%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU621^1 : 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 : n022.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 09:35:40 AM UTC 2026
% Result : Theorem 22.89s 4.85s
% Output : Refutation 22.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 21 unt; 0 typ; 9 def)
% Number of atoms : 2641 ( 684 equ; 0 cnn)
% Maximal formula atoms : 140 ( 28 avg)
% Number of connectives : 1618 ( 93 ~; 91 |; 416 &; 384 @)
% ( 11 <=>; 587 =>; 0 <=; 0 <~>)
% Maximal formula depth : 146 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 726 ( 722 usr; 153 con; 0-4 aty)
% ( 36 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 111 ( 43 ^; 62 !; 6 ?; 111 :)
% 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_181,type,
sK3: $i > $o ).
thf(func_def_188,type,
sK10: $i > $o ).
thf(func_def_194,type,
sK16: $i > $o ).
thf(func_def_196,type,
sK18: $i > $i > $i ).
thf(func_def_202,type,
sK24: ( $i > $o ) > $i ).
thf(func_def_203,type,
sK25: $i > $o ).
thf(func_def_204,type,
sK26: ( $i > $i > $o ) > $i > $i ).
thf(func_def_205,type,
sK27: ( $i > $i > $o ) > $i > $i ).
thf(func_def_206,type,
sK28: $i > $i > $o ).
thf(func_def_208,type,
sK30: $i > $i ).
thf(func_def_209,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_210,type,
sK32: $i > $o ).
thf(func_def_223,type,
sK45: $i > $o ).
thf(func_def_226,type,
sK48: ( $i > $o ) > $i > $i ).
thf(func_def_227,type,
sK49: $i > $o ).
thf(func_def_239,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_240,type,
sK62: $i > $o ).
thf(func_def_253,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_254,type,
sK76: $i > $o ).
thf(func_def_259,type,
sK81: ( $i > $o ) > $i > $i ).
thf(func_def_260,type,
sK82: $i > $o ).
thf(func_def_271,type,
sK93: $i > $o ).
thf(func_def_286,type,
sK108: $i > $o ).
thf(func_def_293,type,
sK115: $i > $i > $i ).
thf(func_def_300,type,
sK122: ( $i > $o ) > $i > $i ).
thf(func_def_301,type,
sK123: $i > $o ).
thf(func_def_304,type,
sK126: $i > $i ).
thf(func_def_311,type,
sK133: $i > $i ).
thf(func_def_312,type,
sK134: $i > $i > $i > $i ).
thf(func_def_313,type,
sK135: $i > $i > $i ).
thf(func_def_314,type,
sK136: $i > $i > $i ).
thf(func_def_315,type,
sK137: $i > $i > $i ).
thf(func_def_316,type,
sK138: $i > $i > $i ).
thf(func_def_318,type,
sK140: $i > $i ).
thf(func_def_319,type,
sK141: $i > $i ).
thf(func_def_320,type,
sK142: $i > $i ).
thf(func_def_321,type,
sK143: $i > $i ).
thf(func_def_322,type,
sK144: $i > $i ).
thf(func_def_323,type,
sK145: $i > $i ).
thf(func_def_324,type,
sK146: $i > $i ).
thf(func_def_325,type,
sK147: $i > $i ).
thf(func_def_326,type,
sK148: $i > $i > $i > $i ).
thf(func_def_327,type,
sK149: $i > $i > $i ).
thf(func_def_328,type,
sK150: $i > $i > $i ).
thf(func_def_329,type,
sK151: $i > $i > $i > $i ).
thf(func_def_330,type,
sK152: $i > $i > $i > $i ).
thf(func_def_331,type,
sK153: $i > $i > $i ).
thf(func_def_332,type,
sK154: $i > $i > $i > $i ).
thf(func_def_333,type,
sK155: $i > $i > $i > $i ).
thf(func_def_334,type,
sK156: $i > $i > $i > $i ).
thf(func_def_335,type,
sK157: $i > $i > $i > $i ).
thf(func_def_336,type,
sK158: $i > $i ).
thf(func_def_337,type,
sK159: $i > $i ).
thf(func_def_338,type,
sK160: $i > $i ).
thf(func_def_339,type,
sK161: $i > $i ).
thf(func_def_340,type,
sK162: $i > $i > $i > $i ).
thf(func_def_341,type,
sK163: $i > $i > $i ).
thf(func_def_342,type,
sK164: $i > $i > $i > $i ).
thf(func_def_343,type,
sK165: $i > $i > $i > $i ).
thf(func_def_344,type,
sK166: $i > $i > $i > $i ).
thf(func_def_345,type,
sK167: $i > $i > $i ).
thf(func_def_346,type,
sK168: $i > $i > $i ).
thf(func_def_347,type,
sK169: $i > $i > $i > $i ).
thf(func_def_348,type,
sK170: $i > $i > $i ).
thf(func_def_349,type,
sK171: $i > $i > $i ).
thf(func_def_350,type,
sK172: $i > $i ).
thf(func_def_351,type,
sK173: $i > $i ).
thf(func_def_352,type,
sK174: $i > $i ).
thf(func_def_353,type,
sK175: $i > $i > $i ).
thf(func_def_354,type,
sK176: $i > $i > $i > $i ).
thf(func_def_355,type,
sK177: $i > $i > $i > $i ).
thf(func_def_356,type,
sK178: $i > $i > $i > $i ).
thf(func_def_357,type,
sK179: $i > $i > $i > $i ).
thf(func_def_358,type,
sK180: $i > $i > $i ).
thf(func_def_359,type,
sK181: $i > $i > $i > $i ).
thf(func_def_360,type,
sK182: $i > $i > $i > $i ).
thf(func_def_361,type,
sK183: $i > $i > $i > $i ).
thf(func_def_362,type,
sK184: $i > $i > $i > $i ).
thf(func_def_363,type,
sK185: $i > $i ).
thf(func_def_364,type,
sK186: $i > $i ).
thf(func_def_365,type,
sK187: $i > $i ).
thf(func_def_366,type,
sK188: $i > $i ).
thf(func_def_367,type,
sK189: $i > $i ).
thf(func_def_368,type,
sK190: $i > $i ).
thf(func_def_369,type,
sK191: $i > $i ).
thf(func_def_370,type,
sK192: $i > $i ).
thf(func_def_371,type,
sK193: $i > $i > $i > $i ).
thf(func_def_372,type,
sK194: $i > $i > $i ).
thf(func_def_373,type,
sK195: $i > $i > $i > $i ).
thf(func_def_374,type,
sK196: $i > $i > $i > $i ).
thf(func_def_375,type,
sK197: $i > $i > $i ).
thf(func_def_376,type,
sK198: $i > $i > $i > $i ).
thf(func_def_377,type,
sK199: $i > $i > $i > $i ).
thf(func_def_378,type,
sK200: $i > $i > $i > $i ).
thf(func_def_379,type,
sK201: $i > $i > $i > $i ).
thf(func_def_380,type,
sK202: $i > $i ).
thf(func_def_381,type,
sK203: $i > $i > $i > $i ).
thf(func_def_382,type,
sK204: $i > $i > $i ).
thf(func_def_383,type,
sK205: $i > $i > $i ).
thf(func_def_384,type,
sK206: $i > $i > $i > $i ).
thf(func_def_385,type,
sK207: $i > $i > $i > $i ).
thf(func_def_386,type,
sK208: $i > $i > $i ).
thf(func_def_387,type,
sK209: $i > $i > $i ).
thf(func_def_388,type,
sK210: $i > $i > $i > $i ).
thf(func_def_389,type,
sK211: $i > $i > $i ).
thf(func_def_390,type,
sK212: $i > $i ).
thf(func_def_391,type,
sK213: $i > $i > $i > $i ).
thf(func_def_392,type,
sK214: $i > $i > $i ).
thf(func_def_393,type,
sK215: $i > $i > $i > $i ).
thf(func_def_394,type,
sK216: $i > $i > $i > $i ).
thf(func_def_395,type,
sK217: $i > $i > $i ).
thf(func_def_396,type,
sK218: $i > $i > $i > $i ).
thf(func_def_397,type,
sK219: $i > $i > $i > $i ).
thf(func_def_398,type,
sK220: $i > $i > $i > $i ).
thf(func_def_399,type,
sK221: $i > $i > $i > $i ).
thf(func_def_400,type,
sK222: $i > $i ).
thf(func_def_401,type,
sK223: $i > $i ).
thf(func_def_402,type,
sK224: $i > $i ).
thf(func_def_403,type,
sK225: $i > $i ).
thf(func_def_404,type,
sK226: $i > $i ).
thf(func_def_405,type,
sK227: $i > $i ).
thf(func_def_406,type,
sK228: $i > $i ).
thf(func_def_407,type,
sK229: $i > $i ).
thf(func_def_408,type,
sK230: $i > $i ).
thf(func_def_409,type,
sK231: $i > $i ).
thf(func_def_410,type,
sK232: $i > $i > $i > $i ).
thf(func_def_411,type,
sK233: $i > $i > $i ).
thf(func_def_412,type,
sK234: $i > $i > $i > $i ).
thf(func_def_413,type,
sK235: $i > $i > $i > $i ).
thf(func_def_414,type,
sK236: $i > $i > $i ).
thf(func_def_415,type,
sK237: $i > $i > $i > $i ).
thf(func_def_416,type,
sK238: $i > $i > $i > $i ).
thf(func_def_417,type,
sK239: $i > $i > $i > $i ).
thf(func_def_418,type,
sK240: $i > $i > $i > $i ).
thf(func_def_419,type,
sK241: $i > $i ).
thf(func_def_420,type,
sK242: $i > $i > $i > $i ).
thf(func_def_421,type,
sK243: $i > $i > $i ).
thf(func_def_422,type,
sK244: $i > $i > $i ).
thf(func_def_423,type,
sK245: $i > $i > $i ).
thf(func_def_424,type,
sK246: $i > $i > $i > $i ).
thf(func_def_425,type,
sK247: $i > $i > $i ).
thf(func_def_426,type,
sK248: $i > $i > $i > $i ).
thf(func_def_427,type,
sK249: $i > $i > $i > $i ).
thf(func_def_428,type,
sK250: $i > $i > $i > $i ).
thf(func_def_429,type,
sK251: $i > $i ).
thf(func_def_430,type,
sK252: $i > $i > $i ).
thf(func_def_431,type,
sK253: $i > $i > $i > $i ).
thf(func_def_432,type,
sK254: $i > $i > $i > $i ).
thf(func_def_433,type,
sK255: $i > $i > $i > $i ).
thf(func_def_434,type,
sK256: $i > $i > $i > $i ).
thf(func_def_435,type,
sK257: $i > $i > $i ).
thf(func_def_436,type,
sK258: $i > $i > $i ).
thf(func_def_437,type,
sK259: $i > $i > $i ).
thf(func_def_438,type,
sK260: $i > $i > $i > $i ).
thf(func_def_439,type,
sK261: $i > $i > $i > $i ).
thf(func_def_440,type,
sK262: $i > $i ).
thf(func_def_441,type,
sK263: $i > $i > $i ).
thf(func_def_442,type,
sK264: $i > $i > $i > $i ).
thf(func_def_443,type,
sK265: $i > $i > $i > $i ).
thf(func_def_444,type,
sK266: $i > $i > $i > $i ).
thf(func_def_445,type,
sK267: $i > $i > $i > $i ).
thf(func_def_446,type,
sK268: $i > $i > $i ).
thf(func_def_447,type,
sK269: $i > $i > $i ).
thf(func_def_448,type,
sK270: $i > $i > $i > $i ).
thf(func_def_449,type,
sK271: $i > $i > $i > $i ).
thf(func_def_450,type,
sK272: $i > $i ).
thf(func_def_451,type,
sK273: $i > $i > $i > $i ).
thf(func_def_452,type,
sK274: $i > $i > $i ).
thf(func_def_453,type,
sK275: $i > $i > $i ).
thf(func_def_454,type,
sK276: $i > $i > $i > $i ).
thf(func_def_455,type,
sK277: $i > $i > $i > $i ).
thf(func_def_456,type,
sK278: $i > $i > $i ).
thf(func_def_457,type,
sK279: $i > $i > $i ).
thf(func_def_458,type,
sK280: $i > $i > $i ).
thf(func_def_459,type,
sK281: $i > $i > $i > $i ).
thf(func_def_460,type,
sK282: $i > $i ).
thf(func_def_461,type,
sK283: $i > $i > $i ).
thf(func_def_462,type,
sK284: $i > $i > $i > $i ).
thf(func_def_463,type,
sK285: $i > $i > $i > $i ).
thf(func_def_464,type,
sK286: $i > $i > $i > $i ).
thf(func_def_465,type,
sK287: $i > $i > $i > $i ).
thf(func_def_466,type,
sK288: $i > $i ).
thf(func_def_467,type,
sK289: $i > $i ).
thf(func_def_468,type,
sK290: $i > $i ).
thf(func_def_469,type,
sK291: $i > $i ).
thf(func_def_470,type,
sK292: $i > $i ).
thf(func_def_471,type,
sK293: $i > $i ).
thf(func_def_472,type,
sK294: $i > $i ).
thf(func_def_473,type,
sK295: $i > $i ).
thf(func_def_474,type,
sK296: $i > $i ).
thf(func_def_475,type,
sK297: $i > $i ).
thf(func_def_476,type,
sK298: $i > $i ).
thf(func_def_477,type,
sK299: $i > $i ).
thf(func_def_478,type,
sK300: $i > $i > $i ).
thf(func_def_479,type,
sK301: $i > $i > $i > $i ).
thf(func_def_480,type,
sK302: $i > $i > $i > $i ).
thf(func_def_481,type,
sK303: $i > $i > $i > $i ).
thf(func_def_482,type,
sK304: $i > $i > $i > $i ).
thf(func_def_483,type,
sK305: $i > $i > $i ).
thf(func_def_484,type,
sK306: $i > $i > $i ).
thf(func_def_485,type,
sK307: $i > $i > $i ).
thf(func_def_486,type,
sK308: $i > $i > $i > $i ).
thf(func_def_487,type,
sK309: $i > $i > $i > $i ).
thf(func_def_488,type,
sK310: $i > $i > $i ).
thf(func_def_489,type,
sK311: $i > $i > $i ).
thf(func_def_490,type,
sK312: $i > $i > $i > $i ).
thf(func_def_491,type,
sK313: $i > $i > $i > $i ).
thf(func_def_492,type,
sK314: $i > $i > $i ).
thf(func_def_493,type,
sK315: $i > $i > $i > $i ).
thf(func_def_494,type,
sK316: $i > $i > $i > $i ).
thf(func_def_495,type,
sK317: $i > $i > $i > $i ).
thf(func_def_496,type,
sK318: $i > $i > $i > $i ).
thf(func_def_497,type,
sK319: $i > $i > $i > $i ).
thf(func_def_498,type,
sK320: $i > $i > $i ).
thf(func_def_499,type,
sK321: $i > $i > $i > $i ).
thf(func_def_500,type,
sK322: $i > $i > $i > $i ).
thf(func_def_501,type,
sK323: $i > $i > $i > $i ).
thf(func_def_502,type,
sK324: $i > $i > $i ).
thf(func_def_503,type,
sK325: $i > $i > $i ).
thf(func_def_504,type,
sK326: $i > $i > $i > $i ).
thf(func_def_505,type,
sK327: $i > $i > $i ).
thf(func_def_506,type,
sK328: $i > $i > $i > $i ).
thf(func_def_507,type,
sK329: $i > $i > $i ).
thf(func_def_508,type,
sK330: $i > $i > $i > $i ).
thf(func_def_509,type,
sK331: $i > $i > $i > $i ).
thf(func_def_510,type,
sK332: $i > $i > $i ).
thf(func_def_511,type,
sK333: $i > $i > $i > $i ).
thf(func_def_512,type,
sK334: $i > $i > $i > $i ).
thf(func_def_513,type,
sK335: $i > $i > $i > $i ).
thf(func_def_514,type,
sK336: $i > $i ).
thf(func_def_515,type,
sK337: $i > $i > $i ).
thf(func_def_516,type,
sK338: $i > $i > $i > $i ).
thf(func_def_517,type,
sK339: $i > $i > $i > $i ).
thf(func_def_518,type,
sK340: $i > $i > $i > $i ).
thf(func_def_519,type,
sK341: $i > $i > $i > $i ).
thf(func_def_520,type,
sK342: $i > $i > $i > $i ).
thf(func_def_521,type,
sK343: $i > $i > $i ).
thf(func_def_522,type,
sK344: $i > $i > $i > $i ).
thf(func_def_523,type,
sK345: $i > $i > $i > $i ).
thf(func_def_524,type,
sK346: $i > $i > $i ).
thf(func_def_525,type,
sK347: $i > $i > $i > $i ).
thf(func_def_526,type,
sK348: $i > $i > $i > $i ).
thf(func_def_527,type,
sK349: $i > $i > $i > $i ).
thf(func_def_528,type,
sK350: $i > $i > $i > $i ).
thf(func_def_529,type,
sK351: $i > $i > $i > $i ).
thf(func_def_530,type,
sK352: $i > $i > $i ).
thf(func_def_531,type,
sK353: $i > $i > $i ).
thf(func_def_532,type,
sK354: $i > $i > $i > $i ).
thf(func_def_533,type,
sK355: $i > $i > $i > $i ).
thf(func_def_534,type,
sK356: $i > $i > $i ).
thf(func_def_535,type,
sK357: $i > $i > $i > $i ).
thf(func_def_536,type,
sK358: $i > $i > $i > $i ).
thf(func_def_537,type,
sK359: $i > $i > $i > $i ).
thf(func_def_538,type,
sK360: $i > $i > $i > $i ).
thf(func_def_539,type,
sK361: $i > $i > $i > $i ).
thf(func_def_540,type,
sK362: $i > $i > $i ).
thf(func_def_541,type,
sK363: $i > $i > $i > $i ).
thf(func_def_542,type,
sK364: $i > $i > $i ).
thf(func_def_543,type,
sK365: $i > $i > $i > $i ).
thf(func_def_544,type,
sK366: $i > $i > $i > $i ).
thf(func_def_545,type,
sK367: $i > $i > $i > $i ).
thf(func_def_546,type,
sK368: $i > $i > $i > $i ).
thf(func_def_547,type,
sK369: $i > $i > $i > $i ).
thf(func_def_548,type,
sK370: $i > $i > $i ).
thf(func_def_549,type,
sK371: $i > $i > $i ).
thf(func_def_550,type,
sK372: $i > $i > $i > $i ).
thf(func_def_551,type,
sK373: $i > $i > $i > $i ).
thf(func_def_552,type,
sK374: $i > $i ).
thf(func_def_553,type,
sK375: $i > $i ).
thf(func_def_554,type,
sK376: $i > $i ).
thf(func_def_555,type,
sK377: $i > $i ).
thf(func_def_556,type,
sK378: $i > $i ).
thf(func_def_557,type,
sK379: $i > $i ).
thf(func_def_558,type,
sK380: $i > $i ).
thf(func_def_559,type,
sK381: $i > $i ).
thf(func_def_560,type,
sK382: $i > $i ).
thf(func_def_561,type,
sK383: $i > $i ).
thf(func_def_562,type,
sK384: $i > $i ).
thf(func_def_563,type,
sK385: $i > $i ).
thf(func_def_564,type,
sK386: $i > $i ).
thf(func_def_565,type,
sK387: $i > $i ).
thf(func_def_566,type,
sK388: $i > $i ).
thf(func_def_567,type,
sK389: $i > $i ).
thf(func_def_568,type,
sK390: $i > $i ).
thf(func_def_569,type,
sK391: $i > $i ).
thf(func_def_570,type,
sK392: $i > $i ).
thf(func_def_571,type,
sK393: $i > $i ).
thf(func_def_572,type,
sK394: $i > $i ).
thf(func_def_573,type,
sK395: $i > $i ).
thf(func_def_574,type,
sK396: $i > $i ).
thf(func_def_575,type,
sK397: $i > $i ).
thf(func_def_576,type,
sK398: $i > $i ).
thf(func_def_577,type,
sK399: $i > $i ).
thf(func_def_578,type,
sK400: $i > $i ).
thf(func_def_579,type,
sK401: $i > $i ).
thf(func_def_580,type,
sK402: $i > $i ).
thf(func_def_581,type,
sK403: $i > $i ).
thf(func_def_582,type,
sK404: $i > $i ).
thf(func_def_583,type,
sK405: $i > $i ).
thf(func_def_584,type,
sK406: $i > $i ).
thf(func_def_585,type,
sK407: $i > $i ).
thf(func_def_586,type,
sK408: $i > $i ).
thf(func_def_587,type,
sK409: $i > $i ).
thf(func_def_588,type,
sK410: $i > $i ).
thf(func_def_589,type,
sK411: $i > $i ).
thf(func_def_590,type,
sK412: $i > $i ).
thf(func_def_591,type,
sK413: $i > $i ).
thf(func_def_592,type,
sK414: $i > $i ).
thf(func_def_593,type,
sK415: $i > $i ).
thf(func_def_594,type,
sK416: $i > $i ).
thf(func_def_595,type,
sK417: $i > $i ).
thf(func_def_596,type,
sK418: $i > $i ).
thf(func_def_597,type,
sK419: $i > $i ).
thf(func_def_598,type,
sK420: $i > $i ).
thf(func_def_599,type,
sK421: $i > $i > $i ).
thf(func_def_600,type,
sK422: $i > $i > $i > $i ).
thf(func_def_601,type,
sK423: $i > $i > $i > $i ).
thf(func_def_602,type,
sK424: $i > $i > $i > $i ).
thf(func_def_603,type,
sK425: $i > $i > $i > $i ).
thf(func_def_604,type,
sK426: $i > $i > $i ).
thf(func_def_605,type,
sK427: $i > $i > $i ).
thf(func_def_606,type,
sK428: $i > $i > $i > $i ).
thf(func_def_607,type,
sK429: $i > $i > $i > $i ).
thf(func_def_608,type,
sK430: $i > $i > $i ).
thf(func_def_609,type,
sK431: $i > $i > $i ).
thf(func_def_610,type,
sK432: $i > $i > $i > $i ).
thf(func_def_611,type,
sK433: $i > $i > $i > $i ).
thf(func_def_612,type,
sK434: $i > $i > $i > $i ).
thf(func_def_613,type,
sK435: $i > $i > $i ).
thf(func_def_614,type,
sK436: $i > $i > $i > $i ).
thf(func_def_615,type,
sK437: $i > $i > $i > $i ).
thf(func_def_616,type,
sK438: $i > $i > $i ).
thf(func_def_617,type,
sK439: $i > $i > $i > $i ).
thf(func_def_618,type,
sK440: $i > $i > $i > $i ).
thf(func_def_619,type,
sK441: $i > $i > $i > $i ).
thf(func_def_620,type,
sK442: $i > $i > $i ).
thf(func_def_621,type,
sK443: $i > $i > $i > $i ).
thf(func_def_622,type,
sK444: $i > $i > $i > $i ).
thf(func_def_623,type,
sK445: $i > $i > $i > $i ).
thf(func_def_624,type,
sK446: $i > $i > $i > $i ).
thf(func_def_625,type,
sK447: $i > $i > $i ).
thf(func_def_626,type,
sK448: $i > $i > $i > $i ).
thf(func_def_627,type,
sK449: $i > $i > $i > $i ).
thf(func_def_628,type,
sK450: $i > $i > $i > $i ).
thf(func_def_629,type,
sK451: $i > $i > $i > $i ).
thf(func_def_630,type,
sK452: $i > $i > $i ).
thf(func_def_631,type,
sK453: $i > $i > $i > $i ).
thf(func_def_632,type,
sK454: $i > $i > $i > $i ).
thf(func_def_633,type,
sK455: $i > $i ).
thf(func_def_634,type,
sK456: $i > $i > $i ).
thf(func_def_635,type,
sK457: $i > $i > $i > $i ).
thf(func_def_636,type,
sK458: $i > $i > $i > $i ).
thf(func_def_637,type,
sK459: $i > $i > $i > $i ).
thf(func_def_638,type,
sK460: $i > $i > $i ).
thf(func_def_639,type,
sK461: $i > $i > $i ).
thf(func_def_640,type,
sK462: $i > $i > $i > $i ).
thf(func_def_641,type,
sK463: $i > $i > $i ).
thf(func_def_642,type,
sK464: $i > $i > $i ).
thf(func_def_643,type,
sK465: $i > $i ).
thf(func_def_644,type,
sK466: $i > $i > $i ).
thf(func_def_645,type,
sK467: $i > $i > $i > $i ).
thf(func_def_646,type,
sK468: $i > $i > $i > $i ).
thf(func_def_647,type,
sK469: $i > $i > $i > $i ).
thf(func_def_648,type,
sK470: $i > $i > $i > $i ).
thf(func_def_649,type,
sK471: $i > $i > $i ).
thf(func_def_650,type,
sK472: $i > $i > $i ).
thf(func_def_651,type,
sK473: $i > $i > $i > $i ).
thf(func_def_652,type,
sK474: $i > $i > $i ).
thf(func_def_653,type,
sK475: $i > $i ).
thf(func_def_654,type,
sK476: $i > $i > $i ).
thf(func_def_655,type,
sK477: $i > $i > $i > $i ).
thf(func_def_656,type,
sK478: $i > $i > $i > $i ).
thf(func_def_657,type,
sK479: $i > $i > $i > $i ).
thf(func_def_658,type,
sK480: $i > $i > $i > $i ).
thf(func_def_659,type,
sK481: $i > $i > $i ).
thf(func_def_660,type,
sK482: $i > $i > $i > $i ).
thf(func_def_661,type,
sK483: $i > $i > $i > $i ).
thf(func_def_662,type,
sK484: $i > $i > $i > $i ).
thf(func_def_663,type,
sK485: $i > $i > $i > $i ).
thf(func_def_664,type,
sK486: $i > $i > $i ).
thf(func_def_665,type,
sK487: $i > $i > $i ).
thf(func_def_666,type,
sK488: $i > $i > $i ).
thf(func_def_667,type,
sK489: $i > $i > $i > $i ).
thf(func_def_668,type,
sK490: $i > $i > $i > $i ).
thf(func_def_669,type,
sK491: $i > $i > $i ).
thf(func_def_670,type,
sK492: $i > $i > $i ).
thf(func_def_671,type,
sK493: $i > $i > $i ).
thf(func_def_672,type,
sK494: $i > $i > $i > $i ).
thf(func_def_673,type,
sK495: $i > $i ).
thf(func_def_674,type,
sK496: $i > $i ).
thf(func_def_675,type,
sK497: $i > $i > $i > $i ).
thf(func_def_676,type,
sK498: $i > $i > $i ).
thf(func_def_677,type,
sK499: $i > $i > $i ).
thf(func_def_678,type,
sK500: $i > $i > $i ).
thf(func_def_679,type,
sK501: $i > $i > $i > $i ).
thf(func_def_680,type,
sK502: $i > $i > $i ).
thf(func_def_681,type,
sK503: $i > $i > $i > $i ).
thf(func_def_682,type,
sK504: $i > $i > $i > $i ).
thf(func_def_683,type,
sK505: $i > $i > $i > $i ).
thf(func_def_684,type,
sK506: $i > $i > $i > $i ).
thf(func_def_685,type,
sK507: $i > $i > $i > $i ).
thf(func_def_686,type,
sK508: $i > $i > $i ).
thf(func_def_687,type,
sK509: $i > $i > $i ).
thf(func_def_688,type,
sK510: $i > $i > $i > $i ).
thf(func_def_689,type,
sK511: $i > $i > $i > $i ).
thf(func_def_690,type,
sK512: $i > $i > $i > $i ).
thf(func_def_691,type,
sK513: $i > $i > $i ).
thf(func_def_692,type,
sK514: $i > $i > $i ).
thf(func_def_693,type,
sK515: $i > $i > $i > $i ).
thf(func_def_694,type,
sK516: $i > $i > $i > $i ).
thf(func_def_695,type,
sK517: $i > $i > $i > $i ).
thf(func_def_696,type,
sK518: $i > $i > $i ).
thf(func_def_697,type,
sK519: $i > $i > $i ).
thf(func_def_698,type,
sK520: $i > $i > $i ).
thf(func_def_699,type,
sK521: $i > $i > $i > $i ).
thf(func_def_700,type,
sK522: $i > $i > $i > $i ).
thf(func_def_701,type,
sK523: $i > $i > $i > $i ).
thf(func_def_702,type,
sK524: $i > $i > $i ).
thf(func_def_703,type,
sK525: $i > $i > $i ).
thf(func_def_704,type,
sK526: $i > $i > $i > $i ).
thf(func_def_705,type,
sK527: $i > $i > $i > $i ).
thf(func_def_706,type,
sK528: $i > $i > $i ).
thf(func_def_707,type,
sK529: $i > $i > $i ).
thf(func_def_708,type,
sK530: $i > $i > $i ).
thf(func_def_709,type,
sK531: $i > $i > $i > $i ).
thf(func_def_710,type,
sK532: $i > $i > $i > $i ).
thf(func_def_711,type,
sK533: $i > $i > $i ).
thf(func_def_712,type,
sK534: $i > $i > $i ).
thf(func_def_713,type,
sK535: $i > $i > $i ).
thf(func_def_714,type,
sK536: $i > $i > $i > $i ).
thf(func_def_715,type,
sK537: $i > $i > $i > $i ).
thf(func_def_716,type,
sK538: $i > $i ).
thf(func_def_717,type,
sK539: $i > $i > $i > $i ).
thf(func_def_718,type,
sK540: $i > $i ).
thf(func_def_719,type,
sK541: $i > $i > $i ).
thf(func_def_720,type,
sK542: $i > $i > $i ).
thf(func_def_721,type,
sK543: $i > $i > $i > $i ).
thf(func_def_722,type,
sK544: $i > $i > $i > $i ).
thf(func_def_723,type,
sK545: $i > $i > $i ).
thf(func_def_724,type,
sK546: $i > $i > $i ).
thf(func_def_725,type,
sK547: $i > $i > $i > $i ).
thf(func_def_726,type,
sK548: $i > $i > $i > $i ).
thf(func_def_727,type,
sK549: $i > $i ).
thf(func_def_728,type,
sK550: $i > $i > $i > $i ).
thf(func_def_729,type,
sK551: $i > $i > $i ).
thf(func_def_730,type,
sK552: $i > $i > $i > $i ).
thf(func_def_731,type,
sK553: $i > $i > $i > $i ).
thf(func_def_732,type,
sK554: $i > $i > $i > $i ).
thf(func_def_733,type,
sK555: $i > $i > $i ).
thf(func_def_734,type,
sK556: $i > $i > $i > $i ).
thf(func_def_735,type,
sK557: $i > $i > $i > $i ).
thf(func_def_736,type,
sK558: $i > $i ).
thf(func_def_737,type,
sK559: $i > $i > $i > $i ).
thf(func_def_738,type,
sK560: $i > $i > $i ).
thf(func_def_739,type,
sK561: $i > $i > $i ).
thf(func_def_740,type,
sK562: $i > $i > $i > $i ).
thf(func_def_741,type,
sK563: $i > $i > $i ).
thf(func_def_742,type,
sK564: $i > $i > $i > $i ).
thf(func_def_743,type,
sK565: $i > $i > $i ).
thf(func_def_744,type,
sK566: $i > $i > $i > $i ).
thf(func_def_745,type,
sK567: $i > $i > $i > $i ).
thf(func_def_746,type,
sK568: $i > $i > $i > $i ).
thf(func_def_747,type,
sK569: $i > $i > $i ).
thf(func_def_748,type,
sK570: $i > $i > $i > $i ).
thf(func_def_749,type,
sK571: $i > $i > $i > $i ).
thf(func_def_750,type,
sK572: $i > $i > $i > $i ).
thf(func_def_751,type,
sK573: $i > $i > $i ).
thf(func_def_752,type,
sK574: $i > $i > $i ).
thf(func_def_753,type,
sK575: $i > $i > $i ).
thf(func_def_754,type,
sK576: $i > $i > $i > $i ).
thf(func_def_755,type,
sK577: $i > $i > $i > $i ).
thf(func_def_764,type,
sK586: $i > $o ).
thf(func_def_767,type,
sK589: ( $i > $o ) > $i ).
thf(func_def_768,type,
sK590: $i > $o ).
thf(func_def_769,type,
sK591: $i > $i ).
thf(func_def_773,type,
sK595: $i > $i ).
thf(func_def_794,type,
sK616: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_795,type,
sK617: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_796,type,
sK618: $i > $o ).
thf(func_def_797,type,
sK619: $i > $o ).
thf(func_def_806,type,
sK628: $i > $i ).
thf(func_def_808,type,
sK630: $i > $o ).
thf(func_def_815,type,
sK637: $i > $o ).
thf(func_def_822,type,
sK644: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_823,type,
sK645: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_824,type,
sK646: $i > $o ).
thf(func_def_825,type,
sK647: $i > $o ).
thf(func_def_831,type,
sK653: ( $i > $o ) > $i > $i ).
thf(func_def_832,type,
sK654: $i > $o ).
thf(func_def_835,type,
sK657: ( $i > $o ) > $i > $i ).
thf(func_def_836,type,
sK658: $i > $o ).
thf(func_def_840,type,
sK662: $i > $o ).
thf(func_def_854,type,
sK676: $i > $i > $i ).
thf(func_def_865,type,
sK687: $i > $i ).
thf(func_def_884,type,
sK706: $i > $i ).
thf(func_def_887,type,
sK709: $i > $i ).
thf(func_def_888,type,
sK710: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_889,type,
sK711: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_892,type,
sK714: $i > $o ).
thf(func_def_893,type,
sK715: $i > $o ).
thf(func_def_896,type,
sK718: $i > $o ).
thf(func_def_897,type,
sK719: $i > $i > $i ).
thf(func_def_906,type,
sK728: $i > $i > $i ).
thf(func_def_907,type,
sK729: $i > $i > $i ).
thf(func_def_908,type,
sK730: $i > $i > $i ).
thf(func_def_914,type,
sK736: ( $i > $o ) > $i ).
thf(func_def_915,type,
sK737: ( $i > $o ) > $i ).
thf(func_def_916,type,
sK738: $i > $o ).
thf(func_def_929,type,
sK751: $i > $i ).
thf(func_def_938,type,
sK760: $i > $o ).
thf(func_def_946,type,
sK768: $i > $o > $i > $i ).
thf(func_def_953,type,
sK775: ( $i > $o ) > $i ).
thf(func_def_954,type,
sK776: $i > $o ).
thf(func_def_955,type,
sK777: $i > $i ).
thf(func_def_956,type,
sK778: $i > $i > $i ).
thf(func_def_969,type,
ph791:
!>[X0: $tType] : X0 ).
thf(func_def_970,type,
sK792: ( $i > $o ) > $i ).
thf(func_def_971,type,
sK793: ( $i > $o ) > $i > $i ).
thf(func_def_972,type,
sK794: $i > $i ).
thf(func_def_973,type,
sK795: $i > $i ).
thf(func_def_974,type,
sK796: $i > $i > $i ).
thf(func_def_975,type,
sK797: $o > $i ).
thf(func_def_976,type,
sK798: $i > $i > $i ).
thf(func_def_977,type,
sK799: $i > $i > $i ).
thf(func_def_978,type,
sK800: $i > $i > $i ).
thf(func_def_979,type,
sK801: $i > $i > $i ).
thf(func_def_980,type,
sK802: $i > $i > $i ).
thf(func_def_982,type,
sK804: $i > $i > $i ).
thf(func_def_1004,type,
sK826: $i > $i > $i ).
thf(func_def_1005,type,
sK827: $o > $i ).
thf(func_def_1006,type,
sK828: $i > $i > $i ).
thf(func_def_1009,type,
sK831: $i > $i > $i ).
thf(func_def_1010,type,
sK832: $i > $i > $i ).
thf(func_def_1011,type,
sK833: $i > $i > $i ).
thf(func_def_1012,type,
sK834: $i > $i ).
thf(func_def_1013,type,
sK835: $i > $i > $i ).
thf(func_def_1014,type,
sK836: $i > $i > $i ).
thf(func_def_1015,type,
sK837: $i > $i > $i ).
thf(func_def_1016,type,
sK838: $i > $i > $i ).
thf(func_def_1017,type,
sK839: $i > $i ).
thf(func_def_1018,type,
sK840: $i > $i > $i ).
thf(func_def_1019,type,
sK841: $i > $i ).
thf(func_def_1020,type,
sK842: $i > $i > $i ).
thf(func_def_1021,type,
sK843: $i > $i ).
thf(func_def_1022,type,
sK844: $i > $i > $i ).
thf(func_def_1023,type,
sK845: $i > $i ).
thf(func_def_1024,type,
sK846: $i > $i > $i ).
thf(func_def_1025,type,
sK847: $i > $i > $i ).
