 = ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ emptyset )
% 0.18/0.39 => $false ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(notinemptyset_type,type,
% 0.18/0.39 notinemptyset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(notinemptyset,definition,
% 0.18/0.39 ( notinemptyset
% 0.18/0.39 = ( ! [Xx: $i] :
% 0.18/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exuE3e_type,type,
% 0.18/0.39 exuE3e: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exuE3e,definition,
% 0.18/0.39 ( exuE3e
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setext_type,type,
% 0.18/0.39 setext: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setext,definition,
% 0.18/0.39 ( setext
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ Xx @ B ) )
% 0.18/0.39 => ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ A ) )
% 0.18/0.39 => ( A = B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptyI_type,type,
% 0.18/0.39 emptyI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptyI,definition,
% 0.18/0.39 ( emptyI
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ~ ( in @ Xx @ A )
% 0.18/0.39 => ( A = emptyset ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(noeltsimpempty_type,type,
% 0.18/0.39 noeltsimpempty: $o ).
% 0.18/0.39
% 0.18/0.39 thf(noeltsimpempty,definition,
% 0.18/0.39 ( noeltsimpempty
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ~ ( in @ Xx @ A )
% 0.18/0.39 => ( A = emptyset ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setbeta_type,type,
% 0.18/0.39 setbeta: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setbeta,definition,
% 0.18/0.39 ( setbeta
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ( in @ Xx
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(nonempty_type,type,
% 0.18/0.39 nonempty: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(nonempty,definition,
% 0.18/0.39 ( nonempty
% 0.18/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(nonemptyE1_type,type,
% 0.18/0.39 nonemptyE1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(nonemptyE1,definition,
% 0.18/0.39 ( nonemptyE1
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ( nonempty @ A )
% 0.18/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(nonemptyI_type,type,
% 0.18/0.39 nonemptyI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(nonemptyI,definition,
% 0.18/0.39 ( nonemptyI
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 => ( nonempty
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(nonemptyI1_type,type,
% 0.18/0.39 nonemptyI1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(nonemptyI1,definition,
% 0.18/0.39 ( nonemptyI1
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinIL_type,type,
% 0.18/0.39 setadjoinIL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinIL,definition,
% 0.18/0.39 ( setadjoinIL
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptyinunitempty_type,type,
% 0.18/0.39 emptyinunitempty: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptyinunitempty,definition,
% 0.18/0.39 ( emptyinunitempty
% 0.18/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinIR_type,type,
% 0.18/0.39 setadjoinIR: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinIR,definition,
% 0.18/0.39 ( setadjoinIR
% 0.18/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ A )
% 0.18/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinE_type,type,
% 0.18/0.39 setadjoinE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinE,definition,
% 0.18/0.39 ( setadjoinE
% 0.18/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.39 => ! [Xphi: $o] :
% 0.18/0.39 ( ( ( Xy = Xx )
% 0.18/0.39 => Xphi )
% 0.18/0.39 => ( ( ( in @ Xy @ A )
% 0.18/0.39 => Xphi )
% 0.18/0.39 => Xphi ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinOr_type,type,
% 0.18/0.39 setadjoinOr: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinOr,definition,
% 0.18/0.39 ( setadjoinOr
% 0.18/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.39 => ( ( Xy = Xx )
% 0.18/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setoftrueEq_type,type,
% 0.18/0.39 setoftrueEq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setoftrueEq,definition,
% 0.18/0.39 ( setoftrueEq
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xx: $i] : $true )
% 0.18/0.39 = A ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(powersetI_type,type,
% 0.18/0.39 powersetI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(powersetI,definition,
% 0.18/0.39 ( powersetI
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ A ) )
% 0.18/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptyinPowerset_type,type,
% 0.18/0.39 emptyinPowerset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptyinPowerset,definition,
% 0.18/0.39 ( emptyinPowerset
% 0.18/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptyInPowerset_type,type,
% 0.18/0.39 emptyInPowerset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptyInPowerset,definition,
% 0.18/0.39 ( emptyInPowerset
% 0.18/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(powersetE_type,type,
% 0.18/0.39 powersetE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(powersetE,definition,
% 0.18/0.39 ( powersetE
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.39 => ( ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setunionI_type,type,
% 0.18/0.39 setunionI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setunionI,definition,
% 0.18/0.39 ( setunionI
% 0.18/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 => ( ( in @ B @ A )
% 0.18/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setunionE_type,type,
% 0.18/0.39 setunionE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setunionE,definition,
% 0.18/0.39 ( setunionE
% 0.18/0.39 = ( ! [A: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.39 => ! [Xphi: $o] :
% 0.18/0.39 ( ! [B: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 => ( ( in @ B @ A )
% 0.18/0.39 => Xphi ) )
% 0.18/0.39 => Xphi ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subPowSU_type,type,
% 0.18/0.39 subPowSU: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subPowSU,definition,
% 0.18/0.39 ( subPowSU
% 0.18/0.39 = ( ! [A: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exuE2_type,type,
% 0.18/0.39 exuE2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exuE2,definition,
% 0.18/0.39 ( exuE2
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ? [Xx: $i] :
% 0.18/0.39 ! [Xy: $i] :
% 0.18/0.39 ( ( Xphi @ Xy )
% 0.18/0.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(nonemptyImpWitness_type,type,
% 0.18/0.39 nonemptyImpWitness: $o ).
% 0.18/0.39
% 0.18/0.39 thf(nonemptyImpWitness,definition,
% 0.18/0.39 ( nonemptyImpWitness
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ( nonempty @ A )
% 0.18/0.39 => ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & $true ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(uniqinunit_type,type,
% 0.18/0.39 uniqinunit: $o ).
% 0.18/0.39
% 0.18/0.39 thf(uniqinunit,definition,
% 0.18/0.39 ( uniqinunit
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(notinsingleton_type,type,
% 0.18/0.39 notinsingleton: $o ).
% 0.18/0.39
% 0.18/0.39 thf(notinsingleton,definition,
% 0.18/0.39 ( notinsingleton
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx != Xy )
% 0.18/0.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(eqinunit_type,type,
% 0.18/0.39 eqinunit: $o ).
% 0.18/0.39
% 0.18/0.39 thf(eqinunit,definition,
% 0.18/0.39 ( eqinunit
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx = Xy )
% 0.18/0.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(singletonsswitch_type,type,
% 0.18/0.39 singletonsswitch: $o ).
% 0.18/0.39
% 0.18/0.39 thf(singletonsswitch,definition,
% 0.18/0.39 ( singletonsswitch
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(upairsetE_type,type,
% 0.18/0.39 upairsetE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairsetE,definition,
% 0.18/0.39 ( upairsetE
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.18/0.39 => ( ( Xz = Xx )
% 0.18/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(upairsetIL_type,type,
% 0.18/0.39 upairsetIL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairsetIL,definition,
% 0.18/0.39 ( upairsetIL
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(upairsetIR_type,type,
% 0.18/0.39 upairsetIR: $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairsetIR,definition,
% 0.18/0.39 ( upairsetIR
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptyE1_type,type,
% 0.18/0.39 emptyE1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptyE1,definition,
% 0.18/0.39 ( emptyE1
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( Xphi @ Xx ) )
% 0.18/0.39 => ( ( ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 = emptyset )
% 0.18/0.39 => $false ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(vacuousDall_type,type,
% 0.18/0.39 vacuousDall: $o ).
% 0.18/0.39
% 0.18/0.39 thf(vacuousDall,definition,
% 0.18/0.39 ( vacuousDall
% 0.18/0.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ emptyset )
% 0.18/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(quantDeMorgan1_type,type,
% 0.18/0.39 quantDeMorgan1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(quantDeMorgan1,definition,
% 0.18/0.39 ( quantDeMorgan1
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ~ ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( Xphi @ Xx ) )
% 0.18/0.39 => ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(quantDeMorgan2_type,type,
% 0.18/0.39 quantDeMorgan2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(quantDeMorgan2,definition,
% 0.18/0.39 ( quantDeMorgan2
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ~ ( Xphi @ Xx ) )
% 0.18/0.39 => ~ ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(quantDeMorgan3_type,type,
% 0.18/0.39 quantDeMorgan3: $o ).
% 0.18/0.39
% 0.18/0.39 thf(quantDeMorgan3,definition,
% 0.18/0.39 ( quantDeMorgan3
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ~ ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( Xphi @ Xx ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(quantDeMorgan4_type,type,
% 0.18/0.39 quantDeMorgan4: $o ).
% 0.18/0.39
% 0.18/0.39 thf(quantDeMorgan4,definition,
% 0.18/0.39 ( quantDeMorgan4
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ~ ( Xphi @ Xx ) )
% 0.18/0.39 => ~ ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(prop2setI_type,type,
% 0.18/0.39 prop2setI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(prop2setI,definition,
% 0.18/0.39 ( prop2setI
% 0.18/0.39 = ( ! [Xphi: $o] :
% 0.18/0.39 ( Xphi
% 0.18/0.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(set2prop_type,type,
% 0.18/0.39 set2prop: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(prop2set2propI_type,type,
% 0.18/0.39 prop2set2propI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(prop2set2propI,definition,
% 0.18/0.39 ( prop2set2propI
% 0.18/0.39 = ( ! [Xphi: $o] :
% 0.18/0.39 ( Xphi
% 0.18/0.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(notdexE_type,type,
% 0.18/0.39 notdexE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(notdexE,definition,
% 0.18/0.39 ( notdexE
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ~ ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( Xphi @ Xx ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(notdallE_type,type,
% 0.18/0.39 notdallE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(notdallE,definition,
% 0.18/0.39 ( notdallE
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ~ ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( Xphi @ Xx ) )
% 0.18/0.39 => ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exuI1_type,type,
% 0.18/0.39 exuI1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exuI1,definition,
% 0.18/0.39 ( exuI1
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ? [Xx: $i] :
% 0.18/0.39 ( ( Xphi @ Xx )
% 0.18/0.39 & ! [Xy: $i] :
% 0.18/0.39 ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) )
% 0.18/0.39 => ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exuI3_type,type,
% 0.18/0.39 exuI3: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exuI3,definition,
% 0.18/0.39 ( exuI3
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.18/0.39 => ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xphi @ Xx )
% 0.18/0.39 => ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) )
% 0.18/0.39 => ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exuI2_type,type,
% 0.18/0.39 exuI2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exuI2,definition,
% 0.18/0.39 ( exuI2
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ? [Xx: $i] :
% 0.18/0.39 ! [Xy: $i] :
% 0.18/0.39 ( ( Xphi @ Xy )
% 0.18/0.39 <=> ( Xy = Xx ) )
% 0.18/0.39 => ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(inCongP_type,type,
% 0.18/0.39 inCongP: $o ).
% 0.18/0.39
% 0.18/0.39 thf(inCongP,definition,
% 0.18/0.39 ( inCongP
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( A = B )
% 0.18/0.39 => ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx = Xy )
% 0.18/0.39 => ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(in__Cong_type,type,
% 0.18/0.39 in__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(in__Cong,definition,
% 0.18/0.39 ( in__Cong
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( A = B )
% 0.18/0.39 => ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx = Xy )
% 0.18/0.39 => ( ( in @ Xx @ A )
% 0.18/0.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exuE3u_type,type,
% 0.18/0.39 exuE3u: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exuE3u,definition,
% 0.18/0.39 ( exuE3u
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xphi @ Xx )
% 0.18/0.39 => ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exu__Cong_type,type,
% 0.18/0.39 exu__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exu__Cong,definition,
% 0.18/0.39 ( exu__Cong
% 0.18/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx = Xy )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.18/0.39 => ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 <=> ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptyset__Cong_type,type,
% 0.18/0.39 emptyset__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptyset__Cong,definition,
% 0.18/0.39 ( emptyset__Cong
% 0.18/0.39 = ( emptyset = emptyset ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoin__Cong_type,type,
% 0.18/0.39 setadjoin__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoin__Cong,definition,
% 0.18/0.39 ( setadjoin__Cong
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx = Xy )
% 0.18/0.39 => ! [Xz: $i,Xu: $i] :
% 0.18/0.39 ( ( Xz = Xu )
% 0.18/0.39 => ( ( setadjoin @ Xx @ Xz )
% 0.18/0.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(powerset__Cong_type,type,
% 0.18/0.39 powerset__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(powerset__Cong,definition,
% 0.18/0.39 ( powerset__Cong
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( A = B )
% 0.18/0.39 => ( ( powerset @ A )
% 0.18/0.39 = ( powerset @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setunion__Cong_type,type,
% 0.18/0.39 setunion__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setunion__Cong,definition,
% 0.18/0.39 ( setunion__Cong
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( A = B )
% 0.18/0.39 => ( ( setunion @ A )
% 0.18/0.39 = ( setunion @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(omega__Cong_type,type,
% 0.18/0.39 omega__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(omega__Cong,definition,
% 0.18/0.39 ( omega__Cong
% 0.18/0.39 = ( omega = omega ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(exuEu_type,type,
% 0.18/0.39 exuEu: $o ).
% 0.18/0.39
% 0.18/0.39 thf(exuEu,definition,
% 0.18/0.39 ( exuEu
% 0.18/0.39 = ( ! [Xphi: $i > $o] :
% 0.18/0.39 ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xphi @ Xx )
% 0.18/0.39 => ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(descr__Cong_type,type,
% 0.18/0.39 descr__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(descr__Cong,definition,
% 0.18/0.39 ( descr__Cong
% 0.18/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx = Xy )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.18/0.39 => ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ( ( exu
% 0.18/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.18/0.39 => ( ( descr
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 = ( descr
% 0.18/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstr__Cong_type,type,
% 0.18/0.39 dsetconstr__Cong: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dsetconstr__Cong,definition,
% 0.18/0.39 ( dsetconstr__Cong
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( A = B )
% 0.18/0.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( ( Xx = Xy )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.18/0.39 => ( ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 = ( dsetconstr @ B
% 0.18/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subset_type,type,
% 0.18/0.39 subset: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(disjoint_type,type,
% 0.18/0.39 disjoint: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(setsmeet_type,type,
% 0.18/0.39 setsmeet: $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(subsetI1_type,type,
% 0.18/0.39 subsetI1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subsetI1,definition,
% 0.18/0.39 ( subsetI1
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ Xx @ B ) )
% 0.18/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(eqimpsubset2_type,type,
% 0.18/0.39 eqimpsubset2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(eqimpsubset2,definition,
% 0.18/0.39 ( eqimpsubset2
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( A = B )
% 0.18/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(eqimpsubset1_type,type,
% 0.18/0.39 eqimpsubset1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(eqimpsubset1,definition,
% 0.18/0.39 ( eqimpsubset1
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( A = B )
% 0.18/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subsetI2_type,type,
% 0.18/0.39 subsetI2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subsetI2,definition,
% 0.18/0.39 ( subsetI2
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ Xx @ B ) )
% 0.18/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(emptysetsubset_type,type,
% 0.18/0.39 emptysetsubset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(emptysetsubset,definition,
% 0.18/0.39 ( emptysetsubset
% 0.18/0.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subsetE_type,type,
% 0.18/0.39 subsetE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subsetE,definition,
% 0.18/0.39 ( subsetE
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subsetE2_type,type,
% 0.18/0.39 subsetE2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subsetE2,definition,
% 0.18/0.39 ( subsetE2
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(notsubsetI_type,type,
% 0.18/0.39 notsubsetI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(notsubsetI,definition,
% 0.18/0.39 ( notsubsetI
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(notequalI1_type,type,
% 0.18/0.39 notequalI1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(notequalI1,definition,
% 0.18/0.39 ( notequalI1
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ~ ( subset @ A @ B )
% 0.18/0.39 => ( A != B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(notequalI2_type,type,
% 0.18/0.39 notequalI2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(notequalI2,definition,
% 0.18/0.39 ( notequalI2
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => ( A != B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subsetRefl_type,type,
% 0.18/0.39 subsetRefl: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subsetRefl,definition,
% 0.18/0.39 ( subsetRefl
% 0.18/0.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subsetTrans_type,type,
% 0.18/0.39 subsetTrans: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subsetTrans,definition,
% 0.18/0.39 ( subsetTrans
% 0.18/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( ( subset @ B @ C )
% 0.18/0.39 => ( subset @ A @ C ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinSub_type,type,
% 0.18/0.39 setadjoinSub: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinSub,definition,
% 0.18/0.39 ( setadjoinSub
% 0.18/0.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinSub2_type,type,
% 0.18/0.39 setadjoinSub2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setadjoinSub2,definition,
% 0.18/0.39 ( setadjoinSub2
% 0.18/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subset2powerset_type,type,
% 0.18/0.39 subset2powerset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subset2powerset,definition,
% 0.18/0.39 ( subset2powerset
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setextsub_type,type,
% 0.18/0.39 setextsub: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setextsub,definition,
% 0.18/0.39 ( setextsub
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( ( subset @ B @ A )
% 0.18/0.39 => ( A = B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(subsetemptysetimpeq_type,type,
% 0.18/0.39 subsetemptysetimpeq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(subsetemptysetimpeq,definition,
% 0.18/0.39 ( subsetemptysetimpeq
% 0.18/0.39 = ( ! [A: $i] :
% 0.18/0.39 ( ( subset @ A @ emptyset )
% 0.18/0.39 => ( A = emptyset ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(powersetI1_type,type,
% 0.18/0.39 powersetI1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(powersetI1,definition,
% 0.18/0.39 ( powersetI1
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( subset @ B @ A )
% 0.18/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(powersetE1_type,type,
% 0.18/0.39 powersetE1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(powersetE1,definition,
% 0.18/0.39 ( powersetE1
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(inPowerset_type,type,
% 0.18/0.39 inPowerset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(inPowerset,definition,
% 0.18/0.39 ( inPowerset
% 0.18/0.39 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(powersetsubset_type,type,
% 0.18/0.39 powersetsubset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(powersetsubset,definition,
% 0.18/0.39 ( powersetsubset
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(sepInPowerset_type,type,
% 0.18/0.39 sepInPowerset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(sepInPowerset,definition,
% 0.18/0.39 ( sepInPowerset
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( in
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 @ ( powerset @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(sepSubset_type,type,
% 0.18/0.39 sepSubset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(sepSubset,definition,
% 0.18/0.39 ( sepSubset
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( subset
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 @ A ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binunion_type,type,
% 0.18/0.39 binunion: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(binunionIL_type,type,
% 0.18/0.39 binunionIL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunionIL,definition,
% 0.18/0.39 ( binunionIL
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(upairset2IR_type,type,
% 0.18/0.39 upairset2IR: $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairset2IR,definition,
% 0.18/0.39 ( upairset2IR
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binunionIR_type,type,
% 0.18/0.39 binunionIR: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunionIR,definition,
% 0.18/0.39 ( binunionIR
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binunionEcases_type,type,
% 0.18/0.39 binunionEcases: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunionEcases,definition,
% 0.18/0.39 ( binunionEcases
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.18/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.18/0.39 => ( ( ( in @ Xx @ A )
% 0.18/0.39 => Xphi )
% 0.18/0.39 => ( ( ( in @ Xx @ B )
% 0.18/0.39 => Xphi )
% 0.18/0.39 => Xphi ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binunionE_type,type,
% 0.18/0.39 binunionE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunionE,definition,
% 0.18/0.39 ( binunionE
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.18/0.39 => ( ( in @ Xx @ A )
% 0.18/0.39 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binunionLsub_type,type,
% 0.18/0.39 binunionLsub: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunionLsub,definition,
% 0.18/0.39 ( binunionLsub
% 0.18/0.39 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binunionRsub_type,type,
% 0.18/0.39 binunionRsub: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binunionRsub,definition,
% 0.18/0.39 ( binunionRsub
% 0.18/0.39 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersect_type,type,
% 0.18/0.39 binintersect: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectI_type,type,
% 0.18/0.39 binintersectI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectI,definition,
% 0.18/0.39 ( binintersectI
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset5_type,type,
% 0.18/0.39 binintersectSubset5: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset5,definition,
% 0.18/0.39 ( binintersectSubset5
% 0.18/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.39 ( ( subset @ C @ A )
% 0.18/0.39 => ( ( subset @ C @ B )
% 0.18/0.39 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectEL_type,type,
% 0.18/0.39 binintersectEL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectEL,definition,
% 0.18/0.39 ( binintersectEL
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.18/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectLsub_type,type,
% 0.18/0.39 binintersectLsub: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectLsub,definition,
% 0.18/0.39 ( binintersectLsub
% 0.18/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset2_type,type,
% 0.18/0.39 binintersectSubset2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset2,definition,
% 0.18/0.39 ( binintersectSubset2
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( ( binintersect @ A @ B )
% 0.18/0.39 = A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset3_type,type,
% 0.18/0.39 binintersectSubset3: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset3,definition,
% 0.18/0.39 ( binintersectSubset3
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( ( binintersect @ A @ B )
% 0.18/0.39 = B )
% 0.18/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectER_type,type,
% 0.18/0.39 binintersectER: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectER,definition,
% 0.18/0.39 ( binintersectER
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.18/0.39 => ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(disjointsetsI1_type,type,
% 0.18/0.39 disjointsetsI1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(disjointsetsI1,definition,
% 0.18/0.39 ( disjointsetsI1
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ~ ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( in @ Xx @ B ) )
% 0.18/0.39 => ( ( binintersect @ A @ B )
% 0.18/0.39 = emptyset ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectRsub_type,type,
% 0.18/0.39 binintersectRsub: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectRsub,definition,
% 0.18/0.39 ( binintersectRsub
% 0.18/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset4_type,type,
% 0.18/0.39 binintersectSubset4: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset4,definition,
% 0.18/0.39 ( binintersectSubset4
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( subset @ B @ A )
% 0.18/0.39 => ( ( binintersect @ A @ B )
% 0.18/0.39 = B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset1_type,type,
% 0.18/0.39 binintersectSubset1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(binintersectSubset1,definition,
% 0.18/0.39 ( binintersectSubset1
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( ( binintersect @ A @ B )
% 0.18/0.39 = A )
% 0.18/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(bs114d_type,type,
% 0.18/0.39 bs114d: $o ).
% 0.18/0.39
% 0.18/0.39 thf(bs114d,definition,
% 0.18/0.39 ( bs114d
% 0.18/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.39 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.18/0.39 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(regular_type,type,
% 0.18/0.39 regular: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminus_type,type,
% 0.18/0.39 setminus: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(setminusI_type,type,
% 0.18/0.39 setminusI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusI,definition,
% 0.18/0.39 ( setminusI
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusEL_type,type,
% 0.18/0.39 setminusEL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusEL,definition,
% 0.18/0.39 ( setminusEL
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusER_type,type,
% 0.18/0.39 setminusER: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusER,definition,
% 0.18/0.39 ( setminusER
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.39 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusSubset2_type,type,
% 0.18/0.39 setminusSubset2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusSubset2,definition,
% 0.18/0.39 ( setminusSubset2
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( subset @ A @ B )
% 0.18/0.39 => ( ( setminus @ A @ B )
% 0.18/0.39 = emptyset ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusERneg_type,type,
% 0.18/0.39 setminusERneg: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusERneg,definition,
% 0.18/0.39 ( setminusERneg
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.39 => ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusELneg_type,type,
% 0.18/0.39 setminusELneg: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusELneg,definition,
% 0.18/0.39 ( setminusELneg
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusILneg_type,type,
% 0.18/0.39 setminusILneg: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusILneg,definition,
% 0.18/0.39 ( setminusILneg
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ~ ( in @ Xx @ A )
% 0.18/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusIRneg_type,type,
% 0.18/0.39 setminusIRneg: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusIRneg,definition,
% 0.18/0.39 ( setminusIRneg
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ B )
% 0.18/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusLsub_type,type,
% 0.18/0.39 setminusLsub: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusLsub,definition,
% 0.18/0.39 ( setminusLsub
% 0.18/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setminusSubset1_type,type,
% 0.18/0.39 setminusSubset1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setminusSubset1,definition,
% 0.18/0.39 ( setminusSubset1
% 0.18/0.39 = ( ! [A: $i,B: $i] :
% 0.18/0.39 ( ( ( setminus @ A @ B )
% 0.18/0.39 = emptyset )
% 0.18/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(symdiff_type,type,
% 0.18/0.39 symdiff: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffE_type,type,
% 0.18/0.39 symdiffE: $o ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffE,definition,
% 0.18/0.39 ( symdiffE
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.18/0.39 => ! [Xphi: $o] :
% 0.18/0.39 ( ( ( in @ Xx @ A )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => Xphi ) )
% 0.18/0.39 => ( ( ~ ( in @ Xx @ A )
% 0.18/0.39 => ( ( in @ Xx @ B )
% 0.18/0.39 => Xphi ) )
% 0.18/0.39 => Xphi ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffI1_type,type,
% 0.18/0.39 symdiffI1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffI1,definition,
% 0.18/0.39 ( symdiffI1
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffI2_type,type,
% 0.18/0.39 symdiffI2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffI2,definition,
% 0.18/0.39 ( symdiffI2
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ~ ( in @ Xx @ A )
% 0.18/0.39 => ( ( in @ Xx @ B )
% 0.18/0.39 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffIneg1_type,type,
% 0.18/0.39 symdiffIneg1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffIneg1,definition,
% 0.18/0.39 ( symdiffIneg1
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ( in @ Xx @ B )
% 0.18/0.39 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffIneg2_type,type,
% 0.18/0.39 symdiffIneg2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(symdiffIneg2,definition,
% 0.18/0.39 ( symdiffIneg2
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ~ ( in @ Xx @ A )
% 0.18/0.39 => ( ~ ( in @ Xx @ B )
% 0.18/0.39 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(iskpair_type,type,
% 0.18/0.39 iskpair: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(secondinupair_type,type,
% 0.18/0.39 secondinupair: $o ).
% 0.18/0.39
% 0.18/0.39 thf(secondinupair,definition,
% 0.18/0.39 ( secondinupair
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairIL_type,type,
% 0.18/0.39 setukpairIL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairIL,definition,
% 0.18/0.39 ( setukpairIL
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairIR_type,type,
% 0.18/0.39 setukpairIR: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairIR,definition,
% 0.18/0.39 ( setukpairIR
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(kpairiskpair_type,type,
% 0.18/0.39 kpairiskpair: $o ).
% 0.18/0.39
% 0.18/0.39 thf(kpairiskpair,definition,
% 0.18/0.39 ( kpairiskpair
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(kpair_type,type,
% 0.18/0.39 kpair: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(kpairp_type,type,
% 0.18/0.39 kpairp: $o ).
% 0.18/0.39
% 0.18/0.39 thf(kpairp,definition,
% 0.18/0.39 ( kpairp
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprod_type,type,
% 0.18/0.39 cartprod: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(singletonsubset_type,type,
% 0.18/0.39 singletonsubset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(singletonsubset,definition,
% 0.18/0.39 ( singletonsubset
% 0.18/0.39 = ( ! [A: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(singletoninpowerset_type,type,
% 0.18/0.39 singletoninpowerset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(singletoninpowerset,definition,
% 0.18/0.39 ( singletoninpowerset
% 0.18/0.39 = ( ! [A: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(singletoninpowunion_type,type,
% 0.18/0.39 singletoninpowunion: $o ).
% 0.18/0.39
% 0.18/0.39 thf(singletoninpowunion,definition,
% 0.18/0.39 ( singletoninpowunion
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(upairset2E_type,type,
% 0.18/0.39 upairset2E: $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairset2E,definition,
% 0.18/0.39 ( upairset2E
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.18/0.39 => ( ( Xz = Xx )
% 0.18/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(upairsubunion_type,type,
% 0.18/0.39 upairsubunion: $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairsubunion,definition,
% 0.18/0.39 ( upairsubunion
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(upairinpowunion_type,type,
% 0.18/0.39 upairinpowunion: $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairinpowunion,definition,
% 0.18/0.39 ( upairinpowunion
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ubforcartprodlem1_type,type,
% 0.18/0.39 ubforcartprodlem1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ubforcartprodlem1,definition,
% 0.18/0.39 ( ubforcartprodlem1
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ubforcartprodlem2_type,type,
% 0.18/0.39 ubforcartprodlem2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ubforcartprodlem2,definition,
% 0.18/0.39 ( ubforcartprodlem2
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ubforcartprodlem3_type,type,
% 0.18/0.39 ubforcartprodlem3: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ubforcartprodlem3,definition,
% 0.18/0.39 ( ubforcartprodlem3
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodpairin_type,type,
% 0.18/0.39 cartprodpairin: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodpairin,definition,
% 0.18/0.39 ( cartprodpairin
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodmempair1_type,type,
% 0.18/0.39 cartprodmempair1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodmempair1,definition,
% 0.18/0.39 ( cartprodmempair1
% 0.18/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.39 => ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ? [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 & ( Xu
% 0.18/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodmempair_type,type,
% 0.18/0.39 cartprodmempair: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodmempair,definition,
% 0.18/0.39 ( cartprodmempair
% 0.18/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.39 => ( iskpair @ Xu ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setunionE2_type,type,
% 0.18/0.39 setunionE2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setunionE2,definition,
% 0.18/0.39 ( setunionE2
% 0.18/0.39 = ( ! [A: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.39 => ? [X: $i] :
% 0.18/0.39 ( ( in @ X @ A )
% 0.18/0.39 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setunionsingleton1_type,type,
% 0.18/0.39 setunionsingleton1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setunionsingleton1,definition,
% 0.18/0.39 ( setunionsingleton1
% 0.18/0.39 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setunionsingleton2_type,type,
% 0.18/0.39 setunionsingleton2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setunionsingleton2,definition,
% 0.18/0.39 ( setunionsingleton2
% 0.18/0.39 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setunionsingleton_type,type,
% 0.18/0.39 setunionsingleton: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setunionsingleton,definition,
% 0.18/0.39 ( setunionsingleton
% 0.18/0.39 = ( ! [Xx: $i] :
% 0.18/0.39 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.18/0.39 = Xx ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(singleton_type,type,
% 0.18/0.39 singleton: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(singleton,definition,
% 0.18/0.39 ( singleton
% 0.18/0.39 = ( ^ [A: $i] :
% 0.18/0.39 ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( A
% 0.18/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(singletonprop_type,type,
% 0.18/0.39 singletonprop: $o ).
% 0.18/0.39
% 0.18/0.39 thf(singletonprop,definition,
% 0.18/0.39 ( singletonprop
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ A )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 => ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) )
% 0.18/0.39 => ( ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( Xphi @ Xx ) )
% 0.18/0.39 => ( singleton
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ex1_type,type,
% 0.18/0.39 ex1: $i > ( $i > $o ) > $o ).
% 0.18/0.39
% 0.18/0.39 thf(ex1,definition,
% 0.18/0.39 ( ex1
% 0.18/0.39 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( singleton
% 0.18/0.39 @ ( dsetconstr @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ex1E1_type,type,
% 0.18/0.39 ex1E1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ex1E1,definition,
% 0.18/0.39 ( ex1E1
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ( ex1 @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ex1I_type,type,
% 0.18/0.39 ex1I: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ex1I,definition,
% 0.18/0.39 ( ex1I
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 => ( ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ A )
% 0.18/0.39 => ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xy = Xx ) ) )
% 0.18/0.39 => ( ex1 @ A
% 0.18/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ex1I2_type,type,
% 0.18/0.39 ex1I2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ex1I2,definition,
% 0.18/0.39 ( ex1I2
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ A )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 => ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) )
% 0.18/0.39 => ( ? [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 & ( Xphi @ Xx ) )
% 0.18/0.39 => ( ex1 @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(singletonsuniq_type,type,
% 0.18/0.39 singletonsuniq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(singletonsuniq,definition,
% 0.18/0.39 ( singletonsuniq
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( ( setadjoin @ Xx @ emptyset )
% 0.18/0.39 = ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(atmost1p_type,type,
% 0.18/0.39 atmost1p: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(atleast2p_type,type,
% 0.18/0.39 atleast2p: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(atmost2p_type,type,
% 0.18/0.39 atmost2p: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairsetp_type,type,
% 0.18/0.39 upairsetp: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjL1_type,type,
% 0.18/0.39 setukpairinjL1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjL1,definition,
% 0.18/0.39 ( setukpairinjL1
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.39 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(kfstsingleton_type,type,
% 0.18/0.39 kfstsingleton: $o ).
% 0.18/0.39
% 0.18/0.39 thf(kfstsingleton,definition,
% 0.18/0.39 ( kfstsingleton
% 0.18/0.39 = ( ! [Xu: $i] :
% 0.18/0.39 ( ( iskpair @ Xu )
% 0.18/0.39 => ( singleton
% 0.18/0.39 @ ( dsetconstr @ ( setunion @ Xu )
% 0.18/0.39 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(theprop_type,type,
% 0.18/0.39 theprop: $o ).
% 0.18/0.39
% 0.18/0.39 thf(theprop,definition,
% 0.18/0.39 ( theprop
% 0.18/0.39 = ( ! [X: $i] :
% 0.18/0.39 ( ( singleton @ X )
% 0.18/0.39 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(kfst_type,type,
% 0.18/0.39 kfst: $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(kfstpairEq_type,type,
% 0.18/0.39 kfstpairEq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(kfstpairEq,definition,
% 0.18/0.39 ( kfstpairEq
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.18/0.39 = Xx ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodfstin_type,type,
% 0.18/0.39 cartprodfstin: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodfstin,definition,
% 0.18/0.39 ( cartprodfstin
% 0.18/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.39 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjL2_type,type,
% 0.18/0.39 setukpairinjL2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjL2,definition,
% 0.18/0.39 ( setukpairinjL2
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjL_type,type,
% 0.18/0.39 setukpairinjL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjL,definition,
% 0.18/0.39 ( setukpairinjL
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.39 ( ( ( kpair @ Xx @ Xy )
% 0.18/0.39 = ( kpair @ Xz @ Xu ) )
% 0.18/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR11_type,type,
% 0.18/0.39 setukpairinjR11: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR11,definition,
% 0.18/0.39 ( setukpairinjR11
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx = Xy )
% 0.18/0.39 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR12_type,type,
% 0.18/0.39 setukpairinjR12: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR12,definition,
% 0.18/0.39 ( setukpairinjR12
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xx = Xy )
% 0.18/0.39 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.39 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR1_type,type,
% 0.18/0.39 setukpairinjR1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR1,definition,
% 0.18/0.39 ( setukpairinjR1
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.39 => ( ( Xz = Xu )
% 0.18/0.39 => ( Xy = Xu ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(upairequniteq_type,type,
% 0.18/0.39 upairequniteq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(upairequniteq,definition,
% 0.18/0.39 ( upairequniteq
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.39 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.39 = ( setadjoin @ Xz @ emptyset ) )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR2_type,type,
% 0.18/0.39 setukpairinjR2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR2,definition,
% 0.18/0.39 ( setukpairinjR2
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.39 => ( Xy = Xu ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR_type,type,
% 0.18/0.39 setukpairinjR: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setukpairinjR,definition,
% 0.18/0.39 ( setukpairinjR
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.39 ( ( ( kpair @ Xx @ Xy )
% 0.18/0.39 = ( kpair @ Xz @ Xu ) )
% 0.18/0.39 => ( Xy = Xu ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ksndsingleton_type,type,
% 0.18/0.39 ksndsingleton: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ksndsingleton,definition,
% 0.18/0.39 ( ksndsingleton
% 0.18/0.39 = ( ! [Xu: $i] :
% 0.18/0.39 ( ( iskpair @ Xu )
% 0.18/0.39 => ( singleton
% 0.18/0.39 @ ( dsetconstr @ ( setunion @ Xu )
% 0.18/0.39 @ ^ [Xx: $i] :
% 0.18/0.39 ( Xu
% 0.18/0.39 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ksnd_type,type,
% 0.18/0.39 ksnd: $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(ksndpairEq_type,type,
% 0.18/0.39 ksndpairEq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ksndpairEq,definition,
% 0.18/0.39 ( ksndpairEq
% 0.18/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.18/0.39 = Xy ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(kpairsurjEq_type,type,
% 0.18/0.39 kpairsurjEq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(kpairsurjEq,definition,
% 0.18/0.39 ( kpairsurjEq
% 0.18/0.39 = ( ! [Xu: $i] :
% 0.18/0.39 ( ( iskpair @ Xu )
% 0.18/0.39 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.18/0.39 = Xu ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodsndin_type,type,
% 0.18/0.39 cartprodsndin: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodsndin,definition,
% 0.18/0.39 ( cartprodsndin
% 0.18/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.39 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodpairmemEL_type,type,
% 0.18/0.39 cartprodpairmemEL: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodpairmemEL,definition,
% 0.18/0.39 ( cartprodpairmemEL
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.18/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodpairmemER_type,type,
% 0.18/0.39 cartprodpairmemER: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodpairmemER,definition,
% 0.18/0.39 ( cartprodpairmemER
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.18/0.39 => ( in @ Xy @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodmempaircEq_type,type,
% 0.18/0.39 cartprodmempaircEq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodmempaircEq,definition,
% 0.18/0.39 ( cartprodmempaircEq
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( ( kpair @ Xx @ Xy )
% 0.18/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodfstpairEq_type,type,
% 0.18/0.39 cartprodfstpairEq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodfstpairEq,definition,
% 0.18/0.39 ( cartprodfstpairEq
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.18/0.39 = Xx ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodsndpairEq_type,type,
% 0.18/0.39 cartprodsndpairEq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodsndpairEq,definition,
% 0.18/0.39 ( cartprodsndpairEq
% 0.18/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.18/0.39 = Xy ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodpairsurjEq_type,type,
% 0.18/0.39 cartprodpairsurjEq: $o ).
% 0.18/0.39
% 0.18/0.39 thf(cartprodpairsurjEq,definition,
% 0.18/0.39 ( cartprodpairsurjEq
% 0.18/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.39 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.18/0.39 = Xu ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(breln_type,type,
% 0.18/0.39 breln: $i > $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(breln,definition,
% 0.18/0.39 ( breln
% 0.18/0.39 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstr_type,type,
% 0.18/0.39 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrI_type,type,
% 0.18/0.39 dpsetconstrI: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrI,definition,
% 0.18/0.39 ( dpsetconstrI
% 0.18/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( ( Xphi @ Xx @ Xy )
% 0.18/0.39 => ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.39 @ ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrSub_type,type,
% 0.18/0.39 dpsetconstrSub: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrSub,definition,
% 0.18/0.39 ( dpsetconstrSub
% 0.18/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.18/0.39 ( subset
% 0.18/0.39 @ ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.18/0.39 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(setOfPairsIsBReln_type,type,
% 0.18/0.39 setOfPairsIsBReln: $o ).
% 0.18/0.39
% 0.18/0.39 thf(setOfPairsIsBReln,definition,
% 0.18/0.39 ( setOfPairsIsBReln
% 0.18/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.18/0.39 ( breln @ A @ B
% 0.18/0.39 @ ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrERa_type,type,
% 0.18/0.39 dpsetconstrERa: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrERa,definition,
% 0.18/0.39 ( dpsetconstrERa
% 0.18/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.39 @ ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.39 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrEL1_type,type,
% 0.18/0.39 dpsetconstrEL1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrEL1,definition,
% 0.18/0.39 ( dpsetconstrEL1
% 0.18/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.39 @ ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrEL2_type,type,
% 0.18/0.39 dpsetconstrEL2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrEL2,definition,
% 0.18/0.39 ( dpsetconstrEL2
% 0.18/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.39 @ ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.39 => ( in @ Xy @ B ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrER_type,type,
% 0.18/0.39 dpsetconstrER: $o ).
% 0.18/0.39
% 0.18/0.39 thf(dpsetconstrER,definition,
% 0.18/0.39 ( dpsetconstrER
% 0.18/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.39 @ ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.39 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(func_type,type,
% 0.18/0.39 func: $i > $i > $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(func,definition,
% 0.18/0.39 ( func
% 0.18/0.39 = ( ^ [A: $i,B: $i,R: $i] :
% 0.18/0.39 ( ( breln @ A @ B @ R )
% 0.18/0.39 & ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( ex1 @ B
% 0.18/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(funcSet_type,type,
% 0.18/0.39 funcSet: $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(funcImageSingleton_type,type,
% 0.18/0.39 funcImageSingleton: $o ).
% 0.18/0.39
% 0.18/0.39 thf(funcImageSingleton,definition,
% 0.18/0.39 ( funcImageSingleton
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.39 ( ( func @ A @ B @ Xf )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( singleton
% 0.18/0.39 @ ( dsetconstr @ B
% 0.18/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(apProp_type,type,
% 0.18/0.39 apProp: $o ).
% 0.18/0.39
% 0.18/0.39 thf(apProp,definition,
% 0.18/0.39 ( apProp
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.39 ( ( func @ A @ B @ Xf )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in
% 0.18/0.39 @ ( setunion
% 0.18/0.39 @ ( dsetconstr @ B
% 0.18/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.18/0.39 @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ap_type,type,
% 0.18/0.39 ap: $i > $i > $i > $i > $i ).
% 0.18/0.39
% 0.18/0.39 thf(ap,definition,
% 0.18/0.39 ( ap
% 0.18/0.39 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 0.18/0.39 ( setunion
% 0.18/0.39 @ ( dsetconstr @ B
% 0.18/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(app_type,type,
% 0.18/0.39 app: $o ).
% 0.18/0.39
% 0.18/0.39 thf(app,definition,
% 0.18/0.39 ( app
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.39 ( ( func @ A @ B @ Xf )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(infuncsetfunc_type,type,
% 0.18/0.39 infuncsetfunc: $o ).
% 0.18/0.39
% 0.18/0.39 thf(infuncsetfunc,definition,
% 0.18/0.39 ( infuncsetfunc
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.39 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.18/0.39 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ap2p_type,type,
% 0.18/0.39 ap2p: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ap2p,definition,
% 0.18/0.39 ( ap2p
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.39 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(funcinfuncset_type,type,
% 0.18/0.39 funcinfuncset: $o ).
% 0.18/0.39
% 0.18/0.39 thf(funcinfuncset,definition,
% 0.18/0.39 ( funcinfuncset
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.39 ( ( func @ A @ B @ Xf )
% 0.18/0.39 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(lamProp_type,type,
% 0.18/0.39 lamProp: $o ).