thf(func_def_1026,type,
sK848: $i > $i ).
thf(func_def_1027,type,
sK849: $i > $i > $i ).
thf(func_def_1028,type,
sK850: $i > $i ).
thf(f17064,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f7568,f7610,f7723,f8238,f12201,f12431,f12687,f15930,f16911,f17063]) ).
thf(f17063,plain,
( ~ spl2_456
| ~ spl2_459 ),
inference(avatar_contradiction_clause,[status(thm)],[f17062]) ).
thf(f17062,plain,
( $false
| ~ spl2_456
| ~ spl2_459 ),
inference(trivial_inequality_removal,[status(thm)],[f17061]) ).
thf(f17061,plain,
( ( $true = $false )
| ~ spl2_456
| ~ spl2_459 ),
inference(backward_demodulation,[status(thm)],[f8224,f8237]) ).
thf(f8237,plain,
( ( notinsingleton = $false )
| ~ spl2_459 ),
inference(avatar_component_clause,[status(thm)],[f8235]) ).
thf(f8235,definition,
( spl2_459
<=> ( notinsingleton = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_459])],[avatar_definition]) ).
thf(f8224,plain,
( ( notinsingleton = $true )
| ~ spl2_456 ),
inference(avatar_component_clause,[status(thm)],[f8222]) ).
thf(f8222,definition,
( spl2_456
<=> ( notinsingleton = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_456])],[avatar_definition]) ).
thf(f16911,plain,
( ~ spl2_312
| ~ spl2_321
| ~ spl2_458 ),
inference(avatar_contradiction_clause,[status(thm)],[f16910]) ).
thf(f16910,plain,
( $false
| ~ spl2_312
| ~ spl2_321
| ~ spl2_458 ),
inference(trivial_inequality_removal,[status(thm)],[f16890]) ).
thf(f16890,plain,
( ( $true = $false )
| ~ spl2_312
| ~ spl2_321
| ~ spl2_458 ),
inference(backward_demodulation,[status(thm)],[f671,f16878]) ).
thf(f16878,plain,
( ( ( in @ sK0 @ sK1 )
= $false )
| ~ spl2_312
| ~ spl2_321
| ~ spl2_458 ),
inference(backward_demodulation,[status(thm)],[f16403,f16856]) ).
thf(f16856,plain,
( ( sK0 = sK830 )
| ~ spl2_312
| ~ spl2_321
| ~ spl2_458 ),
inference(trivial_inequality_removal,[status(thm)],[f16835]) ).
thf(f16835,plain,
( ( sK0 = sK830 )
| ( $true = $false )
| ~ spl2_312
| ~ spl2_321
| ~ spl2_458 ),
inference(superposition,[status(thm)],[f16404,f8233]) ).
thf(f8233,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false )
| ( X1 = X2 ) )
| ~ spl2_458 ),
inference(avatar_component_clause,[status(thm)],[f8232]) ).
thf(f8232,definition,
( spl2_458
<=> ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_458])],[avatar_definition]) ).
thf(f16404,plain,
( ( $true
= ( in @ sK830 @ ( setadjoin @ sK0 @ emptyset ) ) )
| ~ spl2_312
| ~ spl2_321 ),
inference(binary_proxy_clausification,[status(thm)],[f16402]) ).
thf(f16402,plain,
( ( $false
= ( ( in @ sK830 @ ( setadjoin @ sK0 @ emptyset ) )
=> ( in @ sK830 @ sK1 ) ) )
| ~ spl2_312
| ~ spl2_321 ),
inference(beta_eta_normalization,[status(thm)],[f16401]) ).
thf(f16401,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK0 @ emptyset ) )
=> ( in @ Y0 @ sK1 ) )
@ sK830 )
= $false )
| ~ spl2_312
| ~ spl2_321 ),
inference(sigma_clausification,[status(thm)],[f16400]) ).
thf(f16400,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK0 @ emptyset ) )
=> ( in @ Y0 @ sK1 ) ) )
= $false )
| ~ spl2_312
| ~ spl2_321 ),
inference(not_proxy_clausification,[status(thm)],[f16399]) ).
thf(f16399,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK0 @ emptyset ) )
=> ( in @ Y0 @ sK1 ) ) ) ) )
| ~ spl2_312
| ~ spl2_321 ),
inference(boolean_simplification,[status(thm)],[f16340]) ).
thf(f16340,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK0 @ emptyset ) )
=> ( in @ Y0 @ sK1 ) ) )
= $false )
= $true )
| ~ spl2_312
| ~ spl2_321 ),
inference(superposition,[status(thm)],[f7605,f12832]) ).
thf(f12832,plain,
( ( ( in @ ( setadjoin @ sK0 @ emptyset ) @ ( powerset @ sK1 ) )
= $false )
| ~ spl2_312 ),
inference(trivial_inequality_removal,[status(thm)],[f12826]) ).
thf(f12826,plain,
( ( ( in @ ( setadjoin @ sK0 @ emptyset ) @ ( powerset @ sK1 ) )
= $false )
| ( $true != $true )
| ~ spl2_312 ),
inference(superposition,[status(thm)],[f670,f7567]) ).
thf(f7567,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) )
| ~ spl2_312 ),
inference(avatar_component_clause,[status(thm)],[f7566]) ).
thf(f7566,definition,
( spl2_312
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_312])],[avatar_definition]) ).
thf(f670,plain,
( ( subset @ ( setadjoin @ sK0 @ emptyset ) @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f429]) ).
thf(f429,plain,
( ( binunionRsub = $true )
& ( replAx = $true )
& ( quantDeMorgan1 = $true )
& ( ( in @ sK0 @ sK1 )
= $true )
& ( ( subset @ ( setadjoin @ sK0 @ emptyset ) @ sK1 )
!= $true )
& ( setoftrueEq = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset1 = $true )
& ( exuE1 = $true )
& ( emptyInPowerset = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan2 = $true )
& ( exu__Cong = $true )
& ( powersetsubset = $true )
& ( symdiffI2 = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( kpairp = $true )
& ( omega0Ax = $true )
& ( notinsingleton = $true )
& ( subsetTrans = $true )
& ( setextsub = $true )
& ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( binintersectSubset5 = $true )
& ( upairsetIR = $true )
& ( setadjoinE = $true )
& ( setunionE = $true )
& ( in__Cong = $true )
& ( setadjoinSub2 = $true )
& ( noeltsimpempty = $true )
& ( setukpairIL = $true )
& ( uniqinunit = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( binintersectI = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( inPowerset = $true )
& ( foundationAx = $true )
& ( nonemptyI1 = $true )
& ( subsetRefl = $true )
& ( bs114d = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetE = $true )
& ( binunionIL = $true )
& ( dsetconstrEL = $true )
& ( setadjoin__Cong = $true )
& ( subsetE2 = $true )
& ( setext = $true )
& ( powersetE = $true )
& ( symdiffIneg2 = $true )
& ( dsetconstr__Cong = $true )
& ( binintersectSubset2 = $true )
& ( prop2setI = $true )
& ( subset2powerset = $true )
& ( powerset__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetE = $true )
& ( nonemptyE1 = $true )
& ( setadjoinIL = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( setbeta = $true )
& ( subsetemptysetimpeq = $true )
& ( omegaSAx = $true )
& ( setminusSubset1 = $true )
& ( vacuousDall = $true )
& ( powersetAx = $true )
& ( notinemptyset = $true )
& ( disjointsetsI1 = $true )
& ( emptyE1 = $true )
& ( emptyinunitempty = $true )
& ( setminusIRneg = $true )
& ( eqimpsubset1 = $true )
& ( descr__Cong = $true )
& ( subsetI1 = $true )
& ( setukpairIR = $true )
& ( descrp = $true )
& ( notequalI2 = $true )
& ( exuE3u = $true )
& ( setminusER = $true )
& ( singletonsswitch = $true )
& ( eqimpsubset2 = $true )
& ( notequalI1 = $true )
& ( prop2setE = $true )
& ( setunionI = $true )
& ( notdexE = $true )
& ( exuI2 = $true )
& ( setminusERneg = $true )
& ( powersetI = $true )
& ( subsetI2 = $true )
& ( setminusLsub = $true )
& ( upairsetIL = $true )
& ( eqinunit = $true )
& ( sepSubset = $true )
& ( prop2set2propI = $true )
& ( exuE2 = $true )
& ( exuI1 = $true )
& ( setminusEL = $true )
& ( setunion__Cong = $true )
& ( setadjoinIR = $true )
& ( setadjoinSub = $true )
& ( setadjoinAx = $true )
& ( binunionEcases = $true )
& ( exuE3e = $true )
& ( setunionAx = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( subsetE = $true )
& ( symdiffE = $true )
& ( notsubsetI = $true )
& ( omegaIndAx = $true )
& ( binintersectLsub = $true )
& ( setminusI = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset3 = $true )
& ( notdallE = $true )
& ( secondinupair = $true )
& ( binintersectSubset4 = $true )
& ( exuI3 = $true )
& ( binintersectRsub = $true )
& ( exuEu = $true )
& ( binintersectER = $true )
& ( kpairiskpair = $true )
& ( setextAx = $true )
& ( symdiffIneg1 = $true )
& ( binunionE = $true )
& ( inCongP = $true )
& ( symdiffI1 = $true )
& ( binunionLsub = $true )
& ( binintersectEL = $true )
& ( binunionIR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f427,f428]) ).
thf(f428,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= $true ) )
=> ( ( ( in @ sK0 @ sK1 )
= $true )
& ( ( subset @ ( setadjoin @ sK0 @ emptyset ) @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f427,plain,
( ( binunionRsub = $true )
& ( replAx = $true )
& ( quantDeMorgan1 = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= $true ) )
& ( setoftrueEq = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset1 = $true )
& ( exuE1 = $true )
& ( emptyInPowerset = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan2 = $true )
& ( exu__Cong = $true )
& ( powersetsubset = $true )
& ( symdiffI2 = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( kpairp = $true )
& ( omega0Ax = $true )
& ( notinsingleton = $true )
& ( subsetTrans = $true )
& ( setextsub = $true )
& ( dsetconstrI = $true )
& ( dsetconstrER = $true )
& ( binintersectSubset5 = $true )
& ( upairsetIR = $true )
& ( setadjoinE = $true )
& ( setunionE = $true )
& ( in__Cong = $true )
& ( setadjoinSub2 = $true )
& ( noeltsimpempty = $true )
& ( setukpairIL = $true )
& ( uniqinunit = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( emptysetimpfalse = $true )
& ( emptyI = $true )
& ( binintersectI = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( inPowerset = $true )
& ( foundationAx = $true )
& ( nonemptyI1 = $true )
& ( subsetRefl = $true )
& ( bs114d = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetE = $true )
& ( binunionIL = $true )
& ( dsetconstrEL = $true )
& ( setadjoin__Cong = $true )
& ( subsetE2 = $true )
& ( setext = $true )
& ( powersetE = $true )
& ( symdiffIneg2 = $true )
& ( dsetconstr__Cong = $true )
& ( binintersectSubset2 = $true )
& ( prop2setI = $true )
& ( subset2powerset = $true )
& ( powerset__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetE = $true )
& ( nonemptyE1 = $true )
& ( setadjoinIL = $true )
& ( emptyset__Cong = $true )
& ( sepInPowerset = $true )
& ( setbeta = $true )
& ( subsetemptysetimpeq = $true )
& ( omegaSAx = $true )
& ( setminusSubset1 = $true )
& ( vacuousDall = $true )
& ( powersetAx = $true )
& ( notinemptyset = $true )
& ( disjointsetsI1 = $true )
& ( emptyE1 = $true )
& ( emptyinunitempty = $true )
& ( setminusIRneg = $true )
& ( eqimpsubset1 = $true )
& ( descr__Cong = $true )
& ( subsetI1 = $true )
& ( setukpairIR = $true )
& ( descrp = $true )
& ( notequalI2 = $true )
& ( exuE3u = $true )
& ( setminusER = $true )
& ( singletonsswitch = $true )
& ( eqimpsubset2 = $true )
& ( notequalI1 = $true )
& ( prop2setE = $true )
& ( setunionI = $true )
& ( notdexE = $true )
& ( exuI2 = $true )
& ( setminusERneg = $true )
& ( powersetI = $true )
& ( subsetI2 = $true )
& ( setminusLsub = $true )
& ( upairsetIL = $true )
& ( eqinunit = $true )
& ( sepSubset = $true )
& ( prop2set2propI = $true )
& ( exuE2 = $true )
& ( exuI1 = $true )
& ( setminusEL = $true )
& ( setunion__Cong = $true )
& ( setadjoinIR = $true )
& ( setadjoinSub = $true )
& ( setadjoinAx = $true )
& ( binunionEcases = $true )
& ( exuE3e = $true )
& ( setunionAx = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( subsetE = $true )
& ( symdiffE = $true )
& ( notsubsetI = $true )
& ( omegaIndAx = $true )
& ( binintersectLsub = $true )
& ( setminusI = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset3 = $true )
& ( notdallE = $true )
& ( secondinupair = $true )
& ( binintersectSubset4 = $true )
& ( exuI3 = $true )
& ( binintersectRsub = $true )
& ( exuEu = $true )
& ( binintersectER = $true )
& ( kpairiskpair = $true )
& ( setextAx = $true )
& ( symdiffIneg1 = $true )
& ( binunionE = $true )
& ( inCongP = $true )
& ( symdiffI1 = $true )
& ( binunionLsub = $true )
& ( binintersectEL = $true )
& ( binunionIR = $true ) ),
inference(flattening,[status(thm)],[f426]) ).
thf(f426,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
!= $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)],[f256]) ).
thf(f256,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f255]) ).
thf(f255,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
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ X1 )
=> ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f144]) ).
thf(f144,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
=> ! [X1: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ( subset @ ( setadjoin @ X1 @ emptyset ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f143]) ).
thf(f143,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
=> ! [X1: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ( subset @ ( setadjoin @ X1 @ emptyset ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2THF_9200.p',singletonsubset) ).
thf(f7605,plain,
( ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= ( in @ X2 @ ( powerset @ X1 ) ) )
= $true )
| ~ spl2_321 ),
inference(avatar_component_clause,[status(thm)],[f7604]) ).
thf(f7604,definition,
( spl2_321
<=> ! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= ( in @ X2 @ ( powerset @ X1 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_321])],[avatar_definition]) ).
thf(f16403,plain,
( ( ( in @ sK830 @ sK1 )
= $false )
| ~ spl2_312
| ~ spl2_321 ),
inference(binary_proxy_clausification,[status(thm)],[f16402]) ).
thf(f671,plain,
( ( in @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f429]) ).
thf(f15930,plain,
( ~ spl2_320
| ~ spl2_322 ),
inference(avatar_contradiction_clause,[status(thm)],[f15929]) ).
thf(f15929,plain,
( $false
| ~ spl2_320
| ~ spl2_322 ),
inference(trivial_inequality_removal,[status(thm)],[f15928]) ).
thf(f15928,plain,
( ( $true = $false )
| ~ spl2_320
| ~ spl2_322 ),
inference(backward_demodulation,[status(thm)],[f7601,f7609]) ).
thf(f7609,plain,
( ( powersetAx = $false )
| ~ spl2_322 ),
inference(avatar_component_clause,[status(thm)],[f7607]) ).
thf(f7607,definition,
( spl2_322
<=> ( powersetAx = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_322])],[avatar_definition]) ).
thf(f7601,plain,
( ( powersetAx = $true )
| ~ spl2_320 ),
inference(avatar_component_clause,[status(thm)],[f7599]) ).
thf(f7599,definition,
( spl2_320
<=> ( powersetAx = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_320])],[avatar_definition]) ).
thf(f12687,plain,
( ~ spl2_308
| ~ spl2_311 ),
inference(avatar_contradiction_clause,[status(thm)],[f12686]) ).
thf(f12686,plain,
( $false
| ~ spl2_308
| ~ spl2_311 ),
inference(trivial_inequality_removal,[status(thm)],[f12685]) ).
thf(f12685,plain,
( ( $true = $false )
| ~ spl2_308
| ~ spl2_311 ),
inference(forward_demodulation,[status(thm)],[f7550,f7564]) ).
thf(f7564,plain,
( ( powersetE1 = $false )
| ~ spl2_311 ),
inference(avatar_component_clause,[status(thm)],[f7562]) ).
thf(f7562,definition,
( spl2_311
<=> ( powersetE1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_311])],[avatar_definition]) ).
thf(f7550,plain,
( ( powersetE1 = $true )
| ~ spl2_308 ),
inference(avatar_component_clause,[status(thm)],[f7548]) ).
thf(f7548,definition,
( spl2_308
<=> ( powersetE1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_308])],[avatar_definition]) ).
thf(f12431,plain,
spl2_456,
inference(avatar_split_clause,[status(thm)],[f654,f8222]) ).
thf(f654,plain,
notinsingleton = $true,
inference(cnf_transformation,[status(thm)],[f429]) ).
thf(f12201,plain,
spl2_320,
inference(avatar_split_clause,[status(thm)],[f600,f7599]) ).
thf(f600,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f429]) ).
thf(f8238,plain,
( spl2_458
| spl2_459 ),
inference(avatar_split_clause,[status(thm)],[f4700,f8235,f8232]) ).
thf(f4700,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( notinsingleton = $false )
| ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f4699]) ).
thf(f4699,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false )
| ( notinsingleton = $false )
| ( ( X2 = X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f4698]) ).
thf(f4698,plain,
! [X2: $i,X1: $i] :
( ( ( X2 != X1 )
= $false )
| ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false )
| ( notinsingleton = $false ) ),
inference(not_proxy_clausification,[status(thm)],[f4697]) ).
thf(f4697,plain,
! [X2: $i,X1: $i] :
( ( notinsingleton = $false )
| ( $true
= ( ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( ( X2 != X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f4696]) ).
thf(f4696,plain,
! [X2: $i,X1: $i] :
( ( notinsingleton = $false )
| ( ( ( X2 != X1 )
=> ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f4695]) ).
thf(f4695,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( Y0 != X1 )
=> ~ ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 )
= $true )
| ( notinsingleton = $false ) ),
inference(pi_clausification,[status(thm)],[f4694]) ).
thf(f4694,plain,
! [X1: $i] :
( ( notinsingleton = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 != X1 )
=> ~ ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4693]) ).
thf(f4693,plain,
! [X1: $i] :
( ( notinsingleton = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f4692]) ).
thf(f4692,plain,
( ( notinsingleton = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f489]) ).
thf(f489,plain,
( notinsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
thf(f417,plain,
( notinsingleton
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 != Y0 )
=> ~ ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f416]) ).
thf(f416,plain,
( notinsingleton
= ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ~ ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,axiom,
( notinsingleton
= ( ! [X2: $i,X1: $i] :
( ( X1 != X2 )
=> ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2THF_9200.p',notinsingleton) ).
thf(f7723,plain,
spl2_308,
inference(avatar_split_clause,[status(thm)],[f658,f7548]) ).
thf(f658,plain,
powersetE1 = $true,
inference(cnf_transformation,[status(thm)],[f429]) ).
thf(f7610,plain,
( spl2_321
| spl2_322 ),
inference(avatar_split_clause,[status(thm)],[f5156,f7607,f7604]) ).
thf(f5156,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= ( in @ X2 @ ( powerset @ X1 ) ) )
= $true )
| ( powersetAx = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f5155]) ).
thf(f5155,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
= ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 )
= $true )
| ( powersetAx = $false ) ),
inference(pi_clausification,[status(thm)],[f5154]) ).
thf(f5154,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
= ( in @ Y0 @ ( powerset @ X1 ) ) ) ) )
| ( powersetAx = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f5153]) ).
thf(f5153,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 ) )
| ( powersetAx = $false ) ),
inference(pi_clausification,[status(thm)],[f5152]) ).
thf(f5152,plain,
( ( powersetAx = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f441]) ).
thf(f441,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f270]) ).
thf(f270,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
= ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f269]) ).
thf(f269,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
<=> ( in @ X0 @ ( powerset @ X1 ) ) )
= powersetAx ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X4: $i,X3: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
<=> ( in @ X4 @ ( powerset @ X3 ) ) )
= powersetAx ),
file('/export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2THF_9200.p',powersetAx) ).
thf(f7568,plain,
( spl2_311
| spl2_312 ),
inference(avatar_split_clause,[status(thm)],[f5194,f7566,f7562]) ).
thf(f5194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( powersetE1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f5193]) ).
thf(f5193,plain,
! [X2: $i,X1: $i] :
( ( powersetE1 = $false )
| ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f5192]) ).
thf(f5192,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( powersetE1 = $false ) ),
inference(pi_clausification,[status(thm)],[f5191]) ).
thf(f5191,plain,
! [X1: $i] :
( ( powersetE1 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f5190]) ).
thf(f5190,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( powersetE1 = $false ) ),
inference(pi_clausification,[status(thm)],[f5189]) ).
thf(f5189,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) )
| ( powersetE1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f518]) ).
thf(f518,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
thf(f392,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f391]) ).
thf(f391,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
inference(rectify,[status(thm)],[f96]) ).
thf(f96,axiom,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) )
= powersetE1 ),
file('/export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2THF_9200.p',powersetE1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU621^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n022.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 12:28:36 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
% 0.17/0.38 ---- Original DTF file ---
% 0.17/0.38 thf(spec,logic,$$dhol).
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 % File : SEU621^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.38 % Domain : Set Theory
% 0.17/0.38 % Problem : Ordered Pairs - Cartesian Products
% 0.17/0.38 % Version : Especial.
% 0.17/0.38 % English : (! A:i.! x:i.in x A -> subset (setadjoin x emptyset) A)
% 0.17/0.38
% 0.17/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.38 % Source : [Bro08]
% 0.17/0.38 % Names : ZFC123g [Bro08]
% 0.17/0.38
% 0.17/0.38 % Status : Theorem
% 0.17/0.38 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v6.0.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.17/0.38 % Syntax : Number of formulae : 303 ( 142 unt; 160 typ; 142 def)
% 0.17/0.38 % Number of atoms : 748 ( 201 equ; 0 cnn)
% 0.17/0.38 % Maximal formula atoms : 139 ( 5 avg)
% 0.17/0.38 % Number of connectives : 1252 ( 47 ~; 6 |; 32 &; 825 @)
% 0.17/0.38 % ( 14 <=>; 328 =>; 0 <=; 0 <~>)
% 0.17/0.38 % Maximal formula depth : 145 ( 2 avg)
% 0.17/0.38 % Number of types : 2 ( 0 usr)
% 0.17/0.38 % Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% 0.17/0.38 % Number of symbols : 163 ( 160 usr; 141 con; 0-2 aty)
% 0.17/0.38 % Number of variables : 408 ( 36 ^; 339 !; 33 ?; 408 :)
% 0.17/0.38 % SPC : TH0_THM_EQU_NAR
% 0.17/0.38
% 0.17/0.38 % Comments : http://mathgate.info/detsetitem.php?id=178
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 thf(in_type,type,
% 0.17/0.38 in: $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(exu_type,type,
% 0.17/0.38 exu: ( $i > $o ) > $o ).
% 0.17/0.38
% 0.17/0.38 thf(exu,definition,
% 0.17/0.38 ( exu
% 0.17/0.38 = ( ^ [Xphi: $i > $o] :
% 0.17/0.38 ? [Xx: $i] :
% 0.17/0.38 ( ( Xphi @ Xx )
% 0.17/0.38 & ! [Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xy )
% 0.17/0.38 => ( Xx = Xy ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setextAx_type,type,
% 0.17/0.38 setextAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setextAx,definition,
% 0.17/0.38 ( setextAx
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 <=> ( in @ Xx @ B ) )
% 0.17/0.38 => ( A = B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptyset_type,type,
% 0.17/0.38 emptyset: $i ).
% 0.17/0.38
% 0.17/0.38 thf(emptysetAx_type,type,
% 0.17/0.38 emptysetAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptysetAx,definition,
% 0.17/0.38 ( emptysetAx
% 0.17/0.38 = ( ! [Xx: $i] :
% 0.17/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoin_type,type,
% 0.17/0.38 setadjoin: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinAx_type,type,
% 0.17/0.38 setadjoinAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinAx,definition,
% 0.17/0.38 ( setadjoinAx
% 0.17/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.38 <=> ( ( Xy = Xx )
% 0.17/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(powerset_type,type,
% 0.17/0.38 powerset: $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(powersetAx_type,type,
% 0.17/0.38 powersetAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(powersetAx,definition,
% 0.17/0.38 ( powersetAx
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.38 <=> ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setunion_type,type,
% 0.17/0.38 setunion: $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(setunionAx_type,type,
% 0.17/0.38 setunionAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setunionAx,definition,
% 0.17/0.38 ( setunionAx
% 0.17/0.38 = ( ! [A: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.38 <=> ? [B: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 & ( in @ B @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(omega_type,type,
% 0.17/0.38 omega: $i ).
% 0.17/0.38
% 0.17/0.38 thf(omega0Ax_type,type,
% 0.17/0.38 omega0Ax: $o ).
% 0.17/0.38
% 0.17/0.38 thf(omega0Ax,definition,
% 0.17/0.38 ( omega0Ax
% 0.17/0.38 = ( in @ emptyset @ omega ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(omegaSAx_type,type,
% 0.17/0.38 omegaSAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(omegaSAx,definition,
% 0.17/0.38 ( omegaSAx
% 0.17/0.38 = ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ omega )
% 0.17/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(omegaIndAx_type,type,
% 0.17/0.38 omegaIndAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(omegaIndAx,definition,
% 0.17/0.38 ( omegaIndAx
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ( ( in @ emptyset @ A )
% 0.17/0.38 & ! [Xx: $i] :
% 0.17/0.38 ( ( ( in @ Xx @ omega )
% 0.17/0.38 & ( in @ Xx @ A ) )
% 0.17/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.17/0.38 => ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ omega )
% 0.17/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(replAx_type,type,
% 0.17/0.38 replAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(replAx,definition,
% 0.17/0.38 ( replAx
% 0.17/0.38 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( exu
% 0.17/0.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.17/0.38 => ? [B: $i] :
% 0.17/0.38 ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 <=> ? [Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ A )
% 0.17/0.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(foundationAx_type,type,
% 0.17/0.38 foundationAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(foundationAx,definition,
% 0.17/0.38 ( foundationAx
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.38 => ? [B: $i] :
% 0.17/0.38 ( ( in @ B @ A )
% 0.17/0.38 & ~ ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(wellorderingAx_type,type,
% 0.17/0.38 wellorderingAx: $o ).
% 0.17/0.38
% 0.17/0.38 thf(wellorderingAx,definition,
% 0.17/0.38 ( wellorderingAx
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ? [B: $i] :
% 0.17/0.38 ( ! [C: $i] :
% 0.17/0.38 ( ( in @ C @ B )
% 0.17/0.38 => ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ C )
% 0.17/0.38 => ( in @ Xx @ A ) ) )
% 0.17/0.38 & ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( ( in @ Xx @ A )
% 0.17/0.38 & ( in @ Xy @ A ) )
% 0.17/0.38 => ( ! [C: $i] :
% 0.17/0.38 ( ( in @ C @ B )
% 0.17/0.38 => ( ( in @ Xx @ C )
% 0.17/0.38 <=> ( in @ Xy @ C ) ) )
% 0.17/0.38 => ( Xx = Xy ) ) )
% 0.17/0.38 & ! [C: $i,D: $i] :
% 0.17/0.38 ( ( ( in @ C @ B )
% 0.17/0.38 & ( in @ D @ B ) )
% 0.17/0.38 => ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ C )
% 0.17/0.38 => ( in @ Xx @ D ) )
% 0.17/0.38 | ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ D )
% 0.17/0.38 => ( in @ Xx @ C ) ) ) )
% 0.17/0.38 & ! [C: $i] :
% 0.17/0.38 ( ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ C )
% 0.17/0.38 => ( in @ Xx @ A ) )
% 0.17/0.38 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.17/0.38 => ? [D: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ D @ B )
% 0.17/0.38 & ( in @ Xx @ C )
% 0.17/0.38 & ~ ? [Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ D )
% 0.17/0.38 & ( in @ Xy @ C ) )
% 0.17/0.38 & ! [E: $i] :
% 0.17/0.38 ( ( in @ E @ B )
% 0.17/0.38 => ( ! [Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ E )
% 0.17/0.38 => ( in @ Xy @ D ) )
% 0.17/0.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(descr_type,type,
% 0.17/0.38 descr: ( $i > $o ) > $i ).
% 0.17/0.38
% 0.17/0.38 thf(descrp_type,type,
% 0.17/0.38 descrp: $o ).
% 0.17/0.38
% 0.17/0.38 thf(descrp,definition,
% 0.17/0.38 ( descrp
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 => ( Xphi
% 0.17/0.38 @ ( descr
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstr_type,type,
% 0.17/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrI_type,type,
% 0.17/0.38 dsetconstrI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrI,definition,
% 0.17/0.38 ( dsetconstrI
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ( Xphi @ Xx )
% 0.17/0.38 => ( in @ Xx
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrEL_type,type,
% 0.17/0.38 dsetconstrEL: $o ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrEL,definition,
% 0.17/0.38 ( dsetconstrEL
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrER_type,type,
% 0.17/0.38 dsetconstrER: $o ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstrER,definition,
% 0.17/0.38 ( dsetconstrER
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuE1_type,type,
% 0.17/0.38 exuE1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exuE1,definition,
% 0.17/0.38 ( exuE1
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 => ? [Xx: $i] :
% 0.17/0.38 ( ( Xphi @ Xx )
% 0.17/0.38 & ! [Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xy )
% 0.17/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(prop2set_type,type,
% 0.17/0.38 prop2set: $o > $i ).
% 0.17/0.38
% 0.17/0.38 thf(prop2setE_type,type,
% 0.17/0.38 prop2setE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(prop2setE,definition,
% 0.17/0.38 ( prop2setE
% 0.17/0.38 = ( ! [Xphi: $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.17/0.38 => Xphi ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptysetE_type,type,
% 0.17/0.38 emptysetE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptysetE,definition,
% 0.17/0.38 ( emptysetE
% 0.17/0.38 = ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ emptyset )
% 0.17/0.38 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptysetimpfalse_type,type,
% 0.17/0.38 emptysetimpfalse: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptysetimpfalse,definition,
% 0.17/0.38 ( emptysetimpfalse
% 0.17/0.38 = ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ emptyset )
% 0.17/0.38 => $false ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(notinemptyset_type,type,
% 0.17/0.38 notinemptyset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(notinemptyset,definition,
% 0.17/0.38 ( notinemptyset
% 0.17/0.38 = ( ! [Xx: $i] :
% 0.17/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuE3e_type,type,
% 0.17/0.38 exuE3e: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exuE3e,definition,
% 0.17/0.38 ( exuE3e
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setext_type,type,
% 0.17/0.38 setext: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setext,definition,
% 0.17/0.38 ( setext
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ Xx @ B ) )
% 0.17/0.38 => ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ A ) )
% 0.17/0.38 => ( A = B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptyI_type,type,
% 0.17/0.38 emptyI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptyI,definition,
% 0.17/0.38 ( emptyI
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ~ ( in @ Xx @ A )
% 0.17/0.38 => ( A = emptyset ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(noeltsimpempty_type,type,
% 0.17/0.38 noeltsimpempty: $o ).
% 0.17/0.38
% 0.17/0.38 thf(noeltsimpempty,definition,
% 0.17/0.38 ( noeltsimpempty
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ~ ( in @ Xx @ A )
% 0.17/0.38 => ( A = emptyset ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setbeta_type,type,
% 0.17/0.38 setbeta: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setbeta,definition,
% 0.17/0.38 ( setbeta
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ( in @ Xx
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.38 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(nonempty_type,type,
% 0.17/0.38 nonempty: $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(nonempty,definition,
% 0.17/0.38 ( nonempty
% 0.17/0.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(nonemptyE1_type,type,
% 0.17/0.38 nonemptyE1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(nonemptyE1,definition,
% 0.17/0.38 ( nonemptyE1
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ( nonempty @ A )
% 0.17/0.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(nonemptyI_type,type,
% 0.17/0.38 nonemptyI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(nonemptyI,definition,
% 0.17/0.38 ( nonemptyI
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ( Xphi @ Xx )
% 0.17/0.38 => ( nonempty
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(nonemptyI1_type,type,
% 0.17/0.38 nonemptyI1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(nonemptyI1,definition,
% 0.17/0.38 ( nonemptyI1
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.38 => ( nonempty @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinIL_type,type,
% 0.17/0.38 setadjoinIL: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinIL,definition,
% 0.17/0.38 ( setadjoinIL
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptyinunitempty_type,type,
% 0.17/0.38 emptyinunitempty: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptyinunitempty,definition,
% 0.17/0.38 ( emptyinunitempty
% 0.17/0.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinIR_type,type,
% 0.17/0.38 setadjoinIR: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinIR,definition,
% 0.17/0.38 ( setadjoinIR
% 0.17/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ A )
% 0.17/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinE_type,type,
% 0.17/0.38 setadjoinE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinE,definition,
% 0.17/0.38 ( setadjoinE
% 0.17/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.38 => ! [Xphi: $o] :
% 0.17/0.38 ( ( ( Xy = Xx )
% 0.17/0.38 => Xphi )
% 0.17/0.38 => ( ( ( in @ Xy @ A )
% 0.17/0.38 => Xphi )
% 0.17/0.38 => Xphi ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinOr_type,type,
% 0.17/0.38 setadjoinOr: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinOr,definition,
% 0.17/0.38 ( setadjoinOr
% 0.17/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.38 => ( ( Xy = Xx )
% 0.17/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setoftrueEq_type,type,
% 0.17/0.38 setoftrueEq: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setoftrueEq,definition,
% 0.17/0.38 ( setoftrueEq
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xx: $i] : $true )
% 0.17/0.38 = A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(powersetI_type,type,
% 0.17/0.38 powersetI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(powersetI,definition,
% 0.17/0.38 ( powersetI
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ A ) )
% 0.17/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptyinPowerset_type,type,
% 0.17/0.38 emptyinPowerset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptyinPowerset,definition,
% 0.17/0.38 ( emptyinPowerset
% 0.17/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptyInPowerset_type,type,
% 0.17/0.38 emptyInPowerset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptyInPowerset,definition,
% 0.17/0.38 ( emptyInPowerset
% 0.17/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(powersetE_type,type,
% 0.17/0.38 powersetE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(powersetE,definition,
% 0.17/0.38 ( powersetE
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.38 => ( ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setunionI_type,type,
% 0.17/0.38 setunionI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setunionI,definition,
% 0.17/0.38 ( setunionI
% 0.17/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 => ( ( in @ B @ A )
% 0.17/0.38 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setunionE_type,type,
% 0.17/0.38 setunionE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setunionE,definition,
% 0.17/0.38 ( setunionE
% 0.17/0.38 = ( ! [A: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.38 => ! [Xphi: $o] :
% 0.17/0.38 ( ! [B: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 => ( ( in @ B @ A )
% 0.17/0.38 => Xphi ) )
% 0.17/0.38 => Xphi ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subPowSU_type,type,
% 0.17/0.38 subPowSU: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subPowSU,definition,
% 0.17/0.38 ( subPowSU
% 0.17/0.38 = ( ! [A: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuE2_type,type,
% 0.17/0.38 exuE2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exuE2,definition,
% 0.17/0.38 ( exuE2
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 => ? [Xx: $i] :
% 0.17/0.38 ! [Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xy )
% 0.17/0.38 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(nonemptyImpWitness_type,type,
% 0.17/0.38 nonemptyImpWitness: $o ).
% 0.17/0.38
% 0.17/0.38 thf(nonemptyImpWitness,definition,
% 0.17/0.38 ( nonemptyImpWitness
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ( nonempty @ A )
% 0.17/0.38 => ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & $true ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(uniqinunit_type,type,
% 0.17/0.38 uniqinunit: $o ).
% 0.17/0.38
% 0.17/0.38 thf(uniqinunit,definition,
% 0.17/0.38 ( uniqinunit
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(notinsingleton_type,type,
% 0.17/0.38 notinsingleton: $o ).
% 0.17/0.38
% 0.17/0.38 thf(notinsingleton,definition,
% 0.17/0.38 ( notinsingleton
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xx != Xy )
% 0.17/0.38 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(eqinunit_type,type,
% 0.17/0.38 eqinunit: $o ).
% 0.17/0.38
% 0.17/0.38 thf(eqinunit,definition,
% 0.17/0.38 ( eqinunit
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xx = Xy )
% 0.17/0.38 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(singletonsswitch_type,type,
% 0.17/0.38 singletonsswitch: $o ).
% 0.17/0.38
% 0.17/0.38 thf(singletonsswitch,definition,
% 0.17/0.38 ( singletonsswitch
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(upairsetE_type,type,
% 0.17/0.38 upairsetE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(upairsetE,definition,
% 0.17/0.38 ( upairsetE
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.17/0.38 => ( ( Xz = Xx )
% 0.17/0.38 | ( Xz = Xy ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(upairsetIL_type,type,
% 0.17/0.38 upairsetIL: $o ).
% 0.17/0.38
% 0.17/0.38 thf(upairsetIL,definition,
% 0.17/0.38 ( upairsetIL
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(upairsetIR_type,type,
% 0.17/0.38 upairsetIR: $o ).
% 0.17/0.38
% 0.17/0.38 thf(upairsetIR,definition,
% 0.17/0.38 ( upairsetIR
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptyE1_type,type,
% 0.17/0.38 emptyE1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptyE1,definition,
% 0.17/0.38 ( emptyE1
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ( Xphi @ Xx ) )
% 0.17/0.38 => ( ( ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 = emptyset )
% 0.17/0.38 => $false ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(vacuousDall_type,type,
% 0.17/0.38 vacuousDall: $o ).
% 0.17/0.38
% 0.17/0.38 thf(vacuousDall,definition,
% 0.17/0.38 ( vacuousDall
% 0.17/0.38 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ emptyset )
% 0.17/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(quantDeMorgan1_type,type,
% 0.17/0.38 quantDeMorgan1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(quantDeMorgan1,definition,
% 0.17/0.38 ( quantDeMorgan1
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( ~ ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( Xphi @ Xx ) )
% 0.17/0.38 => ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(quantDeMorgan2_type,type,
% 0.17/0.38 quantDeMorgan2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(quantDeMorgan2,definition,
% 0.17/0.38 ( quantDeMorgan2
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ~ ( Xphi @ Xx ) )
% 0.17/0.38 => ~ ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(quantDeMorgan3_type,type,
% 0.17/0.38 quantDeMorgan3: $o ).
% 0.17/0.38
% 0.17/0.38 thf(quantDeMorgan3,definition,
% 0.17/0.38 ( quantDeMorgan3
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( ~ ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ( Xphi @ Xx ) )
% 0.17/0.38 => ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(quantDeMorgan4_type,type,
% 0.17/0.38 quantDeMorgan4: $o ).
% 0.17/0.38
% 0.17/0.38 thf(quantDeMorgan4,definition,
% 0.17/0.38 ( quantDeMorgan4
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ~ ( Xphi @ Xx ) )
% 0.17/0.38 => ~ ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(prop2setI_type,type,
% 0.17/0.38 prop2setI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(prop2setI,definition,
% 0.17/0.38 ( prop2setI
% 0.17/0.38 = ( ! [Xphi: $o] :
% 0.17/0.38 ( Xphi
% 0.17/0.38 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(set2prop_type,type,
% 0.17/0.38 set2prop: $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(prop2set2propI_type,type,
% 0.17/0.38 prop2set2propI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(prop2set2propI,definition,
% 0.17/0.38 ( prop2set2propI
% 0.17/0.38 = ( ! [Xphi: $o] :
% 0.17/0.38 ( Xphi
% 0.17/0.38 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(notdexE_type,type,
% 0.17/0.38 notdexE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(notdexE,definition,
% 0.17/0.38 ( notdexE
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( ~ ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ( Xphi @ Xx ) )
% 0.17/0.38 => ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(notdallE_type,type,
% 0.17/0.38 notdallE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(notdallE,definition,
% 0.17/0.38 ( notdallE
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( ~ ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( Xphi @ Xx ) )
% 0.17/0.38 => ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuI1_type,type,
% 0.17/0.38 exuI1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exuI1,definition,
% 0.17/0.38 ( exuI1
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ? [Xx: $i] :
% 0.17/0.38 ( ( Xphi @ Xx )
% 0.17/0.38 & ! [Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xy )
% 0.17/0.38 => ( Xx = Xy ) ) )
% 0.17/0.38 => ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuI3_type,type,
% 0.17/0.38 exuI3: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exuI3,definition,
% 0.17/0.38 ( exuI3
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.17/0.38 => ( ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xx )
% 0.17/0.38 => ( ( Xphi @ Xy )
% 0.17/0.38 => ( Xx = Xy ) ) )
% 0.17/0.38 => ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuI2_type,type,
% 0.17/0.38 exuI2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exuI2,definition,
% 0.17/0.38 ( exuI2
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ? [Xx: $i] :
% 0.17/0.38 ! [Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xy )
% 0.17/0.38 <=> ( Xy = Xx ) )
% 0.17/0.38 => ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(inCongP_type,type,
% 0.17/0.38 inCongP: $o ).
% 0.17/0.38
% 0.17/0.38 thf(inCongP,definition,
% 0.17/0.38 ( inCongP
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( A = B )
% 0.17/0.38 => ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xx = Xy )
% 0.17/0.38 => ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(in__Cong_type,type,
% 0.17/0.38 in__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(in__Cong,definition,
% 0.17/0.38 ( in__Cong
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( A = B )
% 0.17/0.38 => ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xx = Xy )
% 0.17/0.38 => ( ( in @ Xx @ A )
% 0.17/0.38 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuE3u_type,type,
% 0.17/0.38 exuE3u: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exuE3u,definition,
% 0.17/0.38 ( exuE3u
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 => ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xx )
% 0.17/0.38 => ( ( Xphi @ Xy )
% 0.17/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exu__Cong_type,type,
% 0.17/0.38 exu__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exu__Cong,definition,
% 0.17/0.38 ( exu__Cong
% 0.17/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xx = Xy )
% 0.17/0.38 => ( ( Xphi @ Xx )
% 0.17/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.17/0.38 => ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 <=> ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptyset__Cong_type,type,
% 0.17/0.38 emptyset__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptyset__Cong,definition,
% 0.17/0.38 ( emptyset__Cong
% 0.17/0.38 = ( emptyset = emptyset ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoin__Cong_type,type,
% 0.17/0.38 setadjoin__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoin__Cong,definition,
% 0.17/0.38 ( setadjoin__Cong
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xx = Xy )
% 0.17/0.38 => ! [Xz: $i,Xu: $i] :
% 0.17/0.38 ( ( Xz = Xu )
% 0.17/0.38 => ( ( setadjoin @ Xx @ Xz )
% 0.17/0.38 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(powerset__Cong_type,type,
% 0.17/0.38 powerset__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(powerset__Cong,definition,
% 0.17/0.38 ( powerset__Cong
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( A = B )
% 0.17/0.38 => ( ( powerset @ A )
% 0.17/0.38 = ( powerset @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setunion__Cong_type,type,
% 0.17/0.38 setunion__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setunion__Cong,definition,
% 0.17/0.38 ( setunion__Cong
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( A = B )
% 0.17/0.38 => ( ( setunion @ A )
% 0.17/0.38 = ( setunion @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(omega__Cong_type,type,
% 0.17/0.38 omega__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(omega__Cong,definition,
% 0.17/0.38 ( omega__Cong
% 0.17/0.38 = ( omega = omega ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(exuEu_type,type,
% 0.17/0.38 exuEu: $o ).
% 0.17/0.38
% 0.17/0.38 thf(exuEu,definition,
% 0.17/0.38 ( exuEu
% 0.17/0.38 = ( ! [Xphi: $i > $o] :
% 0.17/0.38 ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 => ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xphi @ Xx )
% 0.17/0.38 => ( ( Xphi @ Xy )
% 0.17/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(descr__Cong_type,type,
% 0.17/0.38 descr__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(descr__Cong,definition,
% 0.17/0.38 ( descr__Cong
% 0.17/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.38 ( ( Xx = Xy )
% 0.17/0.38 => ( ( Xphi @ Xx )
% 0.17/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.17/0.38 => ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 => ( ( exu
% 0.17/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.17/0.38 => ( ( descr
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 = ( descr
% 0.17/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstr__Cong_type,type,
% 0.17/0.38 dsetconstr__Cong: $o ).
% 0.17/0.38
% 0.17/0.38 thf(dsetconstr__Cong,definition,
% 0.17/0.38 ( dsetconstr__Cong
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( A = B )
% 0.17/0.38 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ! [Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ B )
% 0.17/0.38 => ( ( Xx = Xy )
% 0.17/0.38 => ( ( Xphi @ Xx )
% 0.17/0.38 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.17/0.38 => ( ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 = ( dsetconstr @ B
% 0.17/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subset_type,type,
% 0.17/0.38 subset: $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(disjoint_type,type,
% 0.17/0.38 disjoint: $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(setsmeet_type,type,
% 0.17/0.38 setsmeet: $i > $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(subsetI1_type,type,
% 0.17/0.38 subsetI1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subsetI1,definition,
% 0.17/0.38 ( subsetI1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ Xx @ B ) )
% 0.17/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(eqimpsubset2_type,type,
% 0.17/0.38 eqimpsubset2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(eqimpsubset2,definition,
% 0.17/0.38 ( eqimpsubset2
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( A = B )
% 0.17/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(eqimpsubset1_type,type,
% 0.17/0.38 eqimpsubset1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(eqimpsubset1,definition,
% 0.17/0.38 ( eqimpsubset1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( A = B )
% 0.17/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subsetI2_type,type,
% 0.17/0.38 subsetI2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subsetI2,definition,
% 0.17/0.38 ( subsetI2
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ! [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ Xx @ B ) )
% 0.17/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(emptysetsubset_type,type,
% 0.17/0.38 emptysetsubset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(emptysetsubset,definition,
% 0.17/0.38 ( emptysetsubset
% 0.17/0.38 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subsetE_type,type,
% 0.17/0.38 subsetE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subsetE,definition,
% 0.17/0.38 ( subsetE
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subsetE2_type,type,
% 0.17/0.38 subsetE2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subsetE2,definition,
% 0.17/0.38 ( subsetE2
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( ~ ( in @ Xx @ B )
% 0.17/0.38 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(notsubsetI_type,type,
% 0.17/0.38 notsubsetI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(notsubsetI,definition,
% 0.17/0.38 ( notsubsetI
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ~ ( in @ Xx @ B )
% 0.17/0.38 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(notequalI1_type,type,
% 0.17/0.38 notequalI1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(notequalI1,definition,
% 0.17/0.38 ( notequalI1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ~ ( subset @ A @ B )
% 0.17/0.38 => ( A != B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(notequalI2_type,type,
% 0.17/0.38 notequalI2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(notequalI2,definition,
% 0.17/0.38 ( notequalI2
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ~ ( in @ Xx @ B )
% 0.17/0.38 => ( A != B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subsetRefl_type,type,
% 0.17/0.38 subsetRefl: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subsetRefl,definition,
% 0.17/0.38 ( subsetRefl
% 0.17/0.38 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subsetTrans_type,type,
% 0.17/0.38 subsetTrans: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subsetTrans,definition,
% 0.17/0.38 ( subsetTrans
% 0.17/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( ( subset @ B @ C )
% 0.17/0.38 => ( subset @ A @ C ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinSub_type,type,
% 0.17/0.38 setadjoinSub: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinSub,definition,
% 0.17/0.38 ( setadjoinSub
% 0.17/0.38 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinSub2_type,type,
% 0.17/0.38 setadjoinSub2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setadjoinSub2,definition,
% 0.17/0.38 ( setadjoinSub2
% 0.17/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subset2powerset_type,type,
% 0.17/0.38 subset2powerset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subset2powerset,definition,
% 0.17/0.38 ( subset2powerset
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setextsub_type,type,
% 0.17/0.38 setextsub: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setextsub,definition,
% 0.17/0.38 ( setextsub
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( ( subset @ B @ A )
% 0.17/0.38 => ( A = B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(subsetemptysetimpeq_type,type,
% 0.17/0.38 subsetemptysetimpeq: $o ).
% 0.17/0.38
% 0.17/0.38 thf(subsetemptysetimpeq,definition,
% 0.17/0.38 ( subsetemptysetimpeq
% 0.17/0.38 = ( ! [A: $i] :
% 0.17/0.38 ( ( subset @ A @ emptyset )
% 0.17/0.38 => ( A = emptyset ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(powersetI1_type,type,
% 0.17/0.38 powersetI1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(powersetI1,definition,
% 0.17/0.38 ( powersetI1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( subset @ B @ A )
% 0.17/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(powersetE1_type,type,
% 0.17/0.38 powersetE1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(powersetE1,definition,
% 0.17/0.38 ( powersetE1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(inPowerset_type,type,
% 0.17/0.38 inPowerset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(inPowerset,definition,
% 0.17/0.38 ( inPowerset
% 0.17/0.38 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(powersetsubset_type,type,
% 0.17/0.38 powersetsubset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(powersetsubset,definition,
% 0.17/0.38 ( powersetsubset
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sepInPowerset_type,type,
% 0.17/0.38 sepInPowerset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(sepInPowerset,definition,
% 0.17/0.38 ( sepInPowerset
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( in
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 @ ( powerset @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(sepSubset_type,type,
% 0.17/0.38 sepSubset: $o ).
% 0.17/0.38
% 0.17/0.38 thf(sepSubset,definition,
% 0.17/0.38 ( sepSubset
% 0.17/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.38 ( subset
% 0.17/0.38 @ ( dsetconstr @ A
% 0.17/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.38 @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binunion_type,type,
% 0.17/0.38 binunion: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(binunionIL_type,type,
% 0.17/0.38 binunionIL: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binunionIL,definition,
% 0.17/0.38 ( binunionIL
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(upairset2IR_type,type,
% 0.17/0.38 upairset2IR: $o ).
% 0.17/0.38
% 0.17/0.38 thf(upairset2IR,definition,
% 0.17/0.38 ( upairset2IR
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binunionIR_type,type,
% 0.17/0.38 binunionIR: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binunionIR,definition,
% 0.17/0.38 ( binunionIR
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binunionEcases_type,type,
% 0.17/0.38 binunionEcases: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binunionEcases,definition,
% 0.17/0.38 ( binunionEcases
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.17/0.38 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.17/0.38 => ( ( ( in @ Xx @ A )
% 0.17/0.38 => Xphi )
% 0.17/0.38 => ( ( ( in @ Xx @ B )
% 0.17/0.38 => Xphi )
% 0.17/0.38 => Xphi ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binunionE_type,type,
% 0.17/0.38 binunionE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binunionE,definition,
% 0.17/0.38 ( binunionE
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.17/0.38 => ( ( in @ Xx @ A )
% 0.17/0.38 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binunionLsub_type,type,
% 0.17/0.38 binunionLsub: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binunionLsub,definition,
% 0.17/0.38 ( binunionLsub
% 0.17/0.38 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binunionRsub_type,type,
% 0.17/0.38 binunionRsub: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binunionRsub,definition,
% 0.17/0.38 ( binunionRsub
% 0.17/0.38 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersect_type,type,
% 0.17/0.38 binintersect: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectI_type,type,
% 0.17/0.38 binintersectI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectI,definition,
% 0.17/0.38 ( binintersectI
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset5_type,type,
% 0.17/0.38 binintersectSubset5: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset5,definition,
% 0.17/0.38 ( binintersectSubset5
% 0.17/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.38 ( ( subset @ C @ A )
% 0.17/0.38 => ( ( subset @ C @ B )
% 0.17/0.38 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectEL_type,type,
% 0.17/0.38 binintersectEL: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectEL,definition,
% 0.17/0.38 ( binintersectEL
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.17/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectLsub_type,type,
% 0.17/0.38 binintersectLsub: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectLsub,definition,
% 0.17/0.38 ( binintersectLsub
% 0.17/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset2_type,type,
% 0.17/0.38 binintersectSubset2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset2,definition,
% 0.17/0.38 ( binintersectSubset2
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( ( binintersect @ A @ B )
% 0.17/0.38 = A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset3_type,type,
% 0.17/0.38 binintersectSubset3: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset3,definition,
% 0.17/0.38 ( binintersectSubset3
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( ( binintersect @ A @ B )
% 0.17/0.38 = B )
% 0.17/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectER_type,type,
% 0.17/0.38 binintersectER: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectER,definition,
% 0.17/0.38 ( binintersectER
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.17/0.38 => ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(disjointsetsI1_type,type,
% 0.17/0.38 disjointsetsI1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(disjointsetsI1,definition,
% 0.17/0.38 ( disjointsetsI1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ~ ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 & ( in @ Xx @ B ) )
% 0.17/0.38 => ( ( binintersect @ A @ B )
% 0.17/0.38 = emptyset ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectRsub_type,type,
% 0.17/0.38 binintersectRsub: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectRsub,definition,
% 0.17/0.38 ( binintersectRsub
% 0.17/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset4_type,type,
% 0.17/0.38 binintersectSubset4: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset4,definition,
% 0.17/0.38 ( binintersectSubset4
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( subset @ B @ A )
% 0.17/0.38 => ( ( binintersect @ A @ B )
% 0.17/0.38 = B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset1_type,type,
% 0.17/0.38 binintersectSubset1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(binintersectSubset1,definition,
% 0.17/0.38 ( binintersectSubset1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( ( binintersect @ A @ B )
% 0.17/0.38 = A )
% 0.17/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(bs114d_type,type,
% 0.17/0.38 bs114d: $o ).
% 0.17/0.38
% 0.17/0.38 thf(bs114d,definition,
% 0.17/0.38 ( bs114d
% 0.17/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.38 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.17/0.38 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(regular_type,type,
% 0.17/0.38 regular: $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminus_type,type,
% 0.17/0.38 setminus: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(setminusI_type,type,
% 0.17/0.38 setminusI: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusI,definition,
% 0.17/0.38 ( setminusI
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ~ ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusEL_type,type,
% 0.17/0.38 setminusEL: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusEL,definition,
% 0.17/0.38 ( setminusEL
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusER_type,type,
% 0.17/0.38 setminusER: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusER,definition,
% 0.17/0.38 ( setminusER
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.38 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusSubset2_type,type,
% 0.17/0.38 setminusSubset2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusSubset2,definition,
% 0.17/0.38 ( setminusSubset2
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( subset @ A @ B )
% 0.17/0.38 => ( ( setminus @ A @ B )
% 0.17/0.38 = emptyset ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusERneg_type,type,
% 0.17/0.38 setminusERneg: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusERneg,definition,
% 0.17/0.38 ( setminusERneg
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.38 => ( ( in @ Xx @ A )
% 0.17/0.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusELneg_type,type,
% 0.17/0.38 setminusELneg: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusELneg,definition,
% 0.17/0.38 ( setminusELneg
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.38 => ( ~ ( in @ Xx @ B )
% 0.17/0.38 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusILneg_type,type,
% 0.17/0.38 setminusILneg: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusILneg,definition,
% 0.17/0.38 ( setminusILneg
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ~ ( in @ Xx @ A )
% 0.17/0.38 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusIRneg_type,type,
% 0.17/0.38 setminusIRneg: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusIRneg,definition,
% 0.17/0.38 ( setminusIRneg
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ B )
% 0.17/0.38 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusLsub_type,type,
% 0.17/0.38 setminusLsub: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusLsub,definition,
% 0.17/0.38 ( setminusLsub
% 0.17/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setminusSubset1_type,type,
% 0.17/0.38 setminusSubset1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setminusSubset1,definition,
% 0.17/0.38 ( setminusSubset1
% 0.17/0.38 = ( ! [A: $i,B: $i] :
% 0.17/0.38 ( ( ( setminus @ A @ B )
% 0.17/0.38 = emptyset )
% 0.17/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(symdiff_type,type,
% 0.17/0.38 symdiff: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffE_type,type,
% 0.17/0.38 symdiffE: $o ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffE,definition,
% 0.17/0.38 ( symdiffE
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.17/0.38 => ! [Xphi: $o] :
% 0.17/0.38 ( ( ( in @ Xx @ A )
% 0.17/0.38 => ( ~ ( in @ Xx @ B )
% 0.17/0.38 => Xphi ) )
% 0.17/0.38 => ( ( ~ ( in @ Xx @ A )
% 0.17/0.38 => ( ( in @ Xx @ B )
% 0.17/0.38 => Xphi ) )
% 0.17/0.38 => Xphi ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffI1_type,type,
% 0.17/0.38 symdiffI1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffI1,definition,
% 0.17/0.38 ( symdiffI1
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ~ ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffI2_type,type,
% 0.17/0.38 symdiffI2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffI2,definition,
% 0.17/0.38 ( symdiffI2
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ~ ( in @ Xx @ A )
% 0.17/0.38 => ( ( in @ Xx @ B )
% 0.17/0.38 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffIneg1_type,type,
% 0.17/0.38 symdiffIneg1: $o ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffIneg1,definition,
% 0.17/0.38 ( symdiffIneg1
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( ( in @ Xx @ B )
% 0.17/0.38 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffIneg2_type,type,
% 0.17/0.38 symdiffIneg2: $o ).
% 0.17/0.38
% 0.17/0.38 thf(symdiffIneg2,definition,
% 0.17/0.38 ( symdiffIneg2
% 0.17/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.38 ( ~ ( in @ Xx @ A )
% 0.17/0.38 => ( ~ ( in @ Xx @ B )
% 0.17/0.38 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(iskpair_type,type,
% 0.17/0.38 iskpair: $i > $o ).
% 0.17/0.38
% 0.17/0.38 thf(iskpair,definition,
% 0.17/0.38 ( iskpair
% 0.17/0.38 = ( ^ [A: $i] :
% 0.17/0.38 ? [Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.38 & ? [Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ ( setunion @ A ) )
% 0.17/0.38 & ( A
% 0.17/0.38 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(secondinupair_type,type,
% 0.17/0.38 secondinupair: $o ).
% 0.17/0.38
% 0.17/0.38 thf(secondinupair,definition,
% 0.17/0.38 ( secondinupair
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setukpairIL_type,type,
% 0.17/0.38 setukpairIL: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setukpairIL,definition,
% 0.17/0.38 ( setukpairIL
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(setukpairIR_type,type,
% 0.17/0.38 setukpairIR: $o ).
% 0.17/0.38
% 0.17/0.38 thf(setukpairIR,definition,
% 0.17/0.38 ( setukpairIR
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(kpairiskpair_type,type,
% 0.17/0.38 kpairiskpair: $o ).
% 0.17/0.38
% 0.17/0.38 thf(kpairiskpair,definition,
% 0.17/0.38 ( kpairiskpair
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(kpair_type,type,
% 0.17/0.38 kpair: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(kpair,definition,
% 0.17/0.38 ( kpair
% 0.17/0.38 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(kpairp_type,type,
% 0.17/0.38 kpairp: $o ).
% 0.17/0.38
% 0.17/0.38 thf(kpairp,definition,
% 0.17/0.38 ( kpairp
% 0.17/0.38 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(cartprod_type,type,
% 0.17/0.38 cartprod: $i > $i > $i ).
% 0.17/0.38
% 0.17/0.38 thf(cartprod,definition,
% 0.17/0.38 ( cartprod
% 0.17/0.38 = ( ^ [A: $i,B: $i] :
% 0.17/0.38 ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
% 0.17/0.38 @ ^ [Xx: $i] :
% 0.17/0.38 ? [Xy: $i] :
% 0.17/0.38 ( ( in @ Xy @ A )
% 0.17/0.38 & ? [Xz: $i] :
% 0.17/0.38 ( ( in @ Xz @ B )
% 0.17/0.38 & ( Xx
% 0.17/0.38 = ( kpair @ Xy @ Xz ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 thf(singletonsubset,conjecture,
% 0.17/0.38 ( setextAx
% 0.17/0.38 => ( emptysetAx
% 0.17/0.38 => ( setadjoinAx
% 0.17/0.38 => ( powersetAx
% 0.17/0.38 => ( setunionAx
% 0.17/0.38 => ( omega0Ax
% 0.17/0.38 => ( omegaSAx
% 0.17/0.38 => ( omegaIndAx
% 0.17/0.38 => ( replAx
% 0.17/0.38 => ( foundationAx
% 0.17/0.38 => ( wellorderingAx
% 0.17/0.38 => ( descrp
% 0.17/0.38 => ( dsetconstrI
% 0.17/0.38 => ( dsetconstrEL
% 0.17/0.38 => ( dsetconstrER
% 0.17/0.38 => ( exuE1
% 0.17/0.38 => ( prop2setE
% 0.17/0.38 => ( emptysetE
% 0.17/0.38 => ( emptysetimpfalse
% 0.17/0.38 => ( notinemptyset
% 0.17/0.38 => ( exuE3e
% 0.17/0.38 => ( setext
% 0.17/0.38 => ( emptyI
% 0.17/0.38 => ( noeltsimpempty
% 0.17/0.38 => ( setbeta
% 0.17/0.38 => ( nonemptyE1
% 0.17/0.38 => ( nonemptyI
% 0.17/0.38 => ( nonemptyI1
% 0.17/0.38 => ( setadjoinIL
% 0.17/0.38 => ( emptyinunitempty
% 0.17/0.38 => ( setadjoinIR
% 0.17/0.38 => ( setadjoinE
% 0.17/0.38 => ( setadjoinOr
% 0.17/0.38 => ( setoftrueEq
% 0.17/0.38 => ( powersetI
% 0.17/0.38 => ( emptyinPowerset
% 0.17/0.38 => ( emptyInPowerset
% 0.17/0.38 => ( powersetE
% 0.17/0.38 => ( setunionI
% 0.17/0.38 => ( setunionE
% 0.17/0.38 => ( subPowSU
% 0.17/0.38 => ( exuE2
% 0.17/0.38 => ( nonemptyImpWitness
% 0.17/0.38 => ( uniqinunit
% 0.17/0.38 => ( notinsingleton
% 0.17/0.38 => ( eqinunit
% 0.17/0.38 => ( singletonsswitch
% 0.17/0.38 => ( upairsetE
% 0.17/0.38 => ( upairsetIL
% 0.17/0.38 => ( upairsetIR
% 0.17/0.38 => ( emptyE1
% 0.17/0.38 => ( vacuousDall
% 0.17/0.38 => ( quantDeMorgan1
% 0.17/0.38 => ( quantDeMorgan2
% 0.17/0.38 => ( quantDeMorgan3
% 0.17/0.38 => ( quantDeMorgan4
% 0.17/0.38 => ( prop2setI
% 0.17/0.38 => ( prop2set2propI
% 0.17/0.38 => ( notdexE
% 0.17/0.38 => ( notdallE
% 0.17/0.38 => ( exuI1
% 0.17/0.38 => ( exuI3
% 0.17/0.38 => ( exuI2
% 0.17/0.38 => ( inCongP
% 0.17/0.38 => ( in__Cong
% 0.17/0.38 => ( exuE3u
% 0.17/0.38 => ( exu__Cong
% 0.17/0.38 => ( emptyset__Cong
% 0.17/0.38 => ( setadjoin__Cong
% 0.17/0.38 => ( powerset__Cong
% 0.17/0.38 => ( setunion__Cong
% 0.17/0.38 => ( omega__Cong
% 0.17/0.38 => ( exuEu
% 0.17/0.38 => ( descr__Cong
% 0.17/0.38 => ( dsetconstr__Cong
% 0.17/0.38 => ( subsetI1
% 0.17/0.38 => ( eqimpsubset2
% 0.17/0.38 => ( eqimpsubset1
% 0.17/0.38 => ( subsetI2
% 0.17/0.38 => ( emptysetsubset
% 0.17/0.38 => ( subsetE
% 0.17/0.38 => ( subsetE2
% 0.17/0.38 => ( notsubsetI
% 0.17/0.38 => ( notequalI1
% 0.17/0.38 => ( notequalI2
% 0.17/0.38 => ( subsetRefl
% 0.17/0.38 => ( subsetTrans
% 0.17/0.38 => ( setadjoinSub
% 0.17/0.38 => ( setadjoinSub2
% 0.17/0.38 => ( subset2powerset
% 0.17/0.38 => ( setextsub
% 0.17/0.38 => ( subsetemptysetimpeq
% 0.17/0.38 => ( powersetI1
% 0.17/0.38 => ( powersetE1
% 0.17/0.38 => ( inPowerset
% 0.17/0.38 => ( powersetsubset
% 0.17/0.38 => ( sepInPowerset
% 0.17/0.38 => ( sepSubset
% 0.17/0.38 => ( binunionIL
% 0.17/0.38 => ( upairset2IR
% 0.17/0.38 => ( binunionIR
% 0.17/0.38 => ( binunionEcases
% 0.17/0.38 => ( binunionE
% 0.17/0.38 => ( binunionLsub
% 0.17/0.38 => ( binunionRsub
% 0.17/0.38 => ( binintersectI
% 0.17/0.38 => ( binintersectSubset5
% 0.17/0.38 => ( binintersectEL
% 0.17/0.38 => ( binintersectLsub
% 0.17/0.38 => ( binintersectSubset2
% 0.17/0.38 => ( binintersectSubset3
% 0.17/0.38 => ( binintersectER
% 0.17/0.38 => ( disjointsetsI1
% 0.17/0.38 => ( binintersectRsub
% 0.17/0.38 => ( binintersectSubset4
% 0.17/0.38 => ( binintersectSubset1
% 0.17/0.38 => ( bs114d
% 0.17/0.38 => ( setminusI
% 0.17/0.38 => ( setminusEL
% 0.17/0.38 => ( setminusER
% 0.17/0.38 => ( setminusSubset2
% 0.17/0.38 => ( setminusERneg
% 0.17/0.38 => ( setminusELneg
% 0.17/0.38 => ( setminusILneg
% 0.17/0.38 => ( setminusIRneg
% 0.17/0.38 => ( setminusLsub
% 0.17/0.38 => ( setminusSubset1
% 0.17/0.38 => ( symdiffE
% 0.17/0.38 => ( symdiffI1
% 0.17/0.38 => ( symdiffI2
% 0.17/0.38 => ( symdiffIneg1
% 0.17/0.38 => ( symdiffIneg2
% 0.17/0.38 => ( secondinupair
% 0.17/0.38 => ( setukpairIL
% 0.17/0.38 => ( setukpairIR
% 0.17/0.38 => ( kpairiskpair
% 0.17/0.38 => ( kpairp
% 0.17/0.38 => ! [A: $i,Xx: $i] :
% 0.17/0.38 ( ( in @ Xx @ A )
% 0.17/0.38 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.38
% 0.17/0.38 %------------------------------------------------------------------------------
% 0.17/0.38 ------------------------
% 2.51/1.51 ---- Embedded in THF ---
% 2.51/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.51/1.52 %%% Generated on Tue Feb 24 12:28:37 EST 2026
% 2.51/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.51/1.52 %%% Logic specification used:
% 2.51/1.52 %%% thf(spec, logic, $$dhol).
% 2.51/1.52
% 2.51/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2DTF9200.p
% See solution above
% 2.51/1.52 ------------------------
% 2.51/1.54 ---- Cleaned THF ---
% 2.51/1.55 thf(in_type,type,
% 2.51/1.55 in: $i > $i > $o ).
% 2.51/1.55
% 2.51/1.55 thf(exu_type,type,
% 2.51/1.55 exu: ( $i > $o ) > $o ).
% 2.51/1.55
% 2.51/1.55 thf(exu,definition,
% 2.51/1.55 ( exu
% 2.51/1.55 = ( ^ [Xphi: $i > $o] :
% 2.51/1.55 ? [Xx: $i] :
% 2.51/1.55 ( ( Xphi @ Xx )
% 2.51/1.55 & ! [Xy: $i] :
% 2.51/1.55 ( ( Xphi @ Xy )
% 2.51/1.55 => ( Xx = Xy ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setextAx_type,type,
% 2.51/1.55 setextAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setextAx,definition,
% 2.51/1.55 ( setextAx
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 <=> ( in @ Xx @ B ) )
% 2.51/1.55 => ( A = B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptyset_type,type,
% 2.51/1.55 emptyset: $i ).
% 2.51/1.55
% 2.51/1.55 thf(emptysetAx_type,type,
% 2.51/1.55 emptysetAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptysetAx,definition,
% 2.51/1.55 ( emptysetAx
% 2.51/1.55 = ( ! [Xx: $i] :
% 2.51/1.55 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoin_type,type,
% 2.51/1.55 setadjoin: $i > $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinAx_type,type,
% 2.51/1.55 setadjoinAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinAx,definition,
% 2.51/1.55 ( setadjoinAx
% 2.51/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.51/1.55 <=> ( ( Xy = Xx )
% 2.51/1.55 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(powerset_type,type,
% 2.51/1.55 powerset: $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(powersetAx_type,type,
% 2.51/1.55 powersetAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(powersetAx,definition,
% 2.51/1.55 ( powersetAx
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.51/1.55 <=> ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setunion_type,type,
% 2.51/1.55 setunion: $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(setunionAx_type,type,
% 2.51/1.55 setunionAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setunionAx,definition,
% 2.51/1.55 ( setunionAx
% 2.51/1.55 = ( ! [A: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.51/1.55 <=> ? [B: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 & ( in @ B @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(omega_type,type,
% 2.51/1.55 omega: $i ).
% 2.51/1.55
% 2.51/1.55 thf(omega0Ax_type,type,
% 2.51/1.55 omega0Ax: $o ).
% 2.51/1.55
% 2.51/1.55 thf(omega0Ax,definition,
% 2.51/1.55 ( omega0Ax
% 2.51/1.55 = ( in @ emptyset @ omega ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(omegaSAx_type,type,
% 2.51/1.55 omegaSAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(omegaSAx,definition,
% 2.51/1.55 ( omegaSAx
% 2.51/1.55 = ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ omega )
% 2.51/1.55 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(omegaIndAx_type,type,
% 2.51/1.55 omegaIndAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(omegaIndAx,definition,
% 2.51/1.55 ( omegaIndAx
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ( ( in @ emptyset @ A )
% 2.51/1.55 & ! [Xx: $i] :
% 2.51/1.55 ( ( ( in @ Xx @ omega )
% 2.51/1.55 & ( in @ Xx @ A ) )
% 2.51/1.55 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.51/1.55 => ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ omega )
% 2.51/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(replAx_type,type,
% 2.51/1.55 replAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(replAx,definition,
% 2.51/1.55 ( replAx
% 2.51/1.55 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( exu
% 2.51/1.55 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.51/1.55 => ? [B: $i] :
% 2.51/1.55 ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 <=> ? [Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ A )
% 2.51/1.55 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(foundationAx_type,type,
% 2.51/1.55 foundationAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(foundationAx,definition,
% 2.51/1.55 ( foundationAx
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.51/1.55 => ? [B: $i] :
% 2.51/1.55 ( ( in @ B @ A )
% 2.51/1.55 & ~ ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(wellorderingAx_type,type,
% 2.51/1.55 wellorderingAx: $o ).
% 2.51/1.55
% 2.51/1.55 thf(wellorderingAx,definition,
% 2.51/1.55 ( wellorderingAx
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ? [B: $i] :
% 2.51/1.55 ( ! [C: $i] :
% 2.51/1.55 ( ( in @ C @ B )
% 2.51/1.55 => ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ C )
% 2.51/1.55 => ( in @ Xx @ A ) ) )
% 2.51/1.55 & ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( ( in @ Xx @ A )
% 2.51/1.55 & ( in @ Xy @ A ) )
% 2.51/1.55 => ( ! [C: $i] :
% 2.51/1.55 ( ( in @ C @ B )
% 2.51/1.55 => ( ( in @ Xx @ C )
% 2.51/1.55 <=> ( in @ Xy @ C ) ) )
% 2.51/1.55 => ( Xx = Xy ) ) )
% 2.51/1.55 & ! [C: $i,D: $i] :
% 2.51/1.55 ( ( ( in @ C @ B )
% 2.51/1.55 & ( in @ D @ B ) )
% 2.51/1.55 => ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ C )
% 2.51/1.55 => ( in @ Xx @ D ) )
% 2.51/1.55 | ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ D )
% 2.51/1.55 => ( in @ Xx @ C ) ) ) )
% 2.51/1.55 & ! [C: $i] :
% 2.51/1.55 ( ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ C )
% 2.51/1.55 => ( in @ Xx @ A ) )
% 2.51/1.55 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.51/1.55 => ? [D: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ D @ B )
% 2.51/1.55 & ( in @ Xx @ C )
% 2.51/1.55 & ~ ? [Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ D )
% 2.51/1.55 & ( in @ Xy @ C ) )
% 2.51/1.55 & ! [E: $i] :
% 2.51/1.55 ( ( in @ E @ B )
% 2.51/1.55 => ( ! [Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ E )
% 2.51/1.55 => ( in @ Xy @ D ) )
% 2.51/1.55 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(descr_type,type,
% 2.51/1.55 descr: ( $i > $o ) > $i ).
% 2.51/1.55
% 2.51/1.55 thf(descrp_type,type,
% 2.51/1.55 descrp: $o ).