% 0.18/0.39
% 0.18/0.39 thf(lamProp,definition,
% 0.18/0.39 ( lamProp
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.18/0.39 => ( func @ A @ B
% 0.18/0.39 @ ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xf @ Xx )
% 0.18/0.39 = Xy ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(lam_type,type,
% 0.18/0.39 lam: $i > $i > ( $i > $i ) > $i ).
% 0.18/0.39
% 0.18/0.39 thf(lam,definition,
% 0.18/0.39 ( lam
% 0.18/0.39 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.18/0.39 ( dpsetconstr @ A @ B
% 0.18/0.39 @ ^ [Xx: $i,Xy: $i] :
% 0.18/0.39 ( ( Xf @ Xx )
% 0.18/0.39 = Xy ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(lamp_type,type,
% 0.18/0.39 lamp: $o ).
% 0.18/0.39
% 0.18/0.39 thf(lamp,definition,
% 0.18/0.39 ( lamp
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.18/0.39 => ( func @ A @ B
% 0.18/0.39 @ ( lam @ A @ B
% 0.18/0.39 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(lam2p_type,type,
% 0.18/0.39 lam2p: $o ).
% 0.18/0.39
% 0.18/0.39 thf(lam2p,definition,
% 0.18/0.39 ( lam2p
% 0.18/0.39 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.18/0.39 => ( in
% 0.18/0.39 @ ( lam @ A @ B
% 0.18/0.39 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.18/0.39 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(brelnall1_type,type,
% 0.18/0.39 brelnall1: $o ).
% 0.18/0.39
% 0.18/0.39 thf(brelnall1,definition,
% 0.18/0.39 ( brelnall1
% 0.18/0.39 = ( ! [A: $i,B: $i,R: $i] :
% 0.18/0.39 ( ( breln @ A @ B @ R )
% 0.18/0.39 => ! [Xphi: $i > $o] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.39 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ R )
% 0.18/0.39 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(brelnall2_type,type,
% 0.18/0.39 brelnall2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(brelnall2,definition,
% 0.18/0.39 ( brelnall2
% 0.18/0.39 = ( ! [A: $i,B: $i,R: $i] :
% 0.18/0.39 ( ( breln @ A @ B @ R )
% 0.18/0.39 => ! [Xphi: $i > $o] :
% 0.18/0.39 ( ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ B )
% 0.18/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.18/0.39 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ R )
% 0.18/0.39 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(ex1E2_type,type,
% 0.18/0.39 ex1E2: $o ).
% 0.18/0.39
% 0.18/0.39 thf(ex1E2,definition,
% 0.18/0.39 ( ex1E2
% 0.18/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.39 ( ( ex1 @ A
% 0.18/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ! [Xy: $i] :
% 0.18/0.39 ( ( in @ Xy @ A )
% 0.18/0.39 => ( ( Xphi @ Xx )
% 0.18/0.39 => ( ( Xphi @ Xy )
% 0.18/0.39 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(funcGraphProp1,conjecture,
% 0.18/0.39 ( setextAx
% 0.18/0.39 => ( emptysetAx
% 0.18/0.39 => ( setadjoinAx
% 0.18/0.39 => ( powersetAx
% 0.18/0.39 => ( setunionAx
% 0.18/0.39 => ( omega0Ax
% 0.18/0.39 => ( omegaSAx
% 0.18/0.39 => ( omegaIndAx
% 0.18/0.39 => ( replAx
% 0.18/0.39 => ( foundationAx
% 0.18/0.39 => ( wellorderingAx
% 0.18/0.39 => ( descrp
% 0.18/0.39 => ( dsetconstrI
% 0.18/0.39 => ( dsetconstrEL
% 0.18/0.39 => ( dsetconstrER
% 0.18/0.39 => ( exuE1
% 0.18/0.39 => ( prop2setE
% 0.18/0.39 => ( emptysetE
% 0.18/0.39 => ( emptysetimpfalse
% 0.18/0.39 => ( notinemptyset
% 0.18/0.39 => ( exuE3e
% 0.18/0.39 => ( setext
% 0.18/0.39 => ( emptyI
% 0.18/0.39 => ( noeltsimpempty
% 0.18/0.39 => ( setbeta
% 0.18/0.39 => ( nonemptyE1
% 0.18/0.39 => ( nonemptyI
% 0.18/0.39 => ( nonemptyI1
% 0.18/0.39 => ( setadjoinIL
% 0.18/0.39 => ( emptyinunitempty
% 0.18/0.39 => ( setadjoinIR
% 0.18/0.39 => ( setadjoinE
% 0.18/0.39 => ( setadjoinOr
% 0.18/0.39 => ( setoftrueEq
% 0.18/0.39 => ( powersetI
% 0.18/0.39 => ( emptyinPowerset
% 0.18/0.39 => ( emptyInPowerset
% 0.18/0.39 => ( powersetE
% 0.18/0.39 => ( setunionI
% 0.18/0.39 => ( setunionE
% 0.18/0.39 => ( subPowSU
% 0.18/0.39 => ( exuE2
% 0.18/0.39 => ( nonemptyImpWitness
% 0.18/0.39 => ( uniqinunit
% 0.18/0.39 => ( notinsingleton
% 0.18/0.39 => ( eqinunit
% 0.18/0.39 => ( singletonsswitch
% 0.18/0.39 => ( upairsetE
% 0.18/0.39 => ( upairsetIL
% 0.18/0.39 => ( upairsetIR
% 0.18/0.39 => ( emptyE1
% 0.18/0.39 => ( vacuousDall
% 0.18/0.39 => ( quantDeMorgan1
% 0.18/0.39 => ( quantDeMorgan2
% 0.18/0.39 => ( quantDeMorgan3
% 0.18/0.39 => ( quantDeMorgan4
% 0.18/0.39 => ( prop2setI
% 0.18/0.39 => ( prop2set2propI
% 0.18/0.39 => ( notdexE
% 0.18/0.39 => ( notdallE
% 0.18/0.39 => ( exuI1
% 0.18/0.39 => ( exuI3
% 0.18/0.39 => ( exuI2
% 0.18/0.39 => ( inCongP
% 0.18/0.39 => ( in__Cong
% 0.18/0.39 => ( exuE3u
% 0.18/0.39 => ( exu__Cong
% 0.18/0.39 => ( emptyset__Cong
% 0.18/0.39 => ( setadjoin__Cong
% 0.18/0.39 => ( powerset__Cong
% 0.18/0.39 => ( setunion__Cong
% 0.18/0.39 => ( omega__Cong
% 0.18/0.39 => ( exuEu
% 0.18/0.39 => ( descr__Cong
% 0.18/0.39 => ( dsetconstr__Cong
% 0.18/0.39 => ( subsetI1
% 0.18/0.39 => ( eqimpsubset2
% 0.18/0.39 => ( eqimpsubset1
% 0.18/0.39 => ( subsetI2
% 0.18/0.39 => ( emptysetsubset
% 0.18/0.39 => ( subsetE
% 0.18/0.39 => ( subsetE2
% 0.18/0.39 => ( notsubsetI
% 0.18/0.39 => ( notequalI1
% 0.18/0.39 => ( notequalI2
% 0.18/0.39 => ( subsetRefl
% 0.18/0.39 => ( subsetTrans
% 0.18/0.39 => ( setadjoinSub
% 0.18/0.39 => ( setadjoinSub2
% 0.18/0.39 => ( subset2powerset
% 0.18/0.39 => ( setextsub
% 0.18/0.39 => ( subsetemptysetimpeq
% 0.18/0.39 => ( powersetI1
% 0.18/0.39 => ( powersetE1
% 0.18/0.39 => ( inPowerset
% 0.18/0.39 => ( powersetsubset
% 0.18/0.39 => ( sepInPowerset
% 0.18/0.39 => ( sepSubset
% 0.18/0.39 => ( binunionIL
% 0.18/0.39 => ( upairset2IR
% 0.18/0.39 => ( binunionIR
% 0.18/0.39 => ( binunionEcases
% 0.18/0.39 => ( binunionE
% 0.18/0.39 => ( binunionLsub
% 0.18/0.39 => ( binunionRsub
% 0.18/0.39 => ( binintersectI
% 0.18/0.39 => ( binintersectSubset5
% 0.18/0.39 => ( binintersectEL
% 0.18/0.39 => ( binintersectLsub
% 0.18/0.39 => ( binintersectSubset2
% 0.18/0.39 => ( binintersectSubset3
% 0.18/0.39 => ( binintersectER
% 0.18/0.39 => ( disjointsetsI1
% 0.18/0.39 => ( binintersectRsub
% 0.18/0.39 => ( binintersectSubset4
% 0.18/0.39 => ( binintersectSubset1
% 0.18/0.39 => ( bs114d
% 0.18/0.39 => ( setminusI
% 0.18/0.39 => ( setminusEL
% 0.18/0.39 => ( setminusER
% 0.18/0.39 => ( setminusSubset2
% 0.18/0.39 => ( setminusERneg
% 0.18/0.39 => ( setminusELneg
% 0.18/0.39 => ( setminusILneg
% 0.18/0.39 => ( setminusIRneg
% 0.18/0.39 => ( setminusLsub
% 0.18/0.39 => ( setminusSubset1
% 0.18/0.39 => ( symdiffE
% 0.18/0.39 => ( symdiffI1
% 0.18/0.39 => ( symdiffI2
% 0.18/0.39 => ( symdiffIneg1
% 0.18/0.39 => ( symdiffIneg2
% 0.18/0.39 => ( secondinupair
% 0.18/0.39 => ( setukpairIL
% 0.18/0.39 => ( setukpairIR
% 0.18/0.39 => ( kpairiskpair
% 0.18/0.39 => ( kpairp
% 0.18/0.39 => ( singletonsubset
% 0.18/0.39 => ( singletoninpowerset
% 0.18/0.39 => ( singletoninpowunion
% 0.18/0.39 => ( upairset2E
% 0.18/0.39 => ( upairsubunion
% 0.18/0.39 => ( upairinpowunion
% 0.18/0.39 => ( ubforcartprodlem1
% 0.18/0.39 => ( ubforcartprodlem2
% 0.18/0.39 => ( ubforcartprodlem3
% 0.18/0.39 => ( cartprodpairin
% 0.18/0.39 => ( cartprodmempair1
% 0.18/0.39 => ( cartprodmempair
% 0.18/0.39 => ( setunionE2
% 0.18/0.39 => ( setunionsingleton1
% 0.18/0.39 => ( setunionsingleton2
% 0.18/0.39 => ( setunionsingleton
% 0.18/0.39 => ( singletonprop
% 0.18/0.39 => ( ex1E1
% 0.18/0.39 => ( ex1I
% 0.18/0.39 => ( ex1I2
% 0.18/0.39 => ( singletonsuniq
% 0.18/0.39 => ( setukpairinjL1
% 0.18/0.39 => ( kfstsingleton
% 0.18/0.39 => ( theprop
% 0.18/0.39 => ( kfstpairEq
% 0.18/0.39 => ( cartprodfstin
% 0.18/0.39 => ( setukpairinjL2
% 0.18/0.39 => ( setukpairinjL
% 0.18/0.39 => ( setukpairinjR11
% 0.18/0.39 => ( setukpairinjR12
% 0.18/0.39 => ( setukpairinjR1
% 0.18/0.39 => ( upairequniteq
% 0.18/0.39 => ( setukpairinjR2
% 0.18/0.39 => ( setukpairinjR
% 0.18/0.39 => ( ksndsingleton
% 0.18/0.39 => ( ksndpairEq
% 0.18/0.39 => ( kpairsurjEq
% 0.18/0.39 => ( cartprodsndin
% 0.18/0.39 => ( cartprodpairmemEL
% 0.18/0.39 => ( cartprodpairmemER
% 0.18/0.39 => ( cartprodmempaircEq
% 0.18/0.39 => ( cartprodfstpairEq
% 0.18/0.39 => ( cartprodsndpairEq
% 0.18/0.39 => ( cartprodpairsurjEq
% 0.18/0.39 => ( dpsetconstrI
% 0.18/0.39 => ( dpsetconstrSub
% 0.18/0.39 => ( setOfPairsIsBReln
% 0.18/0.39 => ( dpsetconstrERa
% 0.18/0.39 => ( dpsetconstrEL1
% 0.18/0.39 => ( dpsetconstrEL2
% 0.18/0.39 => ( dpsetconstrER
% 0.18/0.39 => ( funcImageSingleton
% 0.18/0.39 => ( apProp
% 0.18/0.39 => ( app
% 0.18/0.39 => ( infuncsetfunc
% 0.18/0.39 => ( ap2p
% 0.18/0.39 => ( funcinfuncset
% 0.18/0.39 => ( lamProp
% 0.18/0.39 => ( lamp
% 0.18/0.39 => ( lam2p
% 0.18/0.39 => ( brelnall1
% 0.18/0.39 => ( brelnall2
% 0.18/0.39 => ( ex1E2
% 0.18/0.39 => ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.39 ( ( func @ A @ B @ Xf )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( in @ Xx @ A )
% 0.18/0.39 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 2.62/1.56 ---- Embedded in THF ---
% 2.62/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.62/1.56 %%% Generated on Tue Feb 24 12:30:40 EST 2026
% 2.62/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.62/1.56 %%% Logic specification used:
% 2.62/1.56 %%% thf(spec, logic, $$dhol).
% 2.62/1.56
% 2.62/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2DTF25541.p
% See solution above
% 2.62/1.56 ------------------------
% 2.80/1.60 ---- Cleaned THF ---
% 2.80/1.61 thf(in_type,type,
% 2.80/1.61 in: $i > $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(exu_type,type,
% 2.80/1.61 exu: ( $i > $o ) > $o ).
% 2.80/1.61
% 2.80/1.61 thf(exu,definition,
% 2.80/1.61 ( exu
% 2.80/1.61 = ( ^ [Xphi: $i > $o] :
% 2.80/1.61 ? [Xx: $i] :
% 2.80/1.61 ( ( Xphi @ Xx )
% 2.80/1.61 & ! [Xy: $i] :
% 2.80/1.61 ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setextAx_type,type,
% 2.80/1.61 setextAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setextAx,definition,
% 2.80/1.61 ( setextAx
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 <=> ( in @ Xx @ B ) )
% 2.80/1.61 => ( A = B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptyset_type,type,
% 2.80/1.61 emptyset: $i ).
% 2.80/1.61
% 2.80/1.61 thf(emptysetAx_type,type,
% 2.80/1.61 emptysetAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptysetAx,definition,
% 2.80/1.61 ( emptysetAx
% 2.80/1.61 = ( ! [Xx: $i] :
% 2.80/1.61 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoin_type,type,
% 2.80/1.61 setadjoin: $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinAx_type,type,
% 2.80/1.61 setadjoinAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinAx,definition,
% 2.80/1.61 ( setadjoinAx
% 2.80/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.80/1.61 <=> ( ( Xy = Xx )
% 2.80/1.61 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(powerset_type,type,
% 2.80/1.61 powerset: $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(powersetAx_type,type,
% 2.80/1.61 powersetAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(powersetAx,definition,
% 2.80/1.61 ( powersetAx
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( in @ B @ ( powerset @ A ) )
% 2.80/1.61 <=> ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setunion_type,type,
% 2.80/1.61 setunion: $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(setunionAx_type,type,
% 2.80/1.61 setunionAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setunionAx,definition,
% 2.80/1.61 ( setunionAx
% 2.80/1.61 = ( ! [A: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 2.80/1.61 <=> ? [B: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 & ( in @ B @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(omega_type,type,
% 2.80/1.61 omega: $i ).
% 2.80/1.61
% 2.80/1.61 thf(omega0Ax_type,type,
% 2.80/1.61 omega0Ax: $o ).
% 2.80/1.61
% 2.80/1.61 thf(omega0Ax,definition,
% 2.80/1.61 ( omega0Ax
% 2.80/1.61 = ( in @ emptyset @ omega ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(omegaSAx_type,type,
% 2.80/1.61 omegaSAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(omegaSAx,definition,
% 2.80/1.61 ( omegaSAx
% 2.80/1.61 = ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ omega )
% 2.80/1.61 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(omegaIndAx_type,type,
% 2.80/1.61 omegaIndAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(omegaIndAx,definition,
% 2.80/1.61 ( omegaIndAx
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ( ( in @ emptyset @ A )
% 2.80/1.61 & ! [Xx: $i] :
% 2.80/1.61 ( ( ( in @ Xx @ omega )
% 2.80/1.61 & ( in @ Xx @ A ) )
% 2.80/1.61 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ omega )
% 2.80/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(replAx_type,type,
% 2.80/1.61 replAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(replAx,definition,
% 2.80/1.61 ( replAx
% 2.80/1.61 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( exu
% 2.80/1.61 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.80/1.61 => ? [B: $i] :
% 2.80/1.61 ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 <=> ? [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ A )
% 2.80/1.61 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(foundationAx_type,type,
% 2.80/1.61 foundationAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(foundationAx,definition,
% 2.80/1.61 ( foundationAx
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.80/1.61 => ? [B: $i] :
% 2.80/1.61 ( ( in @ B @ A )
% 2.80/1.61 & ~ ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(wellorderingAx_type,type,
% 2.80/1.61 wellorderingAx: $o ).
% 2.80/1.61
% 2.80/1.61 thf(wellorderingAx,definition,
% 2.80/1.61 ( wellorderingAx
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ? [B: $i] :
% 2.80/1.61 ( ! [C: $i] :
% 2.80/1.61 ( ( in @ C @ B )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ C )
% 2.80/1.61 => ( in @ Xx @ A ) ) )
% 2.80/1.61 & ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( ( in @ Xx @ A )
% 2.80/1.61 & ( in @ Xy @ A ) )
% 2.80/1.61 => ( ! [C: $i] :
% 2.80/1.61 ( ( in @ C @ B )
% 2.80/1.61 => ( ( in @ Xx @ C )
% 2.80/1.61 <=> ( in @ Xy @ C ) ) )
% 2.80/1.61 => ( Xx = Xy ) ) )
% 2.80/1.61 & ! [C: $i,D: $i] :
% 2.80/1.61 ( ( ( in @ C @ B )
% 2.80/1.61 & ( in @ D @ B ) )
% 2.80/1.61 => ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ C )
% 2.80/1.61 => ( in @ Xx @ D ) )
% 2.80/1.61 | ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ D )
% 2.80/1.61 => ( in @ Xx @ C ) ) ) )
% 2.80/1.61 & ! [C: $i] :
% 2.80/1.61 ( ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ C )
% 2.80/1.61 => ( in @ Xx @ A ) )
% 2.80/1.61 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.80/1.61 => ? [D: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ D @ B )
% 2.80/1.61 & ( in @ Xx @ C )
% 2.80/1.61 & ~ ? [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ D )
% 2.80/1.61 & ( in @ Xy @ C ) )
% 2.80/1.61 & ! [E: $i] :
% 2.80/1.61 ( ( in @ E @ B )
% 2.80/1.61 => ( ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ E )
% 2.80/1.61 => ( in @ Xy @ D ) )
% 2.80/1.61 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(descr_type,type,
% 2.80/1.61 descr: ( $i > $o ) > $i ).
% 2.80/1.61
% 2.80/1.61 thf(descrp_type,type,
% 2.80/1.61 descrp: $o ).
% 2.80/1.61
% 2.80/1.61 thf(descrp,definition,
% 2.80/1.61 ( descrp
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ( Xphi
% 2.80/1.61 @ ( descr
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstr_type,type,
% 2.80/1.61 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstrI_type,type,
% 2.80/1.61 dsetconstrI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstrI,definition,
% 2.80/1.61 ( dsetconstrI
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 => ( in @ Xx
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstrEL_type,type,
% 2.80/1.61 dsetconstrEL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstrEL,definition,
% 2.80/1.61 ( dsetconstrEL
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.80/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstrER_type,type,
% 2.80/1.61 dsetconstrER: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstrER,definition,
% 2.80/1.61 ( dsetconstrER
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.80/1.61 => ( Xphi @ Xx ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exuE1_type,type,
% 2.80/1.61 exuE1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exuE1,definition,
% 2.80/1.61 ( exuE1
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ? [Xx: $i] :
% 2.80/1.61 ( ( Xphi @ Xx )
% 2.80/1.61 & ! [Xy: $i] :
% 2.80/1.61 ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(prop2set_type,type,
% 2.80/1.61 prop2set: $o > $i ).
% 2.80/1.61
% 2.80/1.61 thf(prop2setE_type,type,
% 2.80/1.61 prop2setE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(prop2setE,definition,
% 2.80/1.61 ( prop2setE
% 2.80/1.61 = ( ! [Xphi: $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.80/1.61 => Xphi ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptysetE_type,type,
% 2.80/1.61 emptysetE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptysetE,definition,
% 2.80/1.61 ( emptysetE
% 2.80/1.61 = ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ emptyset )
% 2.80/1.61 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptysetimpfalse_type,type,
% 2.80/1.61 emptysetimpfalse: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptysetimpfalse,definition,
% 2.80/1.61 ( emptysetimpfalse
% 2.80/1.61 = ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ emptyset )
% 2.80/1.61 => $false ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(notinemptyset_type,type,
% 2.80/1.61 notinemptyset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(notinemptyset,definition,
% 2.80/1.61 ( notinemptyset
% 2.80/1.61 = ( ! [Xx: $i] :
% 2.80/1.61 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exuE3e_type,type,
% 2.80/1.61 exuE3e: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exuE3e,definition,
% 2.80/1.61 ( exuE3e
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setext_type,type,
% 2.80/1.61 setext: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setext,definition,
% 2.80/1.61 ( setext
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ Xx @ B ) )
% 2.80/1.61 => ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ A ) )
% 2.80/1.61 => ( A = B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptyI_type,type,
% 2.80/1.61 emptyI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptyI,definition,
% 2.80/1.61 ( emptyI
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ~ ( in @ Xx @ A )
% 2.80/1.61 => ( A = emptyset ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(noeltsimpempty_type,type,
% 2.80/1.61 noeltsimpempty: $o ).
% 2.80/1.61
% 2.80/1.61 thf(noeltsimpempty,definition,
% 2.80/1.61 ( noeltsimpempty
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ~ ( in @ Xx @ A )
% 2.80/1.61 => ( A = emptyset ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setbeta_type,type,
% 2.80/1.61 setbeta: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setbeta,definition,
% 2.80/1.61 ( setbeta
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ( in @ Xx
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.80/1.61 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(nonempty_type,type,
% 2.80/1.61 nonempty: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(nonempty,definition,
% 2.80/1.61 ( nonempty
% 2.80/1.61 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(nonemptyE1_type,type,
% 2.80/1.61 nonemptyE1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(nonemptyE1,definition,
% 2.80/1.61 ( nonemptyE1
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ( nonempty @ A )
% 2.80/1.61 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(nonemptyI_type,type,
% 2.80/1.61 nonemptyI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(nonemptyI,definition,
% 2.80/1.61 ( nonemptyI
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 => ( nonempty
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(nonemptyI1_type,type,
% 2.80/1.61 nonemptyI1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(nonemptyI1,definition,
% 2.80/1.61 ( nonemptyI1
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.80/1.61 => ( nonempty @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinIL_type,type,
% 2.80/1.61 setadjoinIL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinIL,definition,
% 2.80/1.61 ( setadjoinIL
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptyinunitempty_type,type,
% 2.80/1.61 emptyinunitempty: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptyinunitempty,definition,
% 2.80/1.61 ( emptyinunitempty
% 2.80/1.61 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinIR_type,type,
% 2.80/1.61 setadjoinIR: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinIR,definition,
% 2.80/1.61 ( setadjoinIR
% 2.80/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ A )
% 2.80/1.61 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinE_type,type,
% 2.80/1.61 setadjoinE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinE,definition,
% 2.80/1.61 ( setadjoinE
% 2.80/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.80/1.61 => ! [Xphi: $o] :
% 2.80/1.61 ( ( ( Xy = Xx )
% 2.80/1.61 => Xphi )
% 2.80/1.61 => ( ( ( in @ Xy @ A )
% 2.80/1.61 => Xphi )
% 2.80/1.61 => Xphi ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinOr_type,type,
% 2.80/1.61 setadjoinOr: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinOr,definition,
% 2.80/1.61 ( setadjoinOr
% 2.80/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.80/1.61 => ( ( Xy = Xx )
% 2.80/1.61 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setoftrueEq_type,type,
% 2.80/1.61 setoftrueEq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setoftrueEq,definition,
% 2.80/1.61 ( setoftrueEq
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xx: $i] : $true )
% 2.80/1.61 = A ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(powersetI_type,type,
% 2.80/1.61 powersetI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(powersetI,definition,
% 2.80/1.61 ( powersetI
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ A ) )
% 2.80/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptyinPowerset_type,type,
% 2.80/1.61 emptyinPowerset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptyinPowerset,definition,
% 2.80/1.61 ( emptyinPowerset
% 2.80/1.61 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptyInPowerset_type,type,
% 2.80/1.61 emptyInPowerset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptyInPowerset,definition,
% 2.80/1.61 ( emptyInPowerset
% 2.80/1.61 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(powersetE_type,type,
% 2.80/1.61 powersetE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(powersetE,definition,
% 2.80/1.61 ( powersetE
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ B @ ( powerset @ A ) )
% 2.80/1.61 => ( ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setunionI_type,type,
% 2.80/1.61 setunionI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setunionI,definition,
% 2.80/1.61 ( setunionI
% 2.80/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 => ( ( in @ B @ A )
% 2.80/1.61 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setunionE_type,type,
% 2.80/1.61 setunionE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setunionE,definition,
% 2.80/1.61 ( setunionE
% 2.80/1.61 = ( ! [A: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 2.80/1.61 => ! [Xphi: $o] :
% 2.80/1.61 ( ! [B: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 => ( ( in @ B @ A )
% 2.80/1.61 => Xphi ) )
% 2.80/1.61 => Xphi ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subPowSU_type,type,
% 2.80/1.61 subPowSU: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subPowSU,definition,
% 2.80/1.61 ( subPowSU
% 2.80/1.61 = ( ! [A: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exuE2_type,type,
% 2.80/1.61 exuE2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exuE2,definition,
% 2.80/1.61 ( exuE2
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ? [Xx: $i] :
% 2.80/1.61 ! [Xy: $i] :
% 2.80/1.61 ( ( Xphi @ Xy )
% 2.80/1.61 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(nonemptyImpWitness_type,type,
% 2.80/1.61 nonemptyImpWitness: $o ).
% 2.80/1.61
% 2.80/1.61 thf(nonemptyImpWitness,definition,
% 2.80/1.61 ( nonemptyImpWitness
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ( nonempty @ A )
% 2.80/1.61 => ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & $true ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(uniqinunit_type,type,
% 2.80/1.61 uniqinunit: $o ).
% 2.80/1.61
% 2.80/1.61 thf(uniqinunit,definition,
% 2.80/1.61 ( uniqinunit
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(notinsingleton_type,type,
% 2.80/1.61 notinsingleton: $o ).
% 2.80/1.61
% 2.80/1.61 thf(notinsingleton,definition,
% 2.80/1.61 ( notinsingleton
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx != Xy )
% 2.80/1.61 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(eqinunit_type,type,
% 2.80/1.61 eqinunit: $o ).
% 2.80/1.61
% 2.80/1.61 thf(eqinunit,definition,
% 2.80/1.61 ( eqinunit
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx = Xy )
% 2.80/1.61 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(singletonsswitch_type,type,
% 2.80/1.61 singletonsswitch: $o ).
% 2.80/1.61
% 2.80/1.61 thf(singletonsswitch,definition,
% 2.80/1.61 ( singletonsswitch
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.80/1.61 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(upairsetE_type,type,
% 2.80/1.61 upairsetE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairsetE,definition,
% 2.80/1.61 ( upairsetE
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.80/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.80/1.61 => ( ( Xz = Xx )
% 2.80/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(upairsetIL_type,type,
% 2.80/1.61 upairsetIL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairsetIL,definition,
% 2.80/1.61 ( upairsetIL
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(upairsetIR_type,type,
% 2.80/1.61 upairsetIR: $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairsetIR,definition,
% 2.80/1.61 ( upairsetIR
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptyE1_type,type,
% 2.80/1.61 emptyE1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptyE1,definition,
% 2.80/1.61 ( emptyE1
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( Xphi @ Xx ) )
% 2.80/1.61 => ( ( ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 = emptyset )
% 2.80/1.61 => $false ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(vacuousDall_type,type,
% 2.80/1.61 vacuousDall: $o ).
% 2.80/1.61
% 2.80/1.61 thf(vacuousDall,definition,
% 2.80/1.61 ( vacuousDall
% 2.80/1.61 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ emptyset )
% 2.80/1.61 => ( Xphi @ Xx ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(quantDeMorgan1_type,type,
% 2.80/1.61 quantDeMorgan1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(quantDeMorgan1,definition,
% 2.80/1.61 ( quantDeMorgan1
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ~ ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( Xphi @ Xx ) )
% 2.80/1.61 => ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(quantDeMorgan2_type,type,
% 2.80/1.61 quantDeMorgan2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(quantDeMorgan2,definition,
% 2.80/1.61 ( quantDeMorgan2
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ~ ( Xphi @ Xx ) )
% 2.80/1.61 => ~ ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(quantDeMorgan3_type,type,
% 2.80/1.61 quantDeMorgan3: $o ).
% 2.80/1.61
% 2.80/1.61 thf(quantDeMorgan3,definition,
% 2.80/1.61 ( quantDeMorgan3
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ~ ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( Xphi @ Xx ) )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(quantDeMorgan4_type,type,
% 2.80/1.61 quantDeMorgan4: $o ).
% 2.80/1.61
% 2.80/1.61 thf(quantDeMorgan4,definition,
% 2.80/1.61 ( quantDeMorgan4
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ~ ( Xphi @ Xx ) )
% 2.80/1.61 => ~ ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(prop2setI_type,type,
% 2.80/1.61 prop2setI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(prop2setI,definition,
% 2.80/1.61 ( prop2setI
% 2.80/1.61 = ( ! [Xphi: $o] :
% 2.80/1.61 ( Xphi
% 2.80/1.61 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(set2prop_type,type,
% 2.80/1.61 set2prop: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(prop2set2propI_type,type,
% 2.80/1.61 prop2set2propI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(prop2set2propI,definition,
% 2.80/1.61 ( prop2set2propI
% 2.80/1.61 = ( ! [Xphi: $o] :
% 2.80/1.61 ( Xphi
% 2.80/1.61 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(notdexE_type,type,
% 2.80/1.61 notdexE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(notdexE,definition,
% 2.80/1.61 ( notdexE
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ~ ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( Xphi @ Xx ) )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(notdallE_type,type,
% 2.80/1.61 notdallE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(notdallE,definition,
% 2.80/1.61 ( notdallE
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ~ ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( Xphi @ Xx ) )
% 2.80/1.61 => ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exuI1_type,type,
% 2.80/1.61 exuI1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exuI1,definition,
% 2.80/1.61 ( exuI1
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ? [Xx: $i] :
% 2.80/1.61 ( ( Xphi @ Xx )
% 2.80/1.61 & ! [Xy: $i] :
% 2.80/1.61 ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) )
% 2.80/1.61 => ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exuI3_type,type,
% 2.80/1.61 exuI3: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exuI3,definition,
% 2.80/1.61 ( exuI3
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.80/1.61 => ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xphi @ Xx )
% 2.80/1.61 => ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) )
% 2.80/1.61 => ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exuI2_type,type,
% 2.80/1.61 exuI2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exuI2,definition,
% 2.80/1.61 ( exuI2
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ? [Xx: $i] :
% 2.80/1.61 ! [Xy: $i] :
% 2.80/1.61 ( ( Xphi @ Xy )
% 2.80/1.61 <=> ( Xy = Xx ) )
% 2.80/1.61 => ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(inCongP_type,type,
% 2.80/1.61 inCongP: $o ).
% 2.80/1.61
% 2.80/1.61 thf(inCongP,definition,
% 2.80/1.61 ( inCongP
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( A = B )
% 2.80/1.61 => ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx = Xy )
% 2.80/1.61 => ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(in__Cong_type,type,
% 2.80/1.61 in__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(in__Cong,definition,
% 2.80/1.61 ( in__Cong
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( A = B )
% 2.80/1.61 => ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx = Xy )
% 2.80/1.61 => ( ( in @ Xx @ A )
% 2.80/1.61 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exuE3u_type,type,
% 2.80/1.61 exuE3u: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exuE3u,definition,
% 2.80/1.61 ( exuE3u
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xphi @ Xx )
% 2.80/1.61 => ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exu__Cong_type,type,
% 2.80/1.61 exu__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exu__Cong,definition,
% 2.80/1.61 ( exu__Cong
% 2.80/1.61 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.80/1.61 ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx = Xy )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 <=> ( Xpsi @ Xy ) ) )
% 2.80/1.61 => ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 <=> ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptyset__Cong_type,type,
% 2.80/1.61 emptyset__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptyset__Cong,definition,
% 2.80/1.61 ( emptyset__Cong
% 2.80/1.61 = ( emptyset = emptyset ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoin__Cong_type,type,
% 2.80/1.61 setadjoin__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoin__Cong,definition,
% 2.80/1.61 ( setadjoin__Cong
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx = Xy )
% 2.80/1.61 => ! [Xz: $i,Xu: $i] :
% 2.80/1.61 ( ( Xz = Xu )
% 2.80/1.61 => ( ( setadjoin @ Xx @ Xz )
% 2.80/1.61 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(powerset__Cong_type,type,
% 2.80/1.61 powerset__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(powerset__Cong,definition,
% 2.80/1.61 ( powerset__Cong
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( A = B )
% 2.80/1.61 => ( ( powerset @ A )
% 2.80/1.61 = ( powerset @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setunion__Cong_type,type,
% 2.80/1.61 setunion__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setunion__Cong,definition,
% 2.80/1.61 ( setunion__Cong
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( A = B )
% 2.80/1.61 => ( ( setunion @ A )
% 2.80/1.61 = ( setunion @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(omega__Cong_type,type,
% 2.80/1.61 omega__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(omega__Cong,definition,
% 2.80/1.61 ( omega__Cong
% 2.80/1.61 = ( omega = omega ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(exuEu_type,type,
% 2.80/1.61 exuEu: $o ).
% 2.80/1.61
% 2.80/1.61 thf(exuEu,definition,
% 2.80/1.61 ( exuEu
% 2.80/1.61 = ( ! [Xphi: $i > $o] :
% 2.80/1.61 ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xphi @ Xx )
% 2.80/1.61 => ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(descr__Cong_type,type,
% 2.80/1.61 descr__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(descr__Cong,definition,
% 2.80/1.61 ( descr__Cong
% 2.80/1.61 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.80/1.61 ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx = Xy )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 <=> ( Xpsi @ Xy ) ) )
% 2.80/1.61 => ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ( ( exu
% 2.80/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.80/1.61 => ( ( descr
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 = ( descr
% 2.80/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstr__Cong_type,type,
% 2.80/1.61 dsetconstr__Cong: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dsetconstr__Cong,definition,
% 2.80/1.61 ( dsetconstr__Cong
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( A = B )
% 2.80/1.61 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( ( Xx = Xy )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.80/1.61 => ( ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 = ( dsetconstr @ B
% 2.80/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subset_type,type,
% 2.80/1.61 subset: $i > $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(disjoint_type,type,
% 2.80/1.61 disjoint: $i > $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(setsmeet_type,type,
% 2.80/1.61 setsmeet: $i > $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(subsetI1_type,type,
% 2.80/1.61 subsetI1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subsetI1,definition,
% 2.80/1.61 ( subsetI1
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ Xx @ B ) )
% 2.80/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(eqimpsubset2_type,type,
% 2.80/1.61 eqimpsubset2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(eqimpsubset2,definition,
% 2.80/1.61 ( eqimpsubset2
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( A = B )
% 2.80/1.61 => ( subset @ B @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(eqimpsubset1_type,type,
% 2.80/1.61 eqimpsubset1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(eqimpsubset1,definition,
% 2.80/1.61 ( eqimpsubset1
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( A = B )
% 2.80/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subsetI2_type,type,
% 2.80/1.61 subsetI2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subsetI2,definition,
% 2.80/1.61 ( subsetI2
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ Xx @ B ) )
% 2.80/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(emptysetsubset_type,type,
% 2.80/1.61 emptysetsubset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(emptysetsubset,definition,
% 2.80/1.61 ( emptysetsubset
% 2.80/1.61 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subsetE_type,type,
% 2.80/1.61 subsetE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subsetE,definition,
% 2.80/1.61 ( subsetE
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subsetE2_type,type,
% 2.80/1.61 subsetE2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subsetE2,definition,
% 2.80/1.61 ( subsetE2
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( ~ ( in @ Xx @ B )
% 2.80/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(notsubsetI_type,type,
% 2.80/1.61 notsubsetI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(notsubsetI,definition,
% 2.80/1.61 ( notsubsetI
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ~ ( in @ Xx @ B )
% 2.80/1.61 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(notequalI1_type,type,
% 2.80/1.61 notequalI1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(notequalI1,definition,
% 2.80/1.61 ( notequalI1
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ~ ( subset @ A @ B )
% 2.80/1.61 => ( A != B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(notequalI2_type,type,
% 2.80/1.61 notequalI2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(notequalI2,definition,
% 2.80/1.61 ( notequalI2
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ~ ( in @ Xx @ B )
% 2.80/1.61 => ( A != B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subsetRefl_type,type,
% 2.80/1.61 subsetRefl: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subsetRefl,definition,
% 2.80/1.61 ( subsetRefl
% 2.80/1.61 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subsetTrans_type,type,
% 2.80/1.61 subsetTrans: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subsetTrans,definition,
% 2.80/1.61 ( subsetTrans
% 2.80/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( ( subset @ B @ C )
% 2.80/1.61 => ( subset @ A @ C ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinSub_type,type,
% 2.80/1.61 setadjoinSub: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinSub,definition,
% 2.80/1.61 ( setadjoinSub
% 2.80/1.61 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinSub2_type,type,
% 2.80/1.61 setadjoinSub2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setadjoinSub2,definition,
% 2.80/1.61 ( setadjoinSub2
% 2.80/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subset2powerset_type,type,
% 2.80/1.61 subset2powerset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subset2powerset,definition,
% 2.80/1.61 ( subset2powerset
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setextsub_type,type,
% 2.80/1.61 setextsub: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setextsub,definition,
% 2.80/1.61 ( setextsub
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( ( subset @ B @ A )
% 2.80/1.61 => ( A = B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(subsetemptysetimpeq_type,type,
% 2.80/1.61 subsetemptysetimpeq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(subsetemptysetimpeq,definition,
% 2.80/1.61 ( subsetemptysetimpeq
% 2.80/1.61 = ( ! [A: $i] :
% 2.80/1.61 ( ( subset @ A @ emptyset )
% 2.80/1.61 => ( A = emptyset ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(powersetI1_type,type,
% 2.80/1.61 powersetI1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(powersetI1,definition,
% 2.80/1.61 ( powersetI1
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( subset @ B @ A )
% 2.80/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(powersetE1_type,type,
% 2.80/1.61 powersetE1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(powersetE1,definition,
% 2.80/1.61 ( powersetE1
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( in @ B @ ( powerset @ A ) )
% 2.80/1.61 => ( subset @ B @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(inPowerset_type,type,
% 2.80/1.61 inPowerset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(inPowerset,definition,
% 2.80/1.61 ( inPowerset
% 2.80/1.61 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(powersetsubset_type,type,
% 2.80/1.61 powersetsubset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(powersetsubset,definition,
% 2.80/1.61 ( powersetsubset
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(sepInPowerset_type,type,
% 2.80/1.61 sepInPowerset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(sepInPowerset,definition,
% 2.80/1.61 ( sepInPowerset
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( in
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 @ ( powerset @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(sepSubset_type,type,
% 2.80/1.61 sepSubset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(sepSubset,definition,
% 2.80/1.61 ( sepSubset
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( subset
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 @ A ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binunion_type,type,
% 2.80/1.61 binunion: $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(binunionIL_type,type,
% 2.80/1.61 binunionIL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binunionIL,definition,
% 2.80/1.61 ( binunionIL
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(upairset2IR_type,type,
% 2.80/1.61 upairset2IR: $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairset2IR,definition,
% 2.80/1.61 ( upairset2IR
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binunionIR_type,type,
% 2.80/1.61 binunionIR: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binunionIR,definition,
% 2.80/1.61 ( binunionIR
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binunionEcases_type,type,
% 2.80/1.61 binunionEcases: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binunionEcases,definition,
% 2.80/1.61 ( binunionEcases
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.80/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.80/1.61 => ( ( ( in @ Xx @ A )
% 2.80/1.61 => Xphi )
% 2.80/1.61 => ( ( ( in @ Xx @ B )
% 2.80/1.61 => Xphi )
% 2.80/1.61 => Xphi ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binunionE_type,type,
% 2.80/1.61 binunionE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binunionE,definition,
% 2.80/1.61 ( binunionE
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.80/1.61 => ( ( in @ Xx @ A )
% 2.80/1.61 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binunionLsub_type,type,
% 2.80/1.61 binunionLsub: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binunionLsub,definition,
% 2.80/1.61 ( binunionLsub
% 2.80/1.61 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binunionRsub_type,type,
% 2.80/1.61 binunionRsub: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binunionRsub,definition,
% 2.80/1.61 ( binunionRsub
% 2.80/1.61 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersect_type,type,
% 2.80/1.61 binintersect: $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectI_type,type,
% 2.80/1.61 binintersectI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectI,definition,
% 2.80/1.61 ( binintersectI
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset5_type,type,
% 2.80/1.61 binintersectSubset5: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset5,definition,
% 2.80/1.61 ( binintersectSubset5
% 2.80/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.80/1.61 ( ( subset @ C @ A )
% 2.80/1.61 => ( ( subset @ C @ B )
% 2.80/1.61 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectEL_type,type,
% 2.80/1.61 binintersectEL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectEL,definition,
% 2.80/1.61 ( binintersectEL
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.80/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectLsub_type,type,
% 2.80/1.61 binintersectLsub: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectLsub,definition,
% 2.80/1.61 ( binintersectLsub
% 2.80/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset2_type,type,
% 2.80/1.61 binintersectSubset2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset2,definition,
% 2.80/1.61 ( binintersectSubset2
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( ( binintersect @ A @ B )
% 2.80/1.61 = A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset3_type,type,
% 2.80/1.61 binintersectSubset3: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset3,definition,
% 2.80/1.61 ( binintersectSubset3
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( ( binintersect @ A @ B )
% 2.80/1.61 = B )
% 2.80/1.61 => ( subset @ B @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectER_type,type,
% 2.80/1.61 binintersectER: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectER,definition,
% 2.80/1.61 ( binintersectER
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.80/1.61 => ( in @ Xx @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(disjointsetsI1_type,type,
% 2.80/1.61 disjointsetsI1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(disjointsetsI1,definition,
% 2.80/1.61 ( disjointsetsI1
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ~ ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( in @ Xx @ B ) )
% 2.80/1.61 => ( ( binintersect @ A @ B )
% 2.80/1.61 = emptyset ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectRsub_type,type,
% 2.80/1.61 binintersectRsub: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectRsub,definition,
% 2.80/1.61 ( binintersectRsub
% 2.80/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset4_type,type,
% 2.80/1.61 binintersectSubset4: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset4,definition,
% 2.80/1.61 ( binintersectSubset4
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( subset @ B @ A )
% 2.80/1.61 => ( ( binintersect @ A @ B )
% 2.80/1.61 = B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset1_type,type,
% 2.80/1.61 binintersectSubset1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(binintersectSubset1,definition,
% 2.80/1.61 ( binintersectSubset1
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( ( binintersect @ A @ B )
% 2.80/1.61 = A )
% 2.80/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(bs114d_type,type,
% 2.80/1.61 bs114d: $o ).
% 2.80/1.61
% 2.80/1.61 thf(bs114d,definition,
% 2.80/1.61 ( bs114d
% 2.80/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.80/1.61 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.80/1.61 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(regular_type,type,
% 2.80/1.61 regular: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminus_type,type,
% 2.80/1.61 setminus: $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(setminusI_type,type,
% 2.80/1.61 setminusI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusI,definition,
% 2.80/1.61 ( setminusI
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ~ ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusEL_type,type,
% 2.80/1.61 setminusEL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusEL,definition,
% 2.80/1.61 ( setminusEL
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.80/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusER_type,type,
% 2.80/1.61 setminusER: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusER,definition,
% 2.80/1.61 ( setminusER
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.80/1.61 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusSubset2_type,type,
% 2.80/1.61 setminusSubset2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusSubset2,definition,
% 2.80/1.61 ( setminusSubset2
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( subset @ A @ B )
% 2.80/1.61 => ( ( setminus @ A @ B )
% 2.80/1.61 = emptyset ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusERneg_type,type,
% 2.80/1.61 setminusERneg: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusERneg,definition,
% 2.80/1.61 ( setminusERneg
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.80/1.61 => ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusELneg_type,type,
% 2.80/1.61 setminusELneg: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusELneg,definition,
% 2.80/1.61 ( setminusELneg
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.80/1.61 => ( ~ ( in @ Xx @ B )
% 2.80/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusILneg_type,type,
% 2.80/1.61 setminusILneg: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusILneg,definition,
% 2.80/1.61 ( setminusILneg
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ~ ( in @ Xx @ A )
% 2.80/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusIRneg_type,type,
% 2.80/1.61 setminusIRneg: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusIRneg,definition,
% 2.80/1.61 ( setminusIRneg
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ B )
% 2.80/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusLsub_type,type,
% 2.80/1.61 setminusLsub: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusLsub,definition,
% 2.80/1.61 ( setminusLsub
% 2.80/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setminusSubset1_type,type,
% 2.80/1.61 setminusSubset1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setminusSubset1,definition,
% 2.80/1.61 ( setminusSubset1
% 2.80/1.61 = ( ! [A: $i,B: $i] :
% 2.80/1.61 ( ( ( setminus @ A @ B )
% 2.80/1.61 = emptyset )
% 2.80/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(symdiff_type,type,
% 2.80/1.61 symdiff: $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffE_type,type,
% 2.80/1.61 symdiffE: $o ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffE,definition,
% 2.80/1.61 ( symdiffE
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.80/1.61 => ! [Xphi: $o] :
% 2.80/1.61 ( ( ( in @ Xx @ A )
% 2.80/1.61 => ( ~ ( in @ Xx @ B )
% 2.80/1.61 => Xphi ) )
% 2.80/1.61 => ( ( ~ ( in @ Xx @ A )
% 2.80/1.61 => ( ( in @ Xx @ B )
% 2.80/1.61 => Xphi ) )
% 2.80/1.61 => Xphi ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffI1_type,type,
% 2.80/1.61 symdiffI1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffI1,definition,
% 2.80/1.61 ( symdiffI1
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ~ ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffI2_type,type,
% 2.80/1.61 symdiffI2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffI2,definition,
% 2.80/1.61 ( symdiffI2
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ~ ( in @ Xx @ A )
% 2.80/1.61 => ( ( in @ Xx @ B )
% 2.80/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffIneg1_type,type,
% 2.80/1.61 symdiffIneg1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffIneg1,definition,
% 2.80/1.61 ( symdiffIneg1
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ( in @ Xx @ B )
% 2.80/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffIneg2_type,type,
% 2.80/1.61 symdiffIneg2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(symdiffIneg2,definition,
% 2.80/1.61 ( symdiffIneg2
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ~ ( in @ Xx @ A )
% 2.80/1.61 => ( ~ ( in @ Xx @ B )
% 2.80/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(iskpair_type,type,
% 2.80/1.61 iskpair: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(secondinupair_type,type,
% 2.80/1.61 secondinupair: $o ).
% 2.80/1.61
% 2.80/1.61 thf(secondinupair,definition,
% 2.80/1.61 ( secondinupair
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairIL_type,type,
% 2.80/1.61 setukpairIL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairIL,definition,
% 2.80/1.61 ( setukpairIL
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairIR_type,type,
% 2.80/1.61 setukpairIR: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairIR,definition,
% 2.80/1.61 ( setukpairIR
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(kpairiskpair_type,type,
% 2.80/1.61 kpairiskpair: $o ).
% 2.80/1.61
% 2.80/1.61 thf(kpairiskpair,definition,
% 2.80/1.61 ( kpairiskpair
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(kpair_type,type,
% 2.80/1.61 kpair: $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(kpairp_type,type,
% 2.80/1.61 kpairp: $o ).
% 2.80/1.61
% 2.80/1.61 thf(kpairp,definition,
% 2.80/1.61 ( kpairp
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprod_type,type,
% 2.80/1.61 cartprod: $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(singletonsubset_type,type,
% 2.80/1.61 singletonsubset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(singletonsubset,definition,
% 2.80/1.61 ( singletonsubset
% 2.80/1.61 = ( ! [A: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(singletoninpowerset_type,type,
% 2.80/1.61 singletoninpowerset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(singletoninpowerset,definition,
% 2.80/1.61 ( singletoninpowerset
% 2.80/1.61 = ( ! [A: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(singletoninpowunion_type,type,
% 2.80/1.61 singletoninpowunion: $o ).
% 2.80/1.61
% 2.80/1.61 thf(singletoninpowunion,definition,
% 2.80/1.61 ( singletoninpowunion
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(upairset2E_type,type,
% 2.80/1.61 upairset2E: $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairset2E,definition,
% 2.80/1.61 ( upairset2E
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.80/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.80/1.61 => ( ( Xz = Xx )
% 2.80/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(upairsubunion_type,type,
% 2.80/1.61 upairsubunion: $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairsubunion,definition,
% 2.80/1.61 ( upairsubunion
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(upairinpowunion_type,type,
% 2.80/1.61 upairinpowunion: $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairinpowunion,definition,
% 2.80/1.61 ( upairinpowunion
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ubforcartprodlem1_type,type,
% 2.80/1.61 ubforcartprodlem1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ubforcartprodlem1,definition,
% 2.80/1.61 ( ubforcartprodlem1
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ubforcartprodlem2_type,type,
% 2.80/1.61 ubforcartprodlem2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ubforcartprodlem2,definition,
% 2.80/1.61 ( ubforcartprodlem2
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ubforcartprodlem3_type,type,
% 2.80/1.61 ubforcartprodlem3: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ubforcartprodlem3,definition,
% 2.80/1.61 ( ubforcartprodlem3
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodpairin_type,type,
% 2.80/1.61 cartprodpairin: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodpairin,definition,
% 2.80/1.61 ( cartprodpairin
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodmempair1_type,type,
% 2.80/1.61 cartprodmempair1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodmempair1,definition,
% 2.80/1.61 ( cartprodmempair1
% 2.80/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.80/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.80/1.61 => ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ? [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 & ( Xu
% 2.80/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodmempair_type,type,
% 2.80/1.61 cartprodmempair: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodmempair,definition,
% 2.80/1.61 ( cartprodmempair
% 2.80/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.80/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.80/1.61 => ( iskpair @ Xu ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setunionE2_type,type,
% 2.80/1.61 setunionE2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setunionE2,definition,
% 2.80/1.61 ( setunionE2
% 2.80/1.61 = ( ! [A: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 2.80/1.61 => ? [X: $i] :
% 2.80/1.61 ( ( in @ X @ A )
% 2.80/1.61 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setunionsingleton1_type,type,
% 2.80/1.61 setunionsingleton1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setunionsingleton1,definition,
% 2.80/1.61 ( setunionsingleton1
% 2.80/1.61 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setunionsingleton2_type,type,
% 2.80/1.61 setunionsingleton2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setunionsingleton2,definition,
% 2.80/1.61 ( setunionsingleton2
% 2.80/1.61 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setunionsingleton_type,type,
% 2.80/1.61 setunionsingleton: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setunionsingleton,definition,
% 2.80/1.61 ( setunionsingleton
% 2.80/1.61 = ( ! [Xx: $i] :
% 2.80/1.61 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.80/1.61 = Xx ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(singleton_type,type,
% 2.80/1.61 singleton: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(singleton,definition,
% 2.80/1.61 ( singleton
% 2.80/1.61 = ( ^ [A: $i] :
% 2.80/1.61 ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( A
% 2.80/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(singletonprop_type,type,
% 2.80/1.61 singletonprop: $o ).
% 2.80/1.61
% 2.80/1.61 thf(singletonprop,definition,
% 2.80/1.61 ( singletonprop
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ A )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 => ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) )
% 2.80/1.61 => ( ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( Xphi @ Xx ) )
% 2.80/1.61 => ( singleton
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ex1_type,type,
% 2.80/1.61 ex1: $i > ( $i > $o ) > $o ).
% 2.80/1.61
% 2.80/1.61 thf(ex1,definition,
% 2.80/1.61 ( ex1
% 2.80/1.61 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( singleton
% 2.80/1.61 @ ( dsetconstr @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ex1E1_type,type,
% 2.80/1.61 ex1E1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ex1E1,definition,
% 2.80/1.61 ( ex1E1
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ( ex1 @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ex1I_type,type,
% 2.80/1.61 ex1I: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ex1I,definition,
% 2.80/1.61 ( ex1I
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 => ( ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ A )
% 2.80/1.61 => ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xy = Xx ) ) )
% 2.80/1.61 => ( ex1 @ A
% 2.80/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ex1I2_type,type,
% 2.80/1.61 ex1I2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ex1I2,definition,
% 2.80/1.61 ( ex1I2
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ A )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 => ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) )
% 2.80/1.61 => ( ? [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 & ( Xphi @ Xx ) )
% 2.80/1.61 => ( ex1 @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(singletonsuniq_type,type,
% 2.80/1.61 singletonsuniq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(singletonsuniq,definition,
% 2.80/1.61 ( singletonsuniq
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( ( setadjoin @ Xx @ emptyset )
% 2.80/1.61 = ( setadjoin @ Xy @ emptyset ) )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(atmost1p_type,type,
% 2.80/1.61 atmost1p: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(atleast2p_type,type,
% 2.80/1.61 atleast2p: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(atmost2p_type,type,
% 2.80/1.61 atmost2p: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairsetp_type,type,
% 2.80/1.61 upairsetp: $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjL1_type,type,
% 2.80/1.61 setukpairinjL1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjL1,definition,
% 2.80/1.61 ( setukpairinjL1
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.80/1.61 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.80/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(kfstsingleton_type,type,
% 2.80/1.61 kfstsingleton: $o ).
% 2.80/1.61
% 2.80/1.61 thf(kfstsingleton,definition,
% 2.80/1.61 ( kfstsingleton
% 2.80/1.61 = ( ! [Xu: $i] :
% 2.80/1.61 ( ( iskpair @ Xu )
% 2.80/1.61 => ( singleton
% 2.80/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 2.80/1.61 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(theprop_type,type,
% 2.80/1.61 theprop: $o ).
% 2.80/1.61
% 2.80/1.61 thf(theprop,definition,
% 2.80/1.61 ( theprop
% 2.80/1.61 = ( ! [X: $i] :
% 2.80/1.61 ( ( singleton @ X )
% 2.80/1.61 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(kfst_type,type,
% 2.80/1.61 kfst: $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(kfstpairEq_type,type,
% 2.80/1.61 kfstpairEq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(kfstpairEq,definition,
% 2.80/1.61 ( kfstpairEq
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.80/1.61 = Xx ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodfstin_type,type,
% 2.80/1.61 cartprodfstin: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodfstin,definition,
% 2.80/1.61 ( cartprodfstin
% 2.80/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.80/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.80/1.61 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjL2_type,type,
% 2.80/1.61 setukpairinjL2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjL2,definition,
% 2.80/1.61 ( setukpairinjL2
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.80/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.80/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.80/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjL_type,type,
% 2.80/1.61 setukpairinjL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjL,definition,
% 2.80/1.61 ( setukpairinjL
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.80/1.61 ( ( ( kpair @ Xx @ Xy )
% 2.80/1.61 = ( kpair @ Xz @ Xu ) )
% 2.80/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR11_type,type,
% 2.80/1.61 setukpairinjR11: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR11,definition,
% 2.80/1.61 ( setukpairinjR11
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx = Xy )
% 2.80/1.61 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.80/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR12_type,type,
% 2.80/1.61 setukpairinjR12: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR12,definition,
% 2.80/1.61 ( setukpairinjR12
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xx = Xy )
% 2.80/1.61 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.80/1.61 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR1_type,type,
% 2.80/1.61 setukpairinjR1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR1,definition,
% 2.80/1.61 ( setukpairinjR1
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.80/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.80/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.80/1.61 => ( ( Xz = Xu )
% 2.80/1.61 => ( Xy = Xu ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(upairequniteq_type,type,
% 2.80/1.61 upairequniteq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(upairequniteq,definition,
% 2.80/1.61 ( upairequniteq
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.80/1.61 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.80/1.61 = ( setadjoin @ Xz @ emptyset ) )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR2_type,type,
% 2.80/1.61 setukpairinjR2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR2,definition,
% 2.80/1.61 ( setukpairinjR2
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.80/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.80/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.80/1.61 => ( Xy = Xu ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR_type,type,
% 2.80/1.61 setukpairinjR: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setukpairinjR,definition,
% 2.80/1.61 ( setukpairinjR
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.80/1.61 ( ( ( kpair @ Xx @ Xy )
% 2.80/1.61 = ( kpair @ Xz @ Xu ) )
% 2.80/1.61 => ( Xy = Xu ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ksndsingleton_type,type,
% 2.80/1.61 ksndsingleton: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ksndsingleton,definition,
% 2.80/1.61 ( ksndsingleton
% 2.80/1.61 = ( ! [Xu: $i] :
% 2.80/1.61 ( ( iskpair @ Xu )
% 2.80/1.61 => ( singleton
% 2.80/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 2.80/1.61 @ ^ [Xx: $i] :
% 2.80/1.61 ( Xu
% 2.80/1.61 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ksnd_type,type,
% 2.80/1.61 ksnd: $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(ksndpairEq_type,type,
% 2.80/1.61 ksndpairEq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ksndpairEq,definition,
% 2.80/1.61 ( ksndpairEq
% 2.80/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.80/1.61 = Xy ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(kpairsurjEq_type,type,
% 2.80/1.61 kpairsurjEq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(kpairsurjEq,definition,
% 2.80/1.61 ( kpairsurjEq
% 2.80/1.61 = ( ! [Xu: $i] :
% 2.80/1.61 ( ( iskpair @ Xu )
% 2.80/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.80/1.61 = Xu ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodsndin_type,type,
% 2.80/1.61 cartprodsndin: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodsndin,definition,
% 2.80/1.61 ( cartprodsndin
% 2.80/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.80/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.80/1.61 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodpairmemEL_type,type,
% 2.80/1.61 cartprodpairmemEL: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodpairmemEL,definition,
% 2.80/1.61 ( cartprodpairmemEL
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.80/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodpairmemER_type,type,
% 2.80/1.61 cartprodpairmemER: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodpairmemER,definition,
% 2.80/1.61 ( cartprodpairmemER
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.80/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodmempaircEq_type,type,
% 2.80/1.61 cartprodmempaircEq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodmempaircEq,definition,
% 2.80/1.61 ( cartprodmempaircEq
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( ( kpair @ Xx @ Xy )
% 2.80/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodfstpairEq_type,type,
% 2.80/1.61 cartprodfstpairEq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodfstpairEq,definition,
% 2.80/1.61 ( cartprodfstpairEq
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.80/1.61 = Xx ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodsndpairEq_type,type,
% 2.80/1.61 cartprodsndpairEq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodsndpairEq,definition,
% 2.80/1.61 ( cartprodsndpairEq
% 2.80/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.80/1.61 = Xy ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodpairsurjEq_type,type,
% 2.80/1.61 cartprodpairsurjEq: $o ).
% 2.80/1.61
% 2.80/1.61 thf(cartprodpairsurjEq,definition,
% 2.80/1.61 ( cartprodpairsurjEq
% 2.80/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.80/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.80/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.80/1.61 = Xu ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(breln_type,type,
% 2.80/1.61 breln: $i > $i > $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(breln,definition,
% 2.80/1.61 ( breln
% 2.80/1.61 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstr_type,type,
% 2.80/1.61 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrI_type,type,
% 2.80/1.61 dpsetconstrI: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrI,definition,
% 2.80/1.61 ( dpsetconstrI
% 2.80/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( ( Xphi @ Xx @ Xy )
% 2.80/1.61 => ( in @ ( kpair @ Xx @ Xy )
% 2.80/1.61 @ ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrSub_type,type,
% 2.80/1.61 dpsetconstrSub: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrSub,definition,
% 2.80/1.61 ( dpsetconstrSub
% 2.80/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.80/1.61 ( subset
% 2.80/1.61 @ ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.80/1.61 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(setOfPairsIsBReln_type,type,
% 2.80/1.61 setOfPairsIsBReln: $o ).
% 2.80/1.61
% 2.80/1.61 thf(setOfPairsIsBReln,definition,
% 2.80/1.61 ( setOfPairsIsBReln
% 2.80/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.80/1.61 ( breln @ A @ B
% 2.80/1.61 @ ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrERa_type,type,
% 2.80/1.61 dpsetconstrERa: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrERa,definition,
% 2.80/1.61 ( dpsetconstrERa
% 2.80/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.80/1.61 @ ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.80/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrEL1_type,type,
% 2.80/1.61 dpsetconstrEL1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrEL1,definition,
% 2.80/1.61 ( dpsetconstrEL1
% 2.80/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.80/1.61 @ ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.80/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrEL2_type,type,
% 2.80/1.61 dpsetconstrEL2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrEL2,definition,
% 2.80/1.61 ( dpsetconstrEL2
% 2.80/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.80/1.61 @ ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.80/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrER_type,type,
% 2.80/1.61 dpsetconstrER: $o ).
% 2.80/1.61
% 2.80/1.61 thf(dpsetconstrER,definition,
% 2.80/1.61 ( dpsetconstrER
% 2.80/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.80/1.61 @ ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.80/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(func_type,type,
% 2.80/1.61 func: $i > $i > $i > $o ).
% 2.80/1.61
% 2.80/1.61 thf(func,definition,
% 2.80/1.61 ( func
% 2.80/1.61 = ( ^ [A: $i,B: $i,R: $i] :
% 2.80/1.61 ( ( breln @ A @ B @ R )
% 2.80/1.61 & ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( ex1 @ B
% 2.80/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(funcSet_type,type,
% 2.80/1.61 funcSet: $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(funcImageSingleton_type,type,
% 2.80/1.61 funcImageSingleton: $o ).
% 2.80/1.61
% 2.80/1.61 thf(funcImageSingleton,definition,
% 2.80/1.61 ( funcImageSingleton
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.80/1.61 ( ( func @ A @ B @ Xf )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( singleton
% 2.80/1.61 @ ( dsetconstr @ B
% 2.80/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(apProp_type,type,
% 2.80/1.61 apProp: $o ).
% 2.80/1.61
% 2.80/1.61 thf(apProp,definition,
% 2.80/1.61 ( apProp
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.80/1.61 ( ( func @ A @ B @ Xf )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in
% 2.80/1.61 @ ( setunion
% 2.80/1.61 @ ( dsetconstr @ B
% 2.80/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.80/1.61 @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ap_type,type,
% 2.80/1.61 ap: $i > $i > $i > $i > $i ).
% 2.80/1.61
% 2.80/1.61 thf(ap,definition,
% 2.80/1.61 ( ap
% 2.80/1.61 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 2.80/1.61 ( setunion
% 2.80/1.61 @ ( dsetconstr @ B
% 2.80/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(app_type,type,
% 2.80/1.61 app: $o ).
% 2.80/1.61
% 2.80/1.61 thf(app,definition,
% 2.80/1.61 ( app
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.80/1.61 ( ( func @ A @ B @ Xf )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(infuncsetfunc_type,type,
% 2.80/1.61 infuncsetfunc: $o ).
% 2.80/1.61
% 2.80/1.61 thf(infuncsetfunc,definition,
% 2.80/1.61 ( infuncsetfunc
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.80/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.80/1.61 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ap2p_type,type,
% 2.80/1.61 ap2p: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ap2p,definition,
% 2.80/1.61 ( ap2p
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.80/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(funcinfuncset_type,type,
% 2.80/1.61 funcinfuncset: $o ).
% 2.80/1.61
% 2.80/1.61 thf(funcinfuncset,definition,
% 2.80/1.61 ( funcinfuncset
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.80/1.61 ( ( func @ A @ B @ Xf )
% 2.80/1.61 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(lamProp_type,type,
% 2.80/1.61 lamProp: $o ).
% 2.80/1.61
% 2.80/1.61 thf(lamProp,definition,
% 2.80/1.61 ( lamProp
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.80/1.61 => ( func @ A @ B
% 2.80/1.61 @ ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xf @ Xx )
% 2.80/1.61 = Xy ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(lam_type,type,
% 2.80/1.61 lam: $i > $i > ( $i > $i ) > $i ).
% 2.80/1.61
% 2.80/1.61 thf(lam,definition,
% 2.80/1.61 ( lam
% 2.80/1.61 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 2.80/1.61 ( dpsetconstr @ A @ B
% 2.80/1.61 @ ^ [Xx: $i,Xy: $i] :
% 2.80/1.61 ( ( Xf @ Xx )
% 2.80/1.61 = Xy ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(lamp_type,type,
% 2.80/1.61 lamp: $o ).
% 2.80/1.61
% 2.80/1.61 thf(lamp,definition,
% 2.80/1.61 ( lamp
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.80/1.61 => ( func @ A @ B
% 2.80/1.61 @ ( lam @ A @ B
% 2.80/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(lam2p_type,type,
% 2.80/1.61 lam2p: $o ).
% 2.80/1.61
% 2.80/1.61 thf(lam2p,definition,
% 2.80/1.61 ( lam2p
% 2.80/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.80/1.61 => ( in
% 2.80/1.61 @ ( lam @ A @ B
% 2.80/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.80/1.61 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(brelnall1_type,type,
% 2.80/1.61 brelnall1: $o ).
% 2.80/1.61
% 2.80/1.61 thf(brelnall1,definition,
% 2.80/1.61 ( brelnall1
% 2.80/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 2.80/1.61 ( ( breln @ A @ B @ R )
% 2.80/1.61 => ! [Xphi: $i > $o] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.80/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ R )
% 2.80/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(brelnall2_type,type,
% 2.80/1.61 brelnall2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(brelnall2,definition,
% 2.80/1.61 ( brelnall2
% 2.80/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 2.80/1.61 ( ( breln @ A @ B @ R )
% 2.80/1.61 => ! [Xphi: $i > $o] :
% 2.80/1.61 ( ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ B )
% 2.80/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.80/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ R )
% 2.80/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(ex1E2_type,type,
% 2.80/1.61 ex1E2: $o ).
% 2.80/1.61
% 2.80/1.61 thf(ex1E2,definition,
% 2.80/1.61 ( ex1E2
% 2.80/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.80/1.61 ( ( ex1 @ A
% 2.80/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ! [Xy: $i] :
% 2.80/1.61 ( ( in @ Xy @ A )
% 2.80/1.61 => ( ( Xphi @ Xx )
% 2.80/1.61 => ( ( Xphi @ Xy )
% 2.80/1.61 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.80/1.61
% 2.80/1.61 thf(funcGraphProp1,conjecture,
% 2.80/1.61 ( setextAx
% 2.80/1.61 => ( emptysetAx
% 2.80/1.61 => ( setadjoinAx
% 2.80/1.61 => ( powersetAx
% 2.80/1.61 => ( setunionAx
% 2.80/1.61 => ( omega0Ax
% 2.80/1.61 => ( omegaSAx
% 2.80/1.61 => ( omegaIndAx
% 2.80/1.61 => ( replAx
% 2.80/1.61 => ( foundationAx
% 2.80/1.61 => ( wellorderingAx
% 2.80/1.61 => ( descrp
% 2.80/1.61 => ( dsetconstrI
% 2.80/1.61 => ( dsetconstrEL
% 2.80/1.61 => ( dsetconstrER
% 2.80/1.61 => ( exuE1
% 2.80/1.61 => ( prop2setE
% 2.80/1.61 => ( emptysetE
% 2.80/1.61 => ( emptysetimpfalse
% 2.80/1.61 => ( notinemptyset
% 2.80/1.61 => ( exuE3e
% 2.80/1.61 => ( setext
% 2.80/1.61 => ( emptyI
% 2.80/1.61 => ( noeltsimpempty
% 2.80/1.61 => ( setbeta
% 2.80/1.61 => ( nonemptyE1
% 2.80/1.61 => ( nonemptyI
% 2.80/1.61 => ( nonemptyI1
% 2.80/1.61 => ( setadjoinIL
% 2.80/1.61 => ( emptyinunitempty
% 2.80/1.61 => ( setadjoinIR
% 2.80/1.61 => ( setadjoinE
% 2.80/1.61 => ( setadjoinOr
% 2.80/1.61 => ( setoftrueEq
% 2.80/1.61 => ( powersetI
% 2.80/1.61 => ( emptyinPowerset
% 2.80/1.61 => ( emptyInPowerset
% 2.80/1.61 => ( powersetE
% 2.80/1.61 => ( setunionI
% 2.80/1.61 => ( setunionE
% 2.80/1.61 => ( subPowSU
% 2.80/1.61 => ( exuE2
% 2.80/1.61 => ( nonemptyImpWitness
% 2.80/1.61 => ( uniqinunit
% 2.80/1.61 => ( notinsingleton
% 2.80/1.61 => ( eqinunit
% 2.80/1.61 => ( singletonsswitch
% 2.80/1.61 => ( upairsetE
% 2.80/1.61 => ( upairsetIL
% 2.80/1.61 => ( upairsetIR
% 2.80/1.61 => ( emptyE1
% 2.80/1.61 => ( vacuousDall
% 2.80/1.61 => ( quantDeMorgan1
% 2.80/1.61 => ( quantDeMorgan2
% 2.80/1.61 => ( quantDeMorgan3
% 2.80/1.61 => ( quantDeMorgan4
% 2.80/1.61 => ( prop2setI
% 2.80/1.61 => ( prop2set2propI
% 2.80/1.61 => ( notdexE
% 2.80/1.61 => ( notdallE
% 2.80/1.61 => ( exuI1
% 2.80/1.61 => ( exuI3
% 2.80/1.61 => ( exuI2
% 2.80/1.61 => ( inCongP
% 2.80/1.61 => ( in__Cong
% 2.80/1.61 => ( exuE3u
% 2.80/1.61 => ( exu__Cong
% 2.80/1.61 => ( emptyset__Cong
% 2.80/1.61 => ( setadjoin__Cong
% 2.80/1.61 => ( powerset__Cong
% 2.80/1.61 => ( setunion__Cong
% 2.80/1.61 => ( omega__Cong
% 2.80/1.61 => ( exuEu
% 2.80/1.61 => ( descr__Cong
% 2.80/1.61 => ( dsetconstr__Cong
% 2.80/1.61 => ( subsetI1
% 2.80/1.61 => ( eqimpsubset2
% 2.80/1.61 => ( eqimpsubset1
% 2.80/1.61 => ( subsetI2
% 2.80/1.61 => ( emptysetsubset
% 2.80/1.61 => ( subsetE
% 2.80/1.61 => ( subsetE2
% 2.80/1.61 => ( notsubsetI
% 2.80/1.61 => ( notequalI1
% 2.80/1.61 => ( notequalI2
% 2.80/1.61 => ( subsetRefl
% 2.80/1.61 => ( subsetTrans
% 2.80/1.61 => ( setadjoinSub
% 2.80/1.61 => ( setadjoinSub2
% 2.80/1.61 => ( subset2powerset
% 2.80/1.61 => ( setextsub
% 2.80/1.61 => ( subsetemptysetimpeq
% 2.80/1.61 => ( powersetI1
% 2.80/1.61 => ( powersetE1
% 2.80/1.61 => ( inPowerset
% 2.80/1.61 => ( powersetsubset
% 2.80/1.61 => ( sepInPowerset
% 2.80/1.61 => ( sepSubset
% 2.80/1.61 => ( binunionIL
% 2.80/1.61 => ( upairset2IR
% 2.80/1.61 => ( binunionIR
% 2.80/1.61 => ( binunionEcases
% 2.80/1.61 => ( binunionE
% 2.80/1.61 => ( binunionLsub
% 2.80/1.61 => ( binunionRsub
% 2.80/1.61 => ( binintersectI
% 2.80/1.61 => ( binintersectSubset5
% 2.80/1.61 => ( binintersectEL
% 2.80/1.61 => ( binintersectLsub
% 2.80/1.61 => ( binintersectSubset2
% 2.80/1.61 => ( binintersectSubset3
% 2.80/1.61 => ( binintersectER
% 2.80/1.61 => ( disjointsetsI1
% 2.80/1.61 => ( binintersectRsub
% 2.80/1.61 => ( binintersectSubset4
% 2.80/1.61 => ( binintersectSubset1
% 2.80/1.61 => ( bs114d
% 2.80/1.61 => ( setminusI
% 2.80/1.61 => ( setminusEL
% 2.80/1.61 => ( setminusER
% 2.80/1.61 => ( setminusSubset2
% 2.80/1.61 => ( setminusERneg
% 2.80/1.61 => ( setminusELneg
% 2.80/1.61 => ( setminusILneg
% 2.80/1.61 => ( setminusIRneg
% 2.80/1.61 => ( setminusLsub
% 2.80/1.61 => ( setminusSubset1
% 2.80/1.61 => ( symdiffE
% 2.80/1.61 => ( symdiffI1
% 2.80/1.61 => ( symdiffI2
% 2.80/1.61 => ( symdiffIneg1
% 2.80/1.61 => ( symdiffIneg2
% 2.80/1.61 => ( secondinupair
% 2.80/1.61 => ( setukpairIL
% 2.80/1.61 => ( setukpairIR
% 2.80/1.61 => ( kpairiskpair
% 2.80/1.61 => ( kpairp
% 2.80/1.61 => ( singletonsubset
% 2.80/1.61 => ( singletoninpowerset
% 2.80/1.61 => ( singletoninpowunion
% 2.80/1.61 => ( upairset2E
% 2.80/1.61 => ( upairsubunion
% 2.80/1.61 => ( upairinpowunion
% 2.80/1.61 => ( ubforcartprodlem1
% 2.80/1.61 => ( ubforcartprodlem2
% 2.80/1.61 => ( ubforcartprodlem3
% 2.80/1.61 => ( cartprodpairin
% 2.80/1.61 => ( cartprodmempair1
% 2.80/1.61 => ( cartprodmempair
% 2.80/1.61 => ( setunionE2
% 2.80/1.61 => ( setunionsingleton1
% 2.80/1.61 => ( setunionsingleton2
% 2.80/1.61 => ( setunionsingleton
% 2.80/1.61 => ( singletonprop
% 2.80/1.61 => ( ex1E1
% 2.80/1.61 => ( ex1I
% 2.80/1.61 => ( ex1I2
% 2.80/1.61 => ( singletonsuniq
% 2.80/1.61 => ( setukpairinjL1
% 2.80/1.61 => ( kfstsingleton
% 2.80/1.61 => ( theprop
% 2.80/1.61 => ( kfstpairEq
% 2.80/1.61 => ( cartprodfstin
% 2.80/1.61 => ( setukpairinjL2
% 2.80/1.61 => ( setukpairinjL
% 2.80/1.61 => ( setukpairinjR11
% 2.80/1.61 => ( setukpairinjR12
% 2.80/1.61 => ( setukpairinjR1
% 2.80/1.61 => ( upairequniteq
% 2.80/1.61 => ( setukpairinjR2
% 2.80/1.61 => ( setukpairinjR
% 2.80/1.61 => ( ksndsingleton
% 2.80/1.61 => ( ksndpairEq
% 2.80/1.61 => ( kpairsurjEq
% 2.80/1.61 => ( cartprodsndin
% 2.80/1.61 => ( cartprodpairmemEL
% 2.80/1.61 => ( cartprodpairmemER
% 2.80/1.61 => ( cartprodmempaircEq
% 2.80/1.61 => ( cartprodfstpairEq
% 2.80/1.61 => ( cartprodsndpairEq
% 2.80/1.61 => ( cartprodpairsurjEq
% 2.80/1.61 => ( dpsetconstrI
% 2.80/1.61 => ( dpsetconstrSub
% 2.80/1.61 => ( setOfPairsIsBReln
% 2.80/1.61 => ( dpsetconstrERa
% 2.80/1.61 => ( dpsetconstrEL1
% 2.80/1.61 => ( dpsetconstrEL2
% 2.80/1.61 => ( dpsetconstrER
% 2.80/1.61 => ( funcImageSingleton
% 2.80/1.61 => ( apProp
% 2.80/1.61 => ( app
% 2.80/1.61 => ( infuncsetfunc
% 2.80/1.61 => ( ap2p
% 2.80/1.61 => ( funcinfuncset
% 2.80/1.61 => ( lamProp
% 2.80/1.61 => ( lamp
% 2.80/1.61 => ( lam2p
% 2.80/1.61 => ( brelnall1
% 2.80/1.61 => ( brelnall2
% 2.80/1.61 => ( ex1E2
% 2.80/1.61 => ! [A: $i,B: $i,Xf: $i] :
% 2.80/1.61 ( ( func @ A @ B @ Xf )
% 2.80/1.61 => ! [Xx: $i] :
% 2.80/1.61 ( ( in @ Xx @ A )
% 2.80/1.61 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.80/1.61 ------------------------
% 2.80/1.64 % (25644)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/2Mi)
% 2.80/1.64 % (25646)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_25541 for (2999ds/275Mi)
% 2.80/1.64 % (25644)Instruction limit reached!
% 2.80/1.64 % (25644)------------------------------
% 2.80/1.64 % (25644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.64 % (25642)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_25541 for (2999ds/4Mi)
% 2.80/1.64 % (25644)Termination reason: Unknown
% 2.80/1.64 % (25645)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_25541 for (2999ds/2Mi)
% 2.80/1.64 % (25644)Termination phase: shuffling
% 2.80/1.64 % (25647)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/18Mi)
% 2.80/1.64
% 2.80/1.64 % (25644)Memory used [KB]: 1407
% 2.80/1.64 % (25644)Time elapsed: 0.003 s
% 2.80/1.64 % (25644)Instructions burned: 3 (million)
% 2.80/1.64 % (25644)------------------------------
% 2.80/1.64 % (25644)------------------------------
% 2.80/1.64 % (25643)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_25541 for (2999ds/27Mi)
% 2.80/1.64 % (25641)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/183Mi)
% 2.80/1.64 % (25645)Instruction limit reached!
% 2.80/1.64 % (25645)------------------------------
% 2.80/1.64 % (25645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.64 % (25645)Termination reason: Unknown
% 2.80/1.64 % (25645)Termination phase: shuffling
% 2.80/1.64
% 2.80/1.64 % (25645)Memory used [KB]: 1407
% 2.80/1.64 % (25645)Time elapsed: 0.003 s
% 2.80/1.64 % (25645)Instructions burned: 2 (million)
% 2.80/1.64 % (25645)------------------------------
% 2.80/1.64 % (25645)------------------------------
% 2.80/1.65 % (25642)Instruction limit reached!
% 2.80/1.65 % (25642)------------------------------
% 2.80/1.65 % (25642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.65 % (25642)Termination reason: Unknown
% 2.80/1.65 % (25642)Termination phase: shuffling
% 2.80/1.65
% 2.80/1.65 % (25642)Memory used [KB]: 1407
% 2.80/1.65 % (25642)Time elapsed: 0.004 s
% 2.80/1.65 % (25642)Instructions burned: 4 (million)
% 2.80/1.65 % (25642)------------------------------
% 2.80/1.65 % (25642)------------------------------
% 2.80/1.65 % (25647)Instruction limit reached!
% 2.80/1.65 % (25647)------------------------------
% 2.80/1.65 % (25647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.65 % (25647)Termination reason: Unknown
% 2.80/1.65 % (25647)Termination phase: shuffling
% 2.80/1.65
% 2.80/1.65 % (25647)Memory used [KB]: 1663
% 2.80/1.65 % (25647)Time elapsed: 0.011 s
% 2.80/1.65 % (25647)Instructions burned: 18 (million)
% 2.80/1.65 % (25647)------------------------------
% 2.80/1.65 % (25647)------------------------------
% 2.80/1.66 % (25643)Instruction limit reached!
% 2.80/1.66 % (25643)------------------------------
% 2.80/1.66 % (25643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.66 % (25643)Termination reason: Unknown
% 2.80/1.66 % (25643)Termination phase: shuffling
% 2.80/1.66
% 2.80/1.66 % (25643)Memory used [KB]: 1918
% 2.80/1.66 % (25643)Time elapsed: 0.015 s
% 2.80/1.66 % (25643)Instructions burned: 28 (million)
% 2.80/1.66 % (25643)------------------------------
% 2.80/1.66 % (25643)------------------------------
% 2.80/1.66 % (25648)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/3Mi)
% 2.80/1.66 % (25648)Instruction limit reached!
% 2.80/1.66 % (25648)------------------------------
% 2.80/1.66 % (25648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.66 % (25648)Termination reason: Unknown
% 2.80/1.66 % (25648)Termination phase: shuffling
% 2.80/1.66
% 2.80/1.66 % (25648)Memory used [KB]: 1407
% 2.80/1.66 % (25648)Time elapsed: 0.004 s
% 2.80/1.66 % (25648)Instructions burned: 5 (million)
% 2.80/1.66 % (25648)------------------------------
% 2.80/1.66 % (25648)------------------------------
% 2.80/1.66 % (25650)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_25541 for (2999ds/15Mi)
% 2.80/1.66 % (25649)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_25541 for (2999ds/37Mi)
% 2.80/1.67 % (25650)Instruction limit reached!
% 2.80/1.67 % (25650)------------------------------
% 2.80/1.67 % (25650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.67 % (25650)Termination reason: Unknown
% 2.80/1.67 % (25650)Termination phase: shuffling
% 2.80/1.67
% 2.80/1.67 % (25650)Memory used [KB]: 1663
% 2.80/1.67 % (25650)Time elapsed: 0.009 s
% 2.80/1.67 % (25650)Instructions burned: 17 (million)
% 2.80/1.67 % (25650)------------------------------
% 2.80/1.67 % (25650)------------------------------
% 2.80/1.67 % (25651)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_25541 for (2999ds/3Mi)
% 2.80/1.67 % (25651)Instruction limit reached!
% 2.80/1.67 % (25651)------------------------------
% 2.80/1.67 % (25651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.67 % (25651)Termination reason: Unknown
% 2.80/1.67 % (25651)Termination phase: shuffling
% 2.80/1.67
% 2.80/1.67 % (25651)Memory used [KB]: 1407
% 2.80/1.67 % (25651)Time elapsed: 0.004 s
% 2.80/1.67 % (25651)Instructions burned: 4 (million)
% 2.80/1.67 % (25651)------------------------------
% 2.80/1.67 % (25651)------------------------------
% 2.80/1.67 % (25652)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_25541 for (2999ds/1041Mi)
% 2.80/1.67 % (25653)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/7Mi)
% 2.80/1.68 % (25653)Instruction limit reached!
% 2.80/1.68 % (25653)------------------------------
% 2.80/1.68 % (25653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.68 % (25653)Termination reason: Unknown
% 2.80/1.68 % (25653)Termination phase: shuffling
% 2.80/1.68
% 2.80/1.68 % (25653)Memory used [KB]: 1535
% 2.80/1.68 % (25653)Time elapsed: 0.005 s
% 2.80/1.68 % (25653)Instructions burned: 8 (million)
% 2.80/1.68 % (25653)------------------------------
% 2.80/1.68 % (25653)------------------------------
% 2.80/1.68 % (25649)Instruction limit reached!