% 2.51/1.55
% 2.51/1.55 thf(descrp,definition,
% 2.51/1.55 ( descrp
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 => ( Xphi
% 2.51/1.55 @ ( descr
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstr_type,type,
% 2.51/1.55 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstrI_type,type,
% 2.51/1.55 dsetconstrI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstrI,definition,
% 2.51/1.55 ( dsetconstrI
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ( Xphi @ Xx )
% 2.51/1.55 => ( in @ Xx
% 2.51/1.55 @ ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstrEL_type,type,
% 2.51/1.55 dsetconstrEL: $o ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstrEL,definition,
% 2.51/1.55 ( dsetconstrEL
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx
% 2.51/1.55 @ ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.51/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstrER_type,type,
% 2.51/1.55 dsetconstrER: $o ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstrER,definition,
% 2.51/1.55 ( dsetconstrER
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx
% 2.51/1.55 @ ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.51/1.55 => ( Xphi @ Xx ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exuE1_type,type,
% 2.51/1.55 exuE1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exuE1,definition,
% 2.51/1.55 ( exuE1
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 => ? [Xx: $i] :
% 2.51/1.55 ( ( Xphi @ Xx )
% 2.51/1.55 & ! [Xy: $i] :
% 2.51/1.55 ( ( Xphi @ Xy )
% 2.51/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(prop2set_type,type,
% 2.51/1.55 prop2set: $o > $i ).
% 2.51/1.55
% 2.51/1.55 thf(prop2setE_type,type,
% 2.51/1.55 prop2setE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(prop2setE,definition,
% 2.51/1.55 ( prop2setE
% 2.51/1.55 = ( ! [Xphi: $o,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.51/1.55 => Xphi ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptysetE_type,type,
% 2.51/1.55 emptysetE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptysetE,definition,
% 2.51/1.55 ( emptysetE
% 2.51/1.55 = ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ emptyset )
% 2.51/1.55 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptysetimpfalse_type,type,
% 2.51/1.55 emptysetimpfalse: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptysetimpfalse,definition,
% 2.51/1.55 ( emptysetimpfalse
% 2.51/1.55 = ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ emptyset )
% 2.51/1.55 => $false ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(notinemptyset_type,type,
% 2.51/1.55 notinemptyset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(notinemptyset,definition,
% 2.51/1.55 ( notinemptyset
% 2.51/1.55 = ( ! [Xx: $i] :
% 2.51/1.55 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exuE3e_type,type,
% 2.51/1.55 exuE3e: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exuE3e,definition,
% 2.51/1.55 ( exuE3e
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setext_type,type,
% 2.51/1.55 setext: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setext,definition,
% 2.51/1.55 ( setext
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( in @ Xx @ B ) )
% 2.51/1.55 => ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ A ) )
% 2.51/1.55 => ( A = B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptyI_type,type,
% 2.51/1.55 emptyI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptyI,definition,
% 2.51/1.55 ( emptyI
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ~ ( in @ Xx @ A )
% 2.51/1.55 => ( A = emptyset ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(noeltsimpempty_type,type,
% 2.51/1.55 noeltsimpempty: $o ).
% 2.51/1.55
% 2.51/1.55 thf(noeltsimpempty,definition,
% 2.51/1.55 ( noeltsimpempty
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ~ ( in @ Xx @ A )
% 2.51/1.55 => ( A = emptyset ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setbeta_type,type,
% 2.51/1.55 setbeta: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setbeta,definition,
% 2.51/1.55 ( setbeta
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ( in @ Xx
% 2.51/1.55 @ ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.51/1.55 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(nonempty_type,type,
% 2.51/1.55 nonempty: $i > $o ).
% 2.51/1.55
% 2.51/1.55 thf(nonempty,definition,
% 2.51/1.55 ( nonempty
% 2.51/1.55 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(nonemptyE1_type,type,
% 2.51/1.55 nonemptyE1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(nonemptyE1,definition,
% 2.51/1.55 ( nonemptyE1
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ( nonempty @ A )
% 2.51/1.55 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(nonemptyI_type,type,
% 2.51/1.55 nonemptyI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(nonemptyI,definition,
% 2.51/1.55 ( nonemptyI
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ( Xphi @ Xx )
% 2.51/1.55 => ( nonempty
% 2.51/1.55 @ ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(nonemptyI1_type,type,
% 2.51/1.55 nonemptyI1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(nonemptyI1,definition,
% 2.51/1.55 ( nonemptyI1
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.51/1.55 => ( nonempty @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinIL_type,type,
% 2.51/1.55 setadjoinIL: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinIL,definition,
% 2.51/1.55 ( setadjoinIL
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptyinunitempty_type,type,
% 2.51/1.55 emptyinunitempty: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptyinunitempty,definition,
% 2.51/1.55 ( emptyinunitempty
% 2.51/1.55 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinIR_type,type,
% 2.51/1.55 setadjoinIR: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinIR,definition,
% 2.51/1.55 ( setadjoinIR
% 2.51/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ A )
% 2.51/1.55 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinE_type,type,
% 2.51/1.55 setadjoinE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinE,definition,
% 2.51/1.55 ( setadjoinE
% 2.51/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.51/1.55 => ! [Xphi: $o] :
% 2.51/1.55 ( ( ( Xy = Xx )
% 2.51/1.55 => Xphi )
% 2.51/1.55 => ( ( ( in @ Xy @ A )
% 2.51/1.55 => Xphi )
% 2.51/1.55 => Xphi ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinOr_type,type,
% 2.51/1.55 setadjoinOr: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinOr,definition,
% 2.51/1.55 ( setadjoinOr
% 2.51/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.51/1.55 => ( ( Xy = Xx )
% 2.51/1.55 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setoftrueEq_type,type,
% 2.51/1.55 setoftrueEq: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setoftrueEq,definition,
% 2.51/1.55 ( setoftrueEq
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xx: $i] : $true )
% 2.51/1.55 = A ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(powersetI_type,type,
% 2.51/1.55 powersetI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(powersetI,definition,
% 2.51/1.55 ( powersetI
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ A ) )
% 2.51/1.55 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptyinPowerset_type,type,
% 2.51/1.55 emptyinPowerset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptyinPowerset,definition,
% 2.51/1.55 ( emptyinPowerset
% 2.51/1.55 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptyInPowerset_type,type,
% 2.51/1.55 emptyInPowerset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptyInPowerset,definition,
% 2.51/1.55 ( emptyInPowerset
% 2.51/1.55 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(powersetE_type,type,
% 2.51/1.55 powersetE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(powersetE,definition,
% 2.51/1.55 ( powersetE
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.51/1.55 => ( ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setunionI_type,type,
% 2.51/1.55 setunionI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setunionI,definition,
% 2.51/1.55 ( setunionI
% 2.51/1.55 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 => ( ( in @ B @ A )
% 2.51/1.55 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setunionE_type,type,
% 2.51/1.55 setunionE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setunionE,definition,
% 2.51/1.55 ( setunionE
% 2.51/1.55 = ( ! [A: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.51/1.55 => ! [Xphi: $o] :
% 2.51/1.55 ( ! [B: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 => ( ( in @ B @ A )
% 2.51/1.55 => Xphi ) )
% 2.51/1.55 => Xphi ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subPowSU_type,type,
% 2.51/1.55 subPowSU: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subPowSU,definition,
% 2.51/1.55 ( subPowSU
% 2.51/1.55 = ( ! [A: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exuE2_type,type,
% 2.51/1.55 exuE2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exuE2,definition,
% 2.51/1.55 ( exuE2
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 => ? [Xx: $i] :
% 2.51/1.55 ! [Xy: $i] :
% 2.51/1.55 ( ( Xphi @ Xy )
% 2.51/1.55 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(nonemptyImpWitness_type,type,
% 2.51/1.55 nonemptyImpWitness: $o ).
% 2.51/1.55
% 2.51/1.55 thf(nonemptyImpWitness,definition,
% 2.51/1.55 ( nonemptyImpWitness
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ( nonempty @ A )
% 2.51/1.55 => ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & $true ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(uniqinunit_type,type,
% 2.51/1.55 uniqinunit: $o ).
% 2.51/1.55
% 2.51/1.55 thf(uniqinunit,definition,
% 2.51/1.55 ( uniqinunit
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.51/1.55 => ( Xx = Xy ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(notinsingleton_type,type,
% 2.51/1.55 notinsingleton: $o ).
% 2.51/1.55
% 2.51/1.55 thf(notinsingleton,definition,
% 2.51/1.55 ( notinsingleton
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xx != Xy )
% 2.51/1.55 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(eqinunit_type,type,
% 2.51/1.55 eqinunit: $o ).
% 2.51/1.55
% 2.51/1.55 thf(eqinunit,definition,
% 2.51/1.55 ( eqinunit
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xx = Xy )
% 2.51/1.55 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(singletonsswitch_type,type,
% 2.51/1.55 singletonsswitch: $o ).
% 2.51/1.55
% 2.51/1.55 thf(singletonsswitch,definition,
% 2.51/1.55 ( singletonsswitch
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.51/1.55 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(upairsetE_type,type,
% 2.51/1.55 upairsetE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(upairsetE,definition,
% 2.51/1.55 ( upairsetE
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.51/1.55 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.51/1.55 => ( ( Xz = Xx )
% 2.51/1.55 | ( Xz = Xy ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(upairsetIL_type,type,
% 2.51/1.55 upairsetIL: $o ).
% 2.51/1.55
% 2.51/1.55 thf(upairsetIL,definition,
% 2.51/1.55 ( upairsetIL
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(upairsetIR_type,type,
% 2.51/1.55 upairsetIR: $o ).
% 2.51/1.55
% 2.51/1.55 thf(upairsetIR,definition,
% 2.51/1.55 ( upairsetIR
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptyE1_type,type,
% 2.51/1.55 emptyE1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptyE1,definition,
% 2.51/1.55 ( emptyE1
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & ( Xphi @ Xx ) )
% 2.51/1.55 => ( ( ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 = emptyset )
% 2.51/1.55 => $false ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(vacuousDall_type,type,
% 2.51/1.55 vacuousDall: $o ).
% 2.51/1.55
% 2.51/1.55 thf(vacuousDall,definition,
% 2.51/1.55 ( vacuousDall
% 2.51/1.55 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ emptyset )
% 2.51/1.55 => ( Xphi @ Xx ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(quantDeMorgan1_type,type,
% 2.51/1.55 quantDeMorgan1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(quantDeMorgan1,definition,
% 2.51/1.55 ( quantDeMorgan1
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( ~ ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( Xphi @ Xx ) )
% 2.51/1.55 => ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(quantDeMorgan2_type,type,
% 2.51/1.55 quantDeMorgan2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(quantDeMorgan2,definition,
% 2.51/1.55 ( quantDeMorgan2
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ~ ( Xphi @ Xx ) )
% 2.51/1.55 => ~ ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(quantDeMorgan3_type,type,
% 2.51/1.55 quantDeMorgan3: $o ).
% 2.51/1.55
% 2.51/1.55 thf(quantDeMorgan3,definition,
% 2.51/1.55 ( quantDeMorgan3
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( ~ ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & ( Xphi @ Xx ) )
% 2.51/1.55 => ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(quantDeMorgan4_type,type,
% 2.51/1.55 quantDeMorgan4: $o ).
% 2.51/1.55
% 2.51/1.55 thf(quantDeMorgan4,definition,
% 2.51/1.55 ( quantDeMorgan4
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & ~ ( Xphi @ Xx ) )
% 2.51/1.55 => ~ ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(prop2setI_type,type,
% 2.51/1.55 prop2setI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(prop2setI,definition,
% 2.51/1.55 ( prop2setI
% 2.51/1.55 = ( ! [Xphi: $o] :
% 2.51/1.55 ( Xphi
% 2.51/1.55 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(set2prop_type,type,
% 2.51/1.55 set2prop: $i > $o ).
% 2.51/1.55
% 2.51/1.55 thf(prop2set2propI_type,type,
% 2.51/1.55 prop2set2propI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(prop2set2propI,definition,
% 2.51/1.55 ( prop2set2propI
% 2.51/1.55 = ( ! [Xphi: $o] :
% 2.51/1.55 ( Xphi
% 2.51/1.55 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(notdexE_type,type,
% 2.51/1.55 notdexE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(notdexE,definition,
% 2.51/1.55 ( notdexE
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( ~ ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & ( Xphi @ Xx ) )
% 2.51/1.55 => ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(notdallE_type,type,
% 2.51/1.55 notdallE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(notdallE,definition,
% 2.51/1.55 ( notdallE
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( ~ ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( Xphi @ Xx ) )
% 2.51/1.55 => ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exuI1_type,type,
% 2.51/1.55 exuI1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exuI1,definition,
% 2.51/1.55 ( exuI1
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ? [Xx: $i] :
% 2.51/1.55 ( ( Xphi @ Xx )
% 2.51/1.55 & ! [Xy: $i] :
% 2.51/1.55 ( ( Xphi @ Xy )
% 2.51/1.55 => ( Xx = Xy ) ) )
% 2.51/1.55 => ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exuI3_type,type,
% 2.51/1.55 exuI3: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exuI3,definition,
% 2.51/1.55 ( exuI3
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.51/1.55 => ( ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xphi @ Xx )
% 2.51/1.55 => ( ( Xphi @ Xy )
% 2.51/1.55 => ( Xx = Xy ) ) )
% 2.51/1.55 => ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exuI2_type,type,
% 2.51/1.55 exuI2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exuI2,definition,
% 2.51/1.55 ( exuI2
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ? [Xx: $i] :
% 2.51/1.55 ! [Xy: $i] :
% 2.51/1.55 ( ( Xphi @ Xy )
% 2.51/1.55 <=> ( Xy = Xx ) )
% 2.51/1.55 => ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(inCongP_type,type,
% 2.51/1.55 inCongP: $o ).
% 2.51/1.55
% 2.51/1.55 thf(inCongP,definition,
% 2.51/1.55 ( inCongP
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( A = B )
% 2.51/1.55 => ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xx = Xy )
% 2.51/1.55 => ( ( in @ Xx @ A )
% 2.51/1.55 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(in__Cong_type,type,
% 2.51/1.55 in__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(in__Cong,definition,
% 2.51/1.55 ( in__Cong
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( A = B )
% 2.51/1.55 => ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xx = Xy )
% 2.51/1.55 => ( ( in @ Xx @ A )
% 2.51/1.55 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exuE3u_type,type,
% 2.51/1.55 exuE3u: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exuE3u,definition,
% 2.51/1.55 ( exuE3u
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 => ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xphi @ Xx )
% 2.51/1.55 => ( ( Xphi @ Xy )
% 2.51/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exu__Cong_type,type,
% 2.51/1.55 exu__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exu__Cong,definition,
% 2.51/1.55 ( exu__Cong
% 2.51/1.55 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.51/1.55 ( ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xx = Xy )
% 2.51/1.55 => ( ( Xphi @ Xx )
% 2.51/1.55 <=> ( Xpsi @ Xy ) ) )
% 2.51/1.55 => ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 <=> ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptyset__Cong_type,type,
% 2.51/1.55 emptyset__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptyset__Cong,definition,
% 2.51/1.55 ( emptyset__Cong
% 2.51/1.55 = ( emptyset = emptyset ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoin__Cong_type,type,
% 2.51/1.55 setadjoin__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoin__Cong,definition,
% 2.51/1.55 ( setadjoin__Cong
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xx = Xy )
% 2.51/1.55 => ! [Xz: $i,Xu: $i] :
% 2.51/1.55 ( ( Xz = Xu )
% 2.51/1.55 => ( ( setadjoin @ Xx @ Xz )
% 2.51/1.55 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(powerset__Cong_type,type,
% 2.51/1.55 powerset__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(powerset__Cong,definition,
% 2.51/1.55 ( powerset__Cong
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( A = B )
% 2.51/1.55 => ( ( powerset @ A )
% 2.51/1.55 = ( powerset @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setunion__Cong_type,type,
% 2.51/1.55 setunion__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setunion__Cong,definition,
% 2.51/1.55 ( setunion__Cong
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( A = B )
% 2.51/1.55 => ( ( setunion @ A )
% 2.51/1.55 = ( setunion @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(omega__Cong_type,type,
% 2.51/1.55 omega__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(omega__Cong,definition,
% 2.51/1.55 ( omega__Cong
% 2.51/1.55 = ( omega = omega ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(exuEu_type,type,
% 2.51/1.55 exuEu: $o ).
% 2.51/1.55
% 2.51/1.55 thf(exuEu,definition,
% 2.51/1.55 ( exuEu
% 2.51/1.55 = ( ! [Xphi: $i > $o] :
% 2.51/1.55 ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 => ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xphi @ Xx )
% 2.51/1.55 => ( ( Xphi @ Xy )
% 2.51/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(descr__Cong_type,type,
% 2.51/1.55 descr__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(descr__Cong,definition,
% 2.51/1.55 ( descr__Cong
% 2.51/1.55 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.51/1.55 ( ! [Xx: $i,Xy: $i] :
% 2.51/1.55 ( ( Xx = Xy )
% 2.51/1.55 => ( ( Xphi @ Xx )
% 2.51/1.55 <=> ( Xpsi @ Xy ) ) )
% 2.51/1.55 => ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 => ( ( exu
% 2.51/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.51/1.55 => ( ( descr
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 = ( descr
% 2.51/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstr__Cong_type,type,
% 2.51/1.55 dsetconstr__Cong: $o ).
% 2.51/1.55
% 2.51/1.55 thf(dsetconstr__Cong,definition,
% 2.51/1.55 ( dsetconstr__Cong
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( A = B )
% 2.51/1.55 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ! [Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ B )
% 2.51/1.55 => ( ( Xx = Xy )
% 2.51/1.55 => ( ( Xphi @ Xx )
% 2.51/1.55 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.51/1.55 => ( ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 = ( dsetconstr @ B
% 2.51/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subset_type,type,
% 2.51/1.55 subset: $i > $i > $o ).
% 2.51/1.55
% 2.51/1.55 thf(disjoint_type,type,
% 2.51/1.55 disjoint: $i > $i > $o ).
% 2.51/1.55
% 2.51/1.55 thf(setsmeet_type,type,
% 2.51/1.55 setsmeet: $i > $i > $o ).
% 2.51/1.55
% 2.51/1.55 thf(subsetI1_type,type,
% 2.51/1.55 subsetI1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subsetI1,definition,
% 2.51/1.55 ( subsetI1
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( in @ Xx @ B ) )
% 2.51/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(eqimpsubset2_type,type,
% 2.51/1.55 eqimpsubset2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(eqimpsubset2,definition,
% 2.51/1.55 ( eqimpsubset2
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( A = B )
% 2.51/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(eqimpsubset1_type,type,
% 2.51/1.55 eqimpsubset1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(eqimpsubset1,definition,
% 2.51/1.55 ( eqimpsubset1
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( A = B )
% 2.51/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subsetI2_type,type,
% 2.51/1.55 subsetI2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subsetI2,definition,
% 2.51/1.55 ( subsetI2
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ! [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( in @ Xx @ B ) )
% 2.51/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(emptysetsubset_type,type,
% 2.51/1.55 emptysetsubset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(emptysetsubset,definition,
% 2.51/1.55 ( emptysetsubset
% 2.51/1.55 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subsetE_type,type,
% 2.51/1.55 subsetE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subsetE,definition,
% 2.51/1.55 ( subsetE
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( ( in @ Xx @ A )
% 2.51/1.55 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subsetE2_type,type,
% 2.51/1.55 subsetE2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subsetE2,definition,
% 2.51/1.55 ( subsetE2
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( ~ ( in @ Xx @ B )
% 2.51/1.55 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(notsubsetI_type,type,
% 2.51/1.55 notsubsetI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(notsubsetI,definition,
% 2.51/1.55 ( notsubsetI
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ~ ( in @ Xx @ B )
% 2.51/1.55 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(notequalI1_type,type,
% 2.51/1.55 notequalI1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(notequalI1,definition,
% 2.51/1.55 ( notequalI1
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ~ ( subset @ A @ B )
% 2.51/1.55 => ( A != B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(notequalI2_type,type,
% 2.51/1.55 notequalI2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(notequalI2,definition,
% 2.51/1.55 ( notequalI2
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ~ ( in @ Xx @ B )
% 2.51/1.55 => ( A != B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subsetRefl_type,type,
% 2.51/1.55 subsetRefl: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subsetRefl,definition,
% 2.51/1.55 ( subsetRefl
% 2.51/1.55 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subsetTrans_type,type,
% 2.51/1.55 subsetTrans: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subsetTrans,definition,
% 2.51/1.55 ( subsetTrans
% 2.51/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( ( subset @ B @ C )
% 2.51/1.55 => ( subset @ A @ C ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinSub_type,type,
% 2.51/1.55 setadjoinSub: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinSub,definition,
% 2.51/1.55 ( setadjoinSub
% 2.51/1.55 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinSub2_type,type,
% 2.51/1.55 setadjoinSub2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setadjoinSub2,definition,
% 2.51/1.55 ( setadjoinSub2
% 2.51/1.55 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subset2powerset_type,type,
% 2.51/1.55 subset2powerset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subset2powerset,definition,
% 2.51/1.55 ( subset2powerset
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setextsub_type,type,
% 2.51/1.55 setextsub: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setextsub,definition,
% 2.51/1.55 ( setextsub
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( ( subset @ B @ A )
% 2.51/1.55 => ( A = B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(subsetemptysetimpeq_type,type,
% 2.51/1.55 subsetemptysetimpeq: $o ).
% 2.51/1.55
% 2.51/1.55 thf(subsetemptysetimpeq,definition,
% 2.51/1.55 ( subsetemptysetimpeq
% 2.51/1.55 = ( ! [A: $i] :
% 2.51/1.55 ( ( subset @ A @ emptyset )
% 2.51/1.55 => ( A = emptyset ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(powersetI1_type,type,
% 2.51/1.55 powersetI1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(powersetI1,definition,
% 2.51/1.55 ( powersetI1
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( subset @ B @ A )
% 2.51/1.55 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(powersetE1_type,type,
% 2.51/1.55 powersetE1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(powersetE1,definition,
% 2.51/1.55 ( powersetE1
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.51/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(inPowerset_type,type,
% 2.51/1.55 inPowerset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(inPowerset,definition,
% 2.51/1.55 ( inPowerset
% 2.51/1.55 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(powersetsubset_type,type,
% 2.51/1.55 powersetsubset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(powersetsubset,definition,
% 2.51/1.55 ( powersetsubset
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(sepInPowerset_type,type,
% 2.51/1.55 sepInPowerset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(sepInPowerset,definition,
% 2.51/1.55 ( sepInPowerset
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( in
% 2.51/1.55 @ ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 @ ( powerset @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(sepSubset_type,type,
% 2.51/1.55 sepSubset: $o ).
% 2.51/1.55
% 2.51/1.55 thf(sepSubset,definition,
% 2.51/1.55 ( sepSubset
% 2.51/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.51/1.55 ( subset
% 2.51/1.55 @ ( dsetconstr @ A
% 2.51/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.51/1.55 @ A ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binunion_type,type,
% 2.51/1.55 binunion: $i > $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(binunionIL_type,type,
% 2.51/1.55 binunionIL: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binunionIL,definition,
% 2.51/1.55 ( binunionIL
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(upairset2IR_type,type,
% 2.51/1.55 upairset2IR: $o ).
% 2.51/1.55
% 2.51/1.55 thf(upairset2IR,definition,
% 2.51/1.55 ( upairset2IR
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binunionIR_type,type,
% 2.51/1.55 binunionIR: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binunionIR,definition,
% 2.51/1.55 ( binunionIR
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binunionEcases_type,type,
% 2.51/1.55 binunionEcases: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binunionEcases,definition,
% 2.51/1.55 ( binunionEcases
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.51/1.55 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.51/1.55 => ( ( ( in @ Xx @ A )
% 2.51/1.55 => Xphi )
% 2.51/1.55 => ( ( ( in @ Xx @ B )
% 2.51/1.55 => Xphi )
% 2.51/1.55 => Xphi ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binunionE_type,type,
% 2.51/1.55 binunionE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binunionE,definition,
% 2.51/1.55 ( binunionE
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.51/1.55 => ( ( in @ Xx @ A )
% 2.51/1.55 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binunionLsub_type,type,
% 2.51/1.55 binunionLsub: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binunionLsub,definition,
% 2.51/1.55 ( binunionLsub
% 2.51/1.55 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binunionRsub_type,type,
% 2.51/1.55 binunionRsub: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binunionRsub,definition,
% 2.51/1.55 ( binunionRsub
% 2.51/1.55 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersect_type,type,
% 2.51/1.55 binintersect: $i > $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectI_type,type,
% 2.51/1.55 binintersectI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectI,definition,
% 2.51/1.55 ( binintersectI
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset5_type,type,
% 2.51/1.55 binintersectSubset5: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset5,definition,
% 2.51/1.55 ( binintersectSubset5
% 2.51/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.51/1.55 ( ( subset @ C @ A )
% 2.51/1.55 => ( ( subset @ C @ B )
% 2.51/1.55 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectEL_type,type,
% 2.51/1.55 binintersectEL: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectEL,definition,
% 2.51/1.55 ( binintersectEL
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.51/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectLsub_type,type,
% 2.51/1.55 binintersectLsub: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectLsub,definition,
% 2.51/1.55 ( binintersectLsub
% 2.51/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset2_type,type,
% 2.51/1.55 binintersectSubset2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset2,definition,
% 2.51/1.55 ( binintersectSubset2
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( ( binintersect @ A @ B )
% 2.51/1.55 = A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset3_type,type,
% 2.51/1.55 binintersectSubset3: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset3,definition,
% 2.51/1.55 ( binintersectSubset3
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( ( binintersect @ A @ B )
% 2.51/1.55 = B )
% 2.51/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectER_type,type,
% 2.51/1.55 binintersectER: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectER,definition,
% 2.51/1.55 ( binintersectER
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.51/1.55 => ( in @ Xx @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(disjointsetsI1_type,type,
% 2.51/1.55 disjointsetsI1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(disjointsetsI1,definition,
% 2.51/1.55 ( disjointsetsI1
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ~ ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 & ( in @ Xx @ B ) )
% 2.51/1.55 => ( ( binintersect @ A @ B )
% 2.51/1.55 = emptyset ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectRsub_type,type,
% 2.51/1.55 binintersectRsub: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectRsub,definition,
% 2.51/1.55 ( binintersectRsub
% 2.51/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset4_type,type,
% 2.51/1.55 binintersectSubset4: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset4,definition,
% 2.51/1.55 ( binintersectSubset4
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( subset @ B @ A )
% 2.51/1.55 => ( ( binintersect @ A @ B )
% 2.51/1.55 = B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset1_type,type,
% 2.51/1.55 binintersectSubset1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(binintersectSubset1,definition,
% 2.51/1.55 ( binintersectSubset1
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( ( binintersect @ A @ B )
% 2.51/1.55 = A )
% 2.51/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(bs114d_type,type,
% 2.51/1.55 bs114d: $o ).
% 2.51/1.55
% 2.51/1.55 thf(bs114d,definition,
% 2.51/1.55 ( bs114d
% 2.51/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.51/1.55 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.51/1.55 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(regular_type,type,
% 2.51/1.55 regular: $i > $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminus_type,type,
% 2.51/1.55 setminus: $i > $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(setminusI_type,type,
% 2.51/1.55 setminusI: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusI,definition,
% 2.51/1.55 ( setminusI
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ~ ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusEL_type,type,
% 2.51/1.55 setminusEL: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusEL,definition,
% 2.51/1.55 ( setminusEL
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.51/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusER_type,type,
% 2.51/1.55 setminusER: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusER,definition,
% 2.51/1.55 ( setminusER
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.51/1.55 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusSubset2_type,type,
% 2.51/1.55 setminusSubset2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusSubset2,definition,
% 2.51/1.55 ( setminusSubset2
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( subset @ A @ B )
% 2.51/1.55 => ( ( setminus @ A @ B )
% 2.51/1.55 = emptyset ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusERneg_type,type,
% 2.51/1.55 setminusERneg: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusERneg,definition,
% 2.51/1.55 ( setminusERneg
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.51/1.55 => ( ( in @ Xx @ A )
% 2.51/1.55 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusELneg_type,type,
% 2.51/1.55 setminusELneg: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusELneg,definition,
% 2.51/1.55 ( setminusELneg
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.51/1.55 => ( ~ ( in @ Xx @ B )
% 2.51/1.55 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusILneg_type,type,
% 2.51/1.55 setminusILneg: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusILneg,definition,
% 2.51/1.55 ( setminusILneg
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ~ ( in @ Xx @ A )
% 2.51/1.55 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusIRneg_type,type,
% 2.51/1.55 setminusIRneg: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusIRneg,definition,
% 2.51/1.55 ( setminusIRneg
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ B )
% 2.51/1.55 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusLsub_type,type,
% 2.51/1.55 setminusLsub: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusLsub,definition,
% 2.51/1.55 ( setminusLsub
% 2.51/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setminusSubset1_type,type,
% 2.51/1.55 setminusSubset1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setminusSubset1,definition,
% 2.51/1.55 ( setminusSubset1
% 2.51/1.55 = ( ! [A: $i,B: $i] :
% 2.51/1.55 ( ( ( setminus @ A @ B )
% 2.51/1.55 = emptyset )
% 2.51/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(symdiff_type,type,
% 2.51/1.55 symdiff: $i > $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffE_type,type,
% 2.51/1.55 symdiffE: $o ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffE,definition,
% 2.51/1.55 ( symdiffE
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.51/1.55 => ! [Xphi: $o] :
% 2.51/1.55 ( ( ( in @ Xx @ A )
% 2.51/1.55 => ( ~ ( in @ Xx @ B )
% 2.51/1.55 => Xphi ) )
% 2.51/1.55 => ( ( ~ ( in @ Xx @ A )
% 2.51/1.55 => ( ( in @ Xx @ B )
% 2.51/1.55 => Xphi ) )
% 2.51/1.55 => Xphi ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffI1_type,type,
% 2.51/1.55 symdiffI1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffI1,definition,
% 2.51/1.55 ( symdiffI1
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ~ ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffI2_type,type,
% 2.51/1.55 symdiffI2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffI2,definition,
% 2.51/1.55 ( symdiffI2
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ~ ( in @ Xx @ A )
% 2.51/1.55 => ( ( in @ Xx @ B )
% 2.51/1.55 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffIneg1_type,type,
% 2.51/1.55 symdiffIneg1: $o ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffIneg1,definition,
% 2.51/1.55 ( symdiffIneg1
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( ( in @ Xx @ B )
% 2.51/1.55 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffIneg2_type,type,
% 2.51/1.55 symdiffIneg2: $o ).
% 2.51/1.55
% 2.51/1.55 thf(symdiffIneg2,definition,
% 2.51/1.55 ( symdiffIneg2
% 2.51/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.51/1.55 ( ~ ( in @ Xx @ A )
% 2.51/1.55 => ( ~ ( in @ Xx @ B )
% 2.51/1.55 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(iskpair_type,type,
% 2.51/1.55 iskpair: $i > $o ).
% 2.51/1.55
% 2.51/1.55 thf(iskpair,definition,
% 2.51/1.55 ( iskpair
% 2.51/1.55 = ( ^ [A: $i] :
% 2.51/1.55 ? [Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.51/1.55 & ? [Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ ( setunion @ A ) )
% 2.51/1.55 & ( A
% 2.51/1.55 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(secondinupair_type,type,
% 2.51/1.55 secondinupair: $o ).
% 2.51/1.55
% 2.51/1.55 thf(secondinupair,definition,
% 2.51/1.55 ( secondinupair
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setukpairIL_type,type,
% 2.51/1.55 setukpairIL: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setukpairIL,definition,
% 2.51/1.55 ( setukpairIL
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(setukpairIR_type,type,
% 2.51/1.55 setukpairIR: $o ).
% 2.51/1.55
% 2.51/1.55 thf(setukpairIR,definition,
% 2.51/1.55 ( setukpairIR
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(kpairiskpair_type,type,
% 2.51/1.55 kpairiskpair: $o ).
% 2.51/1.55
% 2.51/1.55 thf(kpairiskpair,definition,
% 2.51/1.55 ( kpairiskpair
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(kpair_type,type,
% 2.51/1.55 kpair: $i > $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(kpair,definition,
% 2.51/1.55 ( kpair
% 2.51/1.55 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(kpairp_type,type,
% 2.51/1.55 kpairp: $o ).
% 2.51/1.55
% 2.51/1.55 thf(kpairp,definition,
% 2.51/1.55 ( kpairp
% 2.51/1.55 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(cartprod_type,type,
% 2.51/1.55 cartprod: $i > $i > $i ).
% 2.51/1.55
% 2.51/1.55 thf(cartprod,definition,
% 2.51/1.55 ( cartprod
% 2.51/1.55 = ( ^ [A: $i,B: $i] :
% 2.51/1.55 ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
% 2.51/1.55 @ ^ [Xx: $i] :
% 2.51/1.55 ? [Xy: $i] :
% 2.51/1.55 ( ( in @ Xy @ A )
% 2.51/1.55 & ? [Xz: $i] :
% 2.51/1.55 ( ( in @ Xz @ B )
% 2.51/1.55 & ( Xx
% 2.51/1.55 = ( kpair @ Xy @ Xz ) ) ) ) ) ) ) ).
% 2.51/1.55
% 2.51/1.55 thf(singletonsubset,conjecture,
% 2.51/1.55 ( setextAx
% 2.51/1.55 => ( emptysetAx
% 2.51/1.55 => ( setadjoinAx
% 2.51/1.55 => ( powersetAx
% 2.51/1.55 => ( setunionAx
% 2.51/1.55 => ( omega0Ax
% 2.51/1.55 => ( omegaSAx
% 2.51/1.55 => ( omegaIndAx
% 2.51/1.55 => ( replAx
% 2.51/1.55 => ( foundationAx
% 2.51/1.55 => ( wellorderingAx
% 2.51/1.55 => ( descrp
% 2.51/1.55 => ( dsetconstrI
% 2.51/1.55 => ( dsetconstrEL
% 2.51/1.55 => ( dsetconstrER
% 2.51/1.55 => ( exuE1
% 2.51/1.55 => ( prop2setE
% 2.51/1.55 => ( emptysetE
% 2.51/1.55 => ( emptysetimpfalse
% 2.51/1.55 => ( notinemptyset
% 2.51/1.55 => ( exuE3e
% 2.51/1.55 => ( setext
% 2.51/1.55 => ( emptyI
% 2.51/1.55 => ( noeltsimpempty
% 2.51/1.55 => ( setbeta
% 2.51/1.55 => ( nonemptyE1
% 2.51/1.55 => ( nonemptyI
% 2.51/1.55 => ( nonemptyI1
% 2.51/1.55 => ( setadjoinIL
% 2.51/1.55 => ( emptyinunitempty
% 2.51/1.55 => ( setadjoinIR
% 2.51/1.55 => ( setadjoinE
% 2.51/1.55 => ( setadjoinOr
% 2.51/1.55 => ( setoftrueEq
% 2.51/1.55 => ( powersetI
% 2.51/1.55 => ( emptyinPowerset
% 2.51/1.55 => ( emptyInPowerset
% 2.51/1.55 => ( powersetE
% 2.51/1.55 => ( setunionI
% 2.51/1.55 => ( setunionE
% 2.51/1.55 => ( subPowSU
% 2.51/1.55 => ( exuE2
% 2.51/1.55 => ( nonemptyImpWitness
% 2.51/1.55 => ( uniqinunit
% 2.51/1.55 => ( notinsingleton
% 2.51/1.55 => ( eqinunit
% 2.51/1.55 => ( singletonsswitch
% 2.51/1.55 => ( upairsetE
% 2.51/1.55 => ( upairsetIL
% 2.51/1.55 => ( upairsetIR
% 2.51/1.55 => ( emptyE1
% 2.51/1.55 => ( vacuousDall
% 2.51/1.55 => ( quantDeMorgan1
% 2.51/1.55 => ( quantDeMorgan2
% 2.51/1.55 => ( quantDeMorgan3
% 2.51/1.55 => ( quantDeMorgan4
% 2.51/1.55 => ( prop2setI
% 2.51/1.55 => ( prop2set2propI
% 2.51/1.55 => ( notdexE
% 2.51/1.55 => ( notdallE
% 2.51/1.55 => ( exuI1
% 2.51/1.55 => ( exuI3
% 2.51/1.55 => ( exuI2
% 2.51/1.55 => ( inCongP
% 2.51/1.55 => ( in__Cong
% 2.51/1.55 => ( exuE3u
% 2.51/1.55 => ( exu__Cong
% 2.51/1.55 => ( emptyset__Cong
% 2.51/1.55 => ( setadjoin__Cong
% 2.51/1.55 => ( powerset__Cong
% 2.51/1.55 => ( setunion__Cong
% 2.51/1.55 => ( omega__Cong
% 2.51/1.55 => ( exuEu
% 2.51/1.55 => ( descr__Cong
% 2.51/1.55 => ( dsetconstr__Cong
% 2.51/1.55 => ( subsetI1
% 2.51/1.55 => ( eqimpsubset2
% 2.51/1.55 => ( eqimpsubset1
% 2.51/1.55 => ( subsetI2
% 2.51/1.55 => ( emptysetsubset
% 2.51/1.55 => ( subsetE
% 2.51/1.55 => ( subsetE2
% 2.51/1.55 => ( notsubsetI
% 2.51/1.55 => ( notequalI1
% 2.51/1.55 => ( notequalI2
% 2.51/1.55 => ( subsetRefl
% 2.51/1.55 => ( subsetTrans
% 2.51/1.55 => ( setadjoinSub
% 2.51/1.55 => ( setadjoinSub2
% 2.51/1.55 => ( subset2powerset
% 2.51/1.55 => ( setextsub
% 2.51/1.55 => ( subsetemptysetimpeq
% 2.51/1.55 => ( powersetI1
% 2.51/1.55 => ( powersetE1
% 2.51/1.55 => ( inPowerset
% 2.51/1.55 => ( powersetsubset
% 2.51/1.55 => ( sepInPowerset
% 2.51/1.55 => ( sepSubset
% 2.51/1.55 => ( binunionIL
% 2.51/1.55 => ( upairset2IR
% 2.51/1.55 => ( binunionIR
% 2.51/1.55 => ( binunionEcases
% 2.51/1.55 => ( binunionE
% 2.51/1.55 => ( binunionLsub
% 2.51/1.55 => ( binunionRsub
% 2.51/1.55 => ( binintersectI
% 2.51/1.55 => ( binintersectSubset5
% 2.51/1.55 => ( binintersectEL
% 2.51/1.55 => ( binintersectLsub
% 2.51/1.55 => ( binintersectSubset2
% 2.51/1.55 => ( binintersectSubset3
% 2.51/1.55 => ( binintersectER
% 2.51/1.55 => ( disjointsetsI1
% 2.51/1.55 => ( binintersectRsub
% 2.51/1.55 => ( binintersectSubset4
% 2.51/1.55 => ( binintersectSubset1
% 2.51/1.55 => ( bs114d
% 2.51/1.55 => ( setminusI
% 2.51/1.55 => ( setminusEL
% 2.51/1.55 => ( setminusER
% 2.51/1.55 => ( setminusSubset2
% 2.51/1.55 => ( setminusERneg
% 2.51/1.55 => ( setminusELneg
% 2.51/1.55 => ( setminusILneg
% 2.51/1.55 => ( setminusIRneg
% 2.51/1.55 => ( setminusLsub
% 2.51/1.55 => ( setminusSubset1
% 2.51/1.55 => ( symdiffE
% 2.51/1.55 => ( symdiffI1
% 2.51/1.55 => ( symdiffI2
% 2.51/1.55 => ( symdiffIneg1
% 2.51/1.55 => ( symdiffIneg2
% 2.51/1.55 => ( secondinupair
% 2.51/1.55 => ( setukpairIL
% 2.51/1.55 => ( setukpairIR
% 2.51/1.55 => ( kpairiskpair
% 2.51/1.55 => ( kpairp
% 2.51/1.55 => ! [A: $i,Xx: $i] :
% 2.51/1.55 ( ( in @ Xx @ A )
% 2.51/1.55 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.51/1.55 ------------------------
% 2.51/1.57 % (9301)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/2Mi)
% 2.51/1.57 % (9299)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_9200 for (2999ds/4Mi)
% 2.51/1.57 % (9298)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/183Mi)
% 2.51/1.57 % (9304)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/18Mi)
% 2.51/1.57 % (9302)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_9200 for (2999ds/2Mi)
% 2.51/1.57 % (9300)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_9200 for (2999ds/27Mi)
% 2.51/1.57 % (9303)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_9200 for (2999ds/275Mi)
% 2.51/1.58 % (9301)Instruction limit reached!