% 2.80/1.68 % (25649)------------------------------
% 2.80/1.68 % (25649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.68 % (25649)Termination reason: Unknown
% 2.80/1.68 % (25649)Termination phase: Property scanning
% 2.80/1.68
% 2.80/1.68 % (25649)Memory used [KB]: 2046
% 2.80/1.68 % (25649)Time elapsed: 0.019 s
% 2.80/1.68 % (25649)Instructions burned: 38 (million)
% 2.80/1.68 % (25649)------------------------------
% 2.80/1.68 % (25649)------------------------------
% 2.80/1.68 % (25654)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/16Mi)
% 2.80/1.69 % (25655)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_25541 for (2999ds/3Mi)
% 2.80/1.69 % (25655)Instruction limit reached!
% 2.80/1.69 % (25655)------------------------------
% 2.80/1.69 % (25655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.69 % (25655)Termination reason: Unknown
% 2.80/1.69 % (25655)Termination phase: shuffling
% 2.80/1.69
% 2.80/1.69 % (25655)Memory used [KB]: 1407
% 2.80/1.69 % (25655)Time elapsed: 0.003 s
% 2.80/1.69 % (25655)Instructions burned: 3 (million)
% 2.80/1.69 % (25655)------------------------------
% 2.80/1.69 % (25655)------------------------------
% 2.80/1.69 % (25654)Instruction limit reached!
% 2.80/1.69 % (25654)------------------------------
% 2.80/1.69 % (25654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.69 % (25654)Termination reason: Unknown
% 2.80/1.69 % (25654)Termination phase: shuffling
% 2.80/1.69
% 2.80/1.69 % (25654)Memory used [KB]: 1791
% 2.80/1.69 % (25654)Time elapsed: 0.010 s
% 2.80/1.69 % (25654)Instructions burned: 17 (million)
% 2.80/1.69 % (25654)------------------------------
% 2.80/1.69 % (25654)------------------------------
% 2.80/1.69 % (25656)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_25541 for (2999ds/3Mi)
% 2.80/1.69 % (25657)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/7Mi)
% 2.80/1.70 % (25656)Instruction limit reached!
% 2.80/1.70 % (25656)------------------------------
% 2.80/1.70 % (25656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.70 % (25656)Termination reason: Unknown
% 2.80/1.70 % (25656)Termination phase: shuffling
% 2.80/1.70
% 2.80/1.70 % (25656)Memory used [KB]: 1407
% 2.80/1.70 % (25656)Time elapsed: 0.004 s
% 2.80/1.70 % (25656)Instructions burned: 5 (million)
% 2.80/1.70 % (25656)------------------------------
% 2.80/1.70 % (25656)------------------------------
% 2.84/1.70 % (25657)Instruction limit reached!
% 2.84/1.70 % (25657)------------------------------
% 2.84/1.70 % (25657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.70 % (25657)Termination reason: Unknown
% 2.84/1.70 % (25657)Termination phase: shuffling
% 2.84/1.70
% 2.84/1.70 % (25657)Memory used [KB]: 1535
% 2.84/1.70 % (25657)Time elapsed: 0.005 s
% 2.84/1.70 % (25657)Instructions burned: 7 (million)
% 2.84/1.70 % (25657)------------------------------
% 2.84/1.70 % (25657)------------------------------
% 2.84/1.70 % (25658)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/3Mi)
% 2.84/1.71 % (25658)Instruction limit reached!
% 2.84/1.71 % (25658)------------------------------
% 2.84/1.71 % (25658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.71 % (25658)Termination reason: Unknown
% 2.84/1.71 % (25658)Termination phase: shuffling
% 2.84/1.71
% 2.84/1.71 % (25658)Memory used [KB]: 1407
% 2.84/1.71 % (25658)Time elapsed: 0.003 s
% 2.84/1.71 % (25658)Instructions burned: 3 (million)
% 2.84/1.71 % (25658)------------------------------
% 2.84/1.71 % (25658)------------------------------
% 2.84/1.71 % (25659)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/4Mi)
% 2.84/1.71 % (25659)Instruction limit reached!
% 2.84/1.71 % (25659)------------------------------
% 2.84/1.71 % (25659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.71 % (25659)Termination reason: Unknown
% 2.84/1.71 % (25659)Termination phase: shuffling
% 2.84/1.71
% 2.84/1.71 % (25659)Memory used [KB]: 1407
% 2.84/1.71 % (25659)Time elapsed: 0.004 s
% 2.84/1.71 % (25659)Instructions burned: 5 (million)
% 2.84/1.71 % (25659)------------------------------
% 2.84/1.71 % (25659)------------------------------
% 2.84/1.71 % (25660)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/18Mi)
% 2.84/1.71 % (25661)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/710Mi)
% 2.84/1.72 % (25660)Instruction limit reached!
% 2.84/1.72 % (25660)------------------------------
% 2.84/1.72 % (25660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.72 % (25660)Termination reason: Unknown
% 2.84/1.72 % (25660)Termination phase: shuffling
% 2.84/1.72
% 2.84/1.72 % (25660)Memory used [KB]: 1791
% 2.84/1.72 % (25660)Time elapsed: 0.010 s
% 2.84/1.72 % (25660)Instructions burned: 19 (million)
% 2.84/1.72 % (25660)------------------------------
% 2.84/1.72 % (25660)------------------------------
% 2.84/1.72 % (25662)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25541 for (2999ds/6Mi)
% 2.84/1.73 % (25662)Instruction limit reached!
% 2.84/1.73 % (25662)------------------------------
% 2.84/1.73 % (25662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.73 % (25662)Termination reason: Unknown
% 2.84/1.73 % (25662)Termination phase: shuffling
% 2.84/1.73
% 2.84/1.73 % (25662)Memory used [KB]: 1535
% 2.84/1.73 % (25662)Time elapsed: 0.005 s
% 2.84/1.73 % (25662)Instructions burned: 8 (million)
% 2.84/1.73 % (25662)------------------------------
% 2.84/1.73 % (25662)------------------------------
% 2.84/1.73 % (25641)Instruction limit reached!
% 2.84/1.73 % (25641)------------------------------
% 2.84/1.73 % (25641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.73 % (25641)Termination reason: Unknown
% 2.84/1.73 % (25641)Termination phase: Saturation
% 2.84/1.73
% 2.84/1.73 % (25641)Memory used [KB]: 7419
% 2.84/1.73 % (25641)Time elapsed: 0.084 s
% 2.84/1.73 % (25641)Instructions burned: 184 (million)
% 2.84/1.73 % (25641)------------------------------
% 2.84/1.73 % (25641)------------------------------
% 2.84/1.73 % (25663)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_25541 for (2999ds/902Mi)
% 2.84/1.74 % (25664)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_25541 for (2999ds/21Mi)
% 2.84/1.74 % (25665)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25541 for (2998ds/5Mi)
% 2.84/1.74 % (25666)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_25541 for (2998ds/6Mi)
% 2.84/1.74 % (25665)Instruction limit reached!
% 2.84/1.74 % (25665)------------------------------
% 2.84/1.74 % (25665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.74 % (25665)Termination reason: Unknown
% 2.84/1.74 % (25665)Termination phase: shuffling
% 2.84/1.74
% 2.84/1.74 % (25665)Memory used [KB]: 1407
% 2.84/1.74 % (25665)Time elapsed: 0.004 s
% 2.84/1.74 % (25665)Instructions burned: 5 (million)
% 2.84/1.74 % (25665)------------------------------
% 2.84/1.74 % (25665)------------------------------
% 2.84/1.75 % (25664)Instruction limit reached!
% 2.84/1.75 % (25664)------------------------------
% 2.84/1.75 % (25664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.75 % (25664)Termination reason: Unknown
% 2.84/1.75 % (25664)Termination phase: shuffling
% 2.84/1.75
% 2.84/1.75 % (25664)Memory used [KB]: 1791
% 2.84/1.75 % (25664)Time elapsed: 0.012 s
% 2.84/1.75 % (25664)Instructions burned: 23 (million)
% 2.84/1.75 % (25664)------------------------------
% 2.84/1.75 % (25664)------------------------------
% 2.84/1.75 % (25666)Instruction limit reached!
% 2.84/1.75 % (25666)------------------------------
% 2.84/1.75 % (25666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.75 % (25666)Termination reason: Unknown
% 2.84/1.75 % (25666)Termination phase: shuffling
% 2.84/1.75
% 2.84/1.75 % (25666)Memory used [KB]: 1535
% 2.84/1.75 % (25666)Time elapsed: 0.005 s
% 2.84/1.75 % (25666)Instructions burned: 7 (million)
% 2.84/1.75 % (25666)------------------------------
% 2.84/1.75 % (25666)------------------------------
% 2.84/1.76 % (25668)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_25541 for (2998ds/779Mi)
% 2.84/1.76 % (25667)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25541 for (2998ds/377Mi)
% 2.84/1.76 % (25669)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_25541 for (2998ds/19Mi)
% 2.84/1.77 % (25669)Instruction limit reached!
% 2.84/1.77 % (25669)------------------------------
% 2.84/1.77 % (25669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.77 % (25669)Termination reason: Unknown
% 2.84/1.77 % (25669)Termination phase: shuffling
% 2.84/1.77
% 2.84/1.77 % (25669)Memory used [KB]: 1791
% 2.84/1.77 % (25669)Time elapsed: 0.010 s
% 2.84/1.77 % (25669)Instructions burned: 19 (million)
% 2.84/1.77 % (25669)------------------------------
% 2.84/1.77 % (25669)------------------------------
% 2.84/1.78 % (25646)Instruction limit reached!
% 2.84/1.78 % (25646)------------------------------
% 2.84/1.78 % (25646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.78 % (25646)Termination reason: Unknown
% 2.84/1.78 % (25646)Termination phase: Saturation
% 2.84/1.78
% 2.84/1.78 % (25646)Memory used [KB]: 8699
% 2.84/1.78 % (25646)Time elapsed: 0.135 s
% 2.84/1.78 % (25646)Instructions burned: 275 (million)
% 2.84/1.78 % (25646)------------------------------
% 2.84/1.78 % (25646)------------------------------
% 2.84/1.79 % (25670)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25541 for (2998ds/879Mi)
% 2.84/1.79 % (25671)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25541 for (2998ds/17Mi)
% 2.84/1.80 % (25671)Instruction limit reached!
% 2.84/1.80 % (25671)------------------------------
% 2.84/1.80 % (25671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.80 % (25671)Termination reason: Unknown
% 2.84/1.80 % (25671)Termination phase: shuffling
% 2.84/1.80
% 2.84/1.80 % (25671)Memory used [KB]: 1791
% 2.84/1.80 % (25671)Time elapsed: 0.011 s
% 2.84/1.80 % (25671)Instructions burned: 18 (million)
% 2.84/1.80 % (25671)------------------------------
% 2.84/1.80 % (25671)------------------------------
% 2.84/1.82 % (25672)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25541 for (2998ds/3Mi)
% 2.84/1.82 % (25672)Instruction limit reached!
% 2.84/1.82 % (25672)------------------------------
% 2.84/1.82 % (25672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.82 % (25672)Termination reason: Unknown
% 2.84/1.82 % (25672)Termination phase: shuffling
% 2.84/1.82
% 2.84/1.82 % (25672)Memory used [KB]: 1407
% 2.84/1.82 % (25672)Time elapsed: 0.004 s
% 2.84/1.82 % (25672)Instructions burned: 4 (million)
% 2.84/1.82 % (25672)------------------------------
% 2.84/1.82 % (25672)------------------------------
% 2.84/1.84 % (25673)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_25541 for (2998ds/30Mi)
% 2.84/1.85 % (25673)Instruction limit reached!
% 2.84/1.85 % (25673)------------------------------
% 2.84/1.85 % (25673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.85 % (25673)Termination reason: Unknown
% 2.84/1.85 % (25673)Termination phase: shuffling
% 2.84/1.85
% 2.84/1.85 % (25673)Memory used [KB]: 2046
% 2.84/1.85 % (25673)Time elapsed: 0.016 s
% 2.84/1.85 % (25673)Instructions burned: 31 (million)
% 2.84/1.85 % (25673)------------------------------
% 2.84/1.85 % (25673)------------------------------
% 2.84/1.87 % (25674)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_25541 for (2997ds/127Mi)
% 2.84/1.92 % (25674)Instruction limit reached!
% 2.84/1.92 % (25674)------------------------------
% 2.84/1.92 % (25674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.92 % (25674)Termination reason: Unknown
% 2.84/1.92 % (25674)Termination phase: Saturation
% 2.84/1.92
% 2.84/1.92 % (25674)Memory used [KB]: 6908
% 2.84/1.92 % (25674)Time elapsed: 0.057 s
% 2.84/1.92 % (25674)Instructions burned: 127 (million)
% 2.84/1.92 % (25674)------------------------------
% 2.84/1.92 % (25674)------------------------------
% 2.84/1.94 % (25667)Instruction limit reached!
% 2.84/1.94 % (25667)------------------------------
% 2.84/1.94 % (25667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.94 % (25667)Termination reason: Unknown
% 2.84/1.94 % (25667)Termination phase: Saturation
% 2.84/1.94
% 2.84/1.94 % (25667)Memory used [KB]: 8571
% 2.84/1.94 % (25667)Time elapsed: 0.180 s
% 2.84/1.94 % (25667)Instructions burned: 378 (million)
% 2.84/1.94 % (25667)------------------------------
% 2.84/1.94 % (25667)------------------------------
% 2.84/1.94 % (25675)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_25541 for (2996ds/100Mi)
% 2.84/1.96 % (25676)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_25541 for (2996ds/3Mi)
% 2.84/1.96 % (25676)Instruction limit reached!
% 2.84/1.96 % (25676)------------------------------
% 2.84/1.96 % (25676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.96 % (25676)Termination reason: Unknown
% 2.84/1.96 % (25676)Termination phase: shuffling
% 2.84/1.96
% 2.84/1.96 % (25676)Memory used [KB]: 1407
% 2.84/1.96 % (25676)Time elapsed: 0.003 s
% 2.84/1.96 % (25676)Instructions burned: 3 (million)
% 2.84/1.96 % (25676)------------------------------
% 2.84/1.96 % (25676)------------------------------
% 2.84/1.97 % (25677)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_25541 for (2996ds/20Mi)
% 2.84/1.98 % (25677)Instruction limit reached!
% 2.84/1.98 % (25677)------------------------------
% 2.84/1.98 % (25677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.98 % (25677)Termination reason: Unknown
% 2.84/1.98 % (25677)Termination phase: Property scanning
% 2.84/1.98
% 2.84/1.98 % (25677)Memory used [KB]: 1791
% 2.84/1.98 % (25677)Time elapsed: 0.012 s
% 2.84/1.98 % (25677)Instructions burned: 20 (million)
% 2.84/1.98 % (25677)------------------------------
% 2.84/1.98 % (25677)------------------------------
% 2.84/1.98 % (25675)Instruction limit reached!
% 2.84/1.98 % (25675)------------------------------
% 2.84/1.98 % (25675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.98 % (25675)Termination reason: Unknown
% 2.84/1.98 % (25675)Termination phase: Property scanning
% 2.84/1.98
% 2.84/1.98 % (25675)Memory used [KB]: 2302
% 2.84/1.98 % (25675)Time elapsed: 0.046 s
% 2.84/1.98 % (25675)Instructions burned: 102 (million)
% 2.84/1.98 % (25675)------------------------------
% 2.84/1.98 % (25675)------------------------------
% 2.84/2.00 % (25678)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_25541 for (2996ds/86Mi)
% 2.84/2.00 % (25679)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_25541 for (2996ds/107Mi)
% 5.55/2.04 % (25678)Instruction limit reached!
% 5.55/2.04 % (25678)------------------------------
% 5.55/2.04 % (25678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.04 % (25678)Termination reason: Unknown
% 5.55/2.04 % (25678)Termination phase: Property scanning
% 5.55/2.04
% 5.55/2.04 % (25678)Memory used [KB]: 2302
% 5.55/2.04 % (25678)Time elapsed: 0.040 s
% 5.55/2.04 % (25678)Instructions burned: 86 (million)
% 5.55/2.04 % (25678)------------------------------
% 5.55/2.04 % (25678)------------------------------
% 5.55/2.04 % (25668)Instruction limit reached!
% 5.55/2.04 % (25668)------------------------------
% 5.55/2.04 % (25668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.04 % (25668)Termination reason: Unknown
% 5.55/2.04 % (25668)Termination phase: Saturation
% 5.55/2.04
% 5.55/2.04 % (25668)Memory used [KB]: 7291
% 5.55/2.04 % (25668)Time elapsed: 0.283 s
% 5.55/2.04 % (25668)Instructions burned: 780 (million)
% 5.55/2.04 % (25668)------------------------------
% 5.55/2.04 % (25668)------------------------------
% 5.55/2.05 % (25679)Instruction limit reached!
% 5.55/2.05 % (25679)------------------------------
% 5.55/2.05 % (25679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.05 % (25679)Termination reason: Unknown
% 5.55/2.05 % (25679)Termination phase: Property scanning
% 5.55/2.05
% 5.55/2.05 % (25679)Memory used [KB]: 2302
% 5.55/2.05 % (25679)Time elapsed: 0.047 s
% 5.55/2.05 % (25679)Instructions burned: 108 (million)
% 5.55/2.05 % (25679)------------------------------
% 5.55/2.05 % (25679)------------------------------
% 5.55/2.05 % (25652)Instruction limit reached!
% 5.55/2.05 % (25652)------------------------------
% 5.55/2.05 % (25652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.05 % (25652)Termination reason: Unknown
% 5.55/2.05 % (25652)Termination phase: Saturation
% 5.55/2.05
% 5.55/2.05 % (25652)Memory used [KB]: 11897
% 5.55/2.05 % (25652)Time elapsed: 0.383 s
% 5.55/2.05 % (25652)Instructions burned: 1041 (million)
% 5.55/2.05 % (25652)------------------------------
% 5.55/2.05 % (25652)------------------------------
% 5.55/2.06 % (25680)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_25541 for (2995ds/39Mi)
% 5.55/2.06 % (25681)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_25541 for (2995ds/448Mi)
% 5.55/2.06 % (25682)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_25541 for (2995ds/46Mi)
% 5.55/2.07 % (25661)Instruction limit reached!
% 5.55/2.07 % (25661)------------------------------
% 5.55/2.07 % (25661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.07 % (25661)Termination reason: Unknown
% 5.55/2.07 % (25661)Termination phase: Saturation
% 5.55/2.07
% 5.55/2.07 % (25661)Memory used [KB]: 9850
% 5.55/2.07 % (25661)Time elapsed: 0.353 s
% 5.55/2.07 % (25661)Instructions burned: 710 (million)
% 5.55/2.07 % (25661)------------------------------
% 5.55/2.07 % (25661)------------------------------
% 5.55/2.07 % (25683)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_25541 for (2995ds/98Mi)
% 5.55/2.07 % (25680)Instruction limit reached!
% 5.55/2.07 % (25680)------------------------------
% 5.55/2.07 % (25680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.07 % (25680)Termination reason: Unknown
% 5.55/2.07 % (25680)Termination phase: Property scanning
% 5.55/2.07
% 5.55/2.07 % (25680)Memory used [KB]: 2174
% 5.55/2.07 % (25680)Time elapsed: 0.020 s
% 5.55/2.07 % (25680)Instructions burned: 40 (million)
% 5.55/2.07 % (25680)------------------------------
% 5.55/2.07 % (25680)------------------------------
% 5.55/2.08 % (25684)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_25541 for (2995ds/507Mi)
% 5.55/2.08 % (25682)Instruction limit reached!
% 5.55/2.08 % (25682)------------------------------
% 5.55/2.08 % (25682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.08 % (25682)Termination reason: Unknown
% 5.55/2.08 % (25682)Termination phase: Property scanning
% 5.55/2.08
% 5.55/2.08 % (25682)Memory used [KB]: 2046
% 5.55/2.08 % (25682)Time elapsed: 0.022 s
% 5.55/2.08 % (25682)Instructions burned: 47 (million)
% 5.55/2.08 % (25682)------------------------------
% 5.55/2.08 % (25682)------------------------------
% 5.55/2.09 % (25685)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_25541 for (2995ds/149Mi)
% 5.55/2.10 % (25686)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_25541 for (2995ds/39Mi)
% 5.55/2.11 % (25683)Instruction limit reached!
% 5.55/2.11 % (25683)------------------------------
% 5.55/2.11 % (25683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.11 % (25683)Termination reason: Unknown
% 5.55/2.11 % (25683)Termination phase: Property scanning
% 5.55/2.11
% 5.55/2.11 % (25683)Memory used [KB]: 2302
% 5.55/2.11 % (25683)Time elapsed: 0.044 s
% 5.55/2.11 % (25683)Instructions burned: 99 (million)
% 5.55/2.11 % (25683)------------------------------
% 5.55/2.11 % (25683)------------------------------
% 5.55/2.12 % (25686)Instruction limit reached!
% 5.55/2.12 % (25686)------------------------------
% 5.55/2.12 % (25686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.12 % (25686)Termination reason: Unknown
% 5.55/2.12 % (25686)Termination phase: Property scanning
% 5.55/2.12
% 5.55/2.12 % (25686)Memory used [KB]: 2046
% 5.55/2.12 % (25686)Time elapsed: 0.019 s
% 5.55/2.12 % (25686)Instructions burned: 40 (million)
% 5.55/2.12 % (25686)------------------------------
% 5.55/2.12 % (25686)------------------------------
% 6.08/2.13 % (25687)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_25541 for (2995ds/6Mi)
% 6.08/2.13 % (25688)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_25541 for (2995ds/1087Mi)
% 6.08/2.14 % (25687)Instruction limit reached!
% 6.08/2.14 % (25687)------------------------------
% 6.08/2.14 % (25687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.14 % (25687)Termination reason: Unknown
% 6.08/2.14 % (25687)Termination phase: shuffling
% 6.08/2.14
% 6.08/2.14 % (25687)Memory used [KB]: 1407
% 6.08/2.14 % (25687)Time elapsed: 0.004 s
% 6.08/2.14 % (25687)Instructions burned: 6 (million)
% 6.08/2.14 % (25687)------------------------------
% 6.08/2.14 % (25687)------------------------------
% 6.08/2.14 % (25685)Instruction limit reached!
% 6.08/2.14 % (25685)------------------------------
% 6.08/2.14 % (25685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.14 % (25685)Termination reason: Unknown
% 6.08/2.14 % (25685)Termination phase: Saturation
% 6.08/2.14
% 6.08/2.14 % (25685)Memory used [KB]: 7419
% 6.08/2.14 % (25685)Time elapsed: 0.051 s
% 6.08/2.14 % (25685)Instructions burned: 149 (million)
% 6.08/2.14 % (25685)------------------------------
% 6.08/2.14 % (25685)------------------------------
% 6.08/2.15 % (25690)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_25541 for (2994ds/44Mi)
% 6.08/2.15 % (25689)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_25541 for (2994ds/47Mi)
% 6.08/2.16 % (25663)Instruction limit reached!
% 6.08/2.16 % (25663)------------------------------
% 6.08/2.16 % (25663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.16 % (25663)Termination reason: Unknown
% 6.08/2.16 % (25663)Termination phase: Saturation
% 6.08/2.16
% 6.08/2.16 % (25663)Memory used [KB]: 10490
% 6.08/2.16 % (25663)Time elapsed: 0.431 s
% 6.08/2.16 % (25663)Instructions burned: 903 (million)
% 6.08/2.16 % (25663)------------------------------
% 6.08/2.16 % (25663)------------------------------
% 6.08/2.16 % (25690)Instruction limit reached!
% 6.08/2.16 % (25690)------------------------------
% 6.08/2.16 % (25690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.16 % (25690)Termination reason: Unknown
% 6.08/2.16 % (25690)Termination phase: Property scanning
% 6.08/2.16
% 6.08/2.16 % (25690)Memory used [KB]: 2174
% 6.08/2.16 % (25690)Time elapsed: 0.013 s
% 6.08/2.16 % (25690)Instructions burned: 47 (million)
% 6.08/2.16 % (25690)------------------------------
% 6.08/2.16 % (25690)------------------------------
% 6.08/2.17 % (25689)Instruction limit reached!
% 6.08/2.17 % (25689)------------------------------
% 6.08/2.17 % (25689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.17 % (25692)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_25541 for (2994ds/62Mi)
% 6.08/2.17 % (25689)Termination reason: Unknown
% 6.08/2.17 % (25689)Termination phase: Property scanning
% 6.08/2.17
% 6.08/2.17 % (25689)Memory used [KB]: 2046
% 6.08/2.17 % (25689)Time elapsed: 0.023 s
% 6.08/2.17 % (25689)Instructions burned: 47 (million)
% 6.08/2.17 % (25689)------------------------------
% 6.08/2.17 % (25689)------------------------------
% 6.08/2.17 % (25691)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_25541 for (2994ds/432Mi)
% 6.08/2.19 % (25693)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_25541 for (2994ds/31Mi)
% 6.34/2.20 % (25692)Instruction limit reached!
% 6.34/2.20 % (25692)------------------------------
% 6.34/2.20 % (25692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.20 % (25692)Termination reason: Unknown
% 6.34/2.20 % (25692)Termination phase: Property scanning
% 6.34/2.20
% 6.34/2.20 % (25692)Memory used [KB]: 2174
% 6.34/2.20 % (25692)Time elapsed: 0.029 s
% 6.34/2.20 % (25692)Instructions burned: 62 (million)
% 6.34/2.20 % (25692)------------------------------
% 6.34/2.20 % (25692)------------------------------
% 6.34/2.20 % (25693)Instruction limit reached!
% 6.34/2.20 % (25693)------------------------------
% 6.34/2.20 % (25693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.20 % (25693)Termination reason: Unknown
% 6.34/2.20 % (25693)Termination phase: shuffling
% 6.34/2.20
% 6.34/2.20 % (25693)Memory used [KB]: 1918
% 6.34/2.20 % (25693)Time elapsed: 0.016 s
% 6.34/2.20 % (25693)Instructions burned: 31 (million)
% 6.34/2.20 % (25693)------------------------------
% 6.34/2.20 % (25693)------------------------------
% 6.34/2.21 % (25670)Instruction limit reached!
% 6.34/2.21 % (25670)------------------------------
% 6.34/2.21 % (25670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.21 % (25670)Termination reason: Unknown
% 6.34/2.21 % (25670)Termination phase: Saturation
% 6.34/2.21
% 6.34/2.21 % (25670)Memory used [KB]: 8699
% 6.34/2.21 % (25670)Time elapsed: 0.429 s
% 6.34/2.21 % (25670)Instructions burned: 879 (million)
% 6.34/2.21 % (25670)------------------------------
% 6.34/2.21 % (25670)------------------------------
% 6.34/2.22 % (25694)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_25541 for (2994ds/96Mi)
% 6.34/2.22 % (25695)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_25541 for (2994ds/453Mi)
% 6.34/2.23 % (25681)Instruction limit reached!
% 6.34/2.23 % (25681)------------------------------
% 6.34/2.23 % (25681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.23 % (25681)Termination reason: Unknown
% 6.34/2.23 % (25681)Termination phase: Saturation
% 6.34/2.23
% 6.34/2.23 % (25681)Memory used [KB]: 7164
% 6.34/2.23 % (25681)Time elapsed: 0.175 s
% 6.34/2.23 % (25681)Instructions burned: 449 (million)
% 6.34/2.23 % (25681)------------------------------
% 6.34/2.23 % (25681)------------------------------
% 6.34/2.23 % (25696)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_25541 for (2994ds/71Mi)
% 6.34/2.25 % (25697)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_25541 for (2993ds/83Mi)
% 6.34/2.26 % (25694)Instruction limit reached!
% 6.34/2.26 % (25694)------------------------------
% 6.34/2.26 % (25694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.26 % (25694)Termination reason: Unknown
% 6.34/2.26 % (25694)Termination phase: Property scanning
% 6.34/2.26
% 6.34/2.26 % (25694)Memory used [KB]: 2302
% 6.34/2.26 % (25694)Time elapsed: 0.044 s
% 6.34/2.26 % (25694)Instructions burned: 97 (million)
% 6.34/2.26 % (25694)------------------------------
% 6.34/2.26 % (25694)------------------------------
% 6.34/2.26 % (25696)Instruction limit reached!
% 6.34/2.26 % (25696)------------------------------
% 6.34/2.26 % (25696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.26 % (25696)Termination reason: Unknown
% 6.34/2.26 % (25696)Termination phase: Property scanning
% 6.34/2.26
% 6.34/2.26 % (25696)Memory used [KB]: 2174
% 6.34/2.26 % (25696)Time elapsed: 0.034 s
% 6.34/2.26 % (25696)Instructions burned: 72 (million)
% 6.34/2.26 % (25696)------------------------------
% 6.34/2.26 % (25696)------------------------------
% 6.34/2.28 % (25698)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_25541 for (2993ds/11Mi)
% 6.34/2.28 % (25698)Instruction limit reached!
% 6.34/2.28 % (25698)------------------------------
% 6.34/2.28 % (25698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.28 % (25698)Termination reason: Unknown
% 6.34/2.28 % (25698)Termination phase: shuffling
% 6.34/2.28
% 6.34/2.28 % (25698)Memory used [KB]: 1535
% 6.34/2.28 % (25699)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_25541 for (2993ds/41Mi)
% 6.34/2.28 % (25698)Time elapsed: 0.007 s
% 6.34/2.28 % (25698)Instructions burned: 11 (million)
% 6.34/2.28 % (25698)------------------------------
% 6.34/2.28 % (25698)------------------------------
% 6.34/2.28 % (25697)Instruction limit reached!
% 6.34/2.28 % (25697)------------------------------
% 6.34/2.28 % (25697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.34/2.28 % (25697)Termination reason: Unknown
% 6.34/2.28 % (25697)Termination phase: Property scanning
% 6.34/2.28
% 6.34/2.28 % (25697)Memory used [KB]: 2174
% 6.34/2.28 % (25697)Time elapsed: 0.037 s
% 6.34/2.28 % (25697)Instructions burned: 83 (million)
% 6.34/2.28 % (25697)------------------------------
% 6.34/2.28 % (25697)------------------------------
% 6.34/2.30 % (25700)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25541 for (2993ds/6Mi)
% 6.81/2.30 % (25699)Instruction limit reached!
% 6.81/2.30 % (25699)------------------------------
% 6.81/2.30 % (25699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.30 % (25701)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_25541 for (2993ds/150Mi)
% 6.81/2.30 % (25699)Termination reason: Unknown
% 6.81/2.30 % (25699)Termination phase: Property scanning
% 6.81/2.30
% 6.81/2.30 % (25699)Memory used [KB]: 2174
% 6.81/2.30 % (25699)Time elapsed: 0.021 s
% 6.81/2.30 % (25699)Instructions burned: 42 (million)
% 6.81/2.30 % (25699)------------------------------
% 6.81/2.30 % (25699)------------------------------
% 6.81/2.30 % (25700)Instruction limit reached!
% 6.81/2.30 % (25700)------------------------------
% 6.81/2.30 % (25700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.30 % (25700)Termination reason: Unknown
% 6.81/2.30 % (25700)Termination phase: shuffling
% 6.81/2.30
% 6.81/2.30 % (25700)Memory used [KB]: 1535
% 6.81/2.30 % (25700)Time elapsed: 0.005 s
% 6.81/2.30 % (25700)Instructions burned: 7 (million)
% 6.81/2.30 % (25700)------------------------------
% 6.81/2.30 % (25700)------------------------------
% 6.81/2.31 % (25702)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_25541 for (2993ds/343Mi)
% 6.81/2.32 % (25703)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_25541 for (2993ds/109Mi)
% 6.81/2.32 % (25684)Instruction limit reached!
% 6.81/2.32 % (25684)------------------------------
% 6.81/2.32 % (25684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.32 % (25684)Termination reason: Unknown
% 6.81/2.32 % (25684)Termination phase: Saturation
% 6.81/2.32
% 6.81/2.32 % (25684)Memory used [KB]: 7803
% 6.81/2.32 % (25684)Time elapsed: 0.241 s
% 6.81/2.32 % (25684)Instructions burned: 507 (million)
% 6.81/2.32 % (25684)------------------------------
% 6.81/2.32 % (25684)------------------------------
% 6.81/2.34 % (25704)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_25541 for (2992ds/253Mi)
% 6.81/2.34 % (25691)Instruction limit reached!
% 6.81/2.34 % (25691)------------------------------
% 6.81/2.34 % (25691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.34 % (25691)Termination reason: Unknown
% 6.81/2.34 % (25691)Termination phase: Saturation
% 6.81/2.34
% 6.81/2.34 % (25691)Memory used [KB]: 3198
% 6.81/2.34 % (25691)Time elapsed: 0.172 s
% 6.81/2.34 % (25691)Instructions burned: 433 (million)
% 6.81/2.34 % (25691)------------------------------
% 6.81/2.34 % (25691)------------------------------
% 6.81/2.36 % (25705)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_25541 for (2992ds/140Mi)
% 6.81/2.36 % (25703)Instruction limit reached!
% 6.81/2.36 % (25703)------------------------------
% 6.81/2.36 % (25703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.36 % (25703)Termination reason: Unknown
% 6.81/2.36 % (25703)Termination phase: Property scanning
% 6.81/2.36
% 6.81/2.36 % (25703)Memory used [KB]: 2302
% 6.81/2.36 % (25703)Time elapsed: 0.048 s
% 6.81/2.36 % (25703)Instructions burned: 109 (million)
% 6.81/2.36 % (25703)------------------------------
% 6.81/2.36 % (25703)------------------------------
% 6.81/2.37 % (25701)Instruction limit reached!
% 6.81/2.37 % (25701)------------------------------
% 6.81/2.37 % (25701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.37 % (25701)Termination reason: Unknown
% 6.81/2.37 % (25701)Termination phase: Saturation
% 6.81/2.37
% 6.81/2.37 % (25701)Memory used [KB]: 8315
% 6.81/2.37 % (25701)Time elapsed: 0.071 s
% 6.81/2.37 % (25701)Instructions burned: 150 (million)
% 6.81/2.37 % (25701)------------------------------
% 6.81/2.37 % (25701)------------------------------
% 6.81/2.38 % (25706)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_25541 for (2992ds/614Mi)
% 6.81/2.38 % (25707)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_25541 for (2992ds/202Mi)
% 6.81/2.39 % (25695)Instruction limit reached!
% 6.81/2.39 % (25695)------------------------------
% 6.81/2.39 % (25695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.39 % (25695)Termination reason: Unknown
% 6.81/2.39 % (25695)Termination phase: Saturation
% 6.81/2.39
% 6.81/2.39 % (25695)Memory used [KB]: 7164
% 6.81/2.39 % (25695)Time elapsed: 0.175 s
% 6.81/2.39 % (25695)Instructions burned: 453 (million)
% 6.81/2.39 % (25695)------------------------------
% 6.81/2.39 % (25695)------------------------------
% 7.65/2.41 % (25708)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_25541 for (2992ds/339Mi)
% 7.65/2.42 % (25705)Instruction limit reached!
% 7.65/2.42 % (25705)------------------------------
% 7.65/2.42 % (25705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.42 % (25705)Termination reason: Unknown
% 7.65/2.42 % (25705)Termination phase: Saturation
% 7.65/2.42
% 7.65/2.42 % (25705)Memory used [KB]: 6908
% 7.65/2.42 % (25705)Time elapsed: 0.064 s
% 7.65/2.42 % (25705)Instructions burned: 141 (million)
% 7.65/2.42 % (25705)------------------------------
% 7.65/2.42 % (25705)------------------------------
% 7.65/2.44 % (25709)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_25541 for (2991ds/283Mi)
% 7.65/2.46 % (25704)Instruction limit reached!
% 7.65/2.46 % (25704)------------------------------
% 7.65/2.46 % (25704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.46 % (25704)Termination reason: Unknown
% 7.65/2.46 % (25704)Termination phase: Saturation
% 7.65/2.46
% 7.65/2.46 % (25704)Memory used [KB]: 8955
% 7.65/2.46 % (25704)Time elapsed: 0.121 s
% 7.65/2.46 % (25704)Instructions burned: 253 (million)
% 7.65/2.46 % (25704)------------------------------
% 7.65/2.46 % (25704)------------------------------
% 7.65/2.47 % (25702)Instruction limit reached!
% 7.65/2.47 % (25702)------------------------------
% 7.65/2.47 % (25702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.47 % (25702)Termination reason: Unknown
% 7.65/2.47 % (25702)Termination phase: Saturation
% 7.65/2.47
% 7.65/2.47 % (25702)Memory used [KB]: 8187
% 7.65/2.47 % (25702)Time elapsed: 0.152 s
% 7.65/2.47 % (25702)Instructions burned: 343 (million)
% 7.65/2.47 % (25702)------------------------------
% 7.65/2.47 % (25702)------------------------------
% 7.65/2.47 % (25710)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_25541 for (2991ds/134Mi)
% 7.65/2.48 % (25711)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_25541 for (2991ds/298Mi)
% 7.65/2.48 % (25707)Instruction limit reached!
% 7.65/2.48 % (25707)------------------------------
% 7.65/2.48 % (25707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.48 % (25707)Termination reason: Unknown
% 7.65/2.48 % (25707)Termination phase: Saturation
% 7.65/2.48
% 7.65/2.48 % (25707)Memory used [KB]: 4733
% 7.65/2.48 % (25707)Time elapsed: 0.099 s
% 7.65/2.48 % (25707)Instructions burned: 203 (million)
% 7.65/2.48 % (25707)------------------------------
% 7.65/2.48 % (25707)------------------------------
% 8.15/2.50 % (25712)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_25541 for (2991ds/192Mi)
% 8.15/2.53 % (25710)Instruction limit reached!
% 8.15/2.53 % (25710)------------------------------
% 8.15/2.53 % (25710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.53 % (25710)Termination reason: Unknown
% 8.15/2.53 % (25710)Termination phase: Saturation
% 8.15/2.53
% 8.15/2.53 % (25710)Memory used [KB]: 7036
% 8.15/2.53 % (25710)Time elapsed: 0.061 s
% 8.15/2.53 % (25710)Instructions burned: 135 (million)
% 8.15/2.53 % (25710)------------------------------
% 8.15/2.53 % (25710)------------------------------
% 8.15/2.55 % (25713)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_25541 for (2990ds/258Mi)
% 8.15/2.56 % (25709)Instruction limit reached!
% 8.15/2.56 % (25709)------------------------------
% 8.15/2.56 % (25709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.56 % (25709)Termination reason: Unknown
% 8.15/2.56 % (25709)Termination phase: Saturation
% 8.15/2.56
% 8.15/2.56 % (25709)Memory used [KB]: 7164
% 8.15/2.56 % (25709)Time elapsed: 0.119 s
% 8.15/2.56 % (25709)Instructions burned: 284 (million)
% 8.15/2.56 % (25709)------------------------------
% 8.15/2.56 % (25709)------------------------------
% 8.15/2.56 % (25708)Instruction limit reached!
% 8.15/2.56 % (25708)------------------------------
% 8.15/2.56 % (25708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.56 % (25708)Termination reason: Unknown
% 8.15/2.56 % (25708)Termination phase: Saturation
% 8.15/2.56
% 8.15/2.56 % (25708)Memory used [KB]: 7419
% 8.15/2.56 % (25708)Time elapsed: 0.152 s
% 8.15/2.56 % (25708)Instructions burned: 339 (million)
% 8.15/2.56 % (25708)------------------------------
% 8.15/2.56 % (25708)------------------------------
% 8.15/2.57 % (25714)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_25541 for (2990ds/90Mi)
% 8.15/2.57 % (25715)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_25541 for (2990ds/231Mi)
% 8.15/2.58 % (25712)Instruction limit reached!
% 8.15/2.58 % (25712)------------------------------
% 8.15/2.58 % (25712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.58 % (25712)Termination reason: Unknown
% 8.15/2.58 % (25712)Termination phase: Saturation
% 8.15/2.58
% 8.15/2.58 % (25712)Memory used [KB]: 7547
% 8.15/2.58 % (25712)Time elapsed: 0.086 s
% 8.15/2.58 % (25712)Instructions burned: 193 (million)
% 8.15/2.58 % (25712)------------------------------
% 8.15/2.58 % (25712)------------------------------
% 8.63/2.60 % (25716)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_25541 for (2990ds/458Mi)
% 8.63/2.60 % (25711)Instruction limit reached!
% 8.63/2.60 % (25711)------------------------------
% 8.63/2.60 % (25711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.63/2.60 % (25711)Termination reason: Unknown
% 8.63/2.60 % (25711)Termination phase: Saturation
% 8.63/2.60
% 8.63/2.60 % (25711)Memory used [KB]: 7164
% 8.63/2.60 % (25711)Time elapsed: 0.124 s
% 8.63/2.60 % (25711)Instructions burned: 298 (million)
% 8.63/2.60 % (25711)------------------------------
% 8.63/2.60 % (25711)------------------------------
% 8.63/2.61 % (25714)Instruction limit reached!
% 8.63/2.61 % (25714)------------------------------
% 8.63/2.61 % (25714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.63/2.61 % (25714)Termination reason: Unknown
% 8.63/2.61 % (25714)Termination phase: Twee Goal Transformation
% 8.63/2.61
% 8.63/2.61 % (25714)Memory used [KB]: 2430
% 8.63/2.61 % (25714)Time elapsed: 0.041 s
% 8.63/2.61 % (25714)Instructions burned: 90 (million)
% 8.63/2.61 % (25714)------------------------------
% 8.63/2.61 % (25714)------------------------------
% 8.63/2.62 % (25717)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_25541 for (2990ds/31Mi)
% 8.63/2.63 % (25718)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_25541 for (2990ds/297Mi)
% 8.63/2.63 % (25717)Instruction limit reached!