% 2.51/1.58 % (9301)------------------------------
% 2.51/1.58 % (9301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.58 % (9301)Termination reason: Unknown
% 2.51/1.58 % (9301)Termination phase: shuffling
% 2.51/1.58 % (9302)Instruction limit reached!
% 2.51/1.58 % (9302)------------------------------
% 2.51/1.58 % (9302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.58 % (9302)Termination reason: Unknown
% 2.51/1.58 % (9302)Termination phase: shuffling
% 2.51/1.58
% 2.51/1.58 % (9302)Memory used [KB]: 1279
% 2.51/1.58 % (9302)Time elapsed: 0.003 s
% 2.51/1.58 % (9302)Instructions burned: 3 (million)
% 2.51/1.58 % (9302)------------------------------
% 2.51/1.58 % (9302)------------------------------
% 2.51/1.58
% 2.51/1.58 % (9301)Memory used [KB]: 1279
% 2.51/1.58 % (9301)Time elapsed: 0.003 s
% 2.51/1.58 % (9301)Instructions burned: 3 (million)
% 2.51/1.58 % (9301)------------------------------
% 2.51/1.58 % (9301)------------------------------
% 2.51/1.58 % (9299)Instruction limit reached!
% 2.51/1.58 % (9299)------------------------------
% 2.51/1.58 % (9299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.58 % (9299)Termination reason: Unknown
% 2.51/1.58 % (9299)Termination phase: shuffling
% 2.51/1.58
% 2.51/1.58 % (9299)Memory used [KB]: 1279
% 2.51/1.58 % (9299)Time elapsed: 0.004 s
% 2.51/1.58 % (9299)Instructions burned: 5 (million)
% 2.51/1.58 % (9299)------------------------------
% 2.51/1.58 % (9299)------------------------------
% 2.51/1.58 % (9304)Instruction limit reached!
% 2.51/1.58 % (9304)------------------------------
% 2.51/1.58 % (9304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.58 % (9304)Termination reason: Unknown
% 2.51/1.58 % (9304)Termination phase: Preprocessing 2
% 2.51/1.58
% 2.51/1.58 % (9304)Memory used [KB]: 1535
% 2.51/1.58 % (9304)Time elapsed: 0.011 s
% 2.51/1.58 % (9304)Instructions burned: 20 (million)
% 2.51/1.58 % (9304)------------------------------
% 2.51/1.58 % (9304)------------------------------
% 2.51/1.59 % (9300)Instruction limit reached!
% 2.51/1.59 % (9300)------------------------------
% 2.51/1.59 % (9300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.59 % (9300)Termination reason: Unknown
% 2.51/1.59 % (9300)Termination phase: Property scanning
% 2.51/1.59
% 2.51/1.59 % (9300)Memory used [KB]: 1663
% 2.51/1.59 % (9300)Time elapsed: 0.014 s
% 2.51/1.59 % (9300)Instructions burned: 27 (million)
% 2.51/1.59 % (9300)------------------------------
% 2.51/1.59 % (9300)------------------------------
% 2.51/1.59 % (9305)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/3Mi)
% 2.51/1.59 % (9306)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_9200 for (2999ds/37Mi)
% 2.51/1.59 % (9307)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_9200 for (2999ds/15Mi)
% 2.51/1.59 % (9305)Instruction limit reached!
% 2.51/1.59 % (9305)------------------------------
% 2.51/1.59 % (9305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.51/1.59 % (9305)Termination reason: Unknown
% 2.51/1.59 % (9305)Termination phase: shuffling
% 2.51/1.59
% 2.51/1.59 % (9305)Memory used [KB]: 1279
% 2.51/1.59 % (9305)Time elapsed: 0.003 s
% 2.51/1.59 % (9305)Instructions burned: 4 (million)
% 2.51/1.59 % (9305)------------------------------
% 2.51/1.59 % (9305)------------------------------
% 2.55/1.60 % (9308)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_9200 for (2999ds/3Mi)
% 2.55/1.60 % (9307)Instruction limit reached!
% 2.55/1.60 % (9307)------------------------------
% 2.55/1.60 % (9307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.60 % (9307)Termination reason: Unknown
% 2.55/1.60 % (9307)Termination phase: Property scanning
% 2.55/1.60
% 2.55/1.60 % (9307)Memory used [KB]: 1535
% 2.55/1.60 % (9307)Time elapsed: 0.009 s
% 2.55/1.60 % (9307)Instructions burned: 15 (million)
% 2.55/1.60 % (9307)------------------------------
% 2.55/1.60 % (9307)------------------------------
% 2.55/1.60 % (9308)Instruction limit reached!
% 2.55/1.60 % (9308)------------------------------
% 2.55/1.60 % (9308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.60 % (9308)Termination reason: Unknown
% 2.55/1.60 % (9308)Termination phase: shuffling
% 2.55/1.60
% 2.55/1.60 % (9308)Memory used [KB]: 1279
% 2.55/1.60 % (9308)Time elapsed: 0.003 s
% 2.55/1.60 % (9308)Instructions burned: 3 (million)
% 2.55/1.60 % (9308)------------------------------
% 2.55/1.60 % (9308)------------------------------
% 2.55/1.60 % (9309)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_9200 for (2999ds/1041Mi)
% 2.55/1.61 % (9306)Instruction limit reached!
% 2.55/1.61 % (9306)------------------------------
% 2.55/1.61 % (9306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.61 % (9306)Termination reason: Unknown
% 2.55/1.61 % (9306)Termination phase: Property scanning
% 2.55/1.61
% 2.55/1.61 % (9306)Memory used [KB]: 1663
% 2.55/1.61 % (9306)Time elapsed: 0.018 s
% 2.55/1.61 % (9306)Instructions burned: 37 (million)
% 2.55/1.61 % (9306)------------------------------
% 2.55/1.61 % (9306)------------------------------
% 2.55/1.61 % (9310)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/7Mi)
% 2.55/1.61 % (9310)Instruction limit reached!
% 2.55/1.61 % (9310)------------------------------
% 2.55/1.61 % (9310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.61 % (9310)Termination reason: Unknown
% 2.55/1.61 % (9310)Termination phase: shuffling
% 2.55/1.61
% 2.55/1.61 % (9310)Memory used [KB]: 1407
% 2.55/1.61 % (9310)Time elapsed: 0.005 s
% 2.55/1.61 % (9310)Instructions burned: 8 (million)
% 2.55/1.61 % (9310)------------------------------
% 2.55/1.61 % (9310)------------------------------
% 2.55/1.62 % (9311)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/16Mi)
% 2.55/1.62 % (9312)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_9200 for (2999ds/3Mi)
% 2.55/1.62 % (9312)Instruction limit reached!
% 2.55/1.62 % (9312)------------------------------
% 2.55/1.62 % (9312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.62 % (9312)Termination reason: Unknown
% 2.55/1.62 % (9312)Termination phase: shuffling
% 2.55/1.62
% 2.55/1.62 % (9312)Memory used [KB]: 1279
% 2.55/1.62 % (9312)Time elapsed: 0.003 s
% 2.55/1.62 % (9312)Instructions burned: 3 (million)
% 2.55/1.62 % (9312)------------------------------
% 2.55/1.62 % (9312)------------------------------
% 2.55/1.62 % (9311)Instruction limit reached!
% 2.55/1.62 % (9311)------------------------------
% 2.55/1.62 % (9311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.62 % (9311)Termination reason: Unknown
% 2.55/1.62 % (9311)Termination phase: shuffling
% 2.55/1.62
% 2.55/1.62 % (9311)Memory used [KB]: 1535
% 2.55/1.62 % (9311)Time elapsed: 0.009 s
% 2.55/1.62 % (9311)Instructions burned: 17 (million)
% 2.55/1.62 % (9311)------------------------------
% 2.55/1.62 % (9311)------------------------------
% 2.55/1.62 % (9313)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_9200 for (2999ds/3Mi)
% 2.55/1.63 % (9313)Instruction limit reached!
% 2.55/1.63 % (9313)------------------------------
% 2.55/1.63 % (9313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.63 % (9313)Termination reason: Unknown
% 2.55/1.63 % (9313)Termination phase: shuffling
% 2.55/1.63
% 2.55/1.63 % (9313)Memory used [KB]: 1279
% 2.55/1.63 % (9313)Time elapsed: 0.003 s
% 2.55/1.63 % (9313)Instructions burned: 3 (million)
% 2.55/1.63 % (9313)------------------------------
% 2.55/1.63 % (9313)------------------------------
% 2.55/1.63 % (9314)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/7Mi)
% 2.55/1.63 % (9314)Instruction limit reached!
% 2.55/1.63 % (9314)------------------------------
% 2.55/1.63 % (9314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.63 % (9314)Termination reason: Unknown
% 2.55/1.63 % (9314)Termination phase: shuffling
% 2.55/1.63
% 2.55/1.63 % (9314)Memory used [KB]: 1407
% 2.55/1.63 % (9314)Time elapsed: 0.005 s
% 2.55/1.63 % (9314)Instructions burned: 8 (million)
% 2.55/1.63 % (9314)------------------------------
% 2.55/1.63 % (9314)------------------------------
% 2.55/1.63 % (9315)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/3Mi)
% 2.55/1.64 % (9315)Instruction limit reached!
% 2.55/1.64 % (9315)------------------------------
% 2.55/1.64 % (9315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.64 % (9315)Termination reason: Unknown
% 2.55/1.64 % (9315)Termination phase: shuffling
% 2.55/1.64
% 2.55/1.64 % (9315)Memory used [KB]: 1279
% 2.55/1.64 % (9315)Time elapsed: 0.003 s
% 2.55/1.64 % (9315)Instructions burned: 4 (million)
% 2.55/1.64 % (9315)------------------------------
% 2.55/1.64 % (9315)------------------------------
% 2.55/1.64 % (9316)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/4Mi)
% 2.55/1.64 % (9316)Instruction limit reached!
% 2.55/1.64 % (9316)------------------------------
% 2.55/1.64 % (9316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.64 % (9316)Termination reason: Unknown
% 2.55/1.64 % (9316)Termination phase: shuffling
% 2.55/1.64
% 2.55/1.64 % (9316)Memory used [KB]: 1279
% 2.55/1.64 % (9316)Time elapsed: 0.003 s
% 2.55/1.64 % (9316)Instructions burned: 4 (million)
% 2.55/1.64 % (9316)------------------------------
% 2.55/1.64 % (9316)------------------------------
% 2.55/1.64 % (9317)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/18Mi)
% 2.55/1.65 % (9318)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/710Mi)
% 2.55/1.65 % (9317)Instruction limit reached!
% 2.55/1.65 % (9317)------------------------------
% 2.55/1.65 % (9317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.65 % (9317)Termination reason: Unknown
% 2.55/1.65 % (9317)Termination phase: shuffling
% 2.55/1.65
% 2.55/1.65 % (9317)Memory used [KB]: 1663
% 2.55/1.65 % (9317)Time elapsed: 0.010 s
% 2.55/1.65 % (9317)Instructions burned: 19 (million)
% 2.55/1.65 % (9317)------------------------------
% 2.55/1.65 % (9317)------------------------------
% 2.55/1.65 % (9319)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/6Mi)
% 2.55/1.65 % (9319)Instruction limit reached!
% 2.55/1.65 % (9319)------------------------------
% 2.55/1.65 % (9319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.65 % (9319)Termination reason: Unknown
% 2.55/1.65 % (9319)Termination phase: shuffling
% 2.55/1.65
% 2.55/1.65 % (9319)Memory used [KB]: 1279
% 2.55/1.65 % (9319)Time elapsed: 0.004 s
% 2.55/1.65 % (9319)Instructions burned: 6 (million)
% 2.55/1.65 % (9319)------------------------------
% 2.55/1.65 % (9319)------------------------------
% 2.55/1.66 % (9320)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_9200 for (2999ds/902Mi)
% 2.55/1.66 % (9298)Instruction limit reached!
% 2.55/1.66 % (9298)------------------------------
% 2.55/1.66 % (9298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.66 % (9298)Termination reason: Unknown
% 2.55/1.66 % (9298)Termination phase: Saturation
% 2.55/1.66
% 2.55/1.66 % (9298)Memory used [KB]: 7164
% 2.55/1.66 % (9298)Time elapsed: 0.087 s
% 2.55/1.66 % (9298)Instructions burned: 183 (million)
% 2.55/1.66 % (9298)------------------------------
% 2.55/1.66 % (9298)------------------------------
% 2.55/1.67 % (9321)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_9200 for (2999ds/21Mi)
% 2.55/1.67 % (9322)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9200 for (2999ds/5Mi)
% 2.55/1.67 % (9322)Instruction limit reached!
% 2.55/1.67 % (9322)------------------------------
% 2.55/1.67 % (9322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.67 % (9322)Termination reason: Unknown
% 2.55/1.67 % (9322)Termination phase: shuffling
% 2.55/1.67
% 2.55/1.67 % (9322)Memory used [KB]: 1279
% 2.55/1.67 % (9322)Time elapsed: 0.004 s
% 2.55/1.67 % (9322)Instructions burned: 6 (million)
% 2.55/1.67 % (9322)------------------------------
% 2.55/1.67 % (9322)------------------------------
% 2.55/1.68 % (9323)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_9200 for (2998ds/6Mi)
% 2.55/1.68 % (9321)Instruction limit reached!
% 2.55/1.68 % (9321)------------------------------
% 2.55/1.68 % (9321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.68 % (9321)Termination reason: Unknown
% 2.55/1.68 % (9321)Termination phase: shuffling
% 2.55/1.68
% 2.55/1.68 % (9321)Memory used [KB]: 1663
% 2.55/1.68 % (9321)Time elapsed: 0.011 s
% 2.55/1.68 % (9321)Instructions burned: 21 (million)
% 2.55/1.68 % (9321)------------------------------
% 2.55/1.68 % (9321)------------------------------
% 2.55/1.68 % (9323)Instruction limit reached!
% 2.55/1.68 % (9323)------------------------------
% 2.55/1.68 % (9323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.68 % (9323)Termination reason: Unknown
% 2.55/1.68 % (9323)Termination phase: shuffling
% 2.55/1.68
% 2.55/1.68 % (9323)Memory used [KB]: 1279
% 2.55/1.68 % (9323)Time elapsed: 0.004 s
% 2.55/1.68 % (9323)Instructions burned: 6 (million)
% 2.55/1.68 % (9323)------------------------------
% 2.55/1.68 % (9323)------------------------------
% 2.55/1.69 % (9324)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_9200 for (2998ds/377Mi)
% 2.55/1.69 % (9325)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_9200 for (2998ds/779Mi)
% 2.55/1.69 % (9326)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_9200 for (2998ds/19Mi)
% 2.55/1.70 % (9326)Instruction limit reached!
% 2.55/1.70 % (9326)------------------------------
% 2.55/1.70 % (9326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.70 % (9326)Termination reason: Unknown
% 2.55/1.70 % (9326)Termination phase: shuffling
% 2.55/1.70
% 2.55/1.70 % (9326)Memory used [KB]: 1663
% 2.55/1.70 % (9326)Time elapsed: 0.010 s
% 2.55/1.70 % (9326)Instructions burned: 19 (million)
% 2.55/1.70 % (9326)------------------------------
% 2.55/1.70 % (9326)------------------------------
% 2.55/1.71 % (9303)Instruction limit reached!
% 2.55/1.71 % (9303)------------------------------
% 2.55/1.71 % (9303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.71 % (9303)Termination reason: Unknown
% 2.55/1.71 % (9303)Termination phase: Saturation
% 2.55/1.71
% 2.55/1.71 % (9303)Memory used [KB]: 7931
% 2.55/1.71 % (9303)Time elapsed: 0.139 s
% 2.55/1.71 % (9303)Instructions burned: 275 (million)
% 2.55/1.71 % (9303)------------------------------
% 2.55/1.71 % (9303)------------------------------
% 2.55/1.72 % (9327)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_9200 for (2998ds/879Mi)
% 2.55/1.73 % (9328)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_9200 for (2998ds/17Mi)
% 2.55/1.74 % (9328)Instruction limit reached!
% 2.55/1.74 % (9328)------------------------------
% 2.55/1.74 % (9328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.74 % (9328)Termination reason: Unknown
% 2.55/1.74 % (9328)Termination phase: shuffling
% 2.55/1.74
% 2.55/1.74 % (9328)Memory used [KB]: 1663
% 2.55/1.74 % (9328)Time elapsed: 0.010 s
% 2.55/1.74 % (9328)Instructions burned: 18 (million)
% 2.55/1.74 % (9328)------------------------------
% 2.55/1.74 % (9328)------------------------------
% 2.55/1.75 % (9329)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9200 for (2998ds/3Mi)
% 2.55/1.75 % (9329)Instruction limit reached!
% 2.55/1.75 % (9329)------------------------------
% 2.55/1.75 % (9329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.75 % (9329)Termination reason: Unknown
% 2.55/1.75 % (9329)Termination phase: shuffling
% 2.55/1.75
% 2.55/1.75 % (9329)Memory used [KB]: 1279
% 2.55/1.75 % (9329)Time elapsed: 0.003 s
% 2.55/1.75 % (9329)Instructions burned: 3 (million)
% 2.55/1.75 % (9329)------------------------------
% 2.55/1.75 % (9329)------------------------------
% 2.55/1.77 % (9330)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_9200 for (2998ds/30Mi)
% 2.55/1.78 % (9330)Instruction limit reached!
% 2.55/1.78 % (9330)------------------------------
% 2.55/1.78 % (9330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.78 % (9330)Termination reason: Unknown
% 2.55/1.78 % (9330)Termination phase: Property scanning
% 2.55/1.78
% 2.55/1.78 % (9330)Memory used [KB]: 1663
% 2.55/1.78 % (9330)Time elapsed: 0.015 s
% 2.55/1.78 % (9330)Instructions burned: 30 (million)
% 2.55/1.78 % (9330)------------------------------
% 2.55/1.78 % (9330)------------------------------
% 2.55/1.80 % (9331)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_9200 for (2997ds/127Mi)
% 2.55/1.86 % (9331)Instruction limit reached!
% 2.55/1.86 % (9331)------------------------------
% 2.55/1.86 % (9331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.86 % (9331)Termination reason: Unknown
% 2.55/1.86 % (9331)Termination phase: Saturation
% 2.55/1.86
% 2.55/1.86 % (9331)Memory used [KB]: 6908
% 2.55/1.86 % (9331)Time elapsed: 0.059 s
% 2.55/1.86 % (9331)Instructions burned: 129 (million)
% 2.55/1.86 % (9331)------------------------------
% 2.55/1.86 % (9331)------------------------------
% 2.55/1.87 % (9324)Instruction limit reached!
% 2.55/1.87 % (9324)------------------------------
% 2.55/1.87 % (9324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.87 % (9324)Termination reason: Unknown
% 2.55/1.87 % (9324)Termination phase: Saturation
% 2.55/1.87
% 2.55/1.87 % (9324)Memory used [KB]: 7675
% 2.55/1.87 % (9324)Time elapsed: 0.185 s
% 2.55/1.87 % (9324)Instructions burned: 378 (million)
% 2.55/1.87 % (9324)------------------------------
% 2.55/1.87 % (9324)------------------------------
% 2.55/1.87 % (9332)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_9200 for (2997ds/100Mi)
% 2.55/1.89 % (9333)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_9200 for (2996ds/3Mi)
% 2.55/1.89 % (9333)Instruction limit reached!
% 2.55/1.89 % (9333)------------------------------
% 2.55/1.89 % (9333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.89 % (9333)Termination reason: Unknown
% 2.55/1.89 % (9333)Termination phase: shuffling
% 2.55/1.89
% 2.55/1.89 % (9333)Memory used [KB]: 1279
% 2.55/1.89 % (9333)Time elapsed: 0.003 s
% 2.55/1.89 % (9333)Instructions burned: 3 (million)
% 2.55/1.89 % (9333)------------------------------
% 2.55/1.89 % (9333)------------------------------
% 2.55/1.91 % (9334)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_9200 for (2996ds/20Mi)
% 2.55/1.92 % (9334)Instruction limit reached!
% 2.55/1.92 % (9334)------------------------------
% 2.55/1.92 % (9334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.92 % (9334)Termination reason: Unknown
% 2.55/1.92 % (9334)Termination phase: SInE selection
% 2.55/1.92
% 2.55/1.92 % (9334)Memory used [KB]: 1535
% 2.55/1.92 % (9334)Time elapsed: 0.011 s
% 2.55/1.92 % (9334)Instructions burned: 20 (million)
% 2.55/1.92 % (9334)------------------------------
% 2.55/1.92 % (9334)------------------------------
% 2.55/1.92 % (9332)Instruction limit reached!
% 2.55/1.92 % (9332)------------------------------
% 2.55/1.92 % (9332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.92 % (9332)Termination reason: Unknown
% 2.55/1.92 % (9332)Termination phase: Saturation
% 2.55/1.92
% 2.55/1.92 % (9332)Memory used [KB]: 6524
% 2.55/1.92 % (9332)Time elapsed: 0.047 s
% 2.55/1.92 % (9332)Instructions burned: 100 (million)
% 2.55/1.92 % (9332)------------------------------
% 2.55/1.92 % (9332)------------------------------
% 2.55/1.93 % (9335)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_9200 for (2996ds/86Mi)
% 2.55/1.93 % (9336)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_9200 for (2996ds/107Mi)
% 2.55/1.97 % (9335)Instruction limit reached!
% 2.55/1.97 % (9335)------------------------------
% 2.55/1.97 % (9335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.97 % (9335)Termination reason: Unknown
% 2.55/1.97 % (9335)Termination phase: Saturation
% 2.55/1.97
% 2.55/1.97 % (9335)Memory used [KB]: 6524
% 2.55/1.97 % (9335)Time elapsed: 0.040 s
% 2.55/1.97 % (9335)Instructions burned: 86 (million)
% 2.55/1.97 % (9335)------------------------------
% 2.55/1.97 % (9335)------------------------------
% 2.55/1.97 % (9325)Instruction limit reached!
% 2.55/1.97 % (9325)------------------------------
% 2.55/1.97 % (9325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.97 % (9325)Termination reason: Unknown
% 2.55/1.97 % (9325)Termination phase: Saturation
% 2.55/1.97
% 2.55/1.97 % (9325)Memory used [KB]: 6652
% 2.55/1.97 % (9325)Time elapsed: 0.281 s
% 2.55/1.97 % (9325)Instructions burned: 779 (million)
% 2.55/1.97 % (9325)------------------------------
% 2.55/1.97 % (9325)------------------------------
% 2.55/1.98 % (9336)Instruction limit reached!
% 2.55/1.98 % (9336)------------------------------
% 2.55/1.98 % (9336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.98 % (9336)Termination reason: Unknown
% 2.55/1.98 % (9336)Termination phase: Saturation
% 2.55/1.98
% 2.55/1.98 % (9336)Memory used [KB]: 6780
% 2.55/1.98 % (9336)Time elapsed: 0.050 s
% 2.55/1.98 % (9336)Instructions burned: 109 (million)
% 2.55/1.98 % (9336)------------------------------
% 2.55/1.98 % (9336)------------------------------
% 2.55/1.98 % (9309)Instruction limit reached!
% 2.55/1.98 % (9309)------------------------------
% 2.55/1.98 % (9309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.98 % (9309)Termination reason: Unknown
% 2.55/1.98 % (9309)Termination phase: Saturation
% 2.55/1.98
% 2.55/1.98 % (9309)Memory used [KB]: 8955
% 2.55/1.98 % (9309)Time elapsed: 0.383 s
% 2.55/1.98 % (9309)Instructions burned: 1042 (million)
% 2.55/1.98 % (9309)------------------------------
% 2.55/1.98 % (9309)------------------------------
% 2.55/1.99 % (9337)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_9200 for (2995ds/39Mi)
% 2.55/1.99 % (9338)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_9200 for (2995ds/448Mi)
% 2.55/2.00 % (9339)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_9200 for (2995ds/46Mi)
% 2.55/2.00 % (9340)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_9200 for (2995ds/98Mi)
% 2.55/2.00 % (9337)Instruction limit reached!
% 2.55/2.00 % (9337)------------------------------
% 2.55/2.00 % (9337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/2.00 % (9337)Termination reason: Unknown
% 2.55/2.00 % (9337)Termination phase: Property scanning
% 2.55/2.00
% 2.55/2.00 % (9337)Memory used [KB]: 1663
% 2.55/2.00 % (9337)Time elapsed: 0.019 s
% 2.55/2.00 % (9337)Instructions burned: 39 (million)
% 2.55/2.00 % (9337)------------------------------
% 2.55/2.00 % (9337)------------------------------
% 2.55/2.02 % (9318)Instruction limit reached!
% 2.55/2.02 % (9318)------------------------------
% 2.55/2.02 % (9318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/2.02 % (9318)Termination reason: Unknown
% 2.55/2.02 % (9318)Termination phase: Saturation
% 2.55/2.02
% 2.55/2.02 % (9318)Memory used [KB]: 8955
% 2.55/2.02 % (9318)Time elapsed: 0.367 s
% 2.55/2.02 % (9318)Instructions burned: 711 (million)
% 2.55/2.02 % (9318)------------------------------
% 2.55/2.02 % (9318)------------------------------
% 2.55/2.02 % (9339)Instruction limit reached!
% 2.55/2.02 % (9339)------------------------------
% 2.55/2.02 % (9339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/2.02 % (9339)Termination reason: Unknown
% 2.55/2.02 % (9339)Termination phase: Property scanning
% 2.55/2.02
% 2.55/2.02 % (9339)Memory used [KB]: 1791
% 2.55/2.02 % (9339)Time elapsed: 0.022 s
% 2.55/2.02 % (9339)Instructions burned: 46 (million)
% 2.55/2.02 % (9341)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_9200 for (2995ds/507Mi)
% 2.55/2.02 % (9339)------------------------------
% 2.55/2.02 % (9339)------------------------------
% 5.72/2.03 % (9342)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_9200 for (2995ds/149Mi)
% 5.72/2.04 % (9343)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_9200 for (2995ds/39Mi)
% 5.72/2.04 % (9340)Instruction limit reached!
% 5.72/2.04 % (9340)------------------------------
% 5.72/2.04 % (9340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.04 % (9340)Termination reason: Unknown
% 5.72/2.04 % (9340)Termination phase: Saturation
% 5.72/2.04
% 5.72/2.04 % (9340)Memory used [KB]: 1918
% 5.72/2.04 % (9340)Time elapsed: 0.043 s
% 5.72/2.04 % (9340)Instructions burned: 98 (million)
% 5.72/2.04 % (9340)------------------------------
% 5.72/2.04 % (9340)------------------------------
% 5.72/2.05 % (9343)Instruction limit reached!
% 5.72/2.05 % (9343)------------------------------
% 5.72/2.05 % (9343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.05 % (9343)Termination reason: Unknown
% 5.72/2.05 % (9343)Termination phase: Property scanning
% 5.72/2.05
% 5.72/2.05 % (9343)Memory used [KB]: 1791
% 5.72/2.05 % (9343)Time elapsed: 0.020 s
% 5.72/2.05 % (9343)Instructions burned: 40 (million)
% 5.72/2.05 % (9343)------------------------------
% 5.72/2.05 % (9343)------------------------------
% 5.72/2.06 % (9344)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_9200 for (2995ds/6Mi)
% 5.72/2.06 % (9344)Instruction limit reached!
% 5.72/2.06 % (9344)------------------------------
% 5.72/2.06 % (9344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.06 % (9344)Termination reason: Unknown
% 5.72/2.06 % (9344)Termination phase: shuffling
% 5.72/2.06
% 5.72/2.06 % (9344)Memory used [KB]: 1279
% 5.72/2.06 % (9344)Time elapsed: 0.004 s
% 5.72/2.06 % (9344)Instructions burned: 6 (million)
% 5.72/2.06 % (9344)------------------------------
% 5.72/2.06 % (9344)------------------------------
% 5.72/2.07 % (9345)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_9200 for (2995ds/1087Mi)
% 5.72/2.08 % (9346)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_9200 for (2994ds/47Mi)
% 5.72/2.10 % (9346)Instruction limit reached!
% 5.72/2.10 % (9346)------------------------------
% 5.72/2.10 % (9346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.10 % (9346)Termination reason: Unknown
% 5.72/2.10 % (9346)Termination phase: Function definition elimination
% 5.72/2.10
% 5.72/2.10 % (9346)Memory used [KB]: 1791
% 5.72/2.10 % (9346)Time elapsed: 0.022 s
% 5.72/2.10 % (9346)Instructions burned: 47 (million)
% 5.72/2.10 % (9346)------------------------------
% 5.72/2.10 % (9346)------------------------------
% 5.72/2.10 % (9320)Instruction limit reached!
% 5.72/2.10 % (9320)------------------------------
% 5.72/2.10 % (9320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.10 % (9320)Termination reason: Unknown
% 5.72/2.10 % (9320)Termination phase: Saturation
% 5.72/2.10
% 5.72/2.10 % (9320)Memory used [KB]: 9850
% 5.72/2.10 % (9320)Time elapsed: 0.448 s
% 5.72/2.10 % (9320)Instructions burned: 903 (million)
% 5.72/2.10 % (9320)------------------------------
% 5.72/2.10 % (9320)------------------------------
% 5.72/2.10 % (9342)Instruction limit reached!
% 5.72/2.10 % (9342)------------------------------
% 5.72/2.10 % (9342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.10 % (9342)Termination reason: Unknown
% 5.72/2.10 % (9342)Termination phase: Saturation
% 5.72/2.10
% 5.72/2.10 % (9342)Memory used [KB]: 7036
% 5.72/2.10 % (9342)Time elapsed: 0.074 s
% 5.72/2.10 % (9342)Instructions burned: 150 (million)
% 5.72/2.10 % (9342)------------------------------
% 5.72/2.10 % (9342)------------------------------
% 5.72/2.11 % (9347)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_9200 for (2994ds/44Mi)
% 5.72/2.12 % (9348)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_9200 for (2994ds/432Mi)
% 5.72/2.12 % (9350)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_9200 for (2994ds/62Mi)
% 6.22/2.13 % (9347)Instruction limit reached!
% 6.22/2.13 % (9347)------------------------------
% 6.22/2.13 % (9347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.13 % (9347)Termination reason: Unknown
% 6.22/2.13 % (9347)Termination phase: Property scanning
% 6.22/2.13
% 6.22/2.13 % (9347)Memory used [KB]: 1663
% 6.22/2.13 % (9347)Time elapsed: 0.021 s
% 6.22/2.13 % (9347)Instructions burned: 45 (million)
% 6.22/2.13 % (9347)------------------------------
% 6.22/2.13 % (9347)------------------------------
% 6.22/2.15 % (9327)Instruction limit reached!
% 6.22/2.15 % (9327)------------------------------
% 6.22/2.15 % (9327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.15 % (9327)Termination reason: Unknown
% 6.22/2.15 % (9327)Termination phase: Saturation
% 6.22/2.15
% 6.22/2.15 % (9327)Memory used [KB]: 8059
% 6.22/2.15 % (9327)Time elapsed: 0.431 s
% 6.22/2.15 % (9327)Instructions burned: 879 (million)
% 6.22/2.15 % (9327)------------------------------
% 6.22/2.15 % (9327)------------------------------
% 6.22/2.15 % (9350)Instruction limit reached!
% 6.22/2.15 % (9350)------------------------------
% 6.22/2.15 % (9350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.15 % (9350)Termination reason: Unknown
% 6.22/2.15 % (9350)Termination phase: Property scanning
% 6.22/2.15
% 6.22/2.15 % (9350)Memory used [KB]: 1791
% 6.22/2.15 % (9350)Time elapsed: 0.029 s
% 6.22/2.15 % (9350)Instructions burned: 64 (million)
% 6.22/2.15 % (9350)------------------------------
% 6.22/2.15 % (9350)------------------------------
% 6.22/2.15 % (9351)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_9200 for (2994ds/31Mi)
% 6.22/2.15 % (9338)Instruction limit reached!
% 6.22/2.15 % (9338)------------------------------
% 6.22/2.15 % (9338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.15 % (9338)Termination reason: Unknown
% 6.22/2.15 % (9338)Termination phase: Saturation
% 6.22/2.15
% 6.22/2.15 % (9338)Memory used [KB]: 6524
% 6.22/2.15 % (9338)Time elapsed: 0.165 s
% 6.22/2.15 % (9338)Instructions burned: 449 (million)
% 6.22/2.15 % (9338)------------------------------
% 6.22/2.15 % (9338)------------------------------
% 6.22/2.16 % (9351)Instruction limit reached!
% 6.22/2.16 % (9351)------------------------------
% 6.22/2.16 % (9351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.16 % (9351)Termination reason: Unknown
% 6.22/2.16 % (9351)Termination phase: Property scanning
% 6.22/2.16
% 6.22/2.16 % (9351)Memory used [KB]: 1663
% 6.22/2.16 % (9351)Time elapsed: 0.016 s
% 6.22/2.16 % (9351)Instructions burned: 33 (million)
% 6.22/2.16 % (9351)------------------------------
% 6.22/2.16 % (9351)------------------------------
% 6.22/2.16 % (9352)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_9200 for (2994ds/96Mi)
% 6.22/2.16 % (9353)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_9200 for (2994ds/453Mi)
% 6.22/2.17 % (9354)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_9200 for (2994ds/71Mi)
% 6.22/2.18 % (9355)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_9200 for (2994ds/83Mi)
% 6.40/2.20 % (9354)Instruction limit reached!