% 8.63/2.63 % (25717)------------------------------
% 8.63/2.63 % (25717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.63/2.63 % (25717)Termination reason: Unknown
% 8.63/2.63 % (25717)Termination phase: shuffling
% 8.63/2.63
% 8.63/2.63 % (25717)Memory used [KB]: 2046
% 8.63/2.63 % (25717)Time elapsed: 0.015 s
% 8.63/2.63 % (25717)Instructions burned: 32 (million)
% 8.63/2.63 % (25717)------------------------------
% 8.63/2.63 % (25717)------------------------------
% 8.63/2.65 % (25719)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_25541 for (2989ds/987Mi)
% 8.63/2.66 % (25713)Instruction limit reached!
% 8.63/2.66 % (25713)------------------------------
% 8.63/2.66 % (25713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.63/2.66 % (25713)Termination reason: Unknown
% 8.63/2.66 % (25713)Termination phase: Saturation
% 8.63/2.66
% 8.63/2.66 % (25713)Memory used [KB]: 7803
% 8.63/2.66 % (25713)Time elapsed: 0.114 s
% 8.63/2.66 % (25713)Instructions burned: 259 (million)
% 8.63/2.66 % (25713)------------------------------
% 8.63/2.66 % (25713)------------------------------
% 8.63/2.67 % (25706)Instruction limit reached!
% 8.63/2.67 % (25706)------------------------------
% 8.63/2.67 % (25706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.63/2.67 % (25706)Termination reason: Unknown
% 8.63/2.67 % (25706)Termination phase: Saturation
% 8.63/2.67
% 8.63/2.67 % (25706)Memory used [KB]: 8699
% 8.63/2.67 % (25706)Time elapsed: 0.295 s
% 8.63/2.67 % (25706)Instructions burned: 616 (million)
% 8.63/2.67 % (25706)------------------------------
% 8.63/2.67 % (25706)------------------------------
% 8.63/2.68 % (25688)Instruction limit reached!
% 8.63/2.68 % (25688)------------------------------
% 8.63/2.68 % (25688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.63/2.68 % (25688)Termination reason: Unknown
% 8.63/2.68 % (25688)Termination phase: Saturation
% 8.63/2.68
% 8.63/2.68 % (25688)Memory used [KB]: 10490
% 8.63/2.68 % (25688)Time elapsed: 0.546 s
% 8.63/2.68 % (25688)Instructions burned: 1088 (million)
% 8.63/2.68 % (25688)------------------------------
% 8.63/2.68 % (25688)------------------------------
% 8.63/2.68 % (25720)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_25541 for (2989ds/182Mi)
% 8.63/2.68 % (25715)Instruction limit reached!
% 8.63/2.68 % (25715)------------------------------
% 8.63/2.68 % (25715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.63/2.68 % (25715)Termination reason: Unknown
% 8.63/2.68 % (25715)Termination phase: Saturation
% 8.63/2.68
% 8.63/2.68 % (25715)Memory used [KB]: 12409
% 8.63/2.68 % (25715)Time elapsed: 0.110 s
% 8.63/2.68 % (25715)Instructions burned: 232 (million)
% 8.63/2.68 % (25715)------------------------------
% 8.63/2.68 % (25715)------------------------------
% 8.63/2.69 % (25721)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_25541 for (2989ds/182Mi)
% 8.63/2.69 % (25722)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_25541 for (2989ds/154Mi)
% 9.98/2.70 % (25723)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_25541 for (2989ds/79Mi)
% 9.98/2.74 % (25723)Instruction limit reached!
% 9.98/2.74 % (25723)------------------------------
% 9.98/2.74 % (25723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.74 % (25723)Termination reason: Unknown
% 9.98/2.74 % (25723)Termination phase: Function definition elimination
% 9.98/2.74
% 9.98/2.74 % (25723)Memory used [KB]: 2302
% 9.98/2.74 % (25723)Time elapsed: 0.037 s
% 9.98/2.74 % (25723)Instructions burned: 79 (million)
% 9.98/2.74 % (25723)------------------------------
% 9.98/2.74 % (25723)------------------------------
% 9.98/2.75 % (25718)Instruction limit reached!
% 9.98/2.75 % (25718)------------------------------
% 9.98/2.75 % (25718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.75 % (25718)Termination reason: Unknown
% 9.98/2.75 % (25718)Termination phase: Saturation
% 9.98/2.75
% 9.98/2.75 % (25718)Memory used [KB]: 7164
% 9.98/2.75 % (25718)Time elapsed: 0.122 s
% 9.98/2.75 % (25718)Instructions burned: 297 (million)
% 9.98/2.75 % (25718)------------------------------
% 9.98/2.75 % (25718)------------------------------
% 9.98/2.75 % (25724)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_25541 for (2988ds/216Mi)
% 9.98/2.76 % (25722)Instruction limit reached!
% 9.98/2.76 % (25722)------------------------------
% 9.98/2.76 % (25722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.76 % (25722)Termination reason: Unknown
% 9.98/2.76 % (25722)Termination phase: Saturation
% 9.98/2.76
% 9.98/2.76 % (25722)Memory used [KB]: 6908
% 9.98/2.76 % (25722)Time elapsed: 0.068 s
% 9.98/2.76 % (25722)Instructions burned: 155 (million)
% 9.98/2.76 % (25722)------------------------------
% 9.98/2.76 % (25722)------------------------------
% 9.98/2.76 % (25720)Instruction limit reached!
% 9.98/2.76 % (25720)------------------------------
% 9.98/2.76 % (25720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.76 % (25720)Termination reason: Unknown
% 9.98/2.76 % (25720)Termination phase: Saturation
% 9.98/2.76
% 9.98/2.76 % (25720)Memory used [KB]: 7419
% 9.98/2.76 % (25720)Time elapsed: 0.084 s
% 9.98/2.76 % (25720)Instructions burned: 183 (million)
% 9.98/2.76 % (25720)------------------------------
% 9.98/2.76 % (25720)------------------------------
% 9.98/2.77 % (25725)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_25541 for (2988ds/114Mi)
% 9.98/2.77 % (25721)Instruction limit reached!
% 9.98/2.77 % (25721)------------------------------
% 9.98/2.77 % (25721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.77 % (25721)Termination reason: Unknown
% 9.98/2.77 % (25721)Termination phase: Saturation
% 9.98/2.77
% 9.98/2.77 % (25721)Memory used [KB]: 9978
% 9.98/2.77 % (25721)Time elapsed: 0.088 s
% 9.98/2.77 % (25721)Instructions burned: 182 (million)
% 9.98/2.77 % (25721)------------------------------
% 9.98/2.77 % (25721)------------------------------
% 9.98/2.78 % (25726)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_25541 for (2988ds/922Mi)
% 9.98/2.78 % (25727)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_25541 for (2988ds/182Mi)
% 9.98/2.79 % (25728)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_25541 for (2988ds/164Mi)
% 10.44/2.81 % (25716)Instruction limit reached!
% 10.44/2.81 % (25716)------------------------------
% 10.44/2.81 % (25716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.44/2.81 % (25716)Termination reason: Unknown
% 10.44/2.81 % (25716)Termination phase: Saturation
% 10.44/2.81
% 10.44/2.81 % (25716)Memory used [KB]: 8699
% 10.44/2.81 % (25716)Time elapsed: 0.212 s
% 10.44/2.81 % (25716)Instructions burned: 458 (million)
% 10.44/2.81 % (25716)------------------------------
% 10.44/2.81 % (25716)------------------------------
% 10.44/2.82 % (25725)Instruction limit reached!
% 10.44/2.82 % (25725)------------------------------
% 10.44/2.82 % (25725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.44/2.82 % (25725)Termination reason: Unknown
% 10.44/2.82 % (25725)Termination phase: Saturation
% 10.44/2.82
% 10.44/2.82 % (25725)Memory used [KB]: 6908
% 10.44/2.82 % (25725)Time elapsed: 0.052 s
% 10.44/2.82 % (25725)Instructions burned: 114 (million)
% 10.44/2.82 % (25725)------------------------------
% 10.44/2.82 % (25725)------------------------------
% 10.44/2.83 % (25729)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_25541 for (2988ds/50Mi)
% 10.44/2.83 % (25730)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_25541 for (2988ds/368Mi)
% 10.44/2.84 % (25724)Instruction limit reached!
% 10.44/2.84 % (25724)------------------------------
% 10.44/2.84 % (25724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.44/2.84 % (25724)Termination reason: Unknown
% 10.44/2.84 % (25724)Termination phase: Saturation
% 10.44/2.84
% 10.44/2.84 % (25724)Memory used [KB]: 6908
% 10.44/2.84 % (25724)Time elapsed: 0.090 s
% 10.44/2.84 % (25724)Instructions burned: 216 (million)
% 10.44/2.84 % (25724)------------------------------
% 10.44/2.84 % (25724)------------------------------
% 10.44/2.85 % (25729)Instruction limit reached!
% 10.44/2.85 % (25729)------------------------------
% 10.44/2.85 % (25729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.44/2.85 % (25729)Termination reason: Unknown
% 10.44/2.85 % (25729)Termination phase: Property scanning
% 10.44/2.85
% 10.44/2.85 % (25729)Memory used [KB]: 2174
% 10.44/2.85 % (25729)Time elapsed: 0.024 s
% 10.44/2.85 % (25729)Instructions burned: 50 (million)
% 10.44/2.85 % (25729)------------------------------
% 10.44/2.85 % (25729)------------------------------
% 10.44/2.86 % (25727)Instruction limit reached!
% 10.44/2.86 % (25727)------------------------------
% 10.44/2.86 % (25727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.44/2.86 % (25727)Termination reason: Unknown
% 10.44/2.86 % (25727)Termination phase: Saturation
% 10.44/2.86
% 10.44/2.86 % (25727)Memory used [KB]: 6908
% 10.44/2.86 % (25727)Time elapsed: 0.078 s
% 10.44/2.86 % (25727)Instructions burned: 184 (million)
% 10.44/2.86 % (25727)------------------------------
% 10.44/2.86 % (25727)------------------------------
% 10.44/2.86 % (25731)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_25541 for (2987ds/1021Mi)
% 10.44/2.86 % (25728)Instruction limit reached!
% 10.44/2.86 % (25728)------------------------------
% 10.44/2.86 % (25728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.44/2.86 % (25728)Termination reason: Unknown
% 10.44/2.86 % (25728)Termination phase: Saturation
% 10.44/2.86
% 10.44/2.86 % (25728)Memory used [KB]: 2558
% 10.44/2.86 % (25728)Time elapsed: 0.073 s
% 10.44/2.86 % (25728)Instructions burned: 164 (million)
% 10.44/2.86 % (25728)------------------------------
% 10.44/2.86 % (25728)------------------------------
% 10.44/2.86 % (25732)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_25541 for (2987ds/267Mi)
% 10.44/2.87 % (25733)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_25541 for (2987ds/204Mi)
% 10.44/2.88 % (25734)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_25541 for (2987ds/26Mi)
% 10.44/2.89 % (25734)Instruction limit reached!
% 10.44/2.89 % (25734)------------------------------
% 10.44/2.89 % (25734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.44/2.89 % (25734)Termination reason: Unknown
% 10.44/2.89 % (25734)Termination phase: shuffling
% 10.44/2.89
% 10.44/2.89 % (25734)Memory used [KB]: 1918
% 10.44/2.89 % (25734)Time elapsed: 0.013 s
% 10.44/2.89 % (25734)Instructions burned: 27 (million)
% 10.44/2.89 % (25734)------------------------------
% 10.44/2.89 % (25734)------------------------------
% 11.10/2.91 % (25735)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_25541 for (2987ds/53Mi)
% 11.10/2.93 % (25735)Instruction limit reached!
% 11.10/2.93 % (25735)------------------------------
% 11.10/2.93 % (25735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/2.93 % (25735)Termination reason: Unknown
% 11.10/2.93 % (25735)Termination phase: Property scanning
% 11.10/2.93
% 11.10/2.93 % (25735)Memory used [KB]: 2174
% 11.10/2.93 % (25735)Time elapsed: 0.026 s
% 11.10/2.93 % (25735)Instructions burned: 55 (million)
% 11.10/2.93 % (25735)------------------------------
% 11.10/2.93 % (25735)------------------------------
% 11.10/2.95 % (25736)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_25541 for (2986ds/4436Mi)
% 11.10/2.96 % (25733)Instruction limit reached!
% 11.10/2.96 % (25733)------------------------------
% 11.10/2.96 % (25733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/2.96 % (25733)Termination reason: Unknown
% 11.10/2.96 % (25733)Termination phase: Saturation
% 11.10/2.96
% 11.10/2.96 % (25733)Memory used [KB]: 7547
% 11.10/2.96 % (25733)Time elapsed: 0.089 s
% 11.10/2.96 % (25733)Instructions burned: 204 (million)
% 11.10/2.96 % (25733)------------------------------
% 11.10/2.96 % (25733)------------------------------
% 11.10/2.98 % (25737)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_25541 for (2986ds/1539Mi)
% 11.10/2.98 % (25732)Instruction limit reached!
% 11.10/2.98 % (25732)------------------------------
% 11.10/2.98 % (25732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/2.98 % (25732)Termination reason: Unknown
% 11.10/2.98 % (25732)Termination phase: Saturation
% 11.10/2.98
% 11.10/2.98 % (25732)Memory used [KB]: 7164
% 11.10/2.98 % (25732)Time elapsed: 0.113 s
% 11.10/2.98 % (25732)Instructions burned: 269 (million)
% 11.10/2.98 % (25732)------------------------------
% 11.10/2.98 % (25732)------------------------------
% 11.10/2.99 % (25738)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_25541 for (2986ds/408Mi)
% 11.10/3.00 % (25730)Instruction limit reached!
% 11.10/3.00 % (25730)------------------------------
% 11.10/3.00 % (25730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/3.00 % (25730)Termination reason: Unknown
% 11.10/3.00 % (25730)Termination phase: Saturation
% 11.10/3.00
% 11.10/3.00 % (25730)Memory used [KB]: 8315
% 11.10/3.00 % (25730)Time elapsed: 0.168 s
% 11.10/3.00 % (25730)Instructions burned: 370 (million)
% 11.10/3.00 % (25730)------------------------------
% 11.10/3.00 % (25730)------------------------------
% 11.10/3.02 % (25739)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_25541 for (2986ds/5205Mi)
% 11.10/3.02 % (25719)Instruction limit reached!
% 11.10/3.02 % (25719)------------------------------
% 11.10/3.02 % (25719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/3.02 % (25719)Termination reason: Unknown
% 11.10/3.02 % (25719)Termination phase: Saturation
% 11.10/3.02
% 11.10/3.02 % (25719)Memory used [KB]: 11641
% 11.10/3.02 % (25719)Time elapsed: 0.374 s
% 11.10/3.02 % (25719)Instructions burned: 988 (million)
% 11.10/3.02 % (25719)------------------------------
% 11.10/3.02 % (25719)------------------------------
% 12.15/3.04 % (25740)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_25541 for (2985ds/1913Mi)
% 13.39/3.20 % (25738)Instruction limit reached!
% 13.39/3.20 % (25738)------------------------------
% 13.39/3.20 % (25738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.20 % (25738)Termination reason: Unknown
% 13.39/3.20 % (25738)Termination phase: Saturation
% 13.39/3.20
% 13.39/3.20 % (25738)Memory used [KB]: 9850
% 13.39/3.20 % (25738)Time elapsed: 0.207 s
% 13.39/3.20 % (25738)Instructions burned: 408 (million)
% 13.39/3.20 % (25738)------------------------------
% 13.39/3.20 % (25738)------------------------------
% 13.39/3.22 % (25741)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_25541 for (2984ds/4350Mi)
% 13.39/3.24 % (25726)Instruction limit reached!
% 13.39/3.24 % (25726)------------------------------
% 13.39/3.24 % (25726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.24 % (25726)Termination reason: Unknown
% 13.39/3.24 % (25726)Termination phase: Saturation
% 13.39/3.24
% 13.39/3.24 % (25726)Memory used [KB]: 10234
% 13.39/3.24 % (25726)Time elapsed: 0.460 s
% 13.39/3.24 % (25726)Instructions burned: 922 (million)
% 13.39/3.24 % (25726)------------------------------
% 13.39/3.24 % (25726)------------------------------
% 13.39/3.25 % (25742)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_25541 for (2983ds/68Mi)
% 13.39/3.28 % (25742)Instruction limit reached!
% 13.39/3.28 % (25742)------------------------------
% 13.39/3.28 % (25742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.28 % (25742)Termination reason: Unknown
% 13.39/3.28 % (25742)Termination phase: Preprocessing 3
% 13.39/3.28
% 13.39/3.28 % (25742)Memory used [KB]: 2046
% 13.39/3.28 % (25742)Time elapsed: 0.032 s
% 13.39/3.28 % (25742)Instructions burned: 69 (million)
% 13.39/3.28 % (25742)------------------------------
% 13.39/3.28 % (25742)------------------------------
% 13.81/3.30 % (25743)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_25541 for (2983ds/358Mi)
% 13.81/3.37 % (25731)Instruction limit reached!
% 13.81/3.37 % (25731)------------------------------
% 13.81/3.37 % (25731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.37 % (25731)Termination reason: Unknown
% 13.81/3.37 % (25731)Termination phase: Saturation
% 13.81/3.37
% 13.81/3.37 % (25731)Memory used [KB]: 11385
% 13.81/3.37 % (25731)Time elapsed: 0.510 s
% 13.81/3.37 % (25731)Instructions burned: 1022 (million)
% 13.81/3.37 % (25731)------------------------------
% 13.81/3.37 % (25731)------------------------------
% 13.81/3.38 % (25744)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_25541 for (2982ds/31Mi)
% 14.09/3.40 % (25744)Instruction limit reached!
% 14.09/3.40 % (25744)------------------------------
% 14.09/3.40 % (25744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.40 % (25744)Termination reason: Unknown
% 14.09/3.40 % (25744)Termination phase: shuffling
% 14.09/3.40
% 14.09/3.40 % (25744)Memory used [KB]: 1918
% 14.09/3.40 % (25744)Time elapsed: 0.017 s
% 14.09/3.40 % (25744)Instructions burned: 31 (million)
% 14.09/3.40 % (25744)------------------------------
% 14.09/3.40 % (25744)------------------------------
% 14.09/3.42 % (25745)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_25541 for (2982ds/279Mi)
% 14.09/3.46 % (25743)Instruction limit reached!
% 14.09/3.46 % (25743)------------------------------
% 14.09/3.46 % (25743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.46 % (25743)Termination reason: Unknown
% 14.09/3.46 % (25743)Termination phase: Saturation
% 14.09/3.46
% 14.09/3.46 % (25743)Memory used [KB]: 8187
% 14.09/3.46 % (25743)Time elapsed: 0.165 s
% 14.09/3.46 % (25743)Instructions burned: 358 (million)
% 14.09/3.46 % (25743)------------------------------
% 14.09/3.46 % (25743)------------------------------
% 14.09/3.48 % (25746)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_25541 for (2981ds/258Mi)
% 14.50/3.53 % (25745)Instruction limit reached!
% 14.50/3.53 % (25745)------------------------------
% 14.50/3.53 % (25745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.50/3.53 % (25745)Termination reason: Unknown
% 14.50/3.53 % (25745)Termination phase: Saturation
% 14.50/3.53
% 14.50/3.53 % (25745)Memory used [KB]: 7164
% 14.50/3.53 % (25745)Time elapsed: 0.115 s
% 14.50/3.53 % (25745)Instructions burned: 280 (million)
% 14.50/3.53 % (25745)------------------------------
% 14.50/3.53 % (25745)------------------------------
% 14.50/3.55 % (25747)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_25541 for (2980ds/26Mi)
% 14.50/3.56 % (25747)Instruction limit reached!
% 14.50/3.56 % (25747)------------------------------
% 14.50/3.56 % (25747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.50/3.56 % (25747)Termination reason: Unknown
% 14.50/3.56 % (25747)Termination phase: shuffling
% 14.50/3.56
% 14.50/3.56 % (25747)Memory used [KB]: 1918
% 14.50/3.56 % (25747)Time elapsed: 0.014 s
% 14.50/3.56 % (25747)Instructions burned: 26 (million)
% 14.50/3.56 % (25747)------------------------------
% 14.50/3.56 % (25747)------------------------------
% 14.50/3.57 % (25748)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_25541 for (2980ds/995Mi)
% 14.85/3.60 % (25746)Instruction limit reached!
% 14.85/3.60 % (25746)------------------------------
% 14.85/3.60 % (25746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.85/3.60 % (25746)Termination reason: Unknown
% 14.85/3.60 % (25746)Termination phase: Saturation
% 14.85/3.60
% 14.85/3.60 % (25746)Memory used [KB]: 8315
% 14.85/3.60 % (25746)Time elapsed: 0.118 s
% 14.85/3.60 % (25746)Instructions burned: 258 (million)
% 14.85/3.60 % (25746)------------------------------
% 14.85/3.60 % (25746)------------------------------
% 14.85/3.61 % (25749)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_25541 for (2980ds/373Mi)
% 15.21/3.72 % (25737)Instruction limit reached!
% 15.21/3.72 % (25737)------------------------------
% 15.21/3.72 % (25737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.21/3.72 % (25737)Termination reason: Unknown
% 15.21/3.72 % (25737)Termination phase: Saturation
% 15.21/3.72
% 15.21/3.72 % (25737)Memory used [KB]: 9978
% 15.21/3.72 % (25737)Time elapsed: 0.751 s
% 15.21/3.72 % (25737)Instructions burned: 1539 (million)
% 15.21/3.72 % (25737)------------------------------
% 15.21/3.72 % (25737)------------------------------
% 15.21/3.74 % (25750)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_25541 for (2978ds/253Mi)
% 15.21/3.79 % (25749)Instruction limit reached!
% 15.21/3.79 % (25749)------------------------------
% 15.21/3.79 % (25749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.21/3.79 % (25749)Termination reason: Unknown
% 15.21/3.79 % (25749)Termination phase: Saturation
% 15.21/3.79
% 15.21/3.79 % (25749)Memory used [KB]: 8315
% 15.21/3.79 % (25749)Time elapsed: 0.176 s
% 15.21/3.79 % (25749)Instructions burned: 374 (million)
% 15.21/3.79 % (25749)------------------------------
% 15.21/3.79 % (25749)------------------------------
% 15.54/3.81 % (25751)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_25541 for (2978ds/832Mi)
% 15.54/3.85 % (25750)Instruction limit reached!
% 15.54/3.85 % (25750)------------------------------
% 15.54/3.85 % (25750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.85 % (25750)Termination reason: Unknown
% 15.54/3.85 % (25750)Termination phase: Saturation
% 15.54/3.85
% 15.54/3.85 % (25750)Memory used [KB]: 7164
% 15.54/3.85 % (25750)Time elapsed: 0.107 s
% 15.54/3.85 % (25750)Instructions burned: 254 (million)
% 15.54/3.85 % (25750)------------------------------
% 15.54/3.85 % (25750)------------------------------
% 15.54/3.86 % (25752)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_25541 for (2977ds/668Mi)
% 15.76/3.95 % (25748)Instruction limit reached!
% 15.76/3.95 % (25748)------------------------------
% 15.76/3.95 % (25748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.76/3.95 % (25748)Termination reason: Unknown
% 15.76/3.95 % (25748)Termination phase: Saturation
% 15.76/3.95
% 15.76/3.95 % (25748)Memory used [KB]: 11001
% 15.76/3.95 % (25748)Time elapsed: 0.380 s
% 15.76/3.95 % (25748)Instructions burned: 997 (million)
% 15.76/3.95 % (25748)------------------------------
% 15.76/3.95 % (25748)------------------------------
% 15.76/3.97 % (25740)Instruction limit reached!
% 15.76/3.97 % (25740)------------------------------
% 15.76/3.97 % (25740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.76/3.97 % (25740)Termination reason: Unknown
% 15.76/3.97 % (25740)Termination phase: Saturation
% 15.76/3.97
% 15.76/3.97 % (25740)Memory used [KB]: 4861
% 15.76/3.97 % (25740)Time elapsed: 0.930 s
% 15.76/3.97 % (25740)Instructions burned: 1913 (million)
% 15.76/3.97 % (25740)------------------------------
% 15.76/3.97 % (25740)------------------------------
% 15.76/3.97 % (25753)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_25541 for (2976ds/40Mi)
% 15.76/3.99 % (25754)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_25541 for (2976ds/294Mi)
% 15.76/3.99 % (25753)Instruction limit reached!
% 15.76/3.99 % (25753)------------------------------
% 15.76/3.99 % (25753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.76/3.99 % (25753)Termination reason: Unknown
% 15.76/3.99 % (25753)Termination phase: Property scanning
% 15.76/3.99
% 15.76/3.99 % (25753)Memory used [KB]: 2174
% 15.76/3.99 % (25753)Time elapsed: 0.020 s
% 15.76/3.99 % (25753)Instructions burned: 40 (million)
% 15.76/3.99 % (25753)------------------------------
% 15.76/3.99 % (25753)------------------------------
% 15.76/4.00 % (25755)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_25541 for (2976ds/187Mi)
% 19.56/4.09 % (25755)Instruction limit reached!
% 19.56/4.09 % (25755)------------------------------
% 19.56/4.09 % (25755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.56/4.09 % (25755)Termination reason: Unknown
% 19.56/4.09 % (25755)Termination phase: Saturation
% 19.56/4.09
% 19.56/4.09 % (25755)Memory used [KB]: 7419
% 19.56/4.09 % (25755)Time elapsed: 0.086 s
% 19.56/4.09 % (25755)Instructions burned: 188 (million)
% 19.56/4.09 % (25755)------------------------------
% 19.56/4.09 % (25755)------------------------------
% 19.56/4.11 % (25756)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_25541 for (2975ds/371Mi)
% 19.56/4.11 % (25754)Instruction limit reached!
% 19.56/4.11 % (25754)------------------------------
% 19.56/4.11 % (25754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.56/4.11 % (25754)Termination reason: Unknown
% 19.56/4.11 % (25754)Termination phase: Saturation
% 19.56/4.11
% 19.56/4.11 % (25754)Memory used [KB]: 6908
% 19.56/4.11 % (25754)Time elapsed: 0.123 s
% 19.56/4.11 % (25754)Instructions burned: 294 (million)
% 19.56/4.11 % (25754)------------------------------
% 19.56/4.11 % (25754)------------------------------
% 19.56/4.12 % (25752)Instruction limit reached!
% 19.56/4.12 % (25752)------------------------------
% 19.56/4.12 % (25752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.56/4.12 % (25752)Termination reason: Unknown
% 19.56/4.12 % (25752)Termination phase: Saturation
% 19.56/4.12
% 19.56/4.12 % (25752)Memory used [KB]: 15863
% 19.56/4.12 % (25752)Time elapsed: 0.261 s
% 19.56/4.12 % (25752)Instructions burned: 671 (million)
% 19.56/4.12 % (25752)------------------------------
% 19.56/4.12 % (25752)------------------------------
% 19.56/4.12 % (25757)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_25541 for (2975ds/1827Mi)
% 20.22/4.14 % (25758)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_25541 for (2975ds/70Mi)
% 20.22/4.17 % (25758)Instruction limit reached!
% 20.22/4.17 % (25758)------------------------------
% 20.22/4.17 % (25758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.17 % (25758)Termination reason: Unknown
% 20.22/4.17 % (25758)Termination phase: Property scanning
% 20.22/4.17
% 20.22/4.17 % (25758)Memory used [KB]: 2174
% 20.22/4.17 % (25758)Time elapsed: 0.033 s
% 20.22/4.17 % (25758)Instructions burned: 71 (million)
% 20.22/4.17 % (25758)------------------------------
% 20.22/4.17 % (25758)------------------------------
% 20.22/4.19 % (25759)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_25541 for (2974ds/316Mi)
% 20.57/4.20 % (25751)Instruction limit reached!
% 20.57/4.20 % (25751)------------------------------
% 20.57/4.20 % (25751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.20 % (25751)Termination reason: Unknown
% 20.57/4.20 % (25751)Termination phase: Saturation
% 20.57/4.20
% 20.57/4.20 % (25751)Memory used [KB]: 9722
% 20.57/4.20 % (25751)Time elapsed: 0.397 s
% 20.57/4.20 % (25751)Instructions burned: 832 (million)
% 20.57/4.20 % (25751)------------------------------
% 20.57/4.20 % (25751)------------------------------
% 20.57/4.22 % (25760)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_25541 for (2974ds/932Mi)
% 20.57/4.28 % (25756)Instruction limit reached!
% 20.57/4.28 % (25756)------------------------------
% 20.57/4.28 % (25756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.28 % (25756)Termination reason: Unknown
% 20.57/4.28 % (25756)Termination phase: Saturation
% 20.57/4.28
% 20.57/4.28 % (25756)Memory used [KB]: 8443
% 20.57/4.28 % (25756)Time elapsed: 0.174 s
% 20.57/4.28 % (25756)Instructions burned: 371 (million)
% 20.57/4.28 % (25756)------------------------------
% 20.57/4.28 % (25756)------------------------------
% 20.57/4.30 % (25761)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_25541 for (2973ds/4714Mi)
% 21.06/4.32 % (25759)Instruction limit reached!
% 21.06/4.32 % (25759)------------------------------
% 21.06/4.32 % (25759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.32 % (25759)Termination reason: Unknown
% 21.06/4.32 % (25759)Termination phase: Saturation
% 21.06/4.32
% 21.06/4.32 % (25759)Memory used [KB]: 7164
% 21.06/4.32 % (25759)Time elapsed: 0.130 s
% 21.06/4.32 % (25759)Instructions burned: 318 (million)
% 21.06/4.32 % (25759)------------------------------
% 21.06/4.32 % (25759)------------------------------
% 21.06/4.33 % (25762)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_25541 for (2973ds/8250Mi)
% 21.80/4.59 % (25760)Instruction limit reached!
% 21.80/4.59 % (25760)------------------------------
% 21.80/4.59 % (25760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.59 % (25760)Termination reason: Unknown
% 21.80/4.59 % (25760)Termination phase: Saturation
% 21.80/4.59
% 21.80/4.59 % (25760)Memory used [KB]: 13048
% 21.80/4.59 % (25760)Time elapsed: 0.374 s
% 21.80/4.59 % (25760)Instructions burned: 933 (million)
% 21.80/4.59 % (25760)------------------------------
% 21.80/4.59 % (25760)------------------------------
% 22.49/4.61 % (25763)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_25541 for (2970ds/770Mi)
% 23.39/4.92 % (25739)Instruction limit reached!
% 23.39/4.92 % (25739)------------------------------
% 23.39/4.92 % (25739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.92 % (25739)Termination reason: Unknown
% 23.39/4.92 % (25739)Termination phase: Saturation
% 23.39/4.92
% 23.39/4.92 % (25739)Memory used [KB]: 11897
% 23.39/4.92 % (25739)Time elapsed: 1.907 s
% 23.39/4.92 % (25739)Instructions burned: 5205 (million)
% 23.39/4.92 % (25739)------------------------------
% 23.39/4.92 % (25739)------------------------------
% 23.39/4.94 % (25764)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_25541 for (2967ds/794Mi)
% 23.39/4.95 % (25763)Instruction limit reached!
% 23.39/4.95 % (25763)------------------------------
% 23.39/4.95 % (25763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.95 % (25763)Termination reason: Unknown
% 23.39/4.95 % (25763)Termination phase: Saturation
% 23.39/4.95
% 23.39/4.95 % (25763)Memory used [KB]: 7164
% 23.39/4.95 % (25763)Time elapsed: 0.343 s
% 23.39/4.95 % (25763)Instructions burned: 772 (million)
% 23.39/4.95 % (25763)------------------------------
% 23.39/4.95 % (25763)------------------------------
% 23.39/4.97 % (25765)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_25541 for (2966ds/464Mi)
% 23.39/4.99 % (25757)Instruction limit reached!
% 23.39/4.99 % (25757)------------------------------
% 23.39/4.99 % (25757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.99 % (25757)Termination reason: Unknown
% 23.39/4.99 % (25757)Termination phase: Saturation
% 23.39/4.99
% 23.39/4.99 % (25757)Memory used [KB]: 18038
% 23.39/4.99 % (25757)Time elapsed: 0.866 s
% 23.39/4.99 % (25757)Instructions burned: 1828 (million)
% 23.39/4.99 % (25757)------------------------------
% 23.39/4.99 % (25757)------------------------------
% 23.39/5.01 % (25766)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_25541 for (2966ds/1376Mi)
% 27.24/5.17 % (25736)Instruction limit reached!
% 27.24/5.17 % (25736)------------------------------
% 27.24/5.17 % (25736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.24/5.17 % (25736)Termination reason: Unknown
% 27.24/5.17 % (25736)Termination phase: Saturation
% 27.24/5.17
% 27.24/5.17 % (25736)Memory used [KB]: 17782
% 27.24/5.17 % (25736)Time elapsed: 2.242 s
% 27.24/5.17 % (25736)Instructions burned: 4436 (million)
% 27.24/5.17 % (25736)------------------------------
% 27.24/5.17 % (25736)------------------------------
% 27.24/5.18 % (25767)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_25541 for (2964ds/906Mi)
% 27.24/5.19 % (25765)Instruction limit reached!
% 27.24/5.19 % (25765)------------------------------
% 27.24/5.19 % (25765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.24/5.19 % (25765)Termination reason: Unknown
% 27.24/5.19 % (25765)Termination phase: Saturation
% 27.24/5.19
% 27.24/5.19 % (25765)Memory used [KB]: 8443
% 27.24/5.19 % (25765)Time elapsed: 0.222 s
% 27.24/5.19 % (25765)Instructions burned: 464 (million)
% 27.24/5.19 % (25765)------------------------------
% 27.24/5.19 % (25765)------------------------------
% 27.73/5.20 % (25768)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_25541 for (2964ds/434Mi)
% 28.25/5.33 % (25764)Instruction limit reached!
% 28.25/5.33 % (25764)------------------------------
% 28.25/5.33 % (25764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.25/5.33 % (25764)Termination reason: Unknown
% 28.25/5.33 % (25764)Termination phase: Saturation
% 28.25/5.33
% 28.25/5.33 % (25764)Memory used [KB]: 5117
% 28.25/5.33 % (25764)Time elapsed: 0.392 s
% 28.25/5.33 % (25764)Instructions burned: 795 (million)
% 28.25/5.33 % (25764)------------------------------
% 28.25/5.33 % (25764)------------------------------
% 28.25/5.35 % (25769)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_25541 for (2963ds/865Mi)
% 28.25/5.35 % (25741)Instruction limit reached!
% 28.25/5.35 % (25741)------------------------------
% 28.25/5.35 % (25741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.25/5.35 % (25741)Termination reason: Unknown
% 28.25/5.35 % (25741)Termination phase: Saturation
% 28.25/5.35
% 28.25/5.35 % (25741)Memory used [KB]: 13048
% 28.25/5.35 % (25741)Time elapsed: 2.139 s
% 28.25/5.35 % (25741)Instructions burned: 4350 (million)
% 28.25/5.35 % (25741)------------------------------
% 28.25/5.35 % (25741)------------------------------
% 28.25/5.37 % (25770)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_25541 for (2962ds/593Mi)
% 28.65/5.41 % (25768)Instruction limit reached!
% 28.65/5.41 % (25768)------------------------------
% 28.65/5.41 % (25768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.65/5.41 % (25768)Termination reason: Unknown
% 28.65/5.41 % (25768)Termination phase: Saturation
% 28.65/5.41
% 28.65/5.41 % (25768)Memory used [KB]: 9722
% 28.65/5.41 % (25768)Time elapsed: 0.234 s
% 28.65/5.41 % (25768)Instructions burned: 435 (million)
% 28.65/5.41 % (25768)------------------------------
% 28.65/5.41 % (25768)------------------------------
% 28.65/5.43 % (25771)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_25541 for (2962ds/443Mi)
% 29.17/5.55 % (25766)Instruction limit reached!
% 29.17/5.55 % (25766)------------------------------
% 29.17/5.55 % (25766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.17/5.55 % (25766)Termination reason: Unknown
% 29.17/5.55 % (25766)Termination phase: Saturation
% 29.17/5.55
% 29.17/5.55 % (25766)Memory used [KB]: 8699
% 29.17/5.55 % (25766)Time elapsed: 0.551 s
% 29.17/5.55 % (25766)Instructions burned: 1376 (million)
% 29.17/5.55 % (25766)------------------------------
% 29.17/5.55 % (25766)------------------------------
% 29.17/5.57 % (25772)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_25541 for (2960ds/594Mi)
% 29.17/5.60 % (25770)Instruction limit reached!
% 29.17/5.60 % (25770)------------------------------
% 29.17/5.60 % (25770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.17/5.60 % (25770)Termination reason: Unknown
% 29.17/5.60 % (25770)Termination phase: Saturation
% 29.17/5.60
% 29.17/5.60 % (25770)Memory used [KB]: 7164
% 29.17/5.60 % (25770)Time elapsed: 0.229 s
% 29.17/5.60 % (25770)Instructions burned: 595 (million)
% 29.17/5.60 % (25770)------------------------------
% 29.17/5.60 % (25770)------------------------------
% 29.43/5.61 % (25773)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_25541 for (2960ds/327Mi)
% 29.43/5.62 % (25767)Instruction limit reached!
% 29.43/5.62 % (25767)------------------------------
% 29.43/5.62 % (25767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.43/5.62 % (25767)Termination reason: Unknown
% 29.43/5.62 % (25767)Termination phase: Saturation
% 29.43/5.62
% 29.43/5.62 % (25767)Memory used [KB]: 10490
% 29.43/5.62 % (25767)Time elapsed: 0.460 s
% 29.43/5.62 % (25767)Instructions burned: 906 (million)
% 29.43/5.62 % (25767)------------------------------
% 29.43/5.62 % (25767)------------------------------
% 29.43/5.64 % (25774)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_25541 for (2959ds/5411Mi)
% 29.43/5.64 % (25771)Instruction limit reached!
% 29.43/5.64 % (25771)------------------------------
% 29.43/5.64 % (25771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.43/5.64 % (25771)Termination reason: Unknown
% 29.43/5.64 % (25771)Termination phase: Saturation
% 29.43/5.64
% 29.43/5.64 % (25771)Memory used [KB]: 8443
% 29.43/5.64 % (25771)Time elapsed: 0.236 s
% 29.43/5.64 % (25771)Instructions burned: 444 (million)
% 29.43/5.64 % (25771)------------------------------
% 29.43/5.64 % (25771)------------------------------
% 29.43/5.66 % (25775)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_25541 for (2959ds/1762Mi)
% 30.55/5.74 % (25769)Instruction limit reached!
% 30.55/5.74 % (25769)------------------------------
% 30.55/5.74 % (25769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.55/5.74 % (25769)Termination reason: Unknown
% 30.55/5.74 % (25769)Termination phase: Saturation
% 30.55/5.74
% 30.55/5.74 % (25769)Memory used [KB]: 8827
% 30.55/5.74 % (25769)Time elapsed: 0.399 s
% 30.55/5.74 % (25769)Instructions burned: 867 (million)
% 30.55/5.74 % (25769)------------------------------
% 30.55/5.74 % (25769)------------------------------
% 30.55/5.76 % (25776)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_25541 for (2958ds/96Mi)
% 30.55/5.78 % (25773)Instruction limit reached!
% 30.55/5.78 % (25773)------------------------------
% 30.55/5.78 % (25773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.55/5.78 % (25773)Termination reason: Unknown
% 30.55/5.78 % (25773)Termination phase: Saturation
% 30.55/5.78
% 30.55/5.78 % (25773)Memory used [KB]: 10234
% 30.55/5.78 % (25773)Time elapsed: 0.192 s
% 30.55/5.78 % (25773)Instructions burned: 328 (million)
% 30.55/5.78 % (25773)------------------------------
% 30.55/5.78 % (25773)------------------------------
% 30.55/5.80 % (25777)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_25541 for (2958ds/503Mi)
% 31.36/5.80 % (25776)Instruction limit reached!
% 31.36/5.80 % (25776)------------------------------
% 31.36/5.80 % (25776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.36/5.80 % (25776)Termination reason: Unknown
% 31.36/5.80 % (25776)Termination phase: Property scanning
% 31.36/5.80
% 31.36/5.80 % (25776)Memory used [KB]: 2302
% 31.36/5.80 % (25776)Time elapsed: 0.044 s
% 31.36/5.80 % (25776)Instructions burned: 96 (million)
% 31.36/5.80 % (25776)------------------------------
% 31.36/5.80 % (25776)------------------------------
% 31.36/5.82 % (25778)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_25541 for (2958ds/90Mi)
% 31.36/5.85 % (25772)Instruction limit reached!
% 31.36/5.85 % (25772)------------------------------
% 31.36/5.85 % (25772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.36/5.85 % (25772)Termination reason: Unknown
% 31.36/5.85 % (25772)Termination phase: Saturation
% 31.36/5.85
% 31.36/5.85 % (25772)Memory used [KB]: 8443
% 31.36/5.85 % (25772)Time elapsed: 0.307 s
% 31.36/5.85 % (25772)Instructions burned: 595 (million)
% 31.36/5.85 % (25772)------------------------------
% 31.36/5.85 % (25772)------------------------------
% 31.36/5.86 % (25778)Instruction limit reached!
% 31.36/5.86 % (25778)------------------------------
% 31.36/5.86 % (25778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.36/5.86 % (25778)Termination reason: Unknown
% 31.36/5.86 % (25778)Termination phase: Twee Goal Transformation
% 31.36/5.86
% 31.36/5.86 % (25778)Memory used [KB]: 2558
% 31.36/5.86 % (25778)Time elapsed: 0.042 s
% 31.36/5.86 % (25778)Instructions burned: 91 (million)
% 31.36/5.86 % (25778)------------------------------
% 31.36/5.86 % (25778)------------------------------
% 31.36/5.87 % (25779)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_25541 for (2957ds/593Mi)
% 31.36/5.88 % (25780)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_25541 for (2957ds/1512Mi)
% 33.52/6.03 % (25777)Instruction limit reached!