% 6.40/2.20 % (9354)------------------------------
% 6.40/2.20 % (9354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.20 % (9354)Termination reason: Unknown
% 6.40/2.20 % (9354)Termination phase: Saturation
% 6.40/2.20
% 6.40/2.20 % (9354)Memory used [KB]: 6396
% 6.40/2.20 % (9354)Time elapsed: 0.033 s
% 6.40/2.20 % (9354)Instructions burned: 72 (million)
% 6.40/2.20 % (9354)------------------------------
% 6.40/2.20 % (9354)------------------------------
% 6.40/2.21 % (9352)Instruction limit reached!
% 6.40/2.21 % (9352)------------------------------
% 6.40/2.21 % (9352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.21 % (9352)Termination reason: Unknown
% 6.40/2.21 % (9352)Termination phase: Saturation
% 6.40/2.21
% 6.40/2.21 % (9352)Memory used [KB]: 6780
% 6.40/2.21 % (9352)Time elapsed: 0.045 s
% 6.40/2.21 % (9352)Instructions burned: 98 (million)
% 6.40/2.21 % (9352)------------------------------
% 6.40/2.21 % (9352)------------------------------
% 6.40/2.21 % (9356)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_9200 for (2993ds/11Mi)
% 6.40/2.21 % (9355)Instruction limit reached!
% 6.40/2.21 % (9355)------------------------------
% 6.40/2.21 % (9355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.21 % (9355)Termination reason: Unknown
% 6.40/2.21 % (9355)Termination phase: Saturation
% 6.40/2.21
% 6.40/2.21 % (9355)Memory used [KB]: 6268
% 6.40/2.21 % (9355)Time elapsed: 0.037 s
% 6.40/2.21 % (9355)Instructions burned: 83 (million)
% 6.40/2.21 % (9355)------------------------------
% 6.40/2.21 % (9355)------------------------------
% 6.40/2.22 % (9356)Instruction limit reached!
% 6.40/2.22 % (9356)------------------------------
% 6.40/2.22 % (9356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.22 % (9356)Termination reason: Unknown
% 6.40/2.22 % (9356)Termination phase: shuffling
% 6.40/2.22
% 6.40/2.22 % (9356)Memory used [KB]: 1407
% 6.40/2.22 % (9356)Time elapsed: 0.007 s
% 6.40/2.22 % (9356)Instructions burned: 12 (million)
% 6.40/2.22 % (9356)------------------------------
% 6.40/2.22 % (9356)------------------------------
% 6.40/2.22 % (9357)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_9200 for (2993ds/41Mi)
% 6.40/2.23 % (9358)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9200 for (2993ds/6Mi)
% 6.40/2.23 % (9358)Instruction limit reached!
% 6.40/2.23 % (9358)------------------------------
% 6.40/2.23 % (9358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.23 % (9358)Termination reason: Unknown
% 6.40/2.23 % (9358)Termination phase: shuffling
% 6.40/2.23
% 6.40/2.23 % (9358)Memory used [KB]: 1279
% 6.40/2.23 % (9358)Time elapsed: 0.004 s
% 6.40/2.23 % (9358)Instructions burned: 6 (million)
% 6.40/2.23 % (9358)------------------------------
% 6.40/2.23 % (9358)------------------------------
% 6.40/2.24 % (9359)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_9200 for (2993ds/150Mi)
% 6.40/2.24 % (9357)Instruction limit reached!
% 6.40/2.24 % (9357)------------------------------
% 6.40/2.24 % (9357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.24 % (9357)Termination reason: Unknown
% 6.40/2.24 % (9357)Termination phase: Property scanning
% 6.40/2.24
% 6.40/2.24 % (9357)Memory used [KB]: 1663
% 6.40/2.24 % (9357)Time elapsed: 0.020 s
% 6.40/2.24 % (9357)Instructions burned: 42 (million)
% 6.40/2.24 % (9357)------------------------------
% 6.40/2.24 % (9357)------------------------------
% 6.40/2.25 % (9360)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_9200 for (2993ds/343Mi)
% 6.40/2.26 % (9361)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_9200 for (2993ds/109Mi)
% 6.40/2.26 % (9341)Instruction limit reached!
% 6.40/2.26 % (9341)------------------------------
% 6.40/2.26 % (9341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.26 % (9341)Termination reason: Unknown
% 6.40/2.26 % (9341)Termination phase: Saturation
% 6.40/2.26
% 6.40/2.26 % (9341)Memory used [KB]: 7291
% 6.40/2.26 % (9341)Time elapsed: 0.244 s
% 6.40/2.26 % (9341)Instructions burned: 508 (million)
% 6.40/2.26 % (9341)------------------------------
% 6.40/2.26 % (9341)------------------------------
% 6.40/2.28 % (9362)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_9200 for (2993ds/253Mi)
% 6.40/2.29 % (9348)Instruction limit reached!
% 6.40/2.29 % (9348)------------------------------
% 6.40/2.29 % (9348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.29 % (9348)Termination reason: Unknown
% 6.40/2.29 % (9348)Termination phase: Saturation
% 6.40/2.29
% 6.40/2.29 % (9348)Memory used [KB]: 2814
% 6.40/2.29 % (9348)Time elapsed: 0.174 s
% 6.40/2.29 % (9348)Instructions burned: 432 (million)
% 6.40/2.29 % (9348)------------------------------
% 6.40/2.29 % (9348)------------------------------
% 7.08/2.31 % (9361)Instruction limit reached!
% 7.08/2.31 % (9361)------------------------------
% 7.08/2.31 % (9361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.31 % (9361)Termination reason: Unknown
% 7.08/2.31 % (9361)Termination phase: Saturation
% 7.08/2.31
% 7.08/2.31 % (9361)Memory used [KB]: 6652
% 7.08/2.31 % (9361)Time elapsed: 0.050 s
% 7.08/2.31 % (9361)Instructions burned: 110 (million)
% 7.08/2.31 % (9361)------------------------------
% 7.08/2.31 % (9361)------------------------------
% 7.08/2.31 % (9359)Instruction limit reached!
% 7.08/2.31 % (9359)------------------------------
% 7.08/2.31 % (9359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.31 % (9359)Termination reason: Unknown
% 7.08/2.31 % (9359)Termination phase: Saturation
% 7.08/2.31
% 7.08/2.31 % (9359)Memory used [KB]: 7675
% 7.08/2.31 % (9359)Time elapsed: 0.074 s
% 7.08/2.31 % (9359)Instructions burned: 151 (million)
% 7.08/2.31 % (9359)------------------------------
% 7.08/2.31 % (9359)------------------------------
% 7.08/2.31 % (9363)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_9200 for (2992ds/140Mi)
% 7.08/2.32 % (9364)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_9200 for (2992ds/614Mi)
% 7.08/2.32 % (9365)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_9200 for (2992ds/202Mi)
% 7.08/2.33 % (9353)Instruction limit reached!
% 7.08/2.33 % (9353)------------------------------
% 7.08/2.33 % (9353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.33 % (9353)Termination reason: Unknown
% 7.08/2.33 % (9353)Termination phase: Saturation
% 7.08/2.33
% 7.08/2.33 % (9353)Memory used [KB]: 6524
% 7.08/2.33 % (9353)Time elapsed: 0.169 s
% 7.08/2.33 % (9353)Instructions burned: 453 (million)
% 7.08/2.33 % (9353)------------------------------
% 7.08/2.33 % (9353)------------------------------
% 7.08/2.35 % (9366)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_9200 for (2992ds/339Mi)
% 7.08/2.37 % (9363)Instruction limit reached!
% 7.08/2.37 % (9363)------------------------------
% 7.08/2.37 % (9363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.37 % (9363)Termination reason: Unknown
% 7.08/2.37 % (9363)Termination phase: Saturation
% 7.08/2.37
% 7.08/2.37 % (9363)Memory used [KB]: 6524
% 7.08/2.37 % (9363)Time elapsed: 0.065 s
% 7.08/2.37 % (9363)Instructions burned: 141 (million)
% 7.08/2.37 % (9363)------------------------------
% 7.08/2.37 % (9363)------------------------------
% 7.08/2.39 % (9367)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_9200 for (2991ds/283Mi)
% 7.50/2.40 % (9362)Instruction limit reached!
% 7.50/2.40 % (9362)------------------------------
% 7.50/2.40 % (9362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.40 % (9362)Termination reason: Unknown
% 7.50/2.40 % (9362)Termination phase: Saturation
% 7.50/2.40
% 7.50/2.40 % (9362)Memory used [KB]: 8059
% 7.50/2.40 % (9362)Time elapsed: 0.124 s
% 7.50/2.40 % (9362)Instructions burned: 253 (million)
% 7.50/2.40 % (9362)------------------------------
% 7.50/2.40 % (9362)------------------------------
% 7.50/2.41 % (9360)Instruction limit reached!
% 7.50/2.41 % (9360)------------------------------
% 7.50/2.41 % (9360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.41 % (9360)Termination reason: Unknown
% 7.50/2.41 % (9360)Termination phase: Saturation
% 7.50/2.41
% 7.50/2.41 % (9360)Memory used [KB]: 7675
% 7.50/2.41 % (9360)Time elapsed: 0.164 s
% 7.50/2.41 % (9360)Instructions burned: 343 (million)
% 7.50/2.41 % (9360)------------------------------
% 7.50/2.41 % (9360)------------------------------
% 7.50/2.42 % (9368)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_9200 for (2991ds/134Mi)
% 7.50/2.43 % (9365)Instruction limit reached!
% 7.50/2.43 % (9365)------------------------------
% 7.50/2.43 % (9365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.43 % (9365)Termination reason: Unknown
% 7.50/2.43 % (9365)Termination phase: Saturation
% 7.50/2.43
% 7.50/2.43 % (9365)Memory used [KB]: 8059
% 7.50/2.43 % (9365)Time elapsed: 0.102 s
% 7.50/2.43 % (9365)Instructions burned: 203 (million)
% 7.50/2.43 % (9365)------------------------------
% 7.50/2.43 % (9365)------------------------------
% 7.50/2.43 % (9369)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_9200 for (2991ds/298Mi)
% 7.50/2.44 % (9370)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_9200 for (2991ds/192Mi)
% 7.50/2.48 % (9368)Instruction limit reached!
% 7.50/2.48 % (9368)------------------------------
% 7.50/2.48 % (9368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.48 % (9368)Termination reason: Unknown
% 7.50/2.48 % (9368)Termination phase: Saturation
% 7.50/2.48
% 7.50/2.48 % (9368)Memory used [KB]: 6908
% 7.50/2.48 % (9368)Time elapsed: 0.062 s
% 7.50/2.48 % (9368)Instructions burned: 134 (million)
% 7.50/2.48 % (9368)------------------------------
% 7.50/2.48 % (9368)------------------------------
% 7.50/2.49 % (9371)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_9200 for (2990ds/258Mi)
% 8.01/2.50 % (9367)Instruction limit reached!
% 8.01/2.50 % (9367)------------------------------
% 8.01/2.50 % (9367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.50 % (9367)Termination reason: Unknown
% 8.01/2.50 % (9367)Termination phase: Saturation
% 8.01/2.50
% 8.01/2.50 % (9367)Memory used [KB]: 9210
% 8.01/2.50 % (9367)Time elapsed: 0.116 s
% 8.01/2.50 % (9367)Instructions burned: 284 (million)
% 8.01/2.50 % (9367)------------------------------
% 8.01/2.50 % (9367)------------------------------
% 8.01/2.51 % (9366)Instruction limit reached!
% 8.01/2.51 % (9366)------------------------------
% 8.01/2.51 % (9366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.51 % (9366)Termination reason: Unknown
% 8.01/2.51 % (9366)Termination phase: Saturation
% 8.01/2.51
% 8.01/2.51 % (9366)Memory used [KB]: 8059
% 8.01/2.51 % (9366)Time elapsed: 0.161 s
% 8.01/2.51 % (9366)Instructions burned: 339 (million)
% 8.01/2.51 % (9366)------------------------------
% 8.01/2.51 % (9366)------------------------------
% 8.01/2.52 % (9372)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_9200 for (2990ds/90Mi)
% 8.01/2.52 % (9373)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_9200 for (2990ds/231Mi)
% 8.01/2.53 % (9370)Instruction limit reached!
% 8.01/2.53 % (9370)------------------------------
% 8.01/2.53 % (9370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.53 % (9370)Termination reason: Unknown
% 8.01/2.53 % (9370)Termination phase: Saturation
% 8.01/2.53
% 8.01/2.53 % (9370)Memory used [KB]: 7164
% 8.01/2.53 % (9370)Time elapsed: 0.090 s
% 8.01/2.53 % (9370)Instructions burned: 192 (million)
% 8.01/2.53 % (9370)------------------------------
% 8.01/2.53 % (9370)------------------------------
% 8.01/2.55 % (9374)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_9200 for (2990ds/458Mi)
% 8.01/2.55 % (9369)Instruction limit reached!
% 8.01/2.55 % (9369)------------------------------
% 8.01/2.55 % (9369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.55 % (9369)Termination reason: Unknown
% 8.01/2.55 % (9369)Termination phase: Saturation
% 8.01/2.55
% 8.01/2.55 % (9369)Memory used [KB]: 6524
% 8.01/2.55 % (9369)Time elapsed: 0.125 s
% 8.01/2.55 % (9369)Instructions burned: 298 (million)
% 8.01/2.55 % (9369)------------------------------
% 8.01/2.55 % (9369)------------------------------
% 8.01/2.56 % (9372)Instruction limit reached!
% 8.01/2.56 % (9372)------------------------------
% 8.01/2.56 % (9372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.56 % (9372)Termination reason: Unknown
% 8.01/2.56 % (9372)Termination phase: Saturation
% 8.01/2.56
% 8.01/2.56 % (9372)Memory used [KB]: 6652
% 8.01/2.56 % (9372)Time elapsed: 0.043 s
% 8.01/2.56 % (9372)Instructions burned: 91 (million)
% 8.01/2.56 % (9372)------------------------------
% 8.01/2.56 % (9372)------------------------------
% 8.01/2.57 % (9375)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_9200 for (2989ds/31Mi)
% 8.01/2.58 % (9376)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_9200 for (2989ds/297Mi)
% 8.01/2.58 % (9375)Instruction limit reached!
% 8.01/2.58 % (9375)------------------------------
% 8.01/2.58 % (9375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.58 % (9375)Termination reason: Unknown
% 8.01/2.58 % (9375)Termination phase: Property scanning
% 8.01/2.58
% 8.01/2.58 % (9375)Memory used [KB]: 1663
% 8.01/2.58 % (9375)Time elapsed: 0.016 s
% 8.01/2.58 % (9375)Instructions burned: 32 (million)
% 8.01/2.58 % (9375)------------------------------
% 8.01/2.58 % (9375)------------------------------
% 8.66/2.60 % (9377)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_9200 for (2989ds/987Mi)
% 8.66/2.61 % (9345)Instruction limit reached!
% 8.66/2.61 % (9345)------------------------------
% 8.66/2.61 % (9345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.61 % (9345)Termination reason: Unknown
% 8.66/2.61 % (9345)Termination phase: Saturation
% 8.66/2.61
% 8.66/2.61 % (9345)Memory used [KB]: 10106
% 8.66/2.61 % (9345)Time elapsed: 0.546 s
% 8.66/2.61 % (9345)Instructions burned: 1087 (million)
% 8.66/2.61 % (9345)------------------------------
% 8.66/2.61 % (9345)------------------------------
% 8.66/2.62 % (9371)Instruction limit reached!
% 8.66/2.62 % (9371)------------------------------
% 8.66/2.62 % (9371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.62 % (9371)Termination reason: Unknown
% 8.66/2.62 % (9371)Termination phase: Saturation
% 8.66/2.62
% 8.66/2.62 % (9371)Memory used [KB]: 7291
% 8.66/2.62 % (9371)Time elapsed: 0.124 s
% 8.66/2.62 % (9371)Instructions burned: 259 (million)
% 8.66/2.62 % (9371)------------------------------
% 8.66/2.62 % (9371)------------------------------
% 8.66/2.62 % (9364)Instruction limit reached!
% 8.66/2.62 % (9364)------------------------------
% 8.66/2.62 % (9364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.62 % (9364)Termination reason: Unknown
% 8.66/2.62 % (9364)Termination phase: Saturation
% 8.66/2.62
% 8.66/2.62 % (9364)Memory used [KB]: 8315
% 8.66/2.62 % (9364)Time elapsed: 0.300 s
% 8.66/2.62 % (9364)Instructions burned: 615 (million)
% 8.66/2.62 % (9364)------------------------------
% 8.66/2.62 % (9364)------------------------------
% 8.66/2.63 % (9378)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_9200 for (2989ds/182Mi)
% 8.66/2.63 % (9373)Instruction limit reached!
% 8.66/2.63 % (9373)------------------------------
% 8.66/2.63 % (9373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.63 % (9373)Termination reason: Unknown
% 8.66/2.63 % (9373)Termination phase: Saturation
% 8.66/2.63
% 8.66/2.63 % (9373)Memory used [KB]: 10234
% 8.66/2.63 % (9373)Time elapsed: 0.110 s
% 8.66/2.63 % (9373)Instructions burned: 232 (million)
% 8.66/2.63 % (9373)------------------------------
% 8.66/2.63 % (9373)------------------------------
% 8.66/2.63 % (9379)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_9200 for (2989ds/182Mi)
% 8.66/2.64 % (9380)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_9200 for (2989ds/154Mi)
% 8.66/2.65 % (9381)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_9200 for (2989ds/79Mi)
% 8.66/2.68 % (9381)Instruction limit reached!
% 8.66/2.68 % (9381)------------------------------
% 8.66/2.68 % (9381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.68 % (9381)Termination reason: Unknown
% 8.66/2.68 % (9381)Termination phase: Saturation
% 8.66/2.68
% 8.66/2.68 % (9381)Memory used [KB]: 6524
% 8.66/2.68 % (9381)Time elapsed: 0.037 s
% 8.66/2.68 % (9381)Instructions burned: 80 (million)
% 8.66/2.68 % (9381)------------------------------
% 8.66/2.68 % (9381)------------------------------
% 8.66/2.69 % (9376)Instruction limit reached!
% 8.66/2.69 % (9376)------------------------------
% 8.66/2.69 % (9376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.69 % (9376)Termination reason: Unknown
% 8.66/2.69 % (9376)Termination phase: Saturation
% 8.66/2.69
% 8.66/2.69 % (9376)Memory used [KB]: 8059
% 8.66/2.69 % (9376)Time elapsed: 0.116 s
% 8.66/2.69 % (9376)Instructions burned: 297 (million)
% 8.66/2.69 % (9376)------------------------------
% 8.66/2.69 % (9376)------------------------------
% 9.98/2.70 % (9382)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_9200 for (2988ds/216Mi)
% 9.98/2.70 % (9380)Instruction limit reached!
% 9.98/2.70 % (9380)------------------------------
% 9.98/2.70 % (9380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.70 % (9380)Termination reason: Unknown
% 9.98/2.70 % (9380)Termination phase: Saturation
% 9.98/2.70
% 9.98/2.70 % (9380)Memory used [KB]: 6524
% 9.98/2.70 % (9380)Time elapsed: 0.065 s
% 9.98/2.70 % (9380)Instructions burned: 155 (million)
% 9.98/2.70 % (9380)------------------------------
% 9.98/2.70 % (9380)------------------------------
% 9.98/2.71 % (9383)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_9200 for (2988ds/114Mi)
% 9.98/2.72 % (9378)Instruction limit reached!
% 9.98/2.72 % (9378)------------------------------
% 9.98/2.72 % (9378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.72 % (9378)Termination reason: Unknown
% 9.98/2.72 % (9378)Termination phase: Saturation
% 9.98/2.72
% 9.98/2.72 % (9378)Memory used [KB]: 7036
% 9.98/2.72 % (9378)Time elapsed: 0.086 s
% 9.98/2.72 % (9378)Instructions burned: 183 (million)
% 9.98/2.72 % (9378)------------------------------
% 9.98/2.72 % (9378)------------------------------
% 9.98/2.72 % (9384)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_9200 for (2988ds/922Mi)
% 9.98/2.72 % (9379)Instruction limit reached!
% 9.98/2.72 % (9379)------------------------------
% 9.98/2.72 % (9379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.72 % (9379)Termination reason: Unknown
% 9.98/2.72 % (9379)Termination phase: Saturation
% 9.98/2.72
% 9.98/2.72 % (9379)Memory used [KB]: 9083
% 9.98/2.72 % (9379)Time elapsed: 0.093 s
% 9.98/2.72 % (9379)Instructions burned: 183 (million)
% 9.98/2.72 % (9379)------------------------------
% 9.98/2.72 % (9379)------------------------------
% 9.98/2.73 % (9385)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_9200 for (2988ds/182Mi)
% 9.98/2.74 % (9386)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_9200 for (2988ds/164Mi)
% 9.98/2.76 % (9383)Instruction limit reached!
% 9.98/2.76 % (9383)------------------------------
% 9.98/2.76 % (9383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.76 % (9383)Termination reason: Unknown
% 9.98/2.76 % (9383)Termination phase: Saturation
% 9.98/2.76
% 9.98/2.76 % (9383)Memory used [KB]: 6780
% 9.98/2.76 % (9383)Time elapsed: 0.053 s
% 9.98/2.76 % (9383)Instructions burned: 115 (million)
% 9.98/2.76 % (9383)------------------------------
% 9.98/2.76 % (9383)------------------------------
% 9.98/2.77 % (9374)Instruction limit reached!
% 9.98/2.77 % (9374)------------------------------
% 9.98/2.77 % (9374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.77 % (9374)Termination reason: Unknown
% 9.98/2.77 % (9374)Termination phase: Saturation
% 9.98/2.77
% 9.98/2.77 % (9374)Memory used [KB]: 7803
% 9.98/2.77 % (9374)Time elapsed: 0.224 s
% 9.98/2.77 % (9374)Instructions burned: 459 (million)
% 9.98/2.77 % (9374)------------------------------
% 9.98/2.77 % (9374)------------------------------
% 9.98/2.78 % (9387)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_9200 for (2987ds/50Mi)
% 9.98/2.78 % (9382)Instruction limit reached!
% 9.98/2.78 % (9382)------------------------------
% 9.98/2.78 % (9382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.78 % (9382)Termination reason: Unknown
% 9.98/2.78 % (9382)Termination phase: Saturation
% 9.98/2.78
% 9.98/2.78 % (9382)Memory used [KB]: 6652
% 9.98/2.78 % (9382)Time elapsed: 0.086 s
% 9.98/2.78 % (9382)Instructions burned: 216 (million)
% 9.98/2.78 % (9382)------------------------------
% 9.98/2.78 % (9382)------------------------------
% 9.98/2.79 % (9388)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_9200 for (2987ds/368Mi)
% 10.67/2.80 % (9387)Instruction limit reached!
% 10.67/2.80 % (9387)------------------------------
% 10.67/2.80 % (9387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.67/2.80 % (9387)Termination reason: Unknown
% 10.67/2.80 % (9387)Termination phase: Function definition elimination
% 10.67/2.80
% 10.67/2.80 % (9387)Memory used [KB]: 1663
% 10.67/2.80 % (9387)Time elapsed: 0.023 s
% 10.67/2.80 % (9387)Instructions burned: 50 (million)
% 10.67/2.80 % (9387)------------------------------
% 10.67/2.80 % (9387)------------------------------
% 10.67/2.80 % (9389)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_9200 for (2987ds/1021Mi)
% 10.67/2.80 % (9385)Instruction limit reached!
% 10.67/2.80 % (9385)------------------------------
% 10.67/2.80 % (9385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.67/2.80 % (9385)Termination reason: Unknown
% 10.67/2.80 % (9385)Termination phase: Saturation
% 10.67/2.80
% 10.67/2.80 % (9385)Memory used [KB]: 6524
% 10.67/2.80 % (9385)Time elapsed: 0.074 s
% 10.67/2.80 % (9385)Instructions burned: 184 (million)
% 10.67/2.80 % (9385)------------------------------
% 10.67/2.80 % (9385)------------------------------
% 10.67/2.81 % (9390)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_9200 for (2987ds/267Mi)
% 10.67/2.82 % (9386)Instruction limit reached!
% 10.67/2.82 % (9386)------------------------------
% 10.67/2.82 % (9386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.67/2.82 % (9386)Termination reason: Unknown
% 10.67/2.82 % (9386)Termination phase: Saturation
% 10.67/2.82
% 10.67/2.82 % (9386)Memory used [KB]: 2302
% 10.67/2.82 % (9386)Time elapsed: 0.077 s
% 10.67/2.82 % (9386)Instructions burned: 165 (million)
% 10.67/2.82 % (9386)------------------------------
% 10.67/2.82 % (9386)------------------------------
% 10.67/2.82 % (9391)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_9200 for (2987ds/204Mi)
% 10.67/2.83 % (9392)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_9200 for (2987ds/26Mi)
% 10.67/2.84 % (9392)Instruction limit reached!
% 10.67/2.84 % (9392)------------------------------
% 10.67/2.84 % (9392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.67/2.84 % (9392)Termination reason: Unknown
% 10.67/2.84 % (9392)Termination phase: Property scanning
% 10.67/2.84
% 10.67/2.84 % (9392)Memory used [KB]: 1663
% 10.67/2.84 % (9392)Time elapsed: 0.013 s
% 10.67/2.84 % (9392)Instructions burned: 26 (million)
% 10.67/2.84 % (9392)------------------------------
% 10.67/2.84 % (9392)------------------------------
% 10.67/2.86 % (9393)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_9200 for (2987ds/53Mi)
% 10.67/2.88 % (9393)Instruction limit reached!
% 10.67/2.88 % (9393)------------------------------
% 10.67/2.88 % (9393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.67/2.88 % (9393)Termination reason: Unknown
% 10.67/2.88 % (9393)Termination phase: Property scanning
% 10.67/2.88
% 10.67/2.88 % (9393)Memory used [KB]: 1791
% 10.67/2.88 % (9393)Time elapsed: 0.025 s
% 10.67/2.88 % (9393)Instructions burned: 54 (million)
% 10.67/2.88 % (9393)------------------------------
% 10.67/2.88 % (9393)------------------------------
% 10.95/2.90 % (9394)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_9200 for (2986ds/4436Mi)
% 10.95/2.92 % (9391)Instruction limit reached!
% 10.95/2.92 % (9391)------------------------------
% 10.95/2.92 % (9391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.95/2.92 % (9391)Termination reason: Unknown
% 10.95/2.92 % (9391)Termination phase: Saturation
% 10.95/2.92
% 10.95/2.92 % (9391)Memory used [KB]: 7164
% 10.95/2.92 % (9391)Time elapsed: 0.096 s
% 10.95/2.92 % (9391)Instructions burned: 205 (million)
% 10.95/2.92 % (9391)------------------------------
% 10.95/2.92 % (9391)------------------------------
% 10.95/2.92 % (9390)Instruction limit reached!
% 10.95/2.92 % (9390)------------------------------
% 10.95/2.92 % (9390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.95/2.92 % (9390)Termination reason: Unknown
% 10.95/2.92 % (9390)Termination phase: Saturation
% 10.95/2.92
% 10.95/2.92 % (9390)Memory used [KB]: 8827
% 10.95/2.92 % (9390)Time elapsed: 0.107 s
% 10.95/2.92 % (9390)Instructions burned: 267 (million)
% 10.95/2.92 % (9390)------------------------------
% 10.95/2.92 % (9390)------------------------------
% 10.95/2.93 % (9395)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_9200 for (2986ds/1539Mi)
% 10.95/2.93 % (9396)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_9200 for (2986ds/408Mi)
% 10.95/2.96 % (9377)Instruction limit reached!
% 10.95/2.96 % (9377)------------------------------
% 10.95/2.96 % (9377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.95/2.96 % (9377)Termination reason: Unknown
% 10.95/2.96 % (9377)Termination phase: Saturation
% 10.95/2.96
% 10.95/2.96 % (9377)Memory used [KB]: 8955
% 10.95/2.96 % (9377)Time elapsed: 0.365 s
% 10.95/2.96 % (9377)Instructions burned: 987 (million)
% 10.95/2.96 % (9377)------------------------------
% 10.95/2.96 % (9377)------------------------------
% 10.95/2.96 % (9388)Instruction limit reached!
% 10.95/2.96 % (9388)------------------------------
% 10.95/2.96 % (9388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.95/2.96 % (9388)Termination reason: Unknown
% 10.95/2.96 % (9388)Termination phase: Saturation
% 10.95/2.96
% 10.95/2.96 % (9388)Memory used [KB]: 7547
% 10.95/2.96 % (9388)Time elapsed: 0.180 s
% 10.95/2.96 % (9388)Instructions burned: 370 (million)
% 10.95/2.96 % (9388)------------------------------
% 10.95/2.96 % (9388)------------------------------
% 10.95/2.98 % (9397)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_9200 for (2986ds/5205Mi)
% 10.95/2.98 % (9398)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_9200 for (2986ds/1913Mi)
% 13.44/3.14 % (9396)Instruction limit reached!
% 13.44/3.14 % (9396)------------------------------
% 13.44/3.14 % (9396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.44/3.14 % (9396)Termination reason: Unknown
% 13.44/3.14 % (9396)Termination phase: Saturation
% 13.44/3.14
% 13.44/3.14 % (9396)Memory used [KB]: 9083
% 13.44/3.14 % (9396)Time elapsed: 0.211 s
% 13.44/3.14 % (9396)Instructions burned: 409 (million)
% 13.44/3.14 % (9396)------------------------------
% 13.44/3.14 % (9396)------------------------------
% 13.44/3.16 % (9399)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_9200 for (2984ds/4350Mi)
% 13.44/3.18 % (9384)Instruction limit reached!
% 13.44/3.18 % (9384)------------------------------
% 13.44/3.18 % (9384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.44/3.18 % (9384)Termination reason: Unknown
% 13.44/3.18 % (9384)Termination phase: Saturation
% 13.44/3.18
% 13.44/3.18 % (9384)Memory used [KB]: 9338
% 13.44/3.18 % (9384)Time elapsed: 0.465 s
% 13.44/3.18 % (9384)Instructions burned: 923 (million)
% 13.44/3.18 % (9384)------------------------------
% 13.44/3.18 % (9384)------------------------------
% 13.89/3.20 % (9400)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_9200 for (2983ds/68Mi)
% 13.89/3.23 % (9400)Instruction limit reached!
% 13.89/3.23 % (9400)------------------------------
% 13.89/3.23 % (9400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.89/3.23 % (9400)Termination reason: Unknown
% 13.89/3.23 % (9400)Termination phase: Property scanning
% 13.89/3.23
% 13.89/3.23 % (9400)Memory used [KB]: 1918
% 13.89/3.23 % (9400)Time elapsed: 0.031 s
% 13.89/3.23 % (9400)Instructions burned: 68 (million)
% 13.89/3.23 % (9400)------------------------------
% 13.89/3.23 % (9400)------------------------------
% 13.89/3.24 % (9401)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_9200 for (2983ds/358Mi)
% 14.44/3.32 % (9389)Instruction limit reached!
% 14.44/3.32 % (9389)------------------------------
% 14.44/3.32 % (9389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.32 % (9389)Termination reason: Unknown
% 14.44/3.32 % (9389)Termination phase: Saturation
% 14.44/3.32
% 14.44/3.32 % (9389)Memory used [KB]: 9594
% 14.44/3.32 % (9389)Time elapsed: 0.519 s
% 14.44/3.32 % (9389)Instructions burned: 1022 (million)
% 14.44/3.32 % (9389)------------------------------
% 14.44/3.32 % (9389)------------------------------
% 14.44/3.34 % (9402)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_9200 for (2982ds/31Mi)
% 14.44/3.35 % (9402)Instruction limit reached!
% 14.44/3.35 % (9402)------------------------------
% 14.44/3.35 % (9402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.35 % (9402)Termination reason: Unknown
% 14.44/3.35 % (9402)Termination phase: Property scanning
% 14.44/3.35
% 14.44/3.35 % (9402)Memory used [KB]: 1663
% 14.44/3.35 % (9402)Time elapsed: 0.016 s
% 14.44/3.35 % (9402)Instructions burned: 31 (million)
% 14.44/3.35 % (9402)------------------------------
% 14.44/3.35 % (9402)------------------------------
% 14.44/3.37 % (9403)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_9200 for (2982ds/279Mi)
% 14.90/3.41 % (9401)Instruction limit reached!
% 14.90/3.41 % (9401)------------------------------
% 14.90/3.41 % (9401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.90/3.41 % (9401)Termination reason: Unknown
% 14.90/3.41 % (9401)Termination phase: Saturation
% 14.90/3.41
% 14.90/3.41 % (9401)Memory used [KB]: 7291
% 14.90/3.41 % (9401)Time elapsed: 0.170 s
% 14.90/3.41 % (9401)Instructions burned: 358 (million)
% 14.90/3.41 % (9401)------------------------------
% 14.90/3.41 % (9401)------------------------------
% 14.90/3.43 % (9404)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_9200 for (2981ds/258Mi)
% 14.90/3.47 % (9403)Instruction limit reached!
% 14.90/3.47 % (9403)------------------------------
% 14.90/3.47 % (9403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.90/3.47 % (9403)Termination reason: Unknown
% 14.90/3.47 % (9403)Termination phase: Saturation
% 14.90/3.47
% 14.90/3.47 % (9403)Memory used [KB]: 6524
% 14.90/3.47 % (9403)Time elapsed: 0.109 s
% 14.90/3.47 % (9403)Instructions burned: 281 (million)
% 14.90/3.47 % (9403)------------------------------
% 14.90/3.47 % (9403)------------------------------
% 14.90/3.49 % (9405)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_9200 for (2980ds/26Mi)
% 15.61/3.50 % (9405)Instruction limit reached!
% 15.61/3.50 % (9405)------------------------------
% 15.61/3.50 % (9405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.61/3.50 % (9405)Termination reason: Unknown
% 15.61/3.50 % (9405)Termination phase: Property scanning
% 15.61/3.50
% 15.61/3.50 % (9405)Memory used [KB]: 1663
% 15.61/3.50 % (9405)Time elapsed: 0.014 s
% 15.61/3.50 % (9405)Instructions burned: 27 (million)
% 15.61/3.50 % (9405)------------------------------
% 15.61/3.50 % (9405)------------------------------
% 15.61/3.52 % (9406)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_9200 for (2980ds/995Mi)
% 15.61/3.54 % (9395)Instruction limit reached!
% 15.61/3.54 % (9395)------------------------------
% 15.61/3.54 % (9395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.61/3.54 % (9395)Termination reason: Unknown
% 15.61/3.54 % (9395)Termination phase: Saturation
% 15.61/3.54
% 15.61/3.54 % (9395)Memory used [KB]: 8187
% 15.61/3.54 % (9395)Time elapsed: 0.613 s
% 15.61/3.54 % (9395)Instructions burned: 1541 (million)
% 15.61/3.54 % (9395)------------------------------
% 15.61/3.54 % (9395)------------------------------
% 15.61/3.55 % (9404)Instruction limit reached!
% 15.61/3.55 % (9404)------------------------------
% 15.61/3.55 % (9404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.61/3.55 % (9404)Termination reason: Unknown
% 15.61/3.55 % (9404)Termination phase: Saturation
% 15.61/3.55
% 15.61/3.55 % (9404)Memory used [KB]: 7803
% 15.61/3.55 % (9404)Time elapsed: 0.119 s
% 15.61/3.55 % (9404)Instructions burned: 259 (million)
% 15.61/3.55 % (9404)------------------------------
% 15.61/3.55 % (9404)------------------------------
% 15.61/3.56 % (9407)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_9200 for (2980ds/373Mi)
% 15.61/3.56 % (9408)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_9200 for (2980ds/253Mi)
% 16.13/3.66 % (9408)Instruction limit reached!
% 16.13/3.66 % (9408)------------------------------
% 16.13/3.66 % (9408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.13/3.66 % (9408)Termination reason: Unknown
% 16.13/3.66 % (9408)Termination phase: Saturation
% 16.13/3.66
% 16.13/3.66 % (9408)Memory used [KB]: 6524
% 16.13/3.66 % (9408)Time elapsed: 0.102 s
% 16.13/3.66 % (9408)Instructions burned: 255 (million)
% 16.13/3.66 % (9408)------------------------------
% 16.13/3.66 % (9408)------------------------------
% 16.13/3.68 % (9409)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_9200 for (2979ds/832Mi)
% 16.55/3.74 % (9407)Instruction limit reached!