% 33.52/6.03 % (25777)------------------------------
% 33.52/6.03 % (25777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.52/6.03 % (25777)Termination reason: Unknown
% 33.52/6.03 % (25777)Termination phase: Saturation
% 33.52/6.03
% 33.52/6.03 % (25777)Memory used [KB]: 8571
% 33.52/6.03 % (25777)Time elapsed: 0.239 s
% 33.52/6.03 % (25777)Instructions burned: 504 (million)
% 33.52/6.03 % (25777)------------------------------
% 33.52/6.03 % (25777)------------------------------
% 33.52/6.04 % (25761)Instruction limit reached!
% 33.52/6.04 % (25761)------------------------------
% 33.52/6.04 % (25761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.52/6.04 % (25761)Termination reason: Unknown
% 33.52/6.04 % (25761)Termination phase: Saturation
% 33.52/6.04
% 33.52/6.04 % (25761)Memory used [KB]: 7291
% 33.52/6.04 % (25761)Time elapsed: 1.742 s
% 33.52/6.04 % (25761)Instructions burned: 4715 (million)
% 33.52/6.04 % (25761)------------------------------
% 33.52/6.04 % (25761)------------------------------
% 33.52/6.05 % (25781)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_25541 for (2955ds/569Mi)
% 33.52/6.05 % (25782)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_25541 for (2955ds/501Mi)
% 34.06/6.16 % (25779)Instruction limit reached!
% 34.06/6.16 % (25779)------------------------------
% 34.06/6.16 % (25779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.06/6.16 % (25779)Termination reason: Unknown
% 34.06/6.16 % (25779)Termination phase: Saturation
% 34.06/6.16
% 34.06/6.16 % (25779)Memory used [KB]: 9466
% 34.06/6.16 % (25779)Time elapsed: 0.287 s
% 34.06/6.16 % (25779)Instructions burned: 593 (million)
% 34.06/6.16 % (25779)------------------------------
% 34.06/6.16 % (25779)------------------------------
% 34.06/6.17 % (25783)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_25541 for (2954ds/562Mi)
% 34.40/6.27 % (25781)Instruction limit reached!
% 34.40/6.27 % (25781)------------------------------
% 34.40/6.27 % (25781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.40/6.27 % (25781)Termination reason: Unknown
% 34.40/6.27 % (25781)Termination phase: Saturation
% 34.40/6.27
% 34.40/6.27 % (25781)Memory used [KB]: 11257
% 34.40/6.27 % (25781)Time elapsed: 0.226 s
% 34.40/6.27 % (25781)Instructions burned: 570 (million)
% 34.40/6.27 % (25781)------------------------------
% 34.40/6.27 % (25781)------------------------------
% 34.40/6.29 % (25784)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_25541 for (2953ds/406Mi)
% 35.04/6.30 % (25782)Instruction limit reached!
% 35.04/6.30 % (25782)------------------------------
% 35.04/6.30 % (25782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.30 % (25782)Termination reason: Unknown
% 35.04/6.30 % (25782)Termination phase: Saturation
% 35.04/6.30
% 35.04/6.30 % (25782)Memory used [KB]: 9466
% 35.04/6.30 % (25782)Time elapsed: 0.247 s
% 35.04/6.30 % (25782)Instructions burned: 501 (million)
% 35.04/6.30 % (25782)------------------------------
% 35.04/6.30 % (25782)------------------------------
% 35.04/6.31 % (25785)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_25541 for (2953ds/582Mi)
% 35.04/6.33 % (25775)Instruction limit reached!
% 35.04/6.33 % (25775)------------------------------
% 35.04/6.33 % (25775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.33 % (25775)Termination reason: Unknown
% 35.04/6.33 % (25775)Termination phase: Saturation
% 35.04/6.33
% 35.04/6.33 % (25775)Memory used [KB]: 15607
% 35.04/6.33 % (25775)Time elapsed: 0.672 s
% 35.04/6.33 % (25775)Instructions burned: 1762 (million)
% 35.04/6.33 % (25775)------------------------------
% 35.04/6.33 % (25775)------------------------------
% 35.04/6.35 % (25786)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_25541 for (2952ds/456Mi)
% 35.64/6.44 % (25783)Instruction limit reached!
% 35.64/6.44 % (25783)------------------------------
% 35.64/6.44 % (25783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.64/6.44 % (25783)Termination reason: Unknown
% 35.64/6.44 % (25783)Termination phase: Saturation
% 35.64/6.44
% 35.64/6.44 % (25783)Memory used [KB]: 8315
% 35.64/6.44 % (25783)Time elapsed: 0.268 s
% 35.64/6.44 % (25783)Instructions burned: 563 (million)
% 35.64/6.44 % (25783)------------------------------
% 35.64/6.44 % (25783)------------------------------
% 35.64/6.46 % (25787)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_25541 for (2951ds/393Mi)
% 35.64/6.47 % (25784)Instruction limit reached!
% 35.64/6.47 % (25784)------------------------------
% 35.64/6.47 % (25784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.64/6.47 % (25784)Termination reason: Unknown
% 35.64/6.47 % (25784)Termination phase: Saturation
% 35.64/6.47
% 35.64/6.47 % (25784)Memory used [KB]: 7419
% 35.64/6.47 % (25784)Time elapsed: 0.185 s
% 35.64/6.47 % (25784)Instructions burned: 406 (million)
% 35.64/6.47 % (25784)------------------------------
% 35.64/6.47 % (25784)------------------------------
% 35.64/6.49 % (25788)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_25541 for (2951ds/1335Mi)
% 36.43/6.55 % (25786)Instruction limit reached!
% 36.43/6.55 % (25786)------------------------------
% 36.43/6.55 % (25786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.43/6.55 % (25786)Termination reason: Unknown
% 36.43/6.55 % (25786)Termination phase: Saturation
% 36.43/6.55
% 36.43/6.55 % (25786)Memory used [KB]: 8571
% 36.43/6.55 % (25786)Time elapsed: 0.208 s
% 36.43/6.55 % (25786)Instructions burned: 457 (million)
% 36.43/6.55 % (25786)------------------------------
% 36.43/6.55 % (25786)------------------------------
% 36.43/6.57 % (25789)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_25541 for (2950ds/3373Mi)
% 36.43/6.59 % (25780)Instruction limit reached!
% 36.43/6.59 % (25780)------------------------------
% 36.43/6.59 % (25780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.43/6.59 % (25780)Termination reason: Unknown
% 36.43/6.59 % (25780)Termination phase: Saturation
% 36.43/6.59
% 36.43/6.59 % (25780)Memory used [KB]: 11897
% 36.43/6.59 % (25780)Time elapsed: 0.719 s
% 36.43/6.59 % (25780)Instructions burned: 1513 (million)
% 36.43/6.60 % (25780)------------------------------
% 36.43/6.60 % (25780)------------------------------
% 36.97/6.60 % (25785)Instruction limit reached!
% 36.97/6.60 % (25785)------------------------------
% 36.97/6.60 % (25785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.97/6.60 % (25785)Termination reason: Unknown
% 36.97/6.60 % (25785)Termination phase: Saturation
% 36.97/6.60
% 36.97/6.60 % (25785)Memory used [KB]: 9594
% 36.97/6.60 % (25785)Time elapsed: 0.290 s
% 36.97/6.60 % (25785)Instructions burned: 582 (million)
% 36.97/6.60 % (25785)------------------------------
% 36.97/6.60 % (25785)------------------------------
% 36.97/6.62 % (25790)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_25541 for (2950ds/474Mi)
% 36.97/6.62 % (25791)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_25541 for (2950ds/157Mi)
% 36.97/6.65 % (25787)Instruction limit reached!
% 36.97/6.65 % (25787)------------------------------
% 36.97/6.65 % (25787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.97/6.65 % (25787)Termination reason: Unknown
% 36.97/6.65 % (25787)Termination phase: Saturation
% 36.97/6.65
% 36.97/6.65 % (25787)Memory used [KB]: 9210
% 36.97/6.65 % (25787)Time elapsed: 0.193 s
% 36.97/6.65 % (25787)Instructions burned: 394 (million)
% 36.97/6.65 % (25787)------------------------------
% 36.97/6.65 % (25787)------------------------------
% 36.97/6.67 % (25792)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_25541 for (2949ds/590Mi)
% 36.97/6.69 % (25791)Instruction limit reached!
% 36.97/6.69 % (25791)------------------------------
% 36.97/6.69 % (25791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.97/6.69 % (25791)Termination reason: Unknown
% 36.97/6.69 % (25791)Termination phase: Saturation
% 36.97/6.69
% 36.97/6.69 % (25791)Memory used [KB]: 6908
% 36.97/6.69 % (25791)Time elapsed: 0.069 s
% 36.97/6.69 % (25791)Instructions burned: 157 (million)
% 36.97/6.69 % (25791)------------------------------
% 36.97/6.69 % (25791)------------------------------
% 37.75/6.70 % (25793)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_25541 for (2949ds/104Mi)
% 37.75/6.75 % (25793)Instruction limit reached!
% 37.75/6.75 % (25793)------------------------------
% 37.75/6.75 % (25793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.75/6.75 % (25793)Termination reason: Unknown
% 37.75/6.75 % (25793)Termination phase: Saturation
% 37.75/6.75
% 37.75/6.75 % (25793)Memory used [KB]: 6908
% 37.75/6.75 % (25793)Time elapsed: 0.043 s
% 37.75/6.75 % (25793)Instructions burned: 106 (million)
% 37.75/6.75 % (25793)------------------------------
% 37.75/6.75 % (25793)------------------------------
% 37.75/6.75 % (25790)Instruction limit reached!
% 37.75/6.75 % (25790)------------------------------
% 37.75/6.75 % (25790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.75/6.75 % (25790)Termination reason: Unknown
% 37.75/6.75 % (25790)Termination phase: Saturation
% 37.75/6.75
% 37.75/6.75 % (25790)Memory used [KB]: 11257
% 37.75/6.75 % (25790)Time elapsed: 0.151 s
% 37.75/6.75 % (25790)Instructions burned: 479 (million)
% 37.75/6.75 % (25790)------------------------------
% 37.75/6.75 % (25790)------------------------------
% 37.75/6.76 % (25794)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_25541 for (2948ds/414Mi)
% 37.75/6.76 % (25795)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_25541 for (2948ds/715Mi)
% 38.13/6.86 % (25794)Instruction limit reached!
% 38.13/6.86 % (25794)------------------------------
% 38.13/6.86 % (25794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.13/6.86 % (25794)Termination reason: Unknown
% 38.13/6.86 % (25794)Termination phase: Saturation
% 38.13/6.86
% 38.13/6.86 % (25794)Memory used [KB]: 7164
% 38.13/6.86 % (25794)Time elapsed: 0.102 s
% 38.13/6.86 % (25794)Instructions burned: 414 (million)
% 38.13/6.86 % (25794)------------------------------
% 38.13/6.86 % (25794)------------------------------
% 38.13/6.86 % (25792)Instruction limit reached!
% 38.13/6.86 % (25792)------------------------------
% 38.13/6.86 % (25792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.13/6.86 % (25792)Termination reason: Unknown
% 38.13/6.86 % (25792)Termination phase: Saturation
% 38.13/6.86
% 38.13/6.86 % (25792)Memory used [KB]: 8315
% 38.13/6.86 % (25792)Time elapsed: 0.192 s
% 38.13/6.86 % (25792)Instructions burned: 591 (million)
% 38.13/6.86 % (25792)------------------------------
% 38.13/6.86 % (25792)------------------------------
% 38.13/6.87 % (25796)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_25541 for (2947ds/961Mi)
% 38.13/6.87 % (25797)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_25541 for (2947ds/1213Mi)
% 38.65/6.98 % (25788)Instruction limit reached!
% 38.65/6.98 % (25788)------------------------------
% 38.65/6.98 % (25788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.65/6.98 % (25788)Termination reason: Unknown
% 38.65/6.98 % (25788)Termination phase: Saturation
% 38.65/6.98
% 38.65/6.98 % (25788)Memory used [KB]: 9083
% 38.65/6.98 % (25788)Time elapsed: 0.491 s
% 38.65/6.98 % (25788)Instructions burned: 1337 (million)
% 38.65/6.98 % (25788)------------------------------
% 38.65/6.98 % (25788)------------------------------
% 38.65/6.99 % (25798)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_25541 for (2946ds/1979Mi)
% 40.49/7.08 % (25795)Instruction limit reached!
% 40.49/7.08 % (25795)------------------------------
% 40.49/7.08 % (25795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.49/7.08 % (25795)Termination reason: Unknown
% 40.49/7.08 % (25795)Termination phase: Saturation
% 40.49/7.08
% 40.49/7.08 % (25795)Memory used [KB]: 4221
% 40.49/7.08 % (25795)Time elapsed: 0.327 s
% 40.49/7.08 % (25795)Instructions burned: 715 (million)
% 40.49/7.08 % (25795)------------------------------
% 40.49/7.08 % (25795)------------------------------
% 40.49/7.09 % (25799)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_25541 for (2945ds/481Mi)
% 41.16/7.15 % (25796)Instruction limit reached!
% 41.16/7.15 % (25796)------------------------------
% 41.16/7.15 % (25796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.16/7.15 % (25796)Termination reason: Unknown
% 41.16/7.15 % (25796)Termination phase: Saturation
% 41.16/7.15
% 41.16/7.15 % (25796)Memory used [KB]: 8827
% 41.16/7.15 % (25796)Time elapsed: 0.290 s
% 41.16/7.15 % (25796)Instructions burned: 962 (million)
% 41.16/7.15 % (25796)------------------------------
% 41.16/7.15 % (25796)------------------------------
% 41.16/7.18 % (25800)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_25541 for (2944ds/783Mi)
% 41.55/7.21 % (25799)Instruction limit reached!
% 41.55/7.21 % (25799)------------------------------
% 41.55/7.21 % (25799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.55/7.21 % (25799)Termination reason: Unknown
% 41.55/7.21 % (25799)Termination phase: Saturation
% 41.55/7.21
% 41.55/7.21 % (25799)Memory used [KB]: 11129
% 41.55/7.21 % (25799)Time elapsed: 0.121 s
% 41.55/7.21 % (25799)Instructions burned: 482 (million)
% 41.55/7.21 % (25799)------------------------------
% 41.55/7.21 % (25799)------------------------------
% 41.55/7.22 % (25801)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_25541 for (2944ds/432Mi)
% 41.55/7.24 % (25797)Instruction limit reached!
% 41.55/7.24 % (25797)------------------------------
% 41.55/7.24 % (25797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.55/7.24 % (25797)Termination reason: Unknown
% 41.55/7.24 % (25797)Termination phase: Saturation
% 41.55/7.24
% 41.55/7.24 % (25797)Memory used [KB]: 12920
% 41.55/7.24 % (25797)Time elapsed: 0.372 s
% 41.55/7.24 % (25797)Instructions burned: 1214 (million)
% 41.55/7.24 % (25797)------------------------------
% 41.55/7.24 % (25797)------------------------------
% 41.55/7.25 % (25802)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_25541 for (2943ds/1670Mi)
% 42.12/7.37 % (25801)Instruction limit reached!
% 42.12/7.37 % (25801)------------------------------
% 42.12/7.37 % (25801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.12/7.37 % (25801)Termination reason: Unknown
% 42.12/7.37 % (25801)Termination phase: Saturation
% 42.12/7.37
% 42.12/7.37 % (25801)Memory used [KB]: 8187
% 42.12/7.37 % (25801)Time elapsed: 0.151 s
% 42.12/7.37 % (25801)Instructions burned: 435 (million)
% 42.12/7.37 % (25801)------------------------------
% 42.12/7.37 % (25801)------------------------------
% 42.12/7.38 % (25803)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_25541 for (2942ds/90Mi)
% 42.68/7.41 % (25803)Instruction limit reached!
% 42.68/7.41 % (25803)------------------------------
% 42.68/7.41 % (25803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.68/7.41 % (25803)Termination reason: Unknown
% 42.68/7.41 % (25803)Termination phase: Property scanning
% 42.68/7.41
% 42.68/7.41 % (25803)Memory used [KB]: 2302
% 42.68/7.41 % (25803)Time elapsed: 0.025 s
% 42.68/7.41 % (25803)Instructions burned: 91 (million)
% 42.68/7.41 % (25803)------------------------------
% 42.68/7.41 % (25803)------------------------------
% 42.68/7.42 % (25804)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_25541 for (2942ds/346Mi)
% 42.68/7.45 % (25800)Instruction limit reached!
% 42.68/7.45 % (25800)------------------------------
% 42.68/7.45 % (25800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.68/7.45 % (25800)Termination reason: Unknown
% 42.68/7.45 % (25800)Termination phase: Saturation
% 42.68/7.45
% 42.68/7.45 % (25800)Memory used [KB]: 10746
% 42.68/7.45 % (25800)Time elapsed: 0.301 s
% 42.68/7.45 % (25800)Instructions burned: 784 (million)
% 42.68/7.45 % (25800)------------------------------
% 42.68/7.45 % (25800)------------------------------
% 42.68/7.46 % (25805)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_25541 for (2941ds/401Mi)
% 43.40/7.54 % (25804)Instruction limit reached!
% 43.40/7.54 % (25804)------------------------------
% 43.40/7.54 % (25804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.40/7.54 % (25804)Termination reason: Unknown
% 43.40/7.54 % (25804)Termination phase: Saturation
% 43.40/7.54
% 43.40/7.54 % (25804)Memory used [KB]: 7547
% 43.40/7.54 % (25804)Time elapsed: 0.142 s
% 43.40/7.54 % (25804)Instructions burned: 347 (million)
% 43.40/7.54 % (25804)------------------------------
% 43.40/7.54 % (25804)------------------------------
% 43.40/7.55 % (25806)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_25541 for (2940ds/6454Mi)
% 43.40/7.56 % (25805)Instruction limit reached!
% 43.40/7.56 % (25805)------------------------------
% 43.40/7.56 % (25805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.40/7.56 % (25805)Termination reason: Unknown
% 43.40/7.56 % (25805)Termination phase: Saturation
% 43.40/7.56
% 43.40/7.56 % (25805)Memory used [KB]: 7164
% 43.40/7.56 % (25805)Time elapsed: 0.102 s
% 43.40/7.56 % (25805)Instructions burned: 401 (million)
% 43.40/7.56 % (25805)------------------------------
% 43.40/7.56 % (25805)------------------------------
% 43.40/7.57 % (25807)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_25541 for (2940ds/283Mi)
% 44.03/7.65 % (25807)Instruction limit reached!
% 44.03/7.65 % (25807)------------------------------
% 44.03/7.65 % (25807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.03/7.65 % (25807)Termination reason: Unknown
% 44.03/7.65 % (25807)Termination phase: Saturation
% 44.03/7.65
% 44.03/7.65 % (25807)Memory used [KB]: 8059
% 44.03/7.65 % (25807)Time elapsed: 0.103 s
% 44.03/7.65 % (25807)Instructions burned: 285 (million)
% 44.03/7.65 % (25807)------------------------------
% 44.03/7.65 % (25807)------------------------------
% 44.03/7.66 % (25798)Instruction limit reached!
% 44.03/7.66 % (25798)------------------------------
% 44.03/7.66 % (25798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.03/7.66 % (25798)Termination reason: Unknown
% 44.03/7.66 % (25798)Termination phase: Saturation
% 44.03/7.66
% 44.03/7.66 % (25798)Memory used [KB]: 9594
% 44.03/7.66 % (25798)Time elapsed: 0.667 s
% 44.03/7.66 % (25798)Instructions burned: 1981 (million)
% 44.03/7.66 % (25798)------------------------------
% 44.03/7.66 % (25798)------------------------------
% 44.03/7.66 % (25808)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_25541 for (2939ds/865Mi)
% 44.03/7.67 % (25809)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_25541 for (2939ds/4528Mi)
% 44.03/7.67 % (25802)Instruction limit reached!
% 44.03/7.67 % (25802)------------------------------
% 44.03/7.67 % (25802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.03/7.67 % (25802)Termination reason: Unknown
% 44.03/7.67 % (25802)Termination phase: Saturation
% 44.03/7.67
% 44.03/7.67 % (25802)Memory used [KB]: 12281
% 44.03/7.67 % (25802)Time elapsed: 0.416 s
% 44.03/7.67 % (25802)Instructions burned: 1672 (million)
% 44.03/7.67 % (25802)------------------------------
% 44.03/7.67 % (25802)------------------------------
% 44.03/7.68 % (25810)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_25541 for (2939ds/1001Mi)
% 44.93/7.77 % (25809)Refutation not found, incomplete strategy
% 44.93/7.77 % (25809)------------------------------
% 44.93/7.77 % (25809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.93/7.77 % (25809)Termination reason: Refutation not found, incomplete strategy
% 44.93/7.77
% 44.93/7.77
% 44.93/7.77 % (25809)Memory used [KB]: 2558
% 44.93/7.77 % (25809)Time elapsed: 0.102 s
% 44.93/7.77 % (25809)Instructions burned: 383 (million)
% 44.93/7.77 % (25809)------------------------------
% 44.93/7.77 % (25809)------------------------------
% 44.93/7.78 % (25811)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_25541 for (2938ds/102Mi)
% 44.93/7.78 % (25789)Instruction limit reached!
% 44.93/7.78 % (25789)------------------------------
% 44.93/7.78 % (25789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.93/7.78 % (25789)Termination reason: Unknown
% 44.93/7.78 % (25789)Termination phase: Saturation
% 44.93/7.78
% 44.93/7.78 % (25789)Memory used [KB]: 12409
% 44.93/7.78 % (25789)Time elapsed: 1.211 s
% 44.93/7.78 % (25789)Instructions burned: 3374 (million)
% 44.93/7.78 % (25789)------------------------------
% 44.93/7.78 % (25789)------------------------------
% 44.93/7.79 % (25812)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_25541 for (2938ds/952Mi)
% 45.33/7.81 % (25811)Instruction limit reached!
% 45.33/7.81 % (25811)------------------------------
% 45.33/7.81 % (25811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.33/7.81 % (25811)Termination reason: Unknown
% 45.33/7.81 % (25811)Termination phase: Saturation
% 45.33/7.81
% 45.33/7.81 % (25811)Memory used [KB]: 6780
% 45.33/7.81 % (25811)Time elapsed: 0.028 s
% 45.33/7.81 % (25811)Instructions burned: 104 (million)
% 45.33/7.81 % (25811)------------------------------
% 45.33/7.81 % (25811)------------------------------
% 45.33/7.82 % (25813)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_25541 for (2938ds/578Mi)
% 45.33/7.87 % (25774)Instruction limit reached!
% 45.33/7.87 % (25774)------------------------------
% 45.33/7.87 % (25774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.33/7.87 % (25774)Termination reason: Unknown
% 45.33/7.87 % (25774)Termination phase: Saturation
% 45.33/7.87
% 45.33/7.87 % (25774)Memory used [KB]: 15991
% 45.33/7.87 % (25774)Time elapsed: 2.224 s
% 45.33/7.87 % (25774)Instructions burned: 5412 (million)
% 45.33/7.87 % (25774)------------------------------
% 45.33/7.87 % (25774)------------------------------
% 45.33/7.88 % (25814)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_25541 for (2937ds/643Mi)
% 45.57/7.90 % (25808)Instruction limit reached!
% 45.57/7.90 % (25808)------------------------------
% 45.57/7.90 % (25808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.57/7.90 % (25808)Termination reason: Unknown
% 45.57/7.90 % (25808)Termination phase: Saturation
% 45.57/7.90
% 45.57/7.90 % (25808)Memory used [KB]: 8315
% 45.57/7.90 % (25808)Time elapsed: 0.241 s
% 45.57/7.90 % (25808)Instructions burned: 868 (million)
% 45.57/7.90 % (25808)------------------------------
% 45.57/7.90 % (25808)------------------------------
% 45.57/7.91 % (25815)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_25541 for (2937ds/865Mi)
% 45.57/7.96 % (25813)Instruction limit reached!
% 45.57/7.96 % (25813)------------------------------
% 45.57/7.96 % (25813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.57/7.96 % (25813)Termination reason: Unknown
% 45.57/7.96 % (25813)Termination phase: Saturation
% 45.57/7.96
% 45.57/7.96 % (25813)Memory used [KB]: 8827
% 45.57/7.96 % (25813)Time elapsed: 0.141 s
% 45.57/7.96 % (25813)Instructions burned: 582 (million)
% 45.57/7.96 % (25813)------------------------------
% 45.57/7.96 % (25813)------------------------------
% 45.57/7.97 % (25816)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_25541 for (2936ds/1174Mi)
% 45.57/7.98 % (25810)Instruction limit reached!
% 45.57/7.98 % (25810)------------------------------
% 45.57/7.98 % (25810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.57/7.98 % (25810)Termination reason: Unknown
% 45.57/7.98 % (25810)Termination phase: Saturation
% 45.57/7.98
% 45.57/7.98 % (25810)Memory used [KB]: 11001
% 45.57/7.98 % (25810)Time elapsed: 0.304 s
% 45.57/7.98 % (25810)Instructions burned: 1001 (million)
% 45.57/7.98 % (25810)------------------------------
% 45.57/7.98 % (25810)------------------------------
% 45.57/7.99 % (25817)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_25541 for (2936ds/644Mi)
% 47.43/8.05 % (25814)Instruction limit reached!
% 47.43/8.05 % (25814)------------------------------
% 47.43/8.05 % (25814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.43/8.05 % (25814)Termination reason: Unknown
% 47.43/8.05 % (25814)Termination phase: Saturation
% 47.43/8.05
% 47.43/8.05 % (25814)Memory used [KB]: 11385
% 47.43/8.05 % (25814)Time elapsed: 0.165 s
% 47.43/8.05 % (25814)Instructions burned: 645 (million)
% 47.43/8.05 % (25814)------------------------------
% 47.43/8.05 % (25814)------------------------------
% 47.43/8.06 % (25818)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_25541 for (2935ds/1201Mi)
% 47.43/8.07 % (25812)Instruction limit reached!
% 47.43/8.07 % (25812)------------------------------
% 47.43/8.07 % (25812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.43/8.07 % (25812)Termination reason: Unknown
% 47.43/8.07 % (25812)Termination phase: Saturation
% 47.43/8.07
% 47.43/8.07 % (25812)Memory used [KB]: 8955
% 47.43/8.07 % (25812)Time elapsed: 0.285 s
% 47.43/8.07 % (25812)Instructions burned: 954 (million)
% 47.43/8.07 % (25812)------------------------------
% 47.43/8.07 % (25812)------------------------------
% 47.43/8.08 % (25819)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_25541 for (2935ds/1046Mi)
% 48.03/8.14 % (25815)Instruction limit reached!
% 48.03/8.14 % (25815)------------------------------
% 48.03/8.14 % (25815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.03/8.14 % (25815)Termination reason: Unknown
% 48.03/8.14 % (25815)Termination phase: Saturation
% 48.03/8.14
% 48.03/8.14 % (25815)Memory used [KB]: 7291
% 48.03/8.14 % (25815)Time elapsed: 0.234 s
% 48.03/8.14 % (25815)Instructions burned: 866 (million)
% 48.03/8.14 % (25815)------------------------------
% 48.03/8.14 % (25815)------------------------------
% 48.03/8.15 % (25820)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_25541 for (2934ds/222Mi)
% 48.03/8.18 % (25817)Instruction limit reached!
% 48.03/8.18 % (25817)------------------------------
% 48.03/8.18 % (25817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.03/8.18 % (25817)Termination reason: Unknown
% 48.03/8.18 % (25817)Termination phase: Saturation
% 48.03/8.18
% 48.03/8.18 % (25817)Memory used [KB]: 7803
% 48.03/8.18 % (25817)Time elapsed: 0.191 s
% 48.03/8.18 % (25817)Instructions burned: 645 (million)
% 48.03/8.18 % (25817)------------------------------
% 48.03/8.18 % (25817)------------------------------
% 48.03/8.19 % (25821)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_25541 for (2934ds/68Mi)
% 48.34/8.21 % (25820)Instruction limit reached!
% 48.34/8.21 % (25820)------------------------------
% 48.34/8.21 % (25820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.34/8.21 % (25820)Termination reason: Unknown
% 48.34/8.21 % (25820)Termination phase: Saturation
% 48.34/8.21
% 48.34/8.21 % (25820)Memory used [KB]: 7164
% 48.34/8.21 % (25820)Time elapsed: 0.058 s
% 48.34/8.21 % (25820)Instructions burned: 224 (million)
% 48.34/8.21 % (25820)------------------------------
% 48.34/8.21 % (25820)------------------------------
% 48.34/8.21 % (25821)Instruction limit reached!
% 48.34/8.21 % (25821)------------------------------
% 48.34/8.21 % (25821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.34/8.21 % (25821)Termination reason: Unknown
% 48.34/8.21 % (25821)Termination phase: Property scanning
% 48.34/8.21
% 48.34/8.21 % (25821)Memory used [KB]: 2174
% 48.34/8.21 % (25821)Time elapsed: 0.020 s
% 48.34/8.21 % (25821)Instructions burned: 69 (million)
% 48.34/8.21 % (25821)------------------------------
% 48.34/8.21 % (25821)------------------------------
% 48.34/8.22 % (25822)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_25541 for (2934ds/454Mi)
% 48.34/8.22 % (25823)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_25541 for (2934ds/360Mi)
% 48.34/8.29 % (25762)Instruction limit reached!
% 48.34/8.29 % (25762)------------------------------
% 48.34/8.29 % (25762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.34/8.29 % (25762)Termination reason: Unknown
% 48.34/8.29 % (25762)Termination phase: Saturation
% 48.34/8.29
% 48.34/8.29 % (25762)Memory used [KB]: 21875
% 48.34/8.29 % (25762)Time elapsed: 3.960 s
% 48.34/8.29 % (25762)Instructions burned: 8250 (million)
% 48.34/8.29 % (25762)------------------------------
% 48.34/8.29 % (25762)------------------------------
% 48.73/8.30 % (25824)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_25541 for (2933ds/157Mi)
% 48.73/8.31 % (25823)Instruction limit reached!
% 48.73/8.31 % (25823)------------------------------
% 48.73/8.31 % (25823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.73/8.31 % (25823)Termination reason: Unknown
% 48.73/8.31 % (25823)Termination phase: Saturation
% 48.73/8.31
% 48.73/8.31 % (25823)Memory used [KB]: 7164
% 48.73/8.31 % (25823)Time elapsed: 0.089 s
% 48.73/8.31 % (25823)Instructions burned: 363 (million)
% 48.73/8.31 % (25823)------------------------------
% 48.73/8.31 % (25823)------------------------------
% 48.73/8.32 % (25825)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_25541 for (2933ds/5061Mi)
% 48.73/8.33 % (25822)Instruction limit reached!
% 48.73/8.33 % (25822)------------------------------
% 48.73/8.33 % (25822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.73/8.33 % (25822)Termination reason: Unknown
% 48.73/8.33 % (25822)Termination phase: Saturation
% 48.73/8.33
% 48.73/8.33 % (25822)Memory used [KB]: 15223
% 48.73/8.33 % (25822)Time elapsed: 0.115 s
% 48.73/8.33 % (25822)Instructions burned: 456 (million)
% 48.73/8.33 % (25822)------------------------------
% 48.73/8.33 % (25822)------------------------------
% 48.73/8.33 % (25816)Refutation not found, non-redundant clauses discarded% (25816)------------------------------
% 48.73/8.33 % (25816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.73/8.33 % (25816)Termination reason: Refutation not found, non-redundant clauses discarded
% 48.73/8.33
% 48.73/8.33 % (25816)Memory used [KB]: 9466
% 48.73/8.33 % (25816)Time elapsed: 0.368 s
% 48.73/8.33 % (25816)Instructions burned: 1168 (million)
% 48.73/8.33 % (25816)------------------------------
% 48.73/8.33 % (25816)------------------------------
% 48.73/8.34 % (25824)Instruction limit reached!
% 48.73/8.34 % (25824)------------------------------
% 48.73/8.34 % (25824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.73/8.34 % (25824)Termination reason: Unknown
% 48.73/8.34 % (25824)Termination phase: Saturation
% 48.73/8.34
% 48.73/8.34 % (25824)Memory used [KB]: 6908
% 48.73/8.34 % (25824)Time elapsed: 0.041 s
% 48.73/8.34 % (25824)Instructions burned: 159 (million)
% 48.73/8.34 % (25824)------------------------------
% 48.73/8.34 % (25824)------------------------------
% 48.73/8.34 % (25826)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_25541 for (2932ds/2401Mi)
% 48.73/8.34 % (25819)Instruction limit reached!
% 48.73/8.34 % (25819)------------------------------
% 48.73/8.34 % (25819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.73/8.34 % (25819)Termination reason: Unknown
% 48.73/8.34 % (25819)Termination phase: Saturation
% 48.73/8.34
% 48.73/8.34 % (25819)Memory used [KB]: 7291
% 48.73/8.34 % (25819)Time elapsed: 0.259 s
% 48.73/8.34 % (25819)Instructions burned: 1046 (million)
% 48.73/8.34 % (25819)------------------------------
% 48.73/8.34 % (25819)------------------------------
% 48.73/8.35 % (25828)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_25541 for (2932ds/346Mi)
% 48.73/8.35 % (25827)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_25541 for (2932ds/5798Mi)
% 48.73/8.35 % (25829)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_25541 for (2932ds/1321Mi)
% 49.42/8.43 % (25828)Instruction limit reached!
% 49.42/8.43 % (25828)------------------------------
% 49.42/8.43 % (25828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.42/8.44 % (25828)Termination reason: Unknown
% 49.42/8.44 % (25828)Termination phase: Saturation
% 49.42/8.44
% 49.42/8.44 % (25828)Memory used [KB]: 7547
% 49.42/8.44 % (25828)Time elapsed: 0.086 s
% 49.42/8.44 % (25828)Instructions burned: 348 (million)
% 49.42/8.44 % (25828)------------------------------
% 49.42/8.44 % (25828)------------------------------
% 49.42/8.45 % (25830)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_25541 for (2931ds/1312Mi)
% 49.63/8.50 % (25818)Refutation not found, non-redundant clauses discarded% (25818)------------------------------
% 49.63/8.50 % (25818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.63/8.50 % (25818)Termination reason: Refutation not found, non-redundant clauses discarded
% 49.63/8.50
% 49.63/8.50 % (25818)Memory used [KB]: 10362
% 49.63/8.50 % (25818)Time elapsed: 0.440 s
% 49.63/8.50 % (25818)Instructions burned: 1190 (million)
% 49.63/8.50 % (25818)------------------------------
% 49.63/8.50 % (25818)------------------------------
% 49.63/8.51 % (25831)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_25541 for (2931ds/672Mi)
% 50.26/8.72 % (25831)Instruction limit reached!
% 50.26/8.72 % (25831)------------------------------
% 50.26/8.72 % (25831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.26/8.72 % (25831)Termination reason: Unknown
% 50.26/8.72 % (25831)Termination phase: Saturation
% 50.26/8.72
% 50.26/8.72 % (25831)Memory used [KB]: 9722
% 50.26/8.72 % (25831)Time elapsed: 0.207 s
% 50.26/8.72 % (25831)Instructions burned: 672 (million)
% 50.26/8.72 % (25831)------------------------------
% 50.26/8.72 % (25831)------------------------------
% 50.26/8.73 % (25832)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_25541 for (2929ds/1897Mi)
% 50.26/8.74 % (25829)Instruction limit reached!
% 50.26/8.74 % (25829)------------------------------
% 50.26/8.74 % (25829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.26/8.74 % (25829)Termination reason: Unknown
% 50.26/8.74 % (25829)Termination phase: Saturation
% 50.26/8.74
% 50.26/8.74 % (25829)Memory used [KB]: 6652
% 50.26/8.74 % (25829)Time elapsed: 0.385 s
% 50.26/8.74 % (25829)Instructions burned: 1323 (million)
% 50.26/8.74 % (25829)------------------------------
% 50.26/8.74 % (25829)------------------------------
% 50.26/8.75 % (25833)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_25541 for (2928ds/1202Mi)
% 50.26/8.78 % (25830)Instruction limit reached!
% 50.26/8.78 % (25830)------------------------------
% 50.26/8.78 % (25830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.26/8.78 % (25830)Termination reason: Unknown
% 50.26/8.78 % (25830)Termination phase: Saturation
% 50.26/8.78
% 50.26/8.78 % (25830)Memory used [KB]: 11897
% 50.26/8.78 % (25830)Time elapsed: 0.334 s
% 50.26/8.78 % (25830)Instructions burned: 1312 (million)
% 50.26/8.78 % (25830)------------------------------
% 50.26/8.78 % (25830)------------------------------
% 50.26/8.79 % (25834)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_25541 for (2928ds/1493Mi)
% 54.32/9.06 % (25826)Instruction limit reached!
% 54.32/9.06 % (25826)------------------------------
% 54.32/9.06 % (25826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.32/9.06 % (25826)Termination reason: Unknown
% 54.32/9.06 % (25826)Termination phase: Saturation
% 54.32/9.06
% 54.32/9.06 % (25826)Memory used [KB]: 9722
% 54.32/9.06 % (25826)Time elapsed: 0.720 s
% 54.32/9.06 % (25826)Instructions burned: 2403 (million)
% 54.32/9.06 % (25826)------------------------------
% 54.32/9.06 % (25826)------------------------------
% 54.32/9.07 % (25835)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_25541 for (2925ds/7679Mi)
% 54.32/9.09 % (25833)Instruction limit reached!
% 54.32/9.09 % (25833)------------------------------
% 54.32/9.09 % (25833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.32/9.09 % (25833)Termination reason: Unknown
% 54.32/9.09 % (25833)Termination phase: Saturation
% 54.32/9.09
% 54.32/9.09 % (25833)Memory used [KB]: 7164
% 54.32/9.09 % (25833)Time elapsed: 0.346 s
% 54.32/9.09 % (25833)Instructions burned: 1204 (million)
% 54.32/9.09 % (25833)------------------------------
% 54.32/9.09 % (25833)------------------------------
% 54.32/9.10 % (25836)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_25541 for (2925ds/340Mi)
% 54.97/9.14 % (25834)Instruction limit reached!
% 54.97/9.14 % (25834)------------------------------
% 54.97/9.14 % (25834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.97/9.14 % (25834)Termination reason: Unknown
% 54.97/9.14 % (25834)Termination phase: Saturation
% 54.97/9.14
% 54.97/9.14 % (25834)Memory used [KB]: 7291
% 54.97/9.14 % (25834)Time elapsed: 0.358 s
% 54.97/9.14 % (25834)Instructions burned: 1495 (million)
% 54.97/9.14 % (25834)------------------------------
% 54.97/9.14 % (25834)------------------------------
% 54.97/9.15 % (25837)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_25541 for (2924ds/3672Mi)
% 55.35/9.20 % (25836)Instruction limit reached!
% 55.35/9.20 % (25836)------------------------------
% 55.35/9.20 % (25836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.35/9.20 % (25836)Termination reason: Unknown
% 55.35/9.20 % (25836)Termination phase: Saturation
% 55.35/9.20
% 55.35/9.20 % (25836)Memory used [KB]: 9594
% 55.35/9.20 % (25836)Time elapsed: 0.101 s
% 55.35/9.20 % (25836)Instructions burned: 342 (million)
% 55.35/9.20 % (25836)------------------------------
% 55.35/9.20 % (25836)------------------------------
% 55.35/9.21 % (25838)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_25541 for (2924ds/1535Mi)
% 55.86/9.33 % (25832)Instruction limit reached!
% 55.86/9.33 % (25832)------------------------------
% 55.86/9.33 % (25832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.86/9.33 % (25832)Termination reason: Unknown
% 55.86/9.33 % (25832)Termination phase: Saturation
% 55.86/9.33
% 55.86/9.33 % (25832)Memory used [KB]: 12281
% 55.86/9.33 % (25832)Time elapsed: 0.614 s
% 55.86/9.33 % (25832)Instructions burned: 1898 (million)
% 55.86/9.33 % (25832)------------------------------
% 55.86/9.33 % (25832)------------------------------
% 55.86/9.34 % (25839)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_25541 for (2923ds/4637Mi)
% 56.50/9.51 % (25825)Instruction limit reached!
% 56.50/9.51 % (25825)------------------------------
% 56.50/9.51 % (25825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.50/9.51 % (25825)Termination reason: Unknown
% 56.50/9.51 % (25825)Termination phase: Saturation
% 56.50/9.51
% 56.50/9.51 % (25825)Memory used [KB]: 7931
% 56.50/9.51 % (25825)Time elapsed: 1.195 s
% 56.50/9.51 % (25825)Instructions burned: 5064 (million)
% 56.50/9.51 % (25825)------------------------------
% 56.50/9.51 % (25825)------------------------------
% 56.50/9.52 % (25840)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_25541 for (2921ds/3174Mi)
% 56.50/9.59 % (25838)Instruction limit reached!
% 56.50/9.59 % (25838)------------------------------
% 56.50/9.59 % (25838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.50/9.59 % (25838)Termination reason: Unknown
% 56.50/9.59 % (25838)Termination phase: Saturation
% 56.50/9.59
% 56.50/9.59 % (25838)Memory used [KB]: 11385
% 56.50/9.59 % (25838)Time elapsed: 0.376 s
% 56.50/9.59 % (25838)Instructions burned: 1535 (million)
% 56.50/9.59 % (25838)------------------------------
% 56.50/9.59 % (25838)------------------------------
% 56.50/9.60 % (25841)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_25541 for (2920ds/307Mi)
% 57.11/9.67 % (25841)Instruction limit reached!
% 57.11/9.67 % (25841)------------------------------
% 57.11/9.67 % (25841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.11/9.67 % (25841)Termination reason: Unknown
% 57.11/9.67 % (25841)Termination phase: Saturation
% 57.11/9.67
% 57.11/9.67 % (25841)Memory used [KB]: 7164
% 57.11/9.67 % (25841)Time elapsed: 0.078 s
% 57.11/9.67 % (25841)Instructions burned: 310 (million)
% 57.11/9.67 % (25841)------------------------------
% 57.11/9.67 % (25841)------------------------------
% 57.11/9.68 % (25842)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_25541 for (2919ds/3619Mi)
% 57.39/9.72 % (25806)Instruction limit reached!