% 16.55/3.74 % (9407)------------------------------
% 16.55/3.74 % (9407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.55/3.74 % (9407)Termination reason: Unknown
% 16.55/3.74 % (9407)Termination phase: Saturation
% 16.55/3.74
% 16.55/3.74 % (9407)Memory used [KB]: 7419
% 16.55/3.74 % (9407)Time elapsed: 0.204 s
% 16.55/3.74 % (9407)Instructions burned: 374 (million)
% 16.55/3.74 % (9407)------------------------------
% 16.55/3.74 % (9407)------------------------------
% 16.55/3.76 % (9410)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_9200 for (2978ds/668Mi)
% 17.04/3.87 % (9398)Instruction limit reached!
% 17.04/3.87 % (9398)------------------------------
% 17.04/3.87 % (9398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.04/3.87 % (9398)Termination reason: Unknown
% 17.04/3.87 % (9398)Termination phase: Saturation
% 17.04/3.87
% 17.04/3.87 % (9398)Memory used [KB]: 3454
% 17.04/3.87 % (9398)Time elapsed: 0.891 s
% 17.04/3.87 % (9398)Instructions burned: 1913 (million)
% 17.04/3.87 % (9398)------------------------------
% 17.04/3.87 % (9398)------------------------------
% 17.04/3.89 % (9406)Instruction limit reached!
% 17.04/3.89 % (9406)------------------------------
% 17.04/3.89 % (9406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.04/3.89 % (9406)Termination reason: Unknown
% 17.04/3.89 % (9406)Termination phase: Saturation
% 17.04/3.89
% 17.04/3.89 % (9406)Memory used [KB]: 8699
% 17.04/3.89 % (9406)Time elapsed: 0.370 s
% 17.04/3.89 % (9406)Instructions burned: 996 (million)
% 17.04/3.89 % (9406)------------------------------
% 17.04/3.89 % (9406)------------------------------
% 17.04/3.89 % (9411)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_9200 for (2976ds/40Mi)
% 17.71/3.90 % (9412)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_9200 for (2976ds/294Mi)
% 17.71/3.90 % (9411)Instruction limit reached!
% 17.71/3.90 % (9411)------------------------------
% 17.71/3.90 % (9411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.71/3.90 % (9411)Termination reason: Unknown
% 17.71/3.90 % (9411)Termination phase: Property scanning
% 17.71/3.90
% 17.71/3.90 % (9411)Memory used [KB]: 1663
% 17.71/3.90 % (9411)Time elapsed: 0.020 s
% 17.71/3.90 % (9411)Instructions burned: 41 (million)
% 17.71/3.90 % (9411)------------------------------
% 17.71/3.90 % (9411)------------------------------
% 17.71/3.92 % (9413)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_9200 for (2976ds/187Mi)
% 17.71/4.01 % (9410)Instruction limit reached!
% 17.71/4.01 % (9410)------------------------------
% 17.71/4.01 % (9410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.71/4.01 % (9410)Termination reason: Unknown
% 17.71/4.01 % (9410)Termination phase: Saturation
% 17.71/4.01
% 17.71/4.01 % (9410)Memory used [KB]: 13304
% 17.71/4.01 % (9410)Time elapsed: 0.260 s
% 17.71/4.01 % (9410)Instructions burned: 668 (million)
% 17.71/4.01 % (9410)------------------------------
% 17.71/4.01 % (9410)------------------------------
% 17.71/4.02 % (9413)Instruction limit reached!
% 17.71/4.02 % (9413)------------------------------
% 17.71/4.02 % (9413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.71/4.02 % (9413)Termination reason: Unknown
% 17.71/4.02 % (9413)Termination phase: Saturation
% 17.71/4.02
% 17.71/4.02 % (9413)Memory used [KB]: 7291
% 17.71/4.02 % (9413)Time elapsed: 0.091 s
% 17.71/4.02 % (9413)Instructions burned: 187 (million)
% 17.71/4.02 % (9413)------------------------------
% 17.71/4.02 % (9413)------------------------------
% 17.71/4.03 % (9412)Instruction limit reached!
% 17.71/4.03 % (9412)------------------------------
% 17.71/4.03 % (9412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.71/4.03 % (9412)Termination reason: Unknown
% 17.71/4.03 % (9412)Termination phase: Saturation
% 17.71/4.03
% 17.71/4.03 % (9412)Memory used [KB]: 6396
% 17.71/4.03 % (9412)Time elapsed: 0.126 s
% 17.71/4.03 % (9412)Instructions burned: 295 (million)
% 17.71/4.03 % (9412)------------------------------
% 17.71/4.03 % (9412)------------------------------
% 19.75/4.03 % (9414)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_9200 for (2975ds/371Mi)
% 19.75/4.04 % (9415)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_9200 for (2975ds/1827Mi)
% 19.75/4.04 % (9416)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_9200 for (2975ds/70Mi)
% 19.75/4.07 % (9416)Instruction limit reached!
% 19.75/4.07 % (9416)------------------------------
% 19.75/4.07 % (9416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.75/4.07 % (9416)Termination reason: Unknown
% 19.75/4.07 % (9416)Termination phase: Saturation
% 19.75/4.07
% 19.75/4.07 % (9416)Memory used [KB]: 1791
% 19.75/4.07 % (9416)Time elapsed: 0.032 s
% 19.75/4.07 % (9416)Instructions burned: 71 (million)
% 19.75/4.07 % (9416)------------------------------
% 19.75/4.07 % (9416)------------------------------
% 19.75/4.09 % (9417)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_9200 for (2974ds/316Mi)
% 19.75/4.09 % (9409)Instruction limit reached!
% 19.75/4.09 % (9409)------------------------------
% 19.75/4.09 % (9409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.75/4.09 % (9409)Termination reason: Unknown
% 19.75/4.09 % (9409)Termination phase: Saturation
% 19.75/4.09
% 19.75/4.09 % (9409)Memory used [KB]: 9083
% 19.75/4.09 % (9409)Time elapsed: 0.438 s
% 19.75/4.09 % (9409)Instructions burned: 833 (million)
% 19.75/4.09 % (9409)------------------------------
% 19.75/4.09 % (9409)------------------------------
% 19.75/4.11 % (9418)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_9200 for (2974ds/932Mi)
% 20.39/4.21 % (9414)Instruction limit reached!
% 20.39/4.21 % (9414)------------------------------
% 20.39/4.21 % (9414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.39/4.21 % (9414)Termination reason: Unknown
% 20.39/4.21 % (9414)Termination phase: Saturation
% 20.39/4.21
% 20.39/4.21 % (9414)Memory used [KB]: 7675
% 20.39/4.21 % (9414)Time elapsed: 0.180 s
% 20.39/4.21 % (9414)Instructions burned: 371 (million)
% 20.39/4.21 % (9414)------------------------------
% 20.39/4.21 % (9414)------------------------------
% 20.39/4.22 % (9417)Instruction limit reached!
% 20.39/4.22 % (9417)------------------------------
% 20.39/4.22 % (9417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.39/4.22 % (9417)Termination reason: Unknown
% 20.39/4.22 % (9417)Termination phase: Saturation
% 20.39/4.22
% 20.39/4.22 % (9417)Memory used [KB]: 7291
% 20.39/4.22 % (9417)Time elapsed: 0.129 s
% 20.39/4.22 % (9417)Instructions burned: 316 (million)
% 20.39/4.22 % (9417)------------------------------
% 20.39/4.22 % (9417)------------------------------
% 20.39/4.23 % (9419)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_9200 for (2973ds/4714Mi)
% 20.39/4.23 % (9420)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_9200 for (2973ds/8250Mi)
% 21.32/4.47 % (9418)Instruction limit reached!
% 21.32/4.47 % (9418)------------------------------
% 21.32/4.47 % (9418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.32/4.47 % (9418)Termination reason: Unknown
% 21.32/4.47 % (9418)Termination phase: Saturation
% 21.32/4.47
% 21.32/4.47 % (9418)Memory used [KB]: 9594
% 21.32/4.47 % (9418)Time elapsed: 0.363 s
% 21.32/4.47 % (9418)Instructions burned: 933 (million)
% 21.32/4.47 % (9418)------------------------------
% 21.32/4.47 % (9418)------------------------------
% 21.32/4.49 % (9421)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_9200 for (2970ds/770Mi)
% 22.89/4.83 % (9421)Instruction limit reached!
% 22.89/4.83 % (9421)------------------------------
% 22.89/4.83 % (9421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.89/4.83 % (9421)Termination reason: Unknown
% 22.89/4.83 % (9421)Termination phase: Saturation
% 22.89/4.83
% 22.89/4.83 % (9421)Memory used [KB]: 6780
% 22.89/4.83 % (9421)Time elapsed: 0.342 s
% 22.89/4.83 % (9421)Instructions burned: 770 (million)
% 22.89/4.83 % (9421)------------------------------
% 22.89/4.83 % (9421)------------------------------
% 22.89/4.84 % (9422)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_9200 for (2967ds/794Mi)
% 22.89/4.84 % (9415)First to succeed.
% 22.89/4.85 % (9415)Refutation found. Thanks to Tanya!
% 22.89/4.85 % SZS status Theorem for DTF2THF_9200
% 22.89/4.85 % SZS output start Proof for DTF2THF_9200
% 22.89/4.85 thf(func_def_0, type, in: $i > $i > $o).
% 22.89/4.85 thf(func_def_1, type, exu: ($i > $o) > $o).
% 22.89/4.85 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 22.89/4.85 thf(func_def_8, type, powerset: $i > $i).
% 22.89/4.85 thf(func_def_10, type, setunion: $i > $i).
% 22.89/4.85 thf(func_def_19, type, descr: ($i > $o) > $i).
% 22.89/4.85 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 22.89/4.85 thf(func_def_26, type, prop2set: $o > $i).
% 22.89/4.85 thf(func_def_36, type, nonempty: $i > $o).
% 22.89/4.85 thf(func_def_69, type, set2prop: $i > $o).
% 22.89/4.85 thf(func_def_88, type, subset: $i > $i > $o).
% 22.89/4.85 thf(func_def_89, type, disjoint: $i > $i > $o).
% 22.89/4.85 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 22.89/4.85 thf(func_def_114, type, binunion: $i > $i > $i).
% 22.89/4.85 thf(func_def_122, type, binintersect: $i > $i > $i).
% 22.89/4.85 thf(func_def_135, type, regular: $i > $o).
% 22.89/4.85 thf(func_def_136, type, setminus: $i > $i > $i).
% 22.89/4.85 thf(func_def_147, type, symdiff: $i > $i > $i).
% 22.89/4.85 thf(func_def_153, type, iskpair: $i > $o).
% 22.89/4.85 thf(func_def_158, type, kpair: $i > $i > $i).
% 22.89/4.85 thf(func_def_160, type, cartprod: $i > $i > $i).
% 22.89/4.85 thf(func_def_181, type, sK3: $i > $o).
% 22.89/4.85 thf(func_def_188, type, sK10: $i > $o).
% 22.89/4.85 thf(func_def_194, type, sK16: $i > $o).
% 22.89/4.85 thf(func_def_196, type, sK18: $i > $i > $i).
% 22.89/4.85 thf(func_def_202, type, sK24: ($i > $o) > $i).
% 22.89/4.85 thf(func_def_203, type, sK25: $i > $o).
% 22.89/4.85 thf(func_def_204, type, sK26: ($i > $i > $o) > $i > $i).
% 22.89/4.85 thf(func_def_205, type, sK27: ($i > $i > $o) > $i > $i).
% 22.89/4.85 thf(func_def_206, type, sK28: $i > $i > $o).
% 22.89/4.85 thf(func_def_208, type, sK30: $i > $i).
% 22.89/4.85 thf(func_def_209, type, sK31: ($i > $o) > $i > $i).
% 22.89/4.85 thf(func_def_210, type, sK32: $i > $o).
% 22.89/4.85 thf(func_def_223, type, sK45: $i > $o).
% 22.89/4.85 thf(func_def_226, type, sK48: ($i > $o) > $i > $i).
% 22.89/4.85 thf(func_def_227, type, sK49: $i > $o).
% 22.89/4.85 thf(func_def_239, type, sK61: ($i > $o) > $i > $i).
% 22.89/4.85 thf(func_def_240, type, sK62: $i > $o).
% 22.89/4.85 thf(func_def_253, type, sK75: ($i > $o) > $i > $i).
% 22.89/4.85 thf(func_def_254, type, sK76: $i > $o).
% 22.89/4.85 thf(func_def_259, type, sK81: ($i > $o) > $i > $i).
% 22.89/4.85 thf(func_def_260, type, sK82: $i > $o).
% 22.89/4.85 thf(func_def_271, type, sK93: $i > $o).
% 22.89/4.85 thf(func_def_286, type, sK108: $i > $o).
% 22.89/4.85 thf(func_def_293, type, sK115: $i > $i > $i).
% 22.89/4.85 thf(func_def_300, type, sK122: ($i > $o) > $i > $i).
% 22.89/4.85 thf(func_def_301, type, sK123: $i > $o).
% 22.89/4.85 thf(func_def_304, type, sK126: $i > $i).
% 22.89/4.85 thf(func_def_311, type, sK133: $i > $i).
% 22.89/4.85 thf(func_def_312, type, sK134: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_313, type, sK135: $i > $i > $i).
% 22.89/4.85 thf(func_def_314, type, sK136: $i > $i > $i).
% 22.89/4.85 thf(func_def_315, type, sK137: $i > $i > $i).
% 22.89/4.85 thf(func_def_316, type, sK138: $i > $i > $i).
% 22.89/4.85 thf(func_def_318, type, sK140: $i > $i).
% 22.89/4.85 thf(func_def_319, type, sK141: $i > $i).
% 22.89/4.85 thf(func_def_320, type, sK142: $i > $i).
% 22.89/4.85 thf(func_def_321, type, sK143: $i > $i).
% 22.89/4.85 thf(func_def_322, type, sK144: $i > $i).
% 22.89/4.85 thf(func_def_323, type, sK145: $i > $i).
% 22.89/4.85 thf(func_def_324, type, sK146: $i > $i).
% 22.89/4.85 thf(func_def_325, type, sK147: $i > $i).
% 22.89/4.85 thf(func_def_326, type, sK148: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_327, type, sK149: $i > $i > $i).
% 22.89/4.85 thf(func_def_328, type, sK150: $i > $i > $i).
% 22.89/4.85 thf(func_def_329, type, sK151: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_330, type, sK152: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_331, type, sK153: $i > $i > $i).
% 22.89/4.85 thf(func_def_332, type, sK154: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_333, type, sK155: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_334, type, sK156: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_335, type, sK157: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_336, type, sK158: $i > $i).
% 22.89/4.85 thf(func_def_337, type, sK159: $i > $i).
% 22.89/4.85 thf(func_def_338, type, sK160: $i > $i).
% 22.89/4.85 thf(func_def_339, type, sK161: $i > $i).
% 22.89/4.85 thf(func_def_340, type, sK162: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_341, type, sK163: $i > $i > $i).
% 22.89/4.85 thf(func_def_342, type, sK164: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_343, type, sK165: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_344, type, sK166: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_345, type, sK167: $i > $i > $i).
% 22.89/4.85 thf(func_def_346, type, sK168: $i > $i > $i).
% 22.89/4.85 thf(func_def_347, type, sK169: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_348, type, sK170: $i > $i > $i).
% 22.89/4.85 thf(func_def_349, type, sK171: $i > $i > $i).
% 22.89/4.85 thf(func_def_350, type, sK172: $i > $i).
% 22.89/4.85 thf(func_def_351, type, sK173: $i > $i).
% 22.89/4.85 thf(func_def_352, type, sK174: $i > $i).
% 22.89/4.85 thf(func_def_353, type, sK175: $i > $i > $i).
% 22.89/4.85 thf(func_def_354, type, sK176: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_355, type, sK177: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_356, type, sK178: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_357, type, sK179: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_358, type, sK180: $i > $i > $i).
% 22.89/4.85 thf(func_def_359, type, sK181: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_360, type, sK182: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_361, type, sK183: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_362, type, sK184: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_363, type, sK185: $i > $i).
% 22.89/4.85 thf(func_def_364, type, sK186: $i > $i).
% 22.89/4.85 thf(func_def_365, type, sK187: $i > $i).
% 22.89/4.85 thf(func_def_366, type, sK188: $i > $i).
% 22.89/4.85 thf(func_def_367, type, sK189: $i > $i).
% 22.89/4.85 thf(func_def_368, type, sK190: $i > $i).
% 22.89/4.85 thf(func_def_369, type, sK191: $i > $i).
% 22.89/4.85 thf(func_def_370, type, sK192: $i > $i).
% 22.89/4.85 thf(func_def_371, type, sK193: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_372, type, sK194: $i > $i > $i).
% 22.89/4.85 thf(func_def_373, type, sK195: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_374, type, sK196: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_375, type, sK197: $i > $i > $i).
% 22.89/4.85 thf(func_def_376, type, sK198: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_377, type, sK199: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_378, type, sK200: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_379, type, sK201: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_380, type, sK202: $i > $i).
% 22.89/4.85 thf(func_def_381, type, sK203: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_382, type, sK204: $i > $i > $i).
% 22.89/4.85 thf(func_def_383, type, sK205: $i > $i > $i).
% 22.89/4.85 thf(func_def_384, type, sK206: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_385, type, sK207: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_386, type, sK208: $i > $i > $i).
% 22.89/4.85 thf(func_def_387, type, sK209: $i > $i > $i).
% 22.89/4.85 thf(func_def_388, type, sK210: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_389, type, sK211: $i > $i > $i).
% 22.89/4.85 thf(func_def_390, type, sK212: $i > $i).
% 22.89/4.85 thf(func_def_391, type, sK213: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_392, type, sK214: $i > $i > $i).
% 22.89/4.85 thf(func_def_393, type, sK215: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_394, type, sK216: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_395, type, sK217: $i > $i > $i).
% 22.89/4.85 thf(func_def_396, type, sK218: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_397, type, sK219: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_398, type, sK220: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_399, type, sK221: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_400, type, sK222: $i > $i).
% 22.89/4.85 thf(func_def_401, type, sK223: $i > $i).
% 22.89/4.85 thf(func_def_402, type, sK224: $i > $i).
% 22.89/4.85 thf(func_def_403, type, sK225: $i > $i).
% 22.89/4.85 thf(func_def_404, type, sK226: $i > $i).
% 22.89/4.85 thf(func_def_405, type, sK227: $i > $i).
% 22.89/4.85 thf(func_def_406, type, sK228: $i > $i).
% 22.89/4.85 thf(func_def_407, type, sK229: $i > $i).
% 22.89/4.85 thf(func_def_408, type, sK230: $i > $i).
% 22.89/4.85 thf(func_def_409, type, sK231: $i > $i).
% 22.89/4.85 thf(func_def_410, type, sK232: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_411, type, sK233: $i > $i > $i).
% 22.89/4.85 thf(func_def_412, type, sK234: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_413, type, sK235: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_414, type, sK236: $i > $i > $i).
% 22.89/4.85 thf(func_def_415, type, sK237: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_416, type, sK238: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_417, type, sK239: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_418, type, sK240: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_419, type, sK241: $i > $i).
% 22.89/4.85 thf(func_def_420, type, sK242: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_421, type, sK243: $i > $i > $i).
% 22.89/4.85 thf(func_def_422, type, sK244: $i > $i > $i).
% 22.89/4.85 thf(func_def_423, type, sK245: $i > $i > $i).
% 22.89/4.85 thf(func_def_424, type, sK246: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_425, type, sK247: $i > $i > $i).
% 22.89/4.85 thf(func_def_426, type, sK248: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_427, type, sK249: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_428, type, sK250: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_429, type, sK251: $i > $i).
% 22.89/4.85 thf(func_def_430, type, sK252: $i > $i > $i).
% 22.89/4.85 thf(func_def_431, type, sK253: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_432, type, sK254: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_433, type, sK255: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_434, type, sK256: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_435, type, sK257: $i > $i > $i).
% 22.89/4.85 thf(func_def_436, type, sK258: $i > $i > $i).
% 22.89/4.85 thf(func_def_437, type, sK259: $i > $i > $i).
% 22.89/4.85 thf(func_def_438, type, sK260: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_439, type, sK261: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_440, type, sK262: $i > $i).
% 22.89/4.85 thf(func_def_441, type, sK263: $i > $i > $i).
% 22.89/4.85 thf(func_def_442, type, sK264: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_443, type, sK265: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_444, type, sK266: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_445, type, sK267: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_446, type, sK268: $i > $i > $i).
% 22.89/4.85 thf(func_def_447, type, sK269: $i > $i > $i).
% 22.89/4.85 thf(func_def_448, type, sK270: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_449, type, sK271: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_450, type, sK272: $i > $i).
% 22.89/4.85 thf(func_def_451, type, sK273: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_452, type, sK274: $i > $i > $i).
% 22.89/4.85 thf(func_def_453, type, sK275: $i > $i > $i).
% 22.89/4.85 thf(func_def_454, type, sK276: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_455, type, sK277: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_456, type, sK278: $i > $i > $i).
% 22.89/4.85 thf(func_def_457, type, sK279: $i > $i > $i).
% 22.89/4.85 thf(func_def_458, type, sK280: $i > $i > $i).
% 22.89/4.85 thf(func_def_459, type, sK281: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_460, type, sK282: $i > $i).
% 22.89/4.85 thf(func_def_461, type, sK283: $i > $i > $i).
% 22.89/4.85 thf(func_def_462, type, sK284: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_463, type, sK285: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_464, type, sK286: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_465, type, sK287: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_466, type, sK288: $i > $i).
% 22.89/4.85 thf(func_def_467, type, sK289: $i > $i).
% 22.89/4.85 thf(func_def_468, type, sK290: $i > $i).
% 22.89/4.85 thf(func_def_469, type, sK291: $i > $i).
% 22.89/4.85 thf(func_def_470, type, sK292: $i > $i).
% 22.89/4.85 thf(func_def_471, type, sK293: $i > $i).
% 22.89/4.85 thf(func_def_472, type, sK294: $i > $i).
% 22.89/4.85 thf(func_def_473, type, sK295: $i > $i).
% 22.89/4.85 thf(func_def_474, type, sK296: $i > $i).
% 22.89/4.85 thf(func_def_475, type, sK297: $i > $i).
% 22.89/4.85 thf(func_def_476, type, sK298: $i > $i).
% 22.89/4.85 thf(func_def_477, type, sK299: $i > $i).
% 22.89/4.85 thf(func_def_478, type, sK300: $i > $i > $i).
% 22.89/4.85 thf(func_def_479, type, sK301: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_480, type, sK302: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_481, type, sK303: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_482, type, sK304: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_483, type, sK305: $i > $i > $i).
% 22.89/4.85 thf(func_def_484, type, sK306: $i > $i > $i).
% 22.89/4.85 thf(func_def_485, type, sK307: $i > $i > $i).
% 22.89/4.85 thf(func_def_486, type, sK308: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_487, type, sK309: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_488, type, sK310: $i > $i > $i).
% 22.89/4.85 thf(func_def_489, type, sK311: $i > $i > $i).
% 22.89/4.85 thf(func_def_490, type, sK312: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_491, type, sK313: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_492, type, sK314: $i > $i > $i).
% 22.89/4.85 thf(func_def_493, type, sK315: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_494, type, sK316: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_495, type, sK317: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_496, type, sK318: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_497, type, sK319: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_498, type, sK320: $i > $i > $i).
% 22.89/4.85 thf(func_def_499, type, sK321: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_500, type, sK322: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_501, type, sK323: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_502, type, sK324: $i > $i > $i).
% 22.89/4.85 thf(func_def_503, type, sK325: $i > $i > $i).
% 22.89/4.85 thf(func_def_504, type, sK326: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_505, type, sK327: $i > $i > $i).
% 22.89/4.85 thf(func_def_506, type, sK328: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_507, type, sK329: $i > $i > $i).
% 22.89/4.85 thf(func_def_508, type, sK330: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_509, type, sK331: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_510, type, sK332: $i > $i > $i).
% 22.89/4.85 thf(func_def_511, type, sK333: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_512, type, sK334: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_513, type, sK335: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_514, type, sK336: $i > $i).
% 22.89/4.85 thf(func_def_515, type, sK337: $i > $i > $i).
% 22.89/4.85 thf(func_def_516, type, sK338: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_517, type, sK339: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_518, type, sK340: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_519, type, sK341: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_520, type, sK342: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_521, type, sK343: $i > $i > $i).
% 22.89/4.85 thf(func_def_522, type, sK344: $i > $i > $i > $i).
% 22.89/4.85 thf(func_def_523, type, sK345: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_524, type, sK346: $i > $i > $i).
% 22.89/4.86 thf(func_def_525, type, sK347: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_526, type, sK348: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_527, type, sK349: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_528, type, sK350: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_529, type, sK351: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_530, type, sK352: $i > $i > $i).
% 22.89/4.86 thf(func_def_531, type, sK353: $i > $i > $i).
% 22.89/4.86 thf(func_def_532, type, sK354: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_533, type, sK355: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_534, type, sK356: $i > $i > $i).
% 22.89/4.86 thf(func_def_535, type, sK357: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_536, type, sK358: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_537, type, sK359: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_538, type, sK360: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_539, type, sK361: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_540, type, sK362: $i > $i > $i).
% 22.89/4.86 thf(func_def_541, type, sK363: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_542, type, sK364: $i > $i > $i).
% 22.89/4.86 thf(func_def_543, type, sK365: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_544, type, sK366: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_545, type, sK367: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_546, type, sK368: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_547, type, sK369: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_548, type, sK370: $i > $i > $i).
% 22.89/4.86 thf(func_def_549, type, sK371: $i > $i > $i).
% 22.89/4.86 thf(func_def_550, type, sK372: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_551, type, sK373: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_552, type, sK374: $i > $i).
% 22.89/4.86 thf(func_def_553, type, sK375: $i > $i).
% 22.89/4.86 thf(func_def_554, type, sK376: $i > $i).
% 22.89/4.86 thf(func_def_555, type, sK377: $i > $i).
% 22.89/4.86 thf(func_def_556, type, sK378: $i > $i).
% 22.89/4.86 thf(func_def_557, type, sK379: $i > $i).
% 22.89/4.86 thf(func_def_558, type, sK380: $i > $i).
% 22.89/4.86 thf(func_def_559, type, sK381: $i > $i).
% 22.89/4.86 thf(func_def_560, type, sK382: $i > $i).
% 22.89/4.86 thf(func_def_561, type, sK383: $i > $i).
% 22.89/4.86 thf(func_def_562, type, sK384: $i > $i).
% 22.89/4.86 thf(func_def_563, type, sK385: $i > $i).
% 22.89/4.86 thf(func_def_564, type, sK386: $i > $i).
% 22.89/4.86 thf(func_def_565, type, sK387: $i > $i).
% 22.89/4.86 thf(func_def_566, type, sK388: $i > $i).
% 22.89/4.86 thf(func_def_567, type, sK389: $i > $i).
% 22.89/4.86 thf(func_def_568, type, sK390: $i > $i).
% 22.89/4.86 thf(func_def_569, type, sK391: $i > $i).
% 22.89/4.86 thf(func_def_570, type, sK392: $i > $i).
% 22.89/4.86 thf(func_def_571, type, sK393: $i > $i).
% 22.89/4.86 thf(func_def_572, type, sK394: $i > $i).
% 22.89/4.86 thf(func_def_573, type, sK395: $i > $i).
% 22.89/4.86 thf(func_def_574, type, sK396: $i > $i).
% 22.89/4.86 thf(func_def_575, type, sK397: $i > $i).
% 22.89/4.86 thf(func_def_576, type, sK398: $i > $i).
% 22.89/4.86 thf(func_def_577, type, sK399: $i > $i).
% 22.89/4.86 thf(func_def_578, type, sK400: $i > $i).
% 22.89/4.86 thf(func_def_579, type, sK401: $i > $i).
% 22.89/4.86 thf(func_def_580, type, sK402: $i > $i).
% 22.89/4.86 thf(func_def_581, type, sK403: $i > $i).
% 22.89/4.86 thf(func_def_582, type, sK404: $i > $i).
% 22.89/4.86 thf(func_def_583, type, sK405: $i > $i).
% 22.89/4.86 thf(func_def_584, type, sK406: $i > $i).
% 22.89/4.86 thf(func_def_585, type, sK407: $i > $i).
% 22.89/4.86 thf(func_def_586, type, sK408: $i > $i).
% 22.89/4.86 thf(func_def_587, type, sK409: $i > $i).
% 22.89/4.86 thf(func_def_588, type, sK410: $i > $i).
% 22.89/4.86 thf(func_def_589, type, sK411: $i > $i).
% 22.89/4.86 thf(func_def_590, type, sK412: $i > $i).
% 22.89/4.86 thf(func_def_591, type, sK413: $i > $i).
% 22.89/4.86 thf(func_def_592, type, sK414: $i > $i).
% 22.89/4.86 thf(func_def_593, type, sK415: $i > $i).
% 22.89/4.86 thf(func_def_594, type, sK416: $i > $i).
% 22.89/4.86 thf(func_def_595, type, sK417: $i > $i).
% 22.89/4.86 thf(func_def_596, type, sK418: $i > $i).
% 22.89/4.86 thf(func_def_597, type, sK419: $i > $i).
% 22.89/4.86 thf(func_def_598, type, sK420: $i > $i).
% 22.89/4.86 thf(func_def_599, type, sK421: $i > $i > $i).
% 22.89/4.86 thf(func_def_600, type, sK422: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_601, type, sK423: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_602, type, sK424: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_603, type, sK425: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_604, type, sK426: $i > $i > $i).
% 22.89/4.86 thf(func_def_605, type, sK427: $i > $i > $i).
% 22.89/4.86 thf(func_def_606, type, sK428: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_607, type, sK429: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_608, type, sK430: $i > $i > $i).
% 22.89/4.86 thf(func_def_609, type, sK431: $i > $i > $i).
% 22.89/4.86 thf(func_def_610, type, sK432: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_611, type, sK433: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_612, type, sK434: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_613, type, sK435: $i > $i > $i).
% 22.89/4.86 thf(func_def_614, type, sK436: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_615, type, sK437: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_616, type, sK438: $i > $i > $i).
% 22.89/4.86 thf(func_def_617, type, sK439: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_618, type, sK440: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_619, type, sK441: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_620, type, sK442: $i > $i > $i).
% 22.89/4.86 thf(func_def_621, type, sK443: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_622, type, sK444: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_623, type, sK445: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_624, type, sK446: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_625, type, sK447: $i > $i > $i).
% 22.89/4.86 thf(func_def_626, type, sK448: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_627, type, sK449: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_628, type, sK450: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_629, type, sK451: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_630, type, sK452: $i > $i > $i).
% 22.89/4.86 thf(func_def_631, type, sK453: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_632, type, sK454: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_633, type, sK455: $i > $i).
% 22.89/4.86 thf(func_def_634, type, sK456: $i > $i > $i).
% 22.89/4.86 thf(func_def_635, type, sK457: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_636, type, sK458: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_637, type, sK459: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_638, type, sK460: $i > $i > $i).
% 22.89/4.86 thf(func_def_639, type, sK461: $i > $i > $i).
% 22.89/4.86 thf(func_def_640, type, sK462: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_641, type, sK463: $i > $i > $i).
% 22.89/4.86 thf(func_def_642, type, sK464: $i > $i > $i).
% 22.89/4.86 thf(func_def_643, type, sK465: $i > $i).
% 22.89/4.86 thf(func_def_644, type, sK466: $i > $i > $i).
% 22.89/4.86 thf(func_def_645, type, sK467: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_646, type, sK468: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_647, type, sK469: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_648, type, sK470: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_649, type, sK471: $i > $i > $i).
% 22.89/4.86 thf(func_def_650, type, sK472: $i > $i > $i).
% 22.89/4.86 thf(func_def_651, type, sK473: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_652, type, sK474: $i > $i > $i).
% 22.89/4.86 thf(func_def_653, type, sK475: $i > $i).
% 22.89/4.86 thf(func_def_654, type, sK476: $i > $i > $i).
% 22.89/4.86 thf(func_def_655, type, sK477: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_656, type, sK478: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_657, type, sK479: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_658, type, sK480: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_659, type, sK481: $i > $i > $i).
% 22.89/4.86 thf(func_def_660, type, sK482: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_661, type, sK483: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_662, type, sK484: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_663, type, sK485: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_664, type, sK486: $i > $i > $i).
% 22.89/4.86 thf(func_def_665, type, sK487: $i > $i > $i).
% 22.89/4.86 thf(func_def_666, type, sK488: $i > $i > $i).
% 22.89/4.86 thf(func_def_667, type, sK489: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_668, type, sK490: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_669, type, sK491: $i > $i > $i).
% 22.89/4.86 thf(func_def_670, type, sK492: $i > $i > $i).
% 22.89/4.86 thf(func_def_671, type, sK493: $i > $i > $i).
% 22.89/4.86 thf(func_def_672, type, sK494: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_673, type, sK495: $i > $i).
% 22.89/4.86 thf(func_def_674, type, sK496: $i > $i).
% 22.89/4.86 thf(func_def_675, type, sK497: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_676, type, sK498: $i > $i > $i).
% 22.89/4.86 thf(func_def_677, type, sK499: $i > $i > $i).
% 22.89/4.86 thf(func_def_678, type, sK500: $i > $i > $i).
% 22.89/4.86 thf(func_def_679, type, sK501: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_680, type, sK502: $i > $i > $i).
% 22.89/4.86 thf(func_def_681, type, sK503: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_682, type, sK504: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_683, type, sK505: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_684, type, sK506: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_685, type, sK507: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_686, type, sK508: $i > $i > $i).
% 22.89/4.86 thf(func_def_687, type, sK509: $i > $i > $i).
% 22.89/4.86 thf(func_def_688, type, sK510: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_689, type, sK511: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_690, type, sK512: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_691, type, sK513: $i > $i > $i).
% 22.89/4.86 thf(func_def_692, type, sK514: $i > $i > $i).
% 22.89/4.86 thf(func_def_693, type, sK515: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_694, type, sK516: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_695, type, sK517: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_696, type, sK518: $i > $i > $i).
% 22.89/4.86 thf(func_def_697, type, sK519: $i > $i > $i).
% 22.89/4.86 thf(func_def_698, type, sK520: $i > $i > $i).
% 22.89/4.86 thf(func_def_699, type, sK521: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_700, type, sK522: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_701, type, sK523: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_702, type, sK524: $i > $i > $i).
% 22.89/4.86 thf(func_def_703, type, sK525: $i > $i > $i).
% 22.89/4.86 thf(func_def_704, type, sK526: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_705, type, sK527: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_706, type, sK528: $i > $i > $i).
% 22.89/4.86 thf(func_def_707, type, sK529: $i > $i > $i).
% 22.89/4.86 thf(func_def_708, type, sK530: $i > $i > $i).
% 22.89/4.86 thf(func_def_709, type, sK531: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_710, type, sK532: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_711, type, sK533: $i > $i > $i).
% 22.89/4.86 thf(func_def_712, type, sK534: $i > $i > $i).
% 22.89/4.86 thf(func_def_713, type, sK535: $i > $i > $i).
% 22.89/4.86 thf(func_def_714, type, sK536: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_715, type, sK537: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_716, type, sK538: $i > $i).
% 22.89/4.86 thf(func_def_717, type, sK539: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_718, type, sK540: $i > $i).
% 22.89/4.86 thf(func_def_719, type, sK541: $i > $i > $i).
% 22.89/4.86 thf(func_def_720, type, sK542: $i > $i > $i).
% 22.89/4.86 thf(func_def_721, type, sK543: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_722, type, sK544: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_723, type, sK545: $i > $i > $i).
% 22.89/4.86 thf(func_def_724, type, sK546: $i > $i > $i).
% 22.89/4.86 thf(func_def_725, type, sK547: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_726, type, sK548: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_727, type, sK549: $i > $i).
% 22.89/4.86 thf(func_def_728, type, sK550: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_729, type, sK551: $i > $i > $i).
% 22.89/4.86 thf(func_def_730, type, sK552: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_731, type, sK553: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_732, type, sK554: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_733, type, sK555: $i > $i > $i).
% 22.89/4.86 thf(func_def_734, type, sK556: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_735, type, sK557: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_736, type, sK558: $i > $i).
% 22.89/4.86 thf(func_def_737, type, sK559: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_738, type, sK560: $i > $i > $i).
% 22.89/4.86 thf(func_def_739, type, sK561: $i > $i > $i).
% 22.89/4.86 thf(func_def_740, type, sK562: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_741, type, sK563: $i > $i > $i).
% 22.89/4.86 thf(func_def_742, type, sK564: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_743, type, sK565: $i > $i > $i).
% 22.89/4.86 thf(func_def_744, type, sK566: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_745, type, sK567: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_746, type, sK568: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_747, type, sK569: $i > $i > $i).