% 57.39/9.72 % (25806)------------------------------
% 57.39/9.72 % (25806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.39/9.72 % (25806)Termination reason: Unknown
% 57.39/9.72 % (25806)Termination phase: Saturation
% 57.39/9.72
% 57.39/9.72 % (25806)Memory used [KB]: 12025
% 57.39/9.72 % (25806)Time elapsed: 2.183 s
% 57.39/9.72 % (25806)Instructions burned: 6455 (million)
% 57.39/9.72 % (25806)------------------------------
% 57.39/9.72 % (25806)------------------------------
% 57.39/9.73 % (25843)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_25541 for (2919ds/2325Mi)
% 62.02/10.18 % (25827)Instruction limit reached!
% 62.02/10.18 % (25827)------------------------------
% 62.02/10.18 % (25827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.02/10.18 % (25827)Termination reason: Unknown
% 62.02/10.18 % (25827)Termination phase: Saturation
% 62.02/10.18
% 62.02/10.18 % (25827)Memory used [KB]: 12409
% 62.02/10.18 % (25827)Time elapsed: 1.826 s
% 62.02/10.18 % (25827)Instructions burned: 5800 (million)
% 62.02/10.18 % (25827)------------------------------
% 62.02/10.18 % (25827)------------------------------
% 62.02/10.19 % (25844)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_25541 for (2914ds/2341Mi)
% 62.58/10.29 % (25837)Instruction limit reached!
% 62.58/10.29 % (25837)------------------------------
% 62.58/10.29 % (25837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.58/10.29 % (25837)Termination reason: Unknown
% 62.58/10.29 % (25837)Termination phase: Saturation
% 62.58/10.29
% 62.58/10.29 % (25837)Memory used [KB]: 12153
% 62.58/10.29 % (25837)Time elapsed: 1.139 s
% 62.58/10.29 % (25837)Instructions burned: 3674 (million)
% 62.58/10.29 % (25837)------------------------------
% 62.58/10.29 % (25837)------------------------------
% 63.21/10.30 % (25848)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_25541 for (2913ds/7257Mi)
% 63.70/10.45 % (25843)Instruction limit reached!
% 63.70/10.45 % (25843)------------------------------
% 63.70/10.45 % (25843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.70/10.45 % (25843)Termination reason: Unknown
% 63.70/10.45 % (25843)Termination phase: Saturation
% 63.70/10.45
% 63.70/10.45 % (25843)Memory used [KB]: 14839
% 63.70/10.45 % (25843)Time elapsed: 0.737 s
% 63.70/10.45 % (25843)Instructions burned: 2327 (million)
% 63.70/10.45 % (25843)------------------------------
% 63.70/10.45 % (25843)------------------------------
% 63.70/10.46 % (25906)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_25541 for (2911ds/3710Mi)
% 63.70/10.49 % (25840)Instruction limit reached!
% 63.70/10.49 % (25840)------------------------------
% 63.70/10.49 % (25840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.70/10.49 % (25840)Termination reason: Unknown
% 63.70/10.49 % (25840)Termination phase: Saturation
% 63.70/10.49
% 63.70/10.49 % (25840)Memory used [KB]: 19573
% 63.70/10.49 % (25840)Time elapsed: 0.986 s
% 63.70/10.49 % (25840)Instructions burned: 3175 (million)
% 63.70/10.49 % (25840)------------------------------
% 63.70/10.49 % (25840)------------------------------
% 64.16/10.50 % (25925)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_25541 for (2911ds/326Mi)
% 64.16/10.59 % (25925)Instruction limit reached!
% 64.16/10.59 % (25925)------------------------------
% 64.16/10.59 % (25925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.16/10.59 % (25925)Termination reason: Unknown
% 64.16/10.59 % (25925)Termination phase: Saturation
% 64.16/10.59
% 64.16/10.59 % (25925)Memory used [KB]: 8187
% 64.16/10.59 % (25925)Time elapsed: 0.094 s
% 64.16/10.59 % (25925)Instructions burned: 329 (million)
% 64.16/10.59 % (25925)------------------------------
% 64.16/10.59 % (25925)------------------------------
% 64.57/10.60 % (25974)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_25541 for (2910ds/1100Mi)
% 64.89/10.74 % (25842)Instruction limit reached!
% 64.89/10.74 % (25842)------------------------------
% 64.89/10.74 % (25842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.89/10.74 % (25842)Termination reason: Unknown
% 64.89/10.74 % (25842)Termination phase: Saturation
% 64.89/10.74
% 64.89/10.74 % (25842)Memory used [KB]: 16119
% 64.89/10.74 % (25842)Time elapsed: 1.078 s
% 64.89/10.74 % (25842)Instructions burned: 3621 (million)
% 64.89/10.74 % (25842)------------------------------
% 64.89/10.74 % (25842)------------------------------
% 64.89/10.75 % (26024)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_25541 for (2908ds/406Mi)
% 65.14/10.81 % (25839)Instruction limit reached!
% 65.14/10.81 % (25839)------------------------------
% 65.14/10.81 % (25839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.14/10.81 % (25839)Termination reason: Unknown
% 65.14/10.81 % (25839)Termination phase: Saturation
% 65.14/10.81
% 65.14/10.81 % (25839)Memory used [KB]: 10490
% 65.14/10.81 % (25839)Time elapsed: 1.489 s
% 65.14/10.81 % (25839)Instructions burned: 4637 (million)
% 65.14/10.81 % (25839)------------------------------
% 65.14/10.81 % (25839)------------------------------
% 65.14/10.82 % (26039)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_25541 for (2908ds/1871Mi)
% 65.14/10.86 % (26024)Instruction limit reached!
% 65.14/10.86 % (26024)------------------------------
% 65.14/10.86 % (26024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.14/10.86 % (26024)Termination reason: Unknown
% 65.14/10.86 % (26024)Termination phase: Saturation
% 65.14/10.86
% 65.14/10.86 % (26024)Memory used [KB]: 7291
% 65.14/10.86 % (26024)Time elapsed: 0.114 s
% 65.14/10.86 % (26024)Instructions burned: 407 (million)
% 65.14/10.86 % (26024)------------------------------
% 65.14/10.86 % (26024)------------------------------
% 65.14/10.87 % (26064)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_25541 for (2907ds/1194Mi)
% 65.39/10.91 % (25844)Instruction limit reached!
% 65.39/10.91 % (25844)------------------------------
% 65.39/10.91 % (25844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.39/10.91 % (25844)Termination reason: Unknown
% 65.39/10.91 % (25844)Termination phase: Saturation
% 65.39/10.91
% 65.39/10.91 % (25844)Memory used [KB]: 10234
% 65.39/10.91 % (25844)Time elapsed: 0.740 s
% 65.39/10.91 % (25844)Instructions burned: 2341 (million)
% 65.39/10.91 % (25844)------------------------------
% 65.39/10.91 % (25844)------------------------------
% 65.39/10.92 % (26083)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_25541 for (2907ds/474Mi)
% 65.39/10.95 % (25974)Instruction limit reached!
% 65.39/10.95 % (25974)------------------------------
% 65.39/10.95 % (25974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.39/10.95 % (25974)Termination reason: Unknown
% 65.39/10.95 % (25974)Termination phase: Saturation
% 65.39/10.95
% 65.39/10.95 % (25974)Memory used [KB]: 12792
% 65.39/10.95 % (25974)Time elapsed: 0.352 s
% 65.39/10.95 % (25974)Instructions burned: 1102 (million)
% 65.39/10.95 % (25974)------------------------------
% 65.39/10.95 % (25974)------------------------------
% 65.39/10.96 % (26084)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_25541 for (2906ds/3115Mi)
% 68.32/11.04 % (26083)Instruction limit reached!
% 68.32/11.04 % (26083)------------------------------
% 68.32/11.04 % (26083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.32/11.04 % (26083)Termination reason: Unknown
% 68.32/11.04 % (26083)Termination phase: Saturation
% 68.32/11.04
% 68.32/11.04 % (26083)Memory used [KB]: 11129
% 68.32/11.04 % (26083)Time elapsed: 0.121 s
% 68.32/11.04 % (26083)Instructions burned: 477 (million)
% 68.32/11.04 % (26083)------------------------------
% 68.32/11.04 % (26083)------------------------------
% 68.32/11.05 % (26085)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_25541 for (2905ds/831Mi)
% 69.49/11.25 % (26064)Instruction limit reached!
% 69.49/11.25 % (26064)------------------------------
% 69.49/11.25 % (26064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.49/11.25 % (26064)Termination reason: Unknown
% 69.49/11.25 % (26064)Termination phase: Saturation
% 69.49/11.25
% 69.49/11.25 % (26064)Memory used [KB]: 11513
% 69.49/11.25 % (26064)Time elapsed: 0.381 s
% 69.49/11.25 % (26064)Instructions burned: 1195 (million)
% 69.49/11.25 % (26064)------------------------------
% 69.49/11.25 % (26064)------------------------------
% 69.49/11.26 % (26086)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_25541 for (2903ds/1188Mi)
% 70.05/11.31 % (26085)Instruction limit reached!
% 70.05/11.31 % (26085)------------------------------
% 70.05/11.31 % (26085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.05/11.31 % (26085)Termination reason: Unknown
% 70.05/11.31 % (26085)Termination phase: Saturation
% 70.05/11.31
% 70.05/11.31 % (26085)Memory used [KB]: 8699
% 70.05/11.31 % (26085)Time elapsed: 0.264 s
% 70.05/11.31 % (26085)Instructions burned: 832 (million)
% 70.05/11.31 % (26085)------------------------------
% 70.05/11.31 % (26085)------------------------------
% 70.05/11.32 % (26087)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_25541 for (2903ds/2868Mi)
% 70.05/11.38 % (25835)Instruction limit reached!
% 70.05/11.38 % (25835)------------------------------
% 70.05/11.38 % (25835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.05/11.38 % (25835)Termination reason: Unknown
% 70.05/11.38 % (25835)Termination phase: Saturation
% 70.05/11.38
% 70.05/11.38 % (25835)Memory used [KB]: 17654
% 70.05/11.38 % (25835)Time elapsed: 2.313 s
% 70.05/11.38 % (25835)Instructions burned: 7681 (million)
% 70.05/11.38 % (25835)------------------------------
% 70.05/11.38 % (25835)------------------------------
% 70.05/11.39 % (26088)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_25541 for (2902ds/1516Mi)
% 70.82/11.41 % (25906)Instruction limit reached!
% 70.82/11.41 % (25906)------------------------------
% 70.82/11.41 % (25906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.82/11.41 % (25906)Termination reason: Unknown
% 70.82/11.41 % (25906)Termination phase: Saturation
% 70.82/11.41
% 70.82/11.41 % (25906)Memory used [KB]: 13048
% 70.82/11.41 % (25906)Time elapsed: 0.972 s
% 70.82/11.41 % (25906)Instructions burned: 3712 (million)
% 70.82/11.41 % (25906)------------------------------
% 70.82/11.41 % (25906)------------------------------
% 70.82/11.42 % (26089)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_25541 for (2902ds/2321Mi)
% 70.82/11.45 % (26039)Instruction limit reached!
% 70.82/11.45 % (26039)------------------------------
% 70.82/11.45 % (26039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.82/11.45 % (26039)Termination reason: Unknown
% 70.82/11.45 % (26039)Termination phase: Saturation
% 70.82/11.45
% 70.82/11.45 % (26039)Memory used [KB]: 17142
% 70.82/11.45 % (26039)Time elapsed: 0.631 s
% 70.82/11.45 % (26039)Instructions burned: 1871 (million)
% 70.82/11.45 % (26039)------------------------------
% 70.82/11.45 % (26039)------------------------------
% 70.82/11.46 % (26090)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_25541 for (2901ds/2812Mi)
% 71.11/11.56 % (26086)Instruction limit reached!
% 71.11/11.56 % (26086)------------------------------
% 71.11/11.56 % (26086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.11/11.56 % (26086)Termination reason: Unknown
% 71.11/11.56 % (26086)Termination phase: Saturation
% 71.11/11.56
% 71.11/11.56 % (26086)Memory used [KB]: 12792
% 71.11/11.56 % (26086)Time elapsed: 0.303 s
% 71.11/11.56 % (26086)Instructions burned: 1191 (million)
% 71.11/11.56 % (26086)------------------------------
% 71.11/11.56 % (26086)------------------------------
% 71.11/11.57 % (26091)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_25541 for (2900ds/4604Mi)
% 71.81/11.73 % (26084)Instruction limit reached!
% 71.81/11.73 % (26084)------------------------------
% 71.81/11.73 % (26084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.81/11.73 % (26084)Termination reason: Unknown
% 71.81/11.73 % (26084)Termination phase: Saturation
% 71.81/11.73
% 71.81/11.73 % (26084)Memory used [KB]: 11769
% 71.81/11.73 % (26084)Time elapsed: 0.770 s
% 71.81/11.73 % (26084)Instructions burned: 3118 (million)
% 71.81/11.73 % (26084)------------------------------
% 71.81/11.73 % (26084)------------------------------
% 71.81/11.74 % (26092)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_25541 for (2898ds/2678Mi)
% 71.95/11.86 % (26088)Instruction limit reached!
% 71.95/11.86 % (26088)------------------------------
% 71.95/11.86 % (26088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.95/11.86 % (26088)Termination reason: Unknown
% 71.95/11.86 % (26088)Termination phase: Saturation
% 71.95/11.86
% 71.95/11.86 % (26088)Memory used [KB]: 11385
% 71.95/11.86 % (26088)Time elapsed: 0.462 s
% 71.95/11.86 % (26088)Instructions burned: 1517 (million)
% 71.95/11.86 % (26088)------------------------------
% 71.95/11.86 % (26088)------------------------------
% 71.95/11.87 % (26093)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_25541 for (2897ds/643Mi)
% 72.52/11.99 % (26089)Instruction limit reached!
% 72.52/11.99 % (26089)------------------------------
% 72.52/11.99 % (26089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.52/11.99 % (26089)Termination reason: Unknown
% 72.52/11.99 % (26089)Termination phase: Saturation
% 72.52/11.99
% 72.52/11.99 % (26089)Memory used [KB]: 11385
% 72.52/11.99 % (26089)Time elapsed: 0.574 s
% 72.52/11.99 % (26089)Instructions burned: 2321 (million)
% 72.52/11.99 % (26089)------------------------------
% 72.52/11.99 % (26089)------------------------------
% 72.52/12.00 % (26094)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_25541 for (2896ds/458Mi)
% 75.44/12.03 % (26093)Instruction limit reached!
% 75.44/12.03 % (26093)------------------------------
% 75.44/12.03 % (26093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.44/12.03 % (26093)Termination reason: Unknown
% 75.44/12.03 % (26093)Termination phase: Saturation
% 75.44/12.03
% 75.44/12.03 % (26093)Memory used [KB]: 11385
% 75.44/12.03 % (26093)Time elapsed: 0.161 s
% 75.44/12.03 % (26093)Instructions burned: 646 (million)
% 75.44/12.03 % (26093)------------------------------
% 75.44/12.03 % (26093)------------------------------
% 75.44/12.03 % (26087)Instruction limit reached!
% 75.44/12.03 % (26087)------------------------------
% 75.44/12.03 % (26087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.44/12.03 % (26087)Termination reason: Unknown
% 75.44/12.03 % (26087)Termination phase: Saturation
% 75.44/12.03
% 75.44/12.03 % (26087)Memory used [KB]: 7164
% 75.44/12.03 % (26087)Time elapsed: 0.710 s
% 75.44/12.03 % (26087)Instructions burned: 2869 (million)
% 75.44/12.03 % (26087)------------------------------
% 75.44/12.03 % (26087)------------------------------
% 75.44/12.04 % (26095)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_25541 for (2896ds/2546Mi)
% 75.44/12.04 % (26096)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_25541 for (2895ds/1432Mi)
% 75.44/12.11 % (26094)Instruction limit reached!
% 75.44/12.11 % (26094)------------------------------
% 75.44/12.11 % (26094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.44/12.11 % (26094)Termination reason: Unknown
% 75.44/12.11 % (26094)Termination phase: Saturation
% 75.44/12.11
% 75.44/12.11 % (26094)Memory used [KB]: 11129
% 75.44/12.11 % (26094)Time elapsed: 0.116 s
% 75.44/12.11 % (26094)Instructions burned: 461 (million)
% 75.44/12.11 % (26094)------------------------------
% 75.44/12.11 % (26094)------------------------------
% 75.44/12.12 % (26097)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_25541 for (2894ds/386Mi)
% 76.25/12.22 % (26097)Instruction limit reached!
% 76.25/12.22 % (26097)------------------------------
% 76.25/12.22 % (26097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.25/12.22 % (26097)Termination reason: Unknown
% 76.25/12.22 % (26097)Termination phase: Saturation
% 76.25/12.22
% 76.25/12.22 % (26097)Memory used [KB]: 7164
% 76.25/12.22 % (26097)Time elapsed: 0.095 s
% 76.25/12.22 % (26097)Instructions burned: 387 (million)
% 76.25/12.22 % (26097)------------------------------
% 76.25/12.22 % (26097)------------------------------
% 76.25/12.23 % (26098)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_25541 for (2893ds/360Mi)
% 76.75/12.32 % (26098)Instruction limit reached!
% 76.75/12.32 % (26098)------------------------------
% 76.75/12.32 % (26098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.75/12.32 % (26098)Termination reason: Unknown
% 76.75/12.32 % (26098)Termination phase: Saturation
% 76.75/12.32
% 76.75/12.32 % (26098)Memory used [KB]: 7164
% 76.75/12.32 % (26098)Time elapsed: 0.093 s
% 76.75/12.32 % (26098)Instructions burned: 362 (million)
% 76.75/12.32 % (26098)------------------------------
% 76.75/12.32 % (26098)------------------------------
% 76.75/12.33 % (26099)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_25541 for (2892ds/5446Mi)
% 76.75/12.33 % (26090)Instruction limit reached!
% 76.75/12.33 % (26090)------------------------------
% 76.75/12.33 % (26090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.75/12.33 % (26090)Termination reason: Unknown
% 76.75/12.33 % (26090)Termination phase: Saturation
% 76.75/12.33
% 76.75/12.33 % (26090)Memory used [KB]: 11129
% 76.75/12.33 % (26090)Time elapsed: 0.878 s
% 76.75/12.33 % (26090)Instructions burned: 2812 (million)
% 76.75/12.33 % (26090)------------------------------
% 76.75/12.33 % (26090)------------------------------
% 76.75/12.34 % (26100)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_25541 for (2892ds/2573Mi)
% 76.75/12.38 % (26096)Instruction limit reached!
% 76.75/12.38 % (26096)------------------------------
% 76.75/12.38 % (26096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.75/12.38 % (26096)Termination reason: Unknown
% 76.75/12.38 % (26096)Termination phase: Saturation
% 76.75/12.38
% 76.75/12.38 % (26096)Memory used [KB]: 15223
% 76.75/12.38 % (26096)Time elapsed: 0.343 s
% 76.75/12.38 % (26096)Instructions burned: 1433 (million)
% 76.75/12.38 % (26096)------------------------------
% 76.75/12.38 % (26096)------------------------------
% 76.75/12.39 % (26101)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_25541 for (2892ds/2655Mi)
% 77.57/12.40 % (26092)Instruction limit reached!
% 77.57/12.40 % (26092)------------------------------
% 77.57/12.40 % (26092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.57/12.40 % (26092)Termination reason: Unknown
% 77.57/12.40 % (26092)Termination phase: Saturation
% 77.57/12.40
% 77.57/12.40 % (26092)Memory used [KB]: 15991
% 77.57/12.40 % (26092)Time elapsed: 0.663 s
% 77.57/12.40 % (26092)Instructions burned: 2680 (million)
% 77.57/12.40 % (26092)------------------------------
% 77.57/12.40 % (26092)------------------------------
% 77.57/12.41 % (26102)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_25541 for (2892ds/2781Mi)
% 77.77/12.56 % (25848)Instruction limit reached!
% 77.77/12.56 % (25848)------------------------------
% 77.77/12.56 % (25848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.77/12.56 % (25848)Termination reason: Unknown
% 77.77/12.56 % (25848)Termination phase: Saturation
% 77.77/12.56
% 77.77/12.56 % (25848)Memory used [KB]: 10362
% 77.77/12.56 % (25848)Time elapsed: 2.277 s
% 77.77/12.56 % (25848)Instructions burned: 7257 (million)
% 77.77/12.56 % (25848)------------------------------
% 77.77/12.56 % (25848)------------------------------
% 77.77/12.57 % (26103)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_25541 for (2890ds/307Mi)
% 77.95/12.64 % (26103)Instruction limit reached!
% 77.95/12.64 % (26103)------------------------------
% 77.95/12.64 % (26103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.95/12.64 % (26103)Termination reason: Unknown
% 77.95/12.64 % (26103)Termination phase: Saturation
% 77.95/12.64
% 77.95/12.64 % (26103)Memory used [KB]: 7164
% 77.95/12.64 % (26103)Time elapsed: 0.078 s
% 77.95/12.64 % (26103)Instructions burned: 310 (million)
% 77.95/12.64 % (26103)------------------------------
% 77.95/12.64 % (26103)------------------------------
% 77.95/12.65 % (26104)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_25541 for (2889ds/1548Mi)
% 78.24/12.80 % (26095)Instruction limit reached!
% 78.24/12.80 % (26095)------------------------------
% 78.24/12.80 % (26095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.24/12.80 % (26095)Termination reason: Unknown
% 78.24/12.80 % (26095)Termination phase: Saturation
% 78.24/12.80
% 78.24/12.80 % (26095)Memory used [KB]: 10362
% 78.24/12.80 % (26095)Time elapsed: 0.787 s
% 78.24/12.80 % (26095)Instructions burned: 2546 (million)
% 78.24/12.80 % (26095)------------------------------
% 78.24/12.80 % (26095)------------------------------
% 78.24/12.81 % (26105)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_25541 for (2888ds/5214Mi)
% 79.12/13.00 % (26100)Instruction limit reached!
% 79.12/13.00 % (26100)------------------------------
% 79.12/13.00 % (26100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.12/13.00 % (26100)Termination reason: Unknown
% 79.12/13.00 % (26100)Termination phase: Saturation
% 79.12/13.00
% 79.12/13.00 % (26100)Memory used [KB]: 13304
% 79.12/13.00 % (26100)Time elapsed: 0.654 s
% 79.12/13.00 % (26100)Instructions burned: 2577 (million)
% 79.12/13.00 % (26100)------------------------------
% 79.12/13.00 % (26100)------------------------------
% 79.12/13.00 % (26091)Instruction limit reached!
% 79.12/13.00 % (26091)------------------------------
% 79.12/13.00 % (26091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.12/13.00 % (26091)Termination reason: Unknown
% 79.12/13.00 % (26091)Termination phase: Saturation
% 79.12/13.00
% 79.12/13.00 % (26091)Memory used [KB]: 13304
% 79.12/13.00 % (26091)Time elapsed: 1.432 s
% 79.12/13.00 % (26091)Instructions burned: 4604 (million)
% 79.12/13.00 % (26091)------------------------------
% 79.12/13.00 % (26091)------------------------------
% 79.12/13.01 % (26106)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_25541 for (2886ds/3201Mi)
% 79.12/13.01 % (26107)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_25541 for (2886ds/454Mi)
% 82.42/13.06 % (26101)Instruction limit reached!
% 82.42/13.06 % (26101)------------------------------
% 82.42/13.06 % (26101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.42/13.06 % (26101)Termination reason: Unknown
% 82.42/13.06 % (26101)Termination phase: Saturation
% 82.42/13.06
% 82.42/13.06 % (26101)Memory used [KB]: 4989
% 82.42/13.06 % (26101)Time elapsed: 0.668 s
% 82.42/13.06 % (26101)Instructions burned: 2657 (million)
% 82.42/13.06 % (26101)------------------------------
% 82.42/13.06 % (26101)------------------------------
% 82.42/13.07 % (26108)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_25541 for (2885ds/3049Mi)
% 82.42/13.12 % (26104)Instruction limit reached!
% 82.42/13.12 % (26104)------------------------------
% 82.42/13.12 % (26104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.42/13.12 % (26104)Termination reason: Unknown
% 82.42/13.12 % (26104)Termination phase: Saturation
% 82.42/13.12
% 82.42/13.12 % (26104)Memory used [KB]: 10618
% 82.42/13.12 % (26104)Time elapsed: 0.466 s
% 82.42/13.12 % (26104)Instructions burned: 1550 (million)
% 82.42/13.12 % (26104)------------------------------
% 82.42/13.12 % (26104)------------------------------
% 82.87/13.13 % (26109)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_25541 for (2885ds/7311Mi)
% 82.87/13.13 % (26107)Instruction limit reached!
% 82.87/13.13 % (26107)------------------------------
% 82.87/13.13 % (26107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.87/13.13 % (26107)Termination reason: Unknown
% 82.87/13.13 % (26107)Termination phase: Saturation
% 82.87/13.13
% 82.87/13.13 % (26107)Memory used [KB]: 15991
% 82.87/13.13 % (26107)Time elapsed: 0.116 s
% 82.87/13.13 % (26107)Instructions burned: 456 (million)
% 82.87/13.13 % (26107)------------------------------
% 82.87/13.13 % (26107)------------------------------
% 82.87/13.14 % (26110)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_25541 for (2884ds/6804Mi)
% 83.24/13.25 % (26102)Instruction limit reached!
% 83.24/13.25 % (26102)------------------------------
% 83.24/13.25 % (26102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.24/13.25 % (26102)Termination reason: Unknown
% 83.24/13.25 % (26102)Termination phase: Saturation
% 83.24/13.25
% 83.24/13.25 % (26102)Memory used [KB]: 8059
% 83.24/13.25 % (26102)Time elapsed: 0.840 s
% 83.24/13.25 % (26102)Instructions burned: 2782 (million)
% 83.24/13.25 % (26102)------------------------------
% 83.24/13.25 % (26102)------------------------------
% 83.24/13.26 % (26111)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_25541 for (2883ds/1683Mi)
% 84.30/13.75 % (26111)Instruction limit reached!
% 84.30/13.75 % (26111)------------------------------
% 84.30/13.75 % (26111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.30/13.75 % (26111)Termination reason: Unknown
% 84.30/13.75 % (26111)Termination phase: Saturation
% 84.30/13.75
% 84.30/13.75 % (26111)Memory used [KB]: 17654
% 84.30/13.75 % (26111)Time elapsed: 0.489 s
% 84.30/13.75 % (26111)Instructions burned: 1685 (million)
% 84.30/13.75 % (26111)------------------------------
% 84.30/13.75 % (26111)------------------------------
% 84.30/13.76 % (26112)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_25541 for (2878ds/4688Mi)
% 85.19/14.01 % (26108)Instruction limit reached!
% 85.19/14.01 % (26108)------------------------------
% 85.19/14.01 % (26108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.19/14.01 % (26108)Termination reason: Unknown
% 85.19/14.01 % (26108)Termination phase: Saturation
% 85.19/14.01
% 85.19/14.01 % (26108)Memory used [KB]: 10874
% 85.19/14.01 % (26108)Time elapsed: 0.937 s
% 85.19/14.01 % (26108)Instructions burned: 3052 (million)
% 85.19/14.01 % (26108)------------------------------
% 85.19/14.01 % (26108)------------------------------
% 85.19/14.01 % (26106)Instruction limit reached!
% 85.19/14.01 % (26106)------------------------------
% 85.19/14.01 % (26106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.19/14.01 % (26106)Termination reason: Unknown
% 85.19/14.01 % (26106)Termination phase: Saturation
% 85.19/14.01
% 85.19/14.01 % (26106)Memory used [KB]: 11385
% 85.19/14.01 % (26106)Time elapsed: 1.002 s
% 85.19/14.01 % (26106)Instructions burned: 3202 (million)
% 85.19/14.01 % (26106)------------------------------
% 85.19/14.01 % (26106)------------------------------
% 85.19/14.02 % (26113)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_25541 for (2876ds/2207Mi)
% 85.19/14.02 % (26114)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_25541 for (2876ds/8216Mi)
% 89.47/14.06 % (26099)Instruction limit reached!
% 89.47/14.06 % (26099)------------------------------
% 89.47/14.06 % (26099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.47/14.06 % (26099)Termination reason: Unknown
% 89.47/14.06 % (26099)Termination phase: Saturation
% 89.47/14.06
% 89.47/14.06 % (26099)Memory used [KB]: 16502
% 89.47/14.06 % (26099)Time elapsed: 1.727 s
% 89.47/14.06 % (26099)Instructions burned: 5447 (million)
% 89.47/14.06 % (26099)------------------------------
% 89.47/14.06 % (26099)------------------------------
% 89.47/14.07 % (26115)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_25541 for (2875ds/430Mi)
% 89.91/14.18 % (26115)Instruction limit reached!
% 89.91/14.18 % (26115)------------------------------
% 89.91/14.18 % (26115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.91/14.18 % (26115)Termination reason: Unknown
% 89.91/14.18 % (26115)Termination phase: Saturation
% 89.91/14.18
% 89.91/14.18 % (26115)Memory used [KB]: 11257
% 89.91/14.18 % (26115)Time elapsed: 0.113 s
% 89.91/14.18 % (26115)Instructions burned: 432 (million)
% 89.91/14.18 % (26115)------------------------------
% 89.91/14.18 % (26115)------------------------------
% 89.91/14.19 % (26117)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_25541 for (2874ds/2012Mi)
% 90.73/14.37 % (26105)Instruction limit reached!
% 90.73/14.37 % (26105)------------------------------
% 90.73/14.37 % (26105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.73/14.37 % (26105)Termination reason: Unknown
% 90.73/14.37 % (26105)Termination phase: Saturation
% 90.73/14.37
% 90.73/14.37 % (26105)Memory used [KB]: 10490
% 90.73/14.37 % (26105)Time elapsed: 1.558 s
% 90.73/14.37 % (26105)Instructions burned: 5216 (million)
% 90.73/14.37 % (26105)------------------------------
% 90.73/14.37 % (26105)------------------------------
% 90.73/14.38 % (26164)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_25541 for (2872ds/631Mi)
% 91.11/14.40 % (26112)First to succeed.
% 91.11/14.41 % (26112)Refutation found. Thanks to Tanya!
% 91.11/14.41 % SZS status Theorem for DTF2THF_25541
% 91.11/14.41 % SZS output start Proof for DTF2THF_25541
% 91.11/14.41 thf(func_def_0, type, in: $i > $i > $o).
% 91.11/14.41 thf(func_def_1, type, exu: ($i > $o) > $o).
% 91.11/14.41 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 91.11/14.41 thf(func_def_8, type, powerset: $i > $i).
% 91.11/14.41 thf(func_def_10, type, setunion: $i > $i).
% 91.11/14.41 thf(func_def_19, type, descr: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_26, type, prop2set: $o > $i).
% 91.11/14.41 thf(func_def_36, type, nonempty: $i > $o).
% 91.11/14.41 thf(func_def_69, type, set2prop: $i > $o).
% 91.11/14.41 thf(func_def_88, type, subset: $i > $i > $o).
% 91.11/14.41 thf(func_def_89, type, disjoint: $i > $i > $o).
% 91.11/14.41 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 91.11/14.41 thf(func_def_114, type, binunion: $i > $i > $i).
% 91.11/14.41 thf(func_def_122, type, binintersect: $i > $i > $i).
% 91.11/14.41 thf(func_def_135, type, regular: $i > $o).
% 91.11/14.41 thf(func_def_136, type, setminus: $i > $i > $i).
% 91.11/14.41 thf(func_def_147, type, symdiff: $i > $i > $i).
% 91.11/14.41 thf(func_def_153, type, iskpair: $i > $o).
% 91.11/14.41 thf(func_def_158, type, kpair: $i > $i > $i).
% 91.11/14.41 thf(func_def_160, type, cartprod: $i > $i > $i).
% 91.11/14.41 thf(func_def_177, type, singleton: $i > $o).
% 91.11/14.41 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 91.11/14.41 thf(func_def_184, type, atmost1p: $i > $o).
% 91.11/14.41 thf(func_def_185, type, atleast2p: $i > $o).
% 91.11/14.41 thf(func_def_186, type, atmost2p: $i > $o).
% 91.11/14.41 thf(func_def_187, type, upairsetp: $i > $o).
% 91.11/14.41 thf(func_def_191, type, kfst: $i > $i).
% 91.11/14.41 thf(func_def_203, type, ksnd: $i > $i).
% 91.11/14.41 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 91.11/14.41 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 91.11/14.41 thf(func_def_222, type, func: $i > $i > $i > $o).
% 91.11/14.41 thf(func_def_223, type, funcSet: $i > $i > $i).
% 91.11/14.41 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_251, type, sK0: $i > $i > $i).
% 91.11/14.41 thf(func_def_266, type, sK15: $i > $i).
% 91.11/14.41 thf(func_def_271, type, sK20: $i > $o).
% 91.11/14.41 thf(func_def_274, type, sK23: $i > ($i > $i) > $i > $i).
% 91.11/14.41 thf(func_def_276, type, sK25: $i > $i).
% 91.11/14.41 thf(func_def_289, type, sK38: $i > $o).
% 91.11/14.41 thf(func_def_290, type, sK39: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_295, type, sK44: $i > $i > $o).
% 91.11/14.41 thf(func_def_304, type, sK53: $i > $i).
% 91.11/14.41 thf(func_def_305, type, sK54: ($i > $i) > $i > $i > $i).
% 91.11/14.41 thf(func_def_312, type, sK61: $i > $i > $i).
% 91.11/14.41 thf(func_def_313, type, sK62: $i > $i).
% 91.11/14.41 thf(func_def_314, type, sK63: $i > $i > $i).
% 91.11/14.41 thf(func_def_315, type, sK64: $i > $i > $i).
% 91.11/14.41 thf(func_def_316, type, sK65: $i > $i > $i).
% 91.11/14.41 thf(func_def_317, type, sK66: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_319, type, sK68: $i > $i).
% 91.11/14.41 thf(func_def_320, type, sK69: $i > $i).
% 91.11/14.41 thf(func_def_321, type, sK70: $i > $i).
% 91.11/14.41 thf(func_def_322, type, sK71: $i > $i).
% 91.11/14.41 thf(func_def_323, type, sK72: $i > $i).
% 91.11/14.41 thf(func_def_324, type, sK73: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_325, type, sK74: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_326, type, sK75: $i > $i > $i).
% 91.11/14.41 thf(func_def_327, type, sK76: $i > $i).
% 91.11/14.41 thf(func_def_328, type, sK77: $i > $i).
% 91.11/14.41 thf(func_def_329, type, sK78: $i > $i).
% 91.11/14.41 thf(func_def_330, type, sK79: $i > $i).
% 91.11/14.41 thf(func_def_331, type, sK80: $i > $i).
% 91.11/14.41 thf(func_def_334, type, sK83: $i > $i > $o).
% 91.11/14.41 thf(func_def_347, type, sK96: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_348, type, sK97: $i > $o).
% 91.11/14.41 thf(func_def_349, type, sK98: $i > $i).
% 91.11/14.41 thf(func_def_371, type, sK120: $i > $o).
% 91.11/14.41 thf(func_def_375, type, sK124: $i > $o).
% 91.11/14.41 thf(func_def_379, type, sK128: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_380, type, sK129: $i > $o).
% 91.11/14.41 thf(func_def_386, type, sK135: $i > $i > $o).
% 91.11/14.41 thf(func_def_393, type, sK142: ($i > $o) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_394, type, sK143: ($i > $o) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_398, type, sK147: $i > $o).
% 91.11/14.41 thf(func_def_402, type, sK151: $i > $o).
% 91.11/14.41 thf(func_def_409, type, sK158: $i > $i).
% 91.11/14.41 thf(func_def_413, type, sK162: $o > $i > $i > $i).
% 91.11/14.41 thf(func_def_428, type, sK177: $i > $o).
% 91.11/14.41 thf(func_def_431, type, sK180: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_432, type, sK181: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_433, type, sK182: $i > $i > $i).
% 91.11/14.41 thf(func_def_445, type, sK194: ($i > $o) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_446, type, sK195: ($i > $o) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_450, type, sK199: $i > $o).
% 91.11/14.41 thf(func_def_454, type, sK203: $i > $i > $o).
% 91.11/14.41 thf(func_def_457, type, sK206: ($i > $o) > ($i > $o) > $i > $i > $i).
% 91.11/14.41 thf(func_def_458, type, sK207: ($i > $o) > ($i > $o) > $i > $i > $i).
% 91.11/14.41 thf(func_def_461, type, sK210: $i > $o).
% 91.11/14.41 thf(func_def_462, type, sK211: $i > $o).
% 91.11/14.41 thf(func_def_472, type, sK221: $i > $o).
% 91.11/14.41 thf(func_def_482, type, sK231: $i > $o).
% 91.11/14.41 thf(func_def_484, type, sK233: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_486, type, sK235: $i > $o).
% 91.11/14.41 thf(func_def_488, type, sK237: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_490, type, sK239: $i > $o).
% 91.11/14.41 thf(func_def_492, type, sK241: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_497, type, sK246: $i > $i).
% 91.11/14.41 thf(func_def_500, type, sK249: $i > $i > $i).
% 91.11/14.41 thf(func_def_517, type, sK266: $i > $i > $i).
% 91.11/14.41 thf(func_def_519, type, sK268: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_520, type, sK269: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_521, type, sK270: $i > $o).
% 91.11/14.41 thf(func_def_531, type, sK280: $i > $o).
% 91.11/14.41 thf(func_def_533, type, sK282: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_535, type, sK284: $i > $i > $o).
% 91.11/14.41 thf(func_def_537, type, sK286: $i > $i).
% 91.11/14.41 thf(func_def_540, type, sK289: $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_544, type, sK293: $i > $i > $i).
% 91.11/14.41 thf(func_def_545, type, sK294: $i > $i > $i).
% 91.11/14.41 thf(func_def_548, type, sK297: $i > $i).
% 91.11/14.41 thf(func_def_549, type, sK298: $i > $i).
% 91.11/14.41 thf(func_def_560, type, sK309: $i > $o).
% 91.11/14.41 thf(func_def_564, type, sK313: $i > $o).
% 91.11/14.41 thf(func_def_583, type, sK332: $i > $i > $i).
% 91.11/14.41 thf(func_def_589, type, sK338: $i > $i).
% 91.11/14.41 thf(func_def_605, type, sK354: $i > $o).
% 91.11/14.41 thf(func_def_607, type, sK356: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_611, type, sK360: $i > $o).
% 91.11/14.41 thf(func_def_612, type, sK361: $i > $o).
% 91.11/14.41 thf(func_def_613, type, sK362: ($i > $o) > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_614, type, sK363: ($i > $o) > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_621, type, sK370: $i > $i > $o).
% 91.11/14.41 thf(func_def_626, type, sK375: $i > $o).
% 91.11/14.41 thf(func_def_642, type, sK391: $i > $o).
% 91.11/14.41 thf(func_def_648, type, sK397: $i > $o).
% 91.11/14.41 thf(func_def_653, type, sK402: $i > $o).
% 91.11/14.41 thf(func_def_656, type, sK405: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_676, type, sK425: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_677, type, sK426: $i > $o).
% 91.11/14.41 thf(func_def_678, type, sK427: $i > $i).
% 91.11/14.41 thf(func_def_679, type, sK428: $i > $i > $o).
% 91.11/14.41 thf(func_def_698, type, sK447: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_700, type, sK449: $i > $o).
% 91.11/14.41 thf(func_def_712, type, sK461: $i > $i > $i).
% 91.11/14.41 thf(func_def_715, type, sK464: $i > $i).
% 91.11/14.41 thf(func_def_718, type, sK467: $i > $o).
% 91.11/14.41 thf(func_def_726, type, sK475: $i > $o).
% 91.11/14.41 thf(func_def_728, type, sK477: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_729, type, sK478: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_753, type, sK502: $i > $o).
% 91.11/14.41 thf(func_def_754, type, sK503: $i > $o).
% 91.11/14.41 thf(func_def_755, type, sK504: ($i > $o) > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_756, type, sK505: ($i > $o) > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_762, type, sK511: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_763, type, sK512: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_764, type, sK513: $i > $o).
% 91.11/14.41 thf(func_def_773, type, sK522: $i > $i > $o).
% 91.11/14.41 thf(func_def_775, type, sK524: $i > $i).
% 91.11/14.41 thf(func_def_776, type, sK525: $i > $i).
% 91.11/14.41 thf(func_def_777, type, sK526: $i > ($i > $i > $o) > $i).
% 91.11/14.41 thf(func_def_778, type, sK527: $i > $i > ($i > $i > $o) > $i).
% 91.11/14.41 thf(func_def_779, type, sK528: $i > ($i > $i > $o) > $i).
% 91.11/14.41 thf(func_def_785, type, sK534: $i > $o).
% 91.11/14.41 thf(func_def_788, type, sK537: $i > $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_791, type, sK540: $i > $i > $i).
% 91.11/14.41 thf(func_def_832, type, sK581: $i > $o).
% 91.11/14.41 thf(func_def_835, type, sK584: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_837, type, sK586: $i > $o).
% 91.11/14.41 thf(func_def_839, type, sK588: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_840, type, sK589: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_841, type, sK590: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_842, type, sK591: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_843, type, sK592: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_844, type, sK593: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_845, type, sK594: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_846, type, sK595: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_847, type, sK596: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_848, type, sK597: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_849, type, sK598: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_850, type, sK599: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_851, type, sK600: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_852, type, sK601: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_853, type, sK602: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_854, type, sK603: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_855, type, sK604: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_856, type, sK605: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_857, type, sK606: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_858, type, sK607: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_859, type, sK608: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_860, type, sK609: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_861, type, sK610: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_862, type, sK611: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_863, type, sK612: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_864, type, sK613: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_865, type, sK614: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_866, type, sK615: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_867, type, sK616: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_868, type, sK617: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_869, type, sK618: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_870, type, sK619: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_871, type, sK620: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_872, type, sK621: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_873, type, sK622: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_874, type, sK623: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_875, type, sK624: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_876, type, sK625: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_877, type, sK626: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_878, type, sK627: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_879, type, sK628: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_880, type, sK629: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_881, type, sK630: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_882, type, sK631: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_883, type, sK632: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_884, type, sK633: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_885, type, sK634: $i > $i).