% 22.89/4.86 thf(func_def_748, type, sK570: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_749, type, sK571: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_750, type, sK572: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_751, type, sK573: $i > $i > $i).
% 22.89/4.86 thf(func_def_752, type, sK574: $i > $i > $i).
% 22.89/4.86 thf(func_def_753, type, sK575: $i > $i > $i).
% 22.89/4.86 thf(func_def_754, type, sK576: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_755, type, sK577: $i > $i > $i > $i).
% 22.89/4.86 thf(func_def_764, type, sK586: $i > $o).
% 22.89/4.86 thf(func_def_767, type, sK589: ($i > $o) > $i).
% 22.89/4.86 thf(func_def_768, type, sK590: $i > $o).
% 22.89/4.86 thf(func_def_769, type, sK591: $i > $i).
% 22.89/4.86 thf(func_def_773, type, sK595: $i > $i).
% 22.89/4.86 thf(func_def_794, type, sK616: ($i > $o) > ($i > $o) > $i).
% 22.89/4.86 thf(func_def_795, type, sK617: ($i > $o) > ($i > $o) > $i).
% 22.89/4.86 thf(func_def_796, type, sK618: $i > $o).
% 22.89/4.86 thf(func_def_797, type, sK619: $i > $o).
% 22.89/4.86 thf(func_def_806, type, sK628: $i > $i).
% 22.89/4.86 thf(func_def_808, type, sK630: $i > $o).
% 22.89/4.86 thf(func_def_815, type, sK637: $i > $o).
% 22.89/4.86 thf(func_def_822, type, sK644: ($i > $o) > ($i > $o) > $i).
% 22.89/4.86 thf(func_def_823, type, sK645: ($i > $o) > ($i > $o) > $i).
% 22.89/4.86 thf(func_def_824, type, sK646: $i > $o).
% 22.89/4.86 thf(func_def_825, type, sK647: $i > $o).
% 22.89/4.86 thf(func_def_831, type, sK653: ($i > $o) > $i > $i).
% 22.89/4.86 thf(func_def_832, type, sK654: $i > $o).
% 22.89/4.86 thf(func_def_835, type, sK657: ($i > $o) > $i > $i).
% 22.89/4.86 thf(func_def_836, type, sK658: $i > $o).
% 22.89/4.86 thf(func_def_840, type, sK662: $i > $o).
% 22.89/4.86 thf(func_def_854, type, sK676: $i > $i > $i).
% 22.89/4.86 thf(func_def_865, type, sK687: $i > $i).
% 22.89/4.86 thf(func_def_884, type, sK706: $i > $i).
% 22.89/4.86 thf(func_def_887, type, sK709: $i > $i).
% 22.89/4.86 thf(func_def_888, type, sK710: ($i > $o) > $i > ($i > $o) > $i > $i).
% 22.89/4.86 thf(func_def_889, type, sK711: $i > $i > ($i > $o) > ($i > $o) > $i).
% 22.89/4.86 thf(func_def_892, type, sK714: $i > $o).
% 22.89/4.86 thf(func_def_893, type, sK715: $i > $o).
% 22.89/4.86 thf(func_def_896, type, sK718: $i > $o).
% 22.89/4.86 thf(func_def_897, type, sK719: $i > $i > $i).
% 22.89/4.86 thf(func_def_906, type, sK728: $i > $i > $i).
% 22.89/4.86 thf(func_def_907, type, sK729: $i > $i > $i).
% 22.89/4.86 thf(func_def_908, type, sK730: $i > $i > $i).
% 22.89/4.86 thf(func_def_914, type, sK736: ($i > $o) > $i).
% 22.89/4.86 thf(func_def_915, type, sK737: ($i > $o) > $i).
% 22.89/4.86 thf(func_def_916, type, sK738: $i > $o).
% 22.89/4.86 thf(func_def_929, type, sK751: $i > $i).
% 22.89/4.86 thf(func_def_938, type, sK760: $i > $o).
% 22.89/4.86 thf(func_def_946, type, sK768: $i > $o > $i > $i).
% 22.89/4.86 thf(func_def_953, type, sK775: ($i > $o) > $i).
% 22.89/4.86 thf(func_def_954, type, sK776: $i > $o).
% 22.89/4.86 thf(func_def_955, type, sK777: $i > $i).
% 22.89/4.86 thf(func_def_956, type, sK778: $i > $i > $i).
% 22.89/4.86 thf(func_def_969, type, ph791: !>[X0: $tType]:(X0)).
% 22.89/4.86 thf(func_def_970, type, sK792: ($i > $o) > $i).
% 22.89/4.86 thf(func_def_971, type, sK793: ($i > $o) > $i > $i).
% 22.89/4.86 thf(func_def_972, type, sK794: $i > $i).
% 22.89/4.86 thf(func_def_973, type, sK795: $i > $i).
% 22.89/4.86 thf(func_def_974, type, sK796: $i > $i > $i).
% 22.89/4.86 thf(func_def_975, type, sK797: $o > $i).
% 22.89/4.86 thf(func_def_976, type, sK798: $i > $i > $i).
% 22.89/4.86 thf(func_def_977, type, sK799: $i > $i > $i).
% 22.89/4.86 thf(func_def_978, type, sK800: $i > $i > $i).
% 22.89/4.86 thf(func_def_979, type, sK801: $i > $i > $i).
% 22.89/4.86 thf(func_def_980, type, sK802: $i > $i > $i).
% 22.89/4.86 thf(func_def_982, type, sK804: $i > $i > $i).
% 22.89/4.86 thf(func_def_1004, type, sK826: $i > $i > $i).
% 22.89/4.86 thf(func_def_1005, type, sK827: $o > $i).
% 22.89/4.86 thf(func_def_1006, type, sK828: $i > $i > $i).
% 22.89/4.86 thf(func_def_1009, type, sK831: $i > $i > $i).
% 22.89/4.86 thf(func_def_1010, type, sK832: $i > $i > $i).
% 22.89/4.86 thf(func_def_1011, type, sK833: $i > $i > $i).
% 22.89/4.86 thf(func_def_1012, type, sK834: $i > $i).
% 22.89/4.86 thf(func_def_1013, type, sK835: $i > $i > $i).
% 22.89/4.86 thf(func_def_1014, type, sK836: $i > $i > $i).
% 22.89/4.86 thf(func_def_1015, type, sK837: $i > $i > $i).
% 22.89/4.86 thf(func_def_1016, type, sK838: $i > $i > $i).
% 22.89/4.86 thf(func_def_1017, type, sK839: $i > $i).
% 22.89/4.86 thf(func_def_1018, type, sK840: $i > $i > $i).
% 22.89/4.86 thf(func_def_1019, type, sK841: $i > $i).
% 22.89/4.86 thf(func_def_1020, type, sK842: $i > $i > $i).
% 22.89/4.86 thf(func_def_1021, type, sK843: $i > $i).
% 22.89/4.86 thf(func_def_1022, type, sK844: $i > $i > $i).
% 22.89/4.86 thf(func_def_1023, type, sK845: $i > $i).
% 22.89/4.86 thf(func_def_1024, type, sK846: $i > $i > $i).
% 22.89/4.86 thf(func_def_1025, type, sK847: $i > $i > $i).
% 22.89/4.86 thf(func_def_1026, type, sK848: $i > $i).
% 22.89/4.86 thf(func_def_1027, type, sK849: $i > $i > $i).
% 22.89/4.86 thf(func_def_1028, type, sK850: $i > $i).
% 22.89/4.86 thf(f17064,plain,(
% 22.89/4.86 $false),
% 22.89/4.86 inference(avatar_sat_refutation,[status(thm)],[f7568,f7610,f7723,f8238,f12201,f12431,f12687,f15930,f16911,f17063])).
% 22.89/4.86 thf(f17063,plain,(
% 22.89/4.86 ~spl2_456 | ~spl2_459),
% 22.89/4.86 inference(avatar_contradiction_clause,[status(thm)],[f17062])).
% 22.89/4.86 thf(f17062,plain,(
% 22.89/4.86 $false | (~spl2_456 | ~spl2_459)),
% 22.89/4.86 inference(trivial_inequality_removal,[status(thm)],[f17061])).
% 22.89/4.86 thf(f17061,plain,(
% 22.89/4.86 ($true = $false) | (~spl2_456 | ~spl2_459)),
% 22.89/4.86 inference(backward_demodulation,[status(thm)],[f8224,f8237])).
% 22.89/4.86 thf(f8237,plain,(
% 22.89/4.86 (notinsingleton = $false) | ~spl2_459),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f8235])).
% 22.89/4.86 thf(f8235,definition,(
% 22.89/4.86 spl2_459 <=> (notinsingleton = $false)),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_459])],[avatar_definition])).
% 22.89/4.86 thf(f8224,plain,(
% 22.89/4.86 (notinsingleton = $true) | ~spl2_456),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f8222])).
% 22.89/4.86 thf(f8222,definition,(
% 22.89/4.86 spl2_456 <=> (notinsingleton = $true)),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_456])],[avatar_definition])).
% 22.89/4.86 thf(f16911,plain,(
% 22.89/4.86 ~spl2_312 | ~spl2_321 | ~spl2_458),
% 22.89/4.86 inference(avatar_contradiction_clause,[status(thm)],[f16910])).
% 22.89/4.86 thf(f16910,plain,(
% 22.89/4.86 $false | (~spl2_312 | ~spl2_321 | ~spl2_458)),
% 22.89/4.86 inference(trivial_inequality_removal,[status(thm)],[f16890])).
% 22.89/4.86 thf(f16890,plain,(
% 22.89/4.86 ($true = $false) | (~spl2_312 | ~spl2_321 | ~spl2_458)),
% 22.89/4.86 inference(backward_demodulation,[status(thm)],[f671,f16878])).
% 22.89/4.86 thf(f16878,plain,(
% 22.89/4.86 ((in @ sK0 @ sK1) = $false) | (~spl2_312 | ~spl2_321 | ~spl2_458)),
% 22.89/4.86 inference(backward_demodulation,[status(thm)],[f16403,f16856])).
% 22.89/4.86 thf(f16856,plain,(
% 22.89/4.86 (sK0 = sK830) | (~spl2_312 | ~spl2_321 | ~spl2_458)),
% 22.89/4.86 inference(trivial_inequality_removal,[status(thm)],[f16835])).
% 22.89/4.86 thf(f16835,plain,(
% 22.89/4.86 (sK0 = sK830) | ($true = $false) | (~spl2_312 | ~spl2_321 | ~spl2_458)),
% 22.89/4.86 inference(superposition,[status(thm)],[f16404,f8233])).
% 22.89/4.86 thf(f8233,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false) | (X1 = X2)) ) | ~spl2_458),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f8232])).
% 22.89/4.86 thf(f8232,definition,(
% 22.89/4.86 spl2_458 <=> ! [X2 : $i,X1 : $i] : ((X1 = X2) | ((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false))),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_458])],[avatar_definition])).
% 22.89/4.86 thf(f16404,plain,(
% 22.89/4.86 ($true = (in @ sK830 @ (setadjoin @ sK0 @ emptyset))) | (~spl2_312 | ~spl2_321)),
% 22.89/4.86 inference(binary_proxy_clausification,[status(thm)],[f16402])).
% 22.89/4.86 thf(f16402,plain,(
% 22.89/4.86 ($false = ((in @ sK830 @ (setadjoin @ sK0 @ emptyset)) => (in @ sK830 @ sK1))) | (~spl2_312 | ~spl2_321)),
% 22.89/4.86 inference(beta_eta_normalization,[status(thm)],[f16401])).
% 22.89/4.86 thf(f16401,plain,(
% 22.89/4.86 (((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK0 @ emptyset)) => (in @ Y0 @ sK1))) @ sK830) = $false) | (~spl2_312 | ~spl2_321)),
% 22.89/4.86 inference(sigma_clausification,[status(thm)],[f16400])).
% 22.89/4.86 thf(f16400,plain,(
% 22.89/4.86 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK0 @ emptyset)) => (in @ Y0 @ sK1)))) = $false) | (~spl2_312 | ~spl2_321)),
% 22.89/4.86 inference(not_proxy_clausification,[status(thm)],[f16399])).
% 22.89/4.86 thf(f16399,plain,(
% 22.89/4.86 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK0 @ emptyset)) => (in @ Y0 @ sK1)))))) | (~spl2_312 | ~spl2_321)),
% 22.89/4.86 inference(boolean_simplification,[status(thm)],[f16340])).
% 22.89/4.86 thf(f16340,plain,(
% 22.89/4.86 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK0 @ emptyset)) => (in @ Y0 @ sK1)))) = $false) = $true) | (~spl2_312 | ~spl2_321)),
% 22.89/4.86 inference(superposition,[status(thm)],[f7605,f12832])).
% 22.89/4.86 thf(f12832,plain,(
% 22.89/4.86 ((in @ (setadjoin @ sK0 @ emptyset) @ (powerset @ sK1)) = $false) | ~spl2_312),
% 22.89/4.86 inference(trivial_inequality_removal,[status(thm)],[f12826])).
% 22.89/4.86 thf(f12826,plain,(
% 22.89/4.86 ((in @ (setadjoin @ sK0 @ emptyset) @ (powerset @ sK1)) = $false) | ($true != $true) | ~spl2_312),
% 22.89/4.86 inference(superposition,[status(thm)],[f670,f7567])).
% 22.89/4.86 thf(f7567,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | ((in @ X1 @ (powerset @ X2)) = $false)) ) | ~spl2_312),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f7566])).
% 22.89/4.86 thf(f7566,definition,(
% 22.89/4.86 spl2_312 <=> ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | ((in @ X1 @ (powerset @ X2)) = $false))),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_312])],[avatar_definition])).
% 22.89/4.86 thf(f670,plain,(
% 22.89/4.86 ((subset @ (setadjoin @ sK0 @ emptyset) @ sK1) != $true)),
% 22.89/4.86 inference(cnf_transformation,[status(thm)],[f429])).
% 22.89/4.86 thf(f429,plain,(
% 22.89/4.86 (binunionRsub = $true) & (replAx = $true) & (quantDeMorgan1 = $true) & (((in @ sK0 @ sK1) = $true) & ((subset @ (setadjoin @ sK0 @ emptyset) @ sK1) != $true)) & (setoftrueEq = $true) & (subPowSU = $true) & (wellorderingAx = $true) & (binintersectSubset1 = $true) & (exuE1 = $true) & (emptyInPowerset = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan2 = $true) & (exu__Cong = $true) & (powersetsubset = $true) & (symdiffI2 = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (kpairp = $true) & (omega0Ax = $true) & (notinsingleton = $true) & (subsetTrans = $true) & (setextsub = $true) & (dsetconstrI = $true) & (dsetconstrER = $true) & (binintersectSubset5 = $true) & (upairsetIR = $true) & (setadjoinE = $true) & (setunionE = $true) & (in__Cong = $true) & (setadjoinSub2 = $true) & (noeltsimpempty = $true) & (setukpairIL = $true) & (uniqinunit = $true) & (upairset2IR = $true) & (omega__Cong = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (emptysetimpfalse = $true) & (emptyI = $true) & (binintersectI = $true) & (setadjoinOr = $true) & (emptysetAx = $true) & (inPowerset = $true) & (foundationAx = $true) & (nonemptyI1 = $true) & (subsetRefl = $true) & (bs114d = $true) & (emptysetsubset = $true) & (quantDeMorgan3 = $true) & (upairsetE = $true) & (binunionIL = $true) & (dsetconstrEL = $true) & (setadjoin__Cong = $true) & (subsetE2 = $true) & (setext = $true) & (powersetE = $true) & (symdiffIneg2 = $true) & (dsetconstr__Cong = $true) & (binintersectSubset2 = $true) & (prop2setI = $true) & (subset2powerset = $true) & (powerset__Cong = $true) & (nonemptyImpWitness = $true) & (emptysetE = $true) & (nonemptyE1 = $true) & (setadjoinIL = $true) & (emptyset__Cong = $true) & (sepInPowerset = $true) & (setbeta = $true) & (subsetemptysetimpeq = $true) & (omegaSAx = $true) & (setminusSubset1 = $true) & (vacuousDall = $true) & (powersetAx = $true) & (notinemptyset = $true) & (disjointsetsI1 = $true) & (emptyE1 = $true) & (emptyinunitempty = $true) & (setminusIRneg = $true) & (eqimpsubset1 = $true) & (descr__Cong = $true) & (subsetI1 = $true) & (setukpairIR = $true) & (descrp = $true) & (notequalI2 = $true) & (exuE3u = $true) & (setminusER = $true) & (singletonsswitch = $true) & (eqimpsubset2 = $true) & (notequalI1 = $true) & (prop2setE = $true) & (setunionI = $true) & (notdexE = $true) & (exuI2 = $true) & (setminusERneg = $true) & (powersetI = $true) & (subsetI2 = $true) & (setminusLsub = $true) & (upairsetIL = $true) & (eqinunit = $true) & (sepSubset = $true) & (prop2set2propI = $true) & (exuE2 = $true) & (exuI1 = $true) & (setminusEL = $true) & (setunion__Cong = $true) & (setadjoinIR = $true) & (setadjoinSub = $true) & (setadjoinAx = $true) & (binunionEcases = $true) & (exuE3e = $true) & (setunionAx = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (subsetE = $true) & (symdiffE = $true) & (notsubsetI = $true) & (omegaIndAx = $true) & (binintersectLsub = $true) & (setminusI = $true) & (setminusSubset2 = $true) & (binintersectSubset3 = $true) & (notdallE = $true) & (secondinupair = $true) & (binintersectSubset4 = $true) & (exuI3 = $true) & (binintersectRsub = $true) & (exuEu = $true) & (binintersectER = $true) & (kpairiskpair = $true) & (setextAx = $true) & (symdiffIneg1 = $true) & (binunionE = $true) & (inCongP = $true) & (symdiffI1 = $true) & (binunionLsub = $true) & (binintersectEL = $true) & (binunionIR = $true)),
% 22.89/4.86 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f427,f428])).
% 22.89/4.86 thf(f428,plain,(
% 22.89/4.86 ? [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) & ((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $true)) => (((in @ sK0 @ sK1) = $true) & ((subset @ (setadjoin @ sK0 @ emptyset) @ sK1) != $true))),
% 22.89/4.86 introduced(definition,[],[choice_axiom])).
% 22.89/4.86 thf(f427,plain,(
% 22.89/4.86 (binunionRsub = $true) & (replAx = $true) & (quantDeMorgan1 = $true) & ? [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) & ((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $true)) & (setoftrueEq = $true) & (subPowSU = $true) & (wellorderingAx = $true) & (binintersectSubset1 = $true) & (exuE1 = $true) & (emptyInPowerset = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan2 = $true) & (exu__Cong = $true) & (powersetsubset = $true) & (symdiffI2 = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (kpairp = $true) & (omega0Ax = $true) & (notinsingleton = $true) & (subsetTrans = $true) & (setextsub = $true) & (dsetconstrI = $true) & (dsetconstrER = $true) & (binintersectSubset5 = $true) & (upairsetIR = $true) & (setadjoinE = $true) & (setunionE = $true) & (in__Cong = $true) & (setadjoinSub2 = $true) & (noeltsimpempty = $true) & (setukpairIL = $true) & (uniqinunit = $true) & (upairset2IR = $true) & (omega__Cong = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (emptysetimpfalse = $true) & (emptyI = $true) & (binintersectI = $true) & (setadjoinOr = $true) & (emptysetAx = $true) & (inPowerset = $true) & (foundationAx = $true) & (nonemptyI1 = $true) & (subsetRefl = $true) & (bs114d = $true) & (emptysetsubset = $true) & (quantDeMorgan3 = $true) & (upairsetE = $true) & (binunionIL = $true) & (dsetconstrEL = $true) & (setadjoin__Cong = $true) & (subsetE2 = $true) & (setext = $true) & (powersetE = $true) & (symdiffIneg2 = $true) & (dsetconstr__Cong = $true) & (binintersectSubset2 = $true) & (prop2setI = $true) & (subset2powerset = $true) & (powerset__Cong = $true) & (nonemptyImpWitness = $true) & (emptysetE = $true) & (nonemptyE1 = $true) & (setadjoinIL = $true) & (emptyset__Cong = $true) & (sepInPowerset = $true) & (setbeta = $true) & (subsetemptysetimpeq = $true) & (omegaSAx = $true) & (setminusSubset1 = $true) & (vacuousDall = $true) & (powersetAx = $true) & (notinemptyset = $true) & (disjointsetsI1 = $true) & (emptyE1 = $true) & (emptyinunitempty = $true) & (setminusIRneg = $true) & (eqimpsubset1 = $true) & (descr__Cong = $true) & (subsetI1 = $true) & (setukpairIR = $true) & (descrp = $true) & (notequalI2 = $true) & (exuE3u = $true) & (setminusER = $true) & (singletonsswitch = $true) & (eqimpsubset2 = $true) & (notequalI1 = $true) & (prop2setE = $true) & (setunionI = $true) & (notdexE = $true) & (exuI2 = $true) & (setminusERneg = $true) & (powersetI = $true) & (subsetI2 = $true) & (setminusLsub = $true) & (upairsetIL = $true) & (eqinunit = $true) & (sepSubset = $true) & (prop2set2propI = $true) & (exuE2 = $true) & (exuI1 = $true) & (setminusEL = $true) & (setunion__Cong = $true) & (setadjoinIR = $true) & (setadjoinSub = $true) & (setadjoinAx = $true) & (binunionEcases = $true) & (exuE3e = $true) & (setunionAx = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (subsetE = $true) & (symdiffE = $true) & (notsubsetI = $true) & (omegaIndAx = $true) & (binintersectLsub = $true) & (setminusI = $true) & (setminusSubset2 = $true) & (binintersectSubset3 = $true) & (notdallE = $true) & (secondinupair = $true) & (binintersectSubset4 = $true) & (exuI3 = $true) & (binintersectRsub = $true) & (exuEu = $true) & (binintersectER = $true) & (kpairiskpair = $true) & (setextAx = $true) & (symdiffIneg1 = $true) & (binunionE = $true) & (inCongP = $true) & (symdiffI1 = $true) & (binunionLsub = $true) & (binintersectEL = $true) & (binunionIR = $true)),
% 22.89/4.86 inference(flattening,[status(thm)],[f426])).
% 22.89/4.86 thf(f426,plain,(
% 22.89/4.86 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) & ((subset @ (setadjoin @ X0 @ emptyset) @ X1) != $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)),
% 22.89/4.86 inference(ennf_transformation,[status(thm)],[f256])).
% 22.89/4.86 thf(f256,plain,(
% 22.89/4.86 ~((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) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) => ((subset @ (setadjoin @ X0 @ emptyset) @ X1) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 22.89/4.86 inference(fool_elimination,[status(thm)],[f255])).
% 22.89/4.86 thf(f255,plain,(
% 22.89/4.86 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 22.89/4.86 inference(rectify,[status(thm)],[f144])).
% 22.89/4.86 thf(f144,negated_conjecture,(
% 22.89/4.86 ~(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 => ! [X1 : $i,X3 : $i] : ((in @ X1 @ X3) => (subset @ (setadjoin @ X1 @ emptyset) @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 22.89/4.86 inference(negated_conjecture,[status(cth)],[f143])).
% 22.89/4.86 thf(f143,conjecture,(
% 22.89/4.86 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 => ! [X1 : $i,X3 : $i] : ((in @ X1 @ X3) => (subset @ (setadjoin @ X1 @ emptyset) @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 22.89/4.86 file('/export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2THF_9200.p',singletonsubset)).
% 22.89/4.86 thf(f7605,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = (in @ X2 @ (powerset @ X1))) = $true)) ) | ~spl2_321),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f7604])).
% 22.89/4.86 thf(f7604,definition,(
% 22.89/4.86 spl2_321 <=> ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = (in @ X2 @ (powerset @ X1))) = $true)),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_321])],[avatar_definition])).
% 22.89/4.86 thf(f16403,plain,(
% 22.89/4.86 ((in @ sK830 @ sK1) = $false) | (~spl2_312 | ~spl2_321)),
% 22.89/4.86 inference(binary_proxy_clausification,[status(thm)],[f16402])).
% 22.89/4.86 thf(f671,plain,(
% 22.89/4.86 ((in @ sK0 @ sK1) = $true)),
% 22.89/4.86 inference(cnf_transformation,[status(thm)],[f429])).
% 22.89/4.86 thf(f15930,plain,(
% 22.89/4.86 ~spl2_320 | ~spl2_322),
% 22.89/4.86 inference(avatar_contradiction_clause,[status(thm)],[f15929])).
% 22.89/4.86 thf(f15929,plain,(
% 22.89/4.86 $false | (~spl2_320 | ~spl2_322)),
% 22.89/4.86 inference(trivial_inequality_removal,[status(thm)],[f15928])).
% 22.89/4.86 thf(f15928,plain,(
% 22.89/4.86 ($true = $false) | (~spl2_320 | ~spl2_322)),
% 22.89/4.86 inference(backward_demodulation,[status(thm)],[f7601,f7609])).
% 22.89/4.86 thf(f7609,plain,(
% 22.89/4.86 (powersetAx = $false) | ~spl2_322),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f7607])).
% 22.89/4.86 thf(f7607,definition,(
% 22.89/4.86 spl2_322 <=> (powersetAx = $false)),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_322])],[avatar_definition])).
% 22.89/4.86 thf(f7601,plain,(
% 22.89/4.86 (powersetAx = $true) | ~spl2_320),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f7599])).
% 22.89/4.86 thf(f7599,definition,(
% 22.89/4.86 spl2_320 <=> (powersetAx = $true)),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_320])],[avatar_definition])).
% 22.89/4.86 thf(f12687,plain,(
% 22.89/4.86 ~spl2_308 | ~spl2_311),
% 22.89/4.86 inference(avatar_contradiction_clause,[status(thm)],[f12686])).
% 22.89/4.86 thf(f12686,plain,(
% 22.89/4.86 $false | (~spl2_308 | ~spl2_311)),
% 22.89/4.86 inference(trivial_inequality_removal,[status(thm)],[f12685])).
% 22.89/4.86 thf(f12685,plain,(
% 22.89/4.86 ($true = $false) | (~spl2_308 | ~spl2_311)),
% 22.89/4.86 inference(forward_demodulation,[status(thm)],[f7550,f7564])).
% 22.89/4.86 thf(f7564,plain,(
% 22.89/4.86 (powersetE1 = $false) | ~spl2_311),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f7562])).
% 22.89/4.86 thf(f7562,definition,(
% 22.89/4.86 spl2_311 <=> (powersetE1 = $false)),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_311])],[avatar_definition])).
% 22.89/4.86 thf(f7550,plain,(
% 22.89/4.86 (powersetE1 = $true) | ~spl2_308),
% 22.89/4.86 inference(avatar_component_clause,[status(thm)],[f7548])).
% 22.89/4.86 thf(f7548,definition,(
% 22.89/4.86 spl2_308 <=> (powersetE1 = $true)),
% 22.89/4.86 introduced(definition,[new_symbols(naming,[spl2_308])],[avatar_definition])).
% 22.89/4.86 thf(f12431,plain,(
% 22.89/4.86 spl2_456),
% 22.89/4.86 inference(avatar_split_clause,[status(thm)],[f654,f8222])).
% 22.89/4.86 thf(f654,plain,(
% 22.89/4.86 (notinsingleton = $true)),
% 22.89/4.86 inference(cnf_transformation,[status(thm)],[f429])).
% 22.89/4.86 thf(f12201,plain,(
% 22.89/4.86 spl2_320),
% 22.89/4.86 inference(avatar_split_clause,[status(thm)],[f600,f7599])).
% 22.89/4.86 thf(f600,plain,(
% 22.89/4.86 (powersetAx = $true)),
% 22.89/4.86 inference(cnf_transformation,[status(thm)],[f429])).
% 22.89/4.86 thf(f8238,plain,(
% 22.89/4.86 spl2_458 | spl2_459),
% 22.89/4.86 inference(avatar_split_clause,[status(thm)],[f4700,f8235,f8232])).
% 22.89/4.86 thf(f4700,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((X1 = X2) | (notinsingleton = $false) | ((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false)) )),
% 22.89/4.86 inference(equality_proxy_clausification,[status(thm)],[f4699])).
% 22.89/4.86 thf(f4699,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false) | (notinsingleton = $false) | ((X2 = X1) = $true)) )),
% 22.89/4.86 inference(not_proxy_clausification,[status(thm)],[f4698])).
% 22.89/4.86 thf(f4698,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : (((~ (X2 = X1)) = $false) | ((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false) | (notinsingleton = $false)) )),
% 22.89/4.86 inference(not_proxy_clausification,[status(thm)],[f4697])).
% 22.89/4.86 thf(f4697,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((notinsingleton = $false) | ($true = (~ (in @ X2 @ (setadjoin @ X1 @ emptyset)))) | ((~ (X2 = X1)) = $false)) )),
% 22.89/4.86 inference(binary_proxy_clausification,[status(thm)],[f4696])).
% 22.89/4.86 thf(f4696,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((notinsingleton = $false) | (((~ (X2 = X1)) => (~ (in @ X2 @ (setadjoin @ X1 @ emptyset)))) = $true)) )),
% 22.89/4.86 inference(beta_eta_normalization,[status(thm)],[f4695])).
% 22.89/4.86 thf(f4695,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (Y0 = X1)) => (~ (in @ Y0 @ (setadjoin @ X1 @ emptyset))))) @ X2) = $true) | (notinsingleton = $false)) )),
% 22.89/4.86 inference(pi_clausification,[status(thm)],[f4694])).
% 22.89/4.86 thf(f4694,plain,(
% 22.89/4.86 ( ! [X1 : $i] : ((notinsingleton = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (Y0 = X1)) => (~ (in @ Y0 @ (setadjoin @ X1 @ emptyset)))))))) )),
% 22.89/4.86 inference(beta_eta_normalization,[status(thm)],[f4693])).
% 22.89/4.86 thf(f4693,plain,(
% 22.89/4.86 ( ! [X1 : $i] : ((notinsingleton = $false) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) @ X1) = $true)) )),
% 22.89/4.86 inference(pi_clausification,[status(thm)],[f4692])).
% 22.89/4.86 thf(f4692,plain,(
% 22.89/4.86 (notinsingleton = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 22.89/4.86 inference(binary_proxy_clausification,[status(thm)],[f489])).
% 22.89/4.86 thf(f489,plain,(
% 22.89/4.86 (notinsingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 22.89/4.86 inference(cnf_transformation,[status(thm)],[f417])).
% 22.89/4.86 thf(f417,plain,(
% 22.89/4.86 (notinsingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))))),
% 22.89/4.86 inference(fool_elimination,[status(thm)],[f416])).
% 22.89/4.86 thf(f416,plain,(
% 22.89/4.86 (notinsingleton = ! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 22.89/4.86 inference(rectify,[status(thm)],[f47])).
% 22.89/4.86 thf(f47,axiom,(
% 22.89/4.86 (notinsingleton = ! [X2 : $i,X1 : $i] : ((X1 != X2) => ~(in @ X2 @ (setadjoin @ X1 @ emptyset))))),
% 22.89/4.86 file('/export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2THF_9200.p',notinsingleton)).
% 22.89/4.86 thf(f7723,plain,(
% 22.89/4.86 spl2_308),
% 22.89/4.86 inference(avatar_split_clause,[status(thm)],[f658,f7548])).
% 22.89/4.86 thf(f658,plain,(
% 22.89/4.86 (powersetE1 = $true)),
% 22.89/4.86 inference(cnf_transformation,[status(thm)],[f429])).
% 22.89/4.86 thf(f7610,plain,(
% 22.89/4.86 spl2_321 | spl2_322),
% 22.89/4.86 inference(avatar_split_clause,[status(thm)],[f5156,f7607,f7604])).
% 22.89/4.86 thf(f5156,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = (in @ X2 @ (powerset @ X1))) = $true) | (powersetAx = $false)) )),
% 22.89/4.86 inference(beta_eta_normalization,[status(thm)],[f5155])).
% 22.89/4.86 thf(f5155,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) = (in @ Y0 @ (powerset @ X1)))) @ X2) = $true) | (powersetAx = $false)) )),
% 22.89/4.86 inference(pi_clausification,[status(thm)],[f5154])).
% 22.89/4.86 thf(f5154,plain,(
% 22.89/4.86 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) = (in @ Y0 @ (powerset @ X1)))))) | (powersetAx = $false)) )),
% 22.89/4.86 inference(beta_eta_normalization,[status(thm)],[f5153])).
% 22.89/4.86 thf(f5153,plain,(
% 22.89/4.86 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0)))))) @ X1)) | (powersetAx = $false)) )),
% 22.89/4.86 inference(pi_clausification,[status(thm)],[f5152])).
% 22.89/4.86 thf(f5152,plain,(
% 22.89/4.86 (powersetAx = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 22.89/4.86 inference(binary_proxy_clausification,[status(thm)],[f441])).
% 22.89/4.86 thf(f441,plain,(
% 22.89/4.86 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 22.89/4.86 inference(cnf_transformation,[status(thm)],[f270])).
% 22.89/4.86 thf(f270,plain,(
% 22.89/4.86 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))),
% 22.89/4.86 inference(fool_elimination,[status(thm)],[f269])).
% 22.89/4.86 thf(f269,plain,(
% 22.89/4.86 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) <=> (in @ X0 @ (powerset @ X1))) = powersetAx)),
% 22.89/4.86 inference(rectify,[status(thm)],[f5])).
% 22.89/4.86 thf(f5,axiom,(
% 22.89/4.86 (! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) <=> (in @ X4 @ (powerset @ X3))) = powersetAx)),
% 22.89/4.86 file('/export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2THF_9200.p',powersetAx)).
% 22.89/4.86 thf(f7568,plain,(
% 22.89/4.86 spl2_311 | spl2_312),
% 22.89/4.86 inference(avatar_split_clause,[status(thm)],[f5194,f7566,f7562])).
% 22.89/4.86 thf(f5194,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | ((in @ X1 @ (powerset @ X2)) = $false) | (powersetE1 = $false)) )),
% 22.89/4.86 inference(binary_proxy_clausification,[status(thm)],[f5193])).
% 22.89/4.86 thf(f5193,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((powersetE1 = $false) | ($true = ((in @ X1 @ (powerset @ X2)) => (subset @ X1 @ X2)))) )),
% 22.89/4.86 inference(beta_eta_normalization,[status(thm)],[f5192])).
% 22.89/4.86 thf(f5192,plain,(
% 22.89/4.86 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (subset @ X1 @ Y0))) @ X2) = $true) | (powersetE1 = $false)) )),
% 22.89/4.86 inference(pi_clausification,[status(thm)],[f5191])).
% 22.89/4.86 thf(f5191,plain,(
% 22.89/4.86 ( ! [X1 : $i] : ((powersetE1 = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (subset @ X1 @ Y0)))))) )),
% 22.89/4.86 inference(beta_eta_normalization,[status(thm)],[f5190])).
% 22.89/4.86 thf(f5190,plain,(
% 22.89/4.86 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1))))) @ X1)) | (powersetE1 = $false)) )),
% 22.89/4.86 inference(pi_clausification,[status(thm)],[f5189])).
% 22.89/4.86 thf(f5189,plain,(
% 22.89/4.86 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1))))))) | (powersetE1 = $false)),
% 22.89/4.86 inference(binary_proxy_clausification,[status(thm)],[f518])).
% 22.89/4.86 thf(f518,plain,(
% 22.89/4.86 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))))),
% 22.89/4.86 inference(cnf_transformation,[status(thm)],[f392])).
% 22.89/4.86 thf(f392,plain,(
% 22.89/4.86 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))))),
% 22.89/4.86 inference(fool_elimination,[status(thm)],[f391])).
% 22.89/4.86 thf(f391,plain,(
% 22.89/4.86 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)) = powersetE1)),
% 22.89/4.86 inference(rectify,[status(thm)],[f96])).
% 22.89/4.86 thf(f96,axiom,(
% 22.89/4.86 (! [X3 : $i,X4 : $i] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)) = powersetE1)),
% 22.89/4.86 file('/export/starexec/sandbox/tmp/tmp.mcL7eErk0k/DTF2THF_9200.p',powersetE1)).
% 22.89/4.86 % SZS output end Proof for DTF2THF_9200
% 22.89/4.86 % (9415)------------------------------
% 22.89/4.86 % (9415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.89/4.86 % (9415)Termination reason: Refutation
% 22.89/4.86
% 22.89/4.86 % (9415)Memory used [KB]: 15607
% 22.89/4.86 % (9415)Time elapsed: 0.814 s
% 22.89/4.86 % (9415)Instructions burned: 1680 (million)
% 22.89/4.86 % (9415)------------------------------
% 22.89/4.86 % (9415)------------------------------
% 22.89/4.86 % (9297)Success in time 3.295 s
%------------------------------------------------------------------------------