% 91.11/14.41 thf(func_def_886, type, sK635: $i > $i).
% 91.11/14.41 thf(func_def_889, type, sK638: $i > $i).
% 91.11/14.41 thf(func_def_890, type, sK639: $i > $i).
% 91.11/14.41 thf(func_def_891, type, sK640: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_892, type, sK641: $i > $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_893, type, sK642: $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_894, type, sK643: $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_895, type, sK644: $i > $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_896, type, sK645: $i > $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_897, type, sK646: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_898, type, sK647: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_899, type, sK648: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_900, type, sK649: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_901, type, sK650: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_902, type, sK651: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_903, type, sK652: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_904, type, sK653: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_905, type, sK654: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_906, type, sK655: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_907, type, sK656: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_908, type, sK657: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_909, type, sK658: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_910, type, sK659: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_911, type, sK660: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_912, type, sK661: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_913, type, sK662: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_914, type, sK663: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_915, type, sK664: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_916, type, sK665: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_917, type, sK666: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_918, type, sK667: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_919, type, sK668: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_920, type, sK669: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_921, type, sK670: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_922, type, sK671: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_923, type, sK672: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_924, type, sK673: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_925, type, sK674: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_926, type, sK675: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_927, type, sK676: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_928, type, sK677: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_929, type, sK678: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_930, type, sK679: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_931, type, sK680: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_932, type, sK681: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_933, type, sK682: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_934, type, sK683: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_935, type, sK684: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_936, type, sK685: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_937, type, sK686: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_938, type, sK687: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_939, type, sK688: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_940, type, sK689: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_941, type, sK690: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_942, type, sK691: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_943, type, sK692: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_944, type, sK693: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_945, type, sK694: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_946, type, sK695: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_947, type, sK696: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_948, type, sK697: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_949, type, sK698: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_950, type, sK699: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_951, type, sK700: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_952, type, sK701: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_953, type, sK702: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_954, type, sK703: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_955, type, sK704: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_956, type, sK705: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_957, type, sK706: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_958, type, sK707: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_959, type, sK708: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_960, type, sK709: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_961, type, sK710: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_962, type, sK711: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_963, type, sK712: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_964, type, sK713: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_965, type, sK714: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_966, type, sK715: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_967, type, sK716: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_968, type, sK717: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_969, type, sK718: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_970, type, sK719: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_971, type, sK720: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_972, type, sK721: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_973, type, sK722: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_974, type, sK723: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_975, type, sK724: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_976, type, sK725: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_977, type, sK726: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_978, type, sK727: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_979, type, sK728: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_980, type, sK729: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_981, type, sK730: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_982, type, sK731: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_983, type, sK732: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_984, type, sK733: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_985, type, sK734: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_986, type, sK735: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_987, type, sK736: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_988, type, sK737: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_989, type, sK738: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_990, type, sK739: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_991, type, sK740: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_992, type, sK741: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_993, type, sK742: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_994, type, sK743: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_995, type, sK744: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_996, type, sK745: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_997, type, sK746: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_998, type, sK747: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_999, type, sK748: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1000, type, sK749: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1001, type, sK750: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1002, type, sK751: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1003, type, sK752: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1004, type, sK753: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1005, type, sK754: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1006, type, sK755: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1007, type, sK756: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1008, type, sK757: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1009, type, sK758: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1010, type, sK759: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1011, type, sK760: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1012, type, sK761: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1013, type, sK762: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1014, type, sK763: $i > $i > ($i > $i > $o) > $i).
% 91.11/14.41 thf(func_def_1015, type, sK764: $i > $i > ($i > $i > $o) > $i).
% 91.11/14.41 thf(func_def_1016, type, sK765: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1017, type, sK766: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1018, type, sK767: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1019, type, sK768: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1020, type, sK769: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1021, type, sK770: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1022, type, sK771: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1023, type, sK772: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1024, type, sK773: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1025, type, sK774: ($i > $i) > $i > $i > $i).
% 91.11/14.41 thf(func_def_1026, type, sK775: ($i > $i) > $i > $i > $i).
% 91.11/14.41 thf(func_def_1027, type, sK776: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1028, type, sK777: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1029, type, sK778: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1030, type, sK779: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1031, type, sK780: ($i > $i) > $i > $i > $i).
% 91.11/14.41 thf(func_def_1032, type, sK781: ($i > $i) > $i > $i > $i).
% 91.11/14.41 thf(func_def_1033, type, sK782: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1034, type, sK783: ($i > $i) > $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1035, type, sK784: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1036, type, sK785: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1037, type, sK786: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1038, type, sK787: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1039, type, sK788: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1040, type, sK789: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1041, type, sK790: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1042, type, sK791: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1043, type, sK792: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1044, type, sK793: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1045, type, sK794: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1046, type, sK795: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1047, type, sK796: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1048, type, sK797: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1049, type, sK798: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1050, type, sK799: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1051, type, sK800: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1052, type, sK801: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1053, type, sK802: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1054, type, sK803: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1055, type, sK804: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1056, type, sK805: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1057, type, sK806: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1058, type, sK807: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1059, type, sK808: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1060, type, sK809: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1061, type, sK810: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1062, type, sK811: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1063, type, sK812: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1064, type, sK813: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1065, type, sK814: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1066, type, sK815: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1067, type, sK816: ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1068, type, sK817: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1069, type, sK818: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1070, type, sK819: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1071, type, sK820: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1072, type, sK821: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1073, type, sK822: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1074, type, sK823: $i > $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_1075, type, sK824: $i > $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_1076, type, sK825: $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_1077, type, sK826: $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_1078, type, sK827: $i > $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_1079, type, sK828: $i > $i > $i > ($i > $i) > $i).
% 91.11/14.41 thf(func_def_1080, type, sK829: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1081, type, sK830: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1082, type, sK831: $i > ($i > $i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1083, type, sK832: $i > ($i > $i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1084, type, sK833: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1085, type, sK834: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1086, type, sK835: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1087, type, sK836: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1088, type, sK837: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1089, type, sK838: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1090, type, sK839: $i > $i).
% 91.11/14.41 thf(func_def_1091, type, sK840: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1092, type, sK841: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1093, type, sK842: $i > ($i > $i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1094, type, sK843: $i > ($i > $i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1095, type, sK844: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1096, type, sK845: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1097, type, sK846: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1098, type, sK847: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1099, type, sK848: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1100, type, sK849: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1101, type, sK850: $i > $i).
% 91.11/14.41 thf(func_def_1102, type, sK851: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1103, type, sK852: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1104, type, sK853: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1105, type, sK854: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1106, type, sK855: $i > $i > $i > $i).
% 91.11/14.41 thf(func_def_1107, type, sK856: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1108, type, sK857: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1109, type, sK858: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1110, type, sK859: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1111, type, sK860: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1112, type, sK861: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1113, type, sK862: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1114, type, sK863: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1115, type, sK864: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1116, type, sK865: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1117, type, sK866: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1118, type, sK867: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1119, type, sK868: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1120, type, sK869: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1121, type, sK870: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1122, type, sK871: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1123, type, sK872: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1124, type, sK873: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1125, type, sK874: ($i > $o) > $i > $i).
% 91.11/14.41 thf(func_def_1126, type, sK875: $i > ($i > $o) > $i).
% 91.11/14.41 thf(func_def_1127, type, ph876: !>[X0: $tType]:(X0)).
% 91.11/14.41 thf(f14531,plain,(
% 91.11/14.41 $false),
% 91.11/14.41 inference(trivial_inequality_removal,[status(thm)],[f14521])).
% 91.11/14.41 thf(f14521,plain,(
% 91.11/14.41 ($true = $false)),
% 91.11/14.41 inference(superposition,[status(thm)],[f3196,f14472])).
% 91.11/14.41 thf(f14472,plain,(
% 91.11/14.41 ($false = (in @ sK501 @ sK498))),
% 91.11/14.41 inference(subsumption_resolution,[status(thm)],[f14471,f14462])).
% 91.11/14.41 thf(f14462,plain,(
% 91.11/14.41 ( ! [X0 : $i] : (($false = (in @ X0 @ sK498)) | ($true = (in @ (kpair @ X0 @ (sK634 @ X0)) @ sK499))) )),
% 91.11/14.41 inference(beta_eta_normalization,[status(thm)],[f14461])).
% 91.11/14.41 thf(f14461,plain,(
% 91.11/14.41 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK499)) @ (sK634 @ X0))) | ($false = (in @ X0 @ sK498))) )),
% 91.11/14.41 inference(trivial_inequality_removal,[status(thm)],[f14441])).
% 91.11/14.41 thf(f14441,plain,(
% 91.11/14.41 ( ! [X0 : $i] : (($true != $true) | ($false = (in @ X0 @ sK498)) | ($true = ((^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sK499)) @ (sK634 @ X0)))) )),
% 91.11/14.41 inference(superposition,[status(thm)],[f12671,f6406])).
% 91.11/14.41 thf(f6406,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = (in @ (sK634 @ X1) @ (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499))))) | ($false = (in @ X1 @ sK498))) )),
% 91.11/14.41 inference(trivial_inequality_removal,[status(thm)],[f6405])).
% 91.11/14.41 thf(f6405,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = $false) | ($true = (in @ (sK634 @ X1) @ (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499))))) | ($false = (in @ X1 @ sK498))) )),
% 91.11/14.41 inference(boolean_simplification,[status(thm)],[f6404])).
% 91.11/14.41 thf(f6404,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = (((setadjoin @ (sK634 @ X1) @ emptyset) = (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499)))) & $false)) | ($false = (in @ X1 @ sK498)) | ($true = (in @ (sK634 @ X1) @ (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499)))))) )),
% 91.11/14.41 inference(cases_simplifying,[status(thm)],[f6400])).
% 91.11/14.41 thf(f6400,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($false = (in @ X1 @ sK498)) | ($true = (((setadjoin @ (sK634 @ X1) @ emptyset) = (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499)))) & (in @ (sK634 @ X1) @ (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499))))))) )),
% 91.11/14.41 inference(beta_eta_normalization,[status(thm)],[f6399])).
% 91.11/14.41 thf(f6399,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))) & (in @ Y0 @ (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))))) @ (sK634 @ X1))) | ($false = (in @ X1 @ sK498))) )),
% 91.11/14.41 inference(sigma_clausification,[status(thm)],[f6398])).
% 91.11/14.41 thf(f6398,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($false = (in @ X1 @ sK498)) | ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))) & (in @ Y0 @ (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499))))))))) )),
% 91.11/14.41 inference(trivial_inequality_removal,[status(thm)],[f6397])).
% 91.11/14.41 thf(f6397,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))) & (in @ Y0 @ (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))))))) | ($false = (in @ X1 @ sK498))) )),
% 91.11/14.41 inference(boolean_simplification,[status(thm)],[f6394])).
% 91.11/14.41 thf(f6394,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))) & (in @ Y0 @ (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))))))) | ($true = (~ $true)) | ($false = (in @ X1 @ sK498))) )),
% 91.11/14.41 inference(cases_simplifying,[status(thm)],[f6393])).
% 91.11/14.41 thf(f6393,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = (~ (in @ X1 @ sK498))) | ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))) & (in @ Y0 @ (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499))))))))) )),
% 91.11/14.41 inference(boolean_simplification,[status(thm)],[f6392])).
% 91.11/14.41 thf(f6392,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))) & (in @ Y0 @ (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))))))) | ($true = ((in @ X1 @ sK498) => $false))) )),
% 91.11/14.41 inference(cases_simplifying,[status(thm)],[f6388])).
% 91.11/14.41 thf(f6388,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK498) => (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))) & (in @ Y0 @ (dsetconstr @ sK500 @ (^[Y1 : $i]: (in @ (kpair @ X1 @ Y1) @ sK499)))))))))) )),
% 91.11/14.41 inference(beta_eta_normalization,[status(thm)],[f6387])).
% 91.11/14.41 thf(f6387,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK498) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499)))) & (in @ Y1 @ (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499))))))))) @ X1))) )),
% 91.11/14.41 inference(pi_clausification,[status(thm)],[f6386])).
% 91.11/14.41 thf(f6386,plain,(
% 91.11/14.41 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK498) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499)))) & (in @ Y1 @ (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499)))))))))))),
% 91.11/14.41 inference(trivial_inequality_removal,[status(thm)],[f6385])).
% 91.11/14.41 thf(f6385,plain,(
% 91.11/14.41 ($true = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK498) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499)))) & (in @ Y1 @ (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499)))))))))))),
% 91.11/14.41 inference(boolean_simplification,[status(thm)],[f6384])).
% 91.11/14.41 thf(f6384,plain,(
% 91.11/14.41 ($true = ((subset @ sK499 @ (cartprod @ sK498 @ sK500)) & $false)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK498) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499)))) & (in @ Y1 @ (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499)))))))))))),
% 91.11/14.41 inference(cases_simplifying,[status(thm)],[f6380])).
% 91.11/14.41 thf(f6380,plain,(
% 91.11/14.41 ($true = ((subset @ sK499 @ (cartprod @ sK498 @ sK500)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK498) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499)))) & (in @ Y1 @ (dsetconstr @ sK500 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK499))))))))))))),
% 91.11/14.41 inference(beta_eta_normalization,[status(thm)],[f4797])).
% 91.11/14.41 thf(f4797,plain,(
% 91.11/14.41 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))) @ sK498 @ sK500 @ sK499))),
% 91.11/14.41 inference(definition_unfolding,[status(thm)],[f3198,f3451])).
% 91.11/14.41 thf(f3451,plain,(
% 91.11/14.41 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 91.11/14.41 inference(definition_unfolding,[status(thm)],[f2765,f1835,f3450])).
% 91.11/14.41 thf(f3450,plain,(
% 91.11/14.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 91.11/14.41 inference(definition_unfolding,[status(thm)],[f2992,f2964])).
% 91.11/14.41 thf(f2964,plain,(
% 91.11/14.41 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f411])).
% 91.11/14.41 thf(f411,plain,(
% 91.11/14.41 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 91.11/14.41 inference(fool_elimination,[status(thm)],[f410])).
% 91.11/14.41 thf(f410,plain,(
% 91.11/14.41 ((^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)),
% 91.11/14.41 inference(rectify,[status(thm)],[f156])).
% 91.11/14.41 thf(f156,axiom,(
% 91.11/14.41 ((^[X3 : $i] : (? [X1 : $i] : ((in @ X1 @ X3) & ((setadjoin @ X1 @ emptyset) = X3)))) = singleton)),
% 91.11/14.41 file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',singleton)).
% 91.11/14.41 thf(f2992,plain,(
% 91.11/14.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f515])).
% 91.11/14.41 thf(f515,plain,(
% 91.11/14.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 91.11/14.41 inference(fool_elimination,[status(thm)],[f514])).
% 91.11/14.41 thf(f514,plain,(
% 91.11/14.41 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 91.11/14.41 inference(rectify,[status(thm)],[f158])).
% 91.11/14.41 thf(f158,axiom,(
% 91.11/14.41 ((^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))) = ex1)),
% 91.11/14.41 file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',ex1)).
% 91.11/14.41 thf(f1835,plain,(
% 91.11/14.41 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f465])).
% 91.11/14.41 thf(f465,plain,(
% 91.11/14.41 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 91.11/14.41 inference(fool_elimination,[status(thm)],[f464])).
% 91.11/14.41 thf(f464,plain,(
% 91.11/14.41 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 91.11/14.41 inference(rectify,[status(thm)],[f186])).
% 91.11/14.41 thf(f186,axiom,(
% 91.11/14.41 (breln = (^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))))),
% 91.11/14.41 file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',breln)).
% 91.11/14.41 thf(f2765,plain,(
% 91.11/14.41 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f569])).
% 91.11/14.41 thf(f569,plain,(
% 91.11/14.41 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 91.11/14.41 inference(fool_elimination,[status(thm)],[f568])).
% 91.11/14.41 thf(f568,plain,(
% 91.11/14.41 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))))),
% 91.11/14.41 inference(rectify,[status(thm)],[f194])).
% 91.11/14.41 thf(f194,axiom,(
% 91.11/14.41 (func = (^[X3 : $i, X4 : $i, X12 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (ex1 @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X12)))) & (breln @ X3 @ X4 @ X12))))),
% 91.11/14.41 file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',func)).
% 91.11/14.41 thf(f3198,plain,(
% 91.11/14.41 ($true = (func @ sK498 @ sK500 @ sK499))),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f1655])).
% 91.11/14.41 thf(f1655,plain,(
% 91.11/14.41 (quantDeMorgan4 = $true) & (subsetTrans = $true) & (omegaIndAx = $true) & (setextsub = $true) & (omega__Cong = $true) & (nonemptyImpWitness = $true) & (subsetemptysetimpeq = $true) & (notequalI1 = $true) & (inCongP = $true) & (powersetI1 = $true) & (binintersectER = $true) & (dpsetconstrSub = $true) & (setminusEL = $true) & (ubforcartprodlem2 = $true) & (kpairp = $true) & (binunionRsub = $true) & (ubforcartprodlem1 = $true) & (singletonsswitch = $true) & (replAx = $true) & (binunionE = $true) & (upairsetE = $true) & (exu__Cong = $true) & (binintersectSubset3 = $true) & (exuI1 = $true) & (subsetE2 = $true) & (setukpairinjL1 = $true) & (emptysetimpfalse = $true) & (eqimpsubset1 = $true) & (setukpairIL = $true) & (cartprodmempair1 = $true) & (subsetI2 = $true) & (notequalI2 = $true) & (theprop = $true) & (emptysetAx = $true) & (prop2setE = $true) & (binintersectSubset5 = $true) & (notsubsetI = $true) & (notdexE = $true) & (ex1I = $true) & (symdiffIneg1 = $true) & (singletonprop = $true) & (symdiffIneg2 = $true) & (quantDeMorgan3 = $true) & (cartprodfstin = $true) & (binintersectSubset2 = $true) & (subsetE = $true) & (upairequniteq = $true) & (setadjoinAx = $true) & (setminusELneg = $true) & (setadjoin__Cong = $true) & (wellorderingAx = $true) & (kfstpairEq = $true) & (prop2setI = $true) & (descrp = $true) & (dsetconstrI = $true) & (inPowerset = $true) & (binintersectEL = $true) & (exuE3e = $true) & (upairsetIR = $true) & (setextAx = $true) & (funcImageSingleton = $true) & (binintersectRsub = $true) & (emptyinPowerset = $true) & (setunionsingleton = $true) & (infuncsetfunc = $true) & (setukpairinjR2 = $true) & (cartprodfstpairEq = $true) & (binunionIL = $true) & (setunionI = $true) & (setadjoinIR = $true) & (cartprodsndpairEq = $true) & (powersetsubset = $true) & (symdiffI2 = $true) & (emptyInPowerset = $true) & (setminusSubset1 = $true) & (emptyinunitempty = $true) & (setunionsingleton1 = $true) & (cartprodmempair = $true) & (setminusILneg = $true) & (setbeta = $true) & (powersetI = $true) & (upairsetIL = $true) & (cartprodpairin = $true) & (setunionAx = $true) & (lam2p = $true) & (setukpairinjR = $true) & (setOfPairsIsBReln = $true) & (setunion__Cong = $true) & (setadjoinE = $true) & (apProp = $true) & (descr__Cong = $true) & (emptysetsubset = $true) & (binunionEcases = $true) & (ksndpairEq = $true) & (brelnall1 = $true) & (powersetAx = $true) & (quantDeMorgan2 = $true) & (emptyE1 = $true) & (cartprodpairmemER = $true) & (symdiffI1 = $true) & (exuE1 = $true) & (binunionLsub = $true) & (symdiffE = $true) & (secondinupair = $true) & (ex1E2 = $true) & (bs114d = $true) & (upairset2E = $true) & (brelnall2 = $true) & (powersetE = $true) & (setminusER = $true) & (notdallE = $true) & (setadjoinSub2 = $true) & (cartprodsndin = $true) & (eqinunit = $true) & (omegaSAx = $true) & (quantDeMorgan1 = $true) & (setadjoinOr = $true) & (setminusERneg = $true) & (dsetconstr__Cong = $true) & (binintersectI = $true) & (in__Cong = $true) & (disjointsetsI1 = $true) & (upairsubunion = $true) & (exuE2 = $true) & (setminusI = $true) & (noeltsimpempty = $true) & (setukpairinjR11 = $true) & (emptyI = $true) & (setminusIRneg = $true) & (setoftrueEq = $true) & (ksndsingleton = $true) & (sepInPowerset = $true) & (setadjoinIL = $true) & (dpsetconstrEL1 = $true) & (singletoninpowunion = $true) & (subsetI1 = $true) & (cartprodpairsurjEq = $true) & (($true = (func @ sK498 @ sK500 @ sK499)) & (($true != (in @ (kpair @ sK501 @ (ap @ sK498 @ sK500 @ sK499 @ sK501)) @ sK499)) & ($true = (in @ sK501 @ sK498)))) & (cartprodpairmemEL = $true) & (setminusSubset2 = $true) & (exuEu = $true) & (kfstsingleton = $true) & (dsetconstrER = $true) & (singletoninpowerset = $true) & (funcinfuncset = $true) & (binintersectSubset1 = $true) & (vacuousDall = $true) & (cartprodmempaircEq = $true) & (dpsetconstrEL2 = $true) & (nonemptyE1 = $true) & (binunionIR = $true) & (powersetE1 = $true) & (dpsetconstrI = $true) & (notinsingleton = $true) & (prop2set2propI = $true) & (ex1I2 = $true) & (exuI2 = $true) & (setukpairinjL = $true) & (singletonsuniq = $true) & (lamProp = $true) & (binintersectSubset4 = $true) & (exuI3 = $true) & (setadjoinSub = $true) & (singletonsubset = $true) & (subPowSU = $true) & (app = $true) & (setminusLsub = $true) & (dpsetconstrERa = $true) & (subset2powerset = $true) & (dsetconstrEL = $true) & (sepSubset = $true) & (nonemptyI1 = $true) & (kpairsurjEq = $true) & (lamp = $true) & (setext = $true) & (setukpairIR = $true) & (ubforcartprodlem3 = $true) & (notinemptyset = $true) & (exuE3u = $true) & (setukpairinjR1 = $true) & (ex1E1 = $true) & (eqimpsubset2 = $true) & (setukpairinjL2 = $true) & (powerset__Cong = $true) & (setukpairinjR12 = $true) & (subsetRefl = $true) & (kpairiskpair = $true) & (emptyset__Cong = $true) & (dpsetconstrER = $true) & (setunionsingleton2 = $true) & (ap2p = $true) & (binintersectLsub = $true) & (upairset2IR = $true) & (upairinpowunion = $true) & (foundationAx = $true) & (nonemptyI = $true) & (omega0Ax = $true) & (setunionE2 = $true) & (setunionE = $true) & (uniqinunit = $true) & (emptysetE = $true)),
% 91.11/14.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK498,sK499,sK500,sK501])],[f771,f1654,f1653])).
% 91.11/14.41 thf(f1653,plain,(
% 91.11/14.41 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ X0 @ X2 @ X1 @ X3)) @ X1)) & ($true = (in @ X3 @ X0)))) => (($true = (func @ sK498 @ sK500 @ sK499)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ sK498 @ sK500 @ sK499 @ X3)) @ sK499)) & ($true = (in @ X3 @ sK498))))),
% 91.11/14.41 introduced(definition,[],[choice_axiom])).
% 91.11/14.41 thf(f1654,plain,(
% 91.11/14.41 ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ sK498 @ sK500 @ sK499 @ X3)) @ sK499)) & ($true = (in @ X3 @ sK498))) => (($true != (in @ (kpair @ sK501 @ (ap @ sK498 @ sK500 @ sK499 @ sK501)) @ sK499)) & ($true = (in @ sK501 @ sK498)))),
% 91.11/14.41 introduced(definition,[],[choice_axiom])).
% 91.11/14.41 thf(f771,plain,(
% 91.11/14.41 (quantDeMorgan4 = $true) & (subsetTrans = $true) & (omegaIndAx = $true) & (setextsub = $true) & (omega__Cong = $true) & (nonemptyImpWitness = $true) & (subsetemptysetimpeq = $true) & (notequalI1 = $true) & (inCongP = $true) & (powersetI1 = $true) & (binintersectER = $true) & (dpsetconstrSub = $true) & (setminusEL = $true) & (ubforcartprodlem2 = $true) & (kpairp = $true) & (binunionRsub = $true) & (ubforcartprodlem1 = $true) & (singletonsswitch = $true) & (replAx = $true) & (binunionE = $true) & (upairsetE = $true) & (exu__Cong = $true) & (binintersectSubset3 = $true) & (exuI1 = $true) & (subsetE2 = $true) & (setukpairinjL1 = $true) & (emptysetimpfalse = $true) & (eqimpsubset1 = $true) & (setukpairIL = $true) & (cartprodmempair1 = $true) & (subsetI2 = $true) & (notequalI2 = $true) & (theprop = $true) & (emptysetAx = $true) & (prop2setE = $true) & (binintersectSubset5 = $true) & (notsubsetI = $true) & (notdexE = $true) & (ex1I = $true) & (symdiffIneg1 = $true) & (singletonprop = $true) & (symdiffIneg2 = $true) & (quantDeMorgan3 = $true) & (cartprodfstin = $true) & (binintersectSubset2 = $true) & (subsetE = $true) & (upairequniteq = $true) & (setadjoinAx = $true) & (setminusELneg = $true) & (setadjoin__Cong = $true) & (wellorderingAx = $true) & (kfstpairEq = $true) & (prop2setI = $true) & (descrp = $true) & (dsetconstrI = $true) & (inPowerset = $true) & (binintersectEL = $true) & (exuE3e = $true) & (upairsetIR = $true) & (setextAx = $true) & (funcImageSingleton = $true) & (binintersectRsub = $true) & (emptyinPowerset = $true) & (setunionsingleton = $true) & (infuncsetfunc = $true) & (setukpairinjR2 = $true) & (cartprodfstpairEq = $true) & (binunionIL = $true) & (setunionI = $true) & (setadjoinIR = $true) & (cartprodsndpairEq = $true) & (powersetsubset = $true) & (symdiffI2 = $true) & (emptyInPowerset = $true) & (setminusSubset1 = $true) & (emptyinunitempty = $true) & (setunionsingleton1 = $true) & (cartprodmempair = $true) & (setminusILneg = $true) & (setbeta = $true) & (powersetI = $true) & (upairsetIL = $true) & (cartprodpairin = $true) & (setunionAx = $true) & (lam2p = $true) & (setukpairinjR = $true) & (setOfPairsIsBReln = $true) & (setunion__Cong = $true) & (setadjoinE = $true) & (apProp = $true) & (descr__Cong = $true) & (emptysetsubset = $true) & (binunionEcases = $true) & (ksndpairEq = $true) & (brelnall1 = $true) & (powersetAx = $true) & (quantDeMorgan2 = $true) & (emptyE1 = $true) & (cartprodpairmemER = $true) & (symdiffI1 = $true) & (exuE1 = $true) & (binunionLsub = $true) & (symdiffE = $true) & (secondinupair = $true) & (ex1E2 = $true) & (bs114d = $true) & (upairset2E = $true) & (brelnall2 = $true) & (powersetE = $true) & (setminusER = $true) & (notdallE = $true) & (setadjoinSub2 = $true) & (cartprodsndin = $true) & (eqinunit = $true) & (omegaSAx = $true) & (quantDeMorgan1 = $true) & (setadjoinOr = $true) & (setminusERneg = $true) & (dsetconstr__Cong = $true) & (binintersectI = $true) & (in__Cong = $true) & (disjointsetsI1 = $true) & (upairsubunion = $true) & (exuE2 = $true) & (setminusI = $true) & (noeltsimpempty = $true) & (setukpairinjR11 = $true) & (emptyI = $true) & (setminusIRneg = $true) & (setoftrueEq = $true) & (ksndsingleton = $true) & (sepInPowerset = $true) & (setadjoinIL = $true) & (dpsetconstrEL1 = $true) & (singletoninpowunion = $true) & (subsetI1 = $true) & (cartprodpairsurjEq = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ X0 @ X2 @ X1 @ X3)) @ X1)) & ($true = (in @ X3 @ X0)))) & (cartprodpairmemEL = $true) & (setminusSubset2 = $true) & (exuEu = $true) & (kfstsingleton = $true) & (dsetconstrER = $true) & (singletoninpowerset = $true) & (funcinfuncset = $true) & (binintersectSubset1 = $true) & (vacuousDall = $true) & (cartprodmempaircEq = $true) & (dpsetconstrEL2 = $true) & (nonemptyE1 = $true) & (binunionIR = $true) & (powersetE1 = $true) & (dpsetconstrI = $true) & (notinsingleton = $true) & (prop2set2propI = $true) & (ex1I2 = $true) & (exuI2 = $true) & (setukpairinjL = $true) & (singletonsuniq = $true) & (lamProp = $true) & (binintersectSubset4 = $true) & (exuI3 = $true) & (setadjoinSub = $true) & (singletonsubset = $true) & (subPowSU = $true) & (app = $true) & (setminusLsub = $true) & (dpsetconstrERa = $true) & (subset2powerset = $true) & (dsetconstrEL = $true) & (sepSubset = $true) & (nonemptyI1 = $true) & (kpairsurjEq = $true) & (lamp = $true) & (setext = $true) & (setukpairIR = $true) & (ubforcartprodlem3 = $true) & (notinemptyset = $true) & (exuE3u = $true) & (setukpairinjR1 = $true) & (ex1E1 = $true) & (eqimpsubset2 = $true) & (setukpairinjL2 = $true) & (powerset__Cong = $true) & (setukpairinjR12 = $true) & (subsetRefl = $true) & (kpairiskpair = $true) & (emptyset__Cong = $true) & (dpsetconstrER = $true) & (setunionsingleton2 = $true) & (ap2p = $true) & (binintersectLsub = $true) & (upairset2IR = $true) & (upairinpowunion = $true) & (foundationAx = $true) & (nonemptyI = $true) & (omega0Ax = $true) & (setunionE2 = $true) & (setunionE = $true) & (uniqinunit = $true) & (emptysetE = $true)),
% 91.11/14.41 inference(flattening,[status(thm)],[f770])).
% 91.11/14.41 thf(f770,plain,(
% 91.11/14.41 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ X0 @ X2 @ X1 @ X3)) @ X1)) & ($true = (in @ X3 @ X0)))) & (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)),
% 91.11/14.41 inference(ennf_transformation,[status(thm)],[f565])).
% 91.11/14.41 thf(f565,plain,(
% 91.11/14.41 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X2 @ X1)) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => ($true = (in @ (kpair @ X3 @ (ap @ X0 @ X2 @ X1 @ X3)) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 91.11/14.41 inference(fool_elimination,[status(thm)],[f564])).
% 91.11/14.41 thf(f564,plain,(
% 91.11/14.41 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X2 @ X1 @ X3)) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 91.11/14.41 inference(rectify,[status(thm)],[f210])).
% 91.11/14.41 thf(f210,negated_conjecture,(
% 91.11/14.41 ~(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 => ! [X3 : $i,X13 : $i,X4 : $i] : ((func @ X3 @ X4 @ X13) => ! [X1 : $i] : ((in @ X1 @ X3) => (in @ (kpair @ X1 @ (ap @ X3 @ X4 @ X13 @ X1)) @ X13)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 91.11/14.41 inference(negated_conjecture,[status(cth)],[f209])).
% 91.11/14.41 thf(f209,conjecture,(
% 91.11/14.41 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 => ! [X3 : $i,X13 : $i,X4 : $i] : ((func @ X3 @ X4 @ X13) => ! [X1 : $i] : ((in @ X1 @ X3) => (in @ (kpair @ X1 @ (ap @ X3 @ X4 @ X13 @ X1)) @ X13))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 91.11/14.41 file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',funcGraphProp1)).
% 91.11/14.41 thf(f12671,plain,(
% 91.11/14.41 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != (in @ X2 @ (dsetconstr @ X1 @ X0))) | ((X0 @ X2) = $true)) )),
% 91.11/14.41 inference(beta_eta_normalization,[status(thm)],[f12670])).
% 91.11/14.41 thf(f12670,plain,(
% 91.11/14.41 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) | ((X0 @ X2) = $true)) )),
% 91.11/14.41 inference(trivial_inequality_removal,[status(thm)],[f4313])).
% 91.11/14.41 thf(f4313,plain,(
% 91.11/14.41 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) | ($true != $true)) )),
% 91.11/14.41 inference(definition_unfolding,[status(thm)],[f2643,f3191])).
% 91.11/14.41 thf(f3191,plain,(
% 91.11/14.41 (dsetconstrER = $true)),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f1655])).
% 91.11/14.41 thf(f2643,plain,(
% 91.11/14.41 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) | (dsetconstrER != $true)) )),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f1054])).
% 91.11/14.41 thf(f1054,plain,(
% 91.11/14.41 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (($true != (sK120 @ sK122)) & ($true = (in @ sK122 @ (dsetconstr @ sK121 @ (^[Y0 : $i]: (sK120 @ Y0)))))))),
% 91.11/14.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK120,sK121,sK122])],[f1052,f1053])).
% 91.11/14.41 thf(f1053,plain,(
% 91.11/14.41 ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (X3 @ X5)) & ((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true)) => (($true != (sK120 @ sK122)) & ($true = (in @ sK122 @ (dsetconstr @ sK121 @ (^[Y0 : $i]: (sK120 @ Y0))))))),
% 91.11/14.41 introduced(definition,[],[choice_axiom])).
% 91.11/14.41 thf(f1052,plain,(
% 91.11/14.41 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (X3 @ X5)) & ((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true)))),
% 91.11/14.41 inference(rectify,[status(thm)],[f1051])).
% 91.11/14.41 thf(f1051,plain,(
% 91.11/14.41 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) != $true) & ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))))))),
% 91.11/14.41 inference(nnf_transformation,[status(thm)],[f773])).
% 91.11/14.41 thf(f773,plain,(
% 91.11/14.41 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X2) = $true) | ($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))))) <=> (dsetconstrER = $true)),
% 91.11/14.41 inference(ennf_transformation,[status(thm)],[f262])).
% 91.11/14.41 thf(f262,plain,(
% 91.11/14.41 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) => ((X0 @ X2) = $true)) <=> (dsetconstrER = $true)),
% 91.11/14.41 inference(fool_elimination,[status(thm)],[f261])).
% 91.11/14.41 thf(f261,plain,(
% 91.11/14.41 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 91.11/14.41 inference(rectify,[status(thm)],[f16])).
% 91.11/14.41 thf(f16,axiom,(
% 91.11/14.41 (! [X0 : $i > $o,X3 : $i,X1 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)),
% 91.11/14.41 file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',dsetconstrER)).
% 91.11/14.41 thf(f14471,plain,(
% 91.11/14.41 ($true != (in @ (kpair @ sK501 @ (sK634 @ sK501)) @ sK499)) | ($false = (in @ sK501 @ sK498))),
% 91.11/14.41 inference(forward_demodulation,[status(thm)],[f14464,f5149])).
% 91.11/14.41 thf(f5149,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (((setunion @ (setadjoin @ X1 @ emptyset)) = X1)) )),
% 91.11/14.41 inference(trivial_inequality_removal,[status(thm)],[f4297])).
% 91.11/14.41 thf(f4297,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (((setunion @ (setadjoin @ X1 @ emptyset)) = X1) | ($true != $true)) )),
% 91.11/14.41 inference(definition_unfolding,[status(thm)],[f2624,f3272])).
% 91.11/14.41 thf(f3272,plain,(
% 91.11/14.41 (setunionsingleton = $true)),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f1655])).
% 91.11/14.41 thf(f2624,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (((setunion @ (setadjoin @ X1 @ emptyset)) = X1) | (setunionsingleton != $true)) )),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f1038])).
% 91.11/14.41 thf(f1038,plain,(
% 91.11/14.41 ((setunionsingleton = $true) | (sK110 != (setunion @ (setadjoin @ sK110 @ emptyset)))) & (! [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) = X1) | (setunionsingleton != $true))),
% 91.11/14.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK110])],[f1036,f1037])).
% 91.11/14.41 thf(f1037,plain,(
% 91.11/14.41 ? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0) => (sK110 != (setunion @ (setadjoin @ sK110 @ emptyset)))),
% 91.11/14.41 introduced(definition,[],[choice_axiom])).
% 91.11/14.41 thf(f1036,plain,(
% 91.11/14.41 ((setunionsingleton = $true) | ? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0)) & (! [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) = X1) | (setunionsingleton != $true))),
% 91.11/14.41 inference(rectify,[status(thm)],[f1035])).
% 91.11/14.41 thf(f1035,plain,(
% 91.11/14.41 ((setunionsingleton = $true) | ? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0)) & (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true))),
% 91.11/14.41 inference(nnf_transformation,[status(thm)],[f591])).
% 91.11/14.41 thf(f591,plain,(
% 91.11/14.41 (setunionsingleton = $true) <=> ! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0)),
% 91.11/14.41 inference(fool_elimination,[status(thm)],[f590])).
% 91.11/14.41 thf(f590,plain,(
% 91.11/14.41 (setunionsingleton = ! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0))),
% 91.11/14.41 inference(rectify,[status(thm)],[f155])).
% 91.11/14.41 thf(f155,axiom,(
% 91.11/14.41 (setunionsingleton = ! [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) = X1))),
% 91.11/14.41 file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',setunionsingleton)).
% 91.11/14.41 thf(f14464,plain,(
% 91.11/14.41 ($true != (in @ (kpair @ sK501 @ (setunion @ (setadjoin @ (sK634 @ sK501) @ emptyset))) @ sK499)) | ($false = (in @ sK501 @ sK498))),
% 91.11/14.41 inference(superposition,[status(thm)],[f5104,f6411])).
% 91.11/14.41 thf(f6411,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (((setadjoin @ (sK634 @ X1) @ emptyset) = (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499)))) | ($false = (in @ X1 @ sK498))) )),
% 91.11/14.41 inference(equality_proxy_clausification,[status(thm)],[f6410])).
% 91.11/14.41 thf(f6410,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = ((setadjoin @ (sK634 @ X1) @ emptyset) = (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499))))) | ($false = (in @ X1 @ sK498))) )),
% 91.11/14.41 inference(trivial_inequality_removal,[status(thm)],[f6409])).
% 91.11/14.41 thf(f6409,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($false = (in @ X1 @ sK498)) | ($true = $false) | ($true = ((setadjoin @ (sK634 @ X1) @ emptyset) = (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499)))))) )),
% 91.11/14.41 inference(boolean_simplification,[status(thm)],[f6402])).
% 91.11/14.41 thf(f6402,plain,(
% 91.11/14.41 ( ! [X1 : $i] : (($true = ((setadjoin @ (sK634 @ X1) @ emptyset) = (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499))))) | ($true = ($false & (in @ (sK634 @ X1) @ (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sK499)))))) | ($false = (in @ X1 @ sK498))) )),
% 91.11/14.41 inference(cases_simplifying,[status(thm)],[f6400])).
% 91.11/14.41 thf(f5104,plain,(
% 91.11/14.41 ($true != (in @ (kpair @ sK501 @ (setunion @ (dsetconstr @ sK500 @ (^[Y0 : $i]: (in @ (kpair @ sK501 @ Y0) @ sK499))))) @ sK499))),
% 91.11/14.41 inference(beta_eta_normalization,[status(thm)],[f4798])).
% 91.11/14.41 thf(f4798,plain,(
% 91.11/14.41 ($true != (in @ (kpair @ sK501 @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))) @ sK498 @ sK500 @ sK499 @ sK501)) @ sK499))),
% 91.11/14.41 inference(definition_unfolding,[status(thm)],[f3197,f3098])).
% 91.11/14.41 thf(f3098,plain,(
% 91.11/14.41 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f221])).
% 91.11/14.41 thf(f221,plain,(
% 91.11/14.41 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))),
% 91.11/14.41 inference(fool_elimination,[status(thm)],[f220])).
% 91.11/14.41 thf(f220,plain,(
% 91.11/14.41 (ap = (^[X0 : $i, X1 : $i, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2))))))),
% 91.11/14.41 inference(rectify,[status(thm)],[f197])).
% 91.11/14.41 thf(f197,axiom,(
% 91.11/14.41 (ap = (^[X3 : $i, X4 : $i, X13 : $i, X1 : $i] : (setunion @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13))))))),
% 91.11/14.41 file('/export/starexec/sandbox/tmp/tmp.KZMRZKjQSz/DTF2THF_25541.p',ap)).
% 91.11/14.41 thf(f3197,plain,(
% 91.11/14.41 ($true != (in @ (kpair @ sK501 @ (ap @ sK498 @ sK500 @ sK499 @ sK501)) @ sK499))),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f1655])).
% 91.11/14.41 thf(f3196,plain,(
% 91.11/14.41 ($true = (in @ sK501 @ sK498))),
% 91.11/14.41 inference(cnf_transformation,[status(thm)],[f1655])).
% 91.11/14.41 % SZS output end Proof for DTF2THF_25541
% 91.11/14.41 % (26112)------------------------------
% 91.11/14.41 % (26112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.11/14.41 % (26112)Termination reason: Refutation
% 91.11/14.41
% 91.11/14.41 % (26112)Memory used [KB]: 8443
% 91.11/14.41 % (26112)Time elapsed: 0.647 s
% 91.11/14.41 % (26112)Instructions burned: 2153 (million)
% 91.11/14.41 % (26112)------------------------------
% 91.11/14.41 % (26112)------------------------------
% 91.11/14.41 % (25640)Success in time 12.797 s
%------------------------------------------------------------------------------