%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU681^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:17 AM UTC 2026
% Result : Theorem 43.35s 7.52s
% Output : Refutation 43.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 85 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 3894 (1065 equ; 0 cnn)
% Maximal formula atoms : 204 ( 45 avg)
% Number of connectives : 2460 ( 136 ~; 106 |; 649 &; 723 @)
% ( 10 <=>; 836 =>; 0 <=; 0 <~>)
% Maximal formula depth : 214 ( 22 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 443 ( 440 usr; 215 con; 0-4 aty)
% Number of variables : 244 ( 15 ^; 172 !; 57 ?; 244 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_249,type,
sP1: $i > ( $i > $i > $o ) > $o ).
thf(func_def_260,type,
sP12: ( $i > $o ) > $i > $o ).
thf(func_def_268,type,
sP20: $i > ( $i > $o ) > $o ).
thf(func_def_270,type,
sP22: $i > $i > $i > $o ).
thf(func_def_271,type,
sP23: $i > $i > $o ).
thf(func_def_272,type,
sP24: $i > $o ).
thf(func_def_273,type,
sP25: $i > $i > $o ).
thf(func_def_274,type,
sP26: $i > $i > $o ).
thf(func_def_275,type,
sP27: $i > $i > $o ).
thf(func_def_278,type,
sP30: $i > $i > $i > $o > $o ).
thf(func_def_287,type,
sK39: ( $i > $o ) > $i ).
thf(func_def_288,type,
sK40: $i > $o ).
thf(func_def_289,type,
sK41: $i > $i > $o ).
thf(func_def_301,type,
sK53: $i > $o ).
thf(func_def_307,type,
sK59: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_308,type,
sK60: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_309,type,
sK61: $i > ( $i > $i > $o ) > $i ).
thf(func_def_310,type,
sK62: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_311,type,
sK63: $i > ( $i > $i > $o ) > $i ).
thf(func_def_312,type,
sK64: $i > $i > $o ).
thf(func_def_347,type,
sK99: $i > $i > $o ).
thf(func_def_348,type,
sK100: $i > $o ).
thf(func_def_349,type,
sK101: $i > $i ).
thf(func_def_350,type,
sK102: ( $i > $o ) > $i ).
thf(func_def_352,type,
sK104: $i > $i > $o ).
thf(func_def_370,type,
sK122: $i > $i > $i ).
thf(func_def_380,type,
sK132: $i > $o ).
thf(func_def_381,type,
sK133: $i > $o ).
thf(func_def_382,type,
sK134: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_383,type,
sK135: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_398,type,
sK150: $i > $o ).
thf(func_def_399,type,
sK151: $i > $o ).
thf(func_def_400,type,
sK152: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_401,type,
sK153: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_402,type,
sK154: ( $i > $i ) > $i > $i > $i ).
thf(func_def_405,type,
sK157: $i > $i ).
thf(func_def_421,type,
sK173: $i > $i > $o ).
thf(func_def_428,type,
sK180: $i > $o ).
thf(func_def_432,type,
sK184: $i > $o ).
thf(func_def_446,type,
sK198: $i > $o ).
thf(func_def_448,type,
sK200: $i > $o ).
thf(func_def_450,type,
sK202: $i > ( $i > $o ) > $i ).
thf(func_def_457,type,
sK209: $i > $o ).
thf(func_def_459,type,
sK211: ( $i > $o ) > $i > $i ).
thf(func_def_460,type,
sK212: $i > $o ).
thf(func_def_464,type,
sK216: $i > $i > $i ).
thf(func_def_465,type,
sK217: $i > $i > $i ).
thf(func_def_469,type,
sK221: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_470,type,
sK222: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_471,type,
sK223: $i > $o ).
thf(func_def_472,type,
sK224: $i > $o ).
thf(func_def_477,type,
sK229: $i > $o ).
thf(func_def_479,type,
sK231: ( $i > $o ) > $i > $i ).
thf(func_def_487,type,
sK239: $i > $o ).
thf(func_def_489,type,
sK241: $i > ( $i > $o ) > $i ).
thf(func_def_498,type,
sK250: $i > $i > $i ).
thf(func_def_499,type,
sK251: $i > $o ).
thf(func_def_501,type,
sK253: $i > $o ).
thf(func_def_504,type,
sK256: ( $i > $o ) > $i > $i ).
thf(func_def_505,type,
sK257: ( $i > $o ) > $i > $i ).
thf(func_def_507,type,
sK259: $i > $o ).
thf(func_def_544,type,
sK296: $i > $i ).
thf(func_def_545,type,
sK297: $i > $i ).
thf(func_def_547,type,
sK299: $i > $o ).
thf(func_def_555,type,
sK307: $i > $o ).
thf(func_def_557,type,
sK309: ( $i > $o ) > $i ).
thf(func_def_558,type,
sK310: ( $i > $o ) > $i ).
thf(func_def_567,type,
sK319: $i > $o ).
thf(func_def_570,type,
sK322: $i > ( $i > $o ) > $i ).
thf(func_def_575,type,
sK327: $i > $i ).
thf(func_def_581,type,
sK333: $i > $i ).
thf(func_def_586,type,
sK338: $i > $o ).
thf(func_def_589,type,
sK341: $i > $i > ( $i > $o ) > $i ).
thf(func_def_590,type,
sK342: $i > $o ).
thf(func_def_595,type,
sK347: $i > $i > $i ).
thf(func_def_600,type,
sK352: $i > $i > $i ).
thf(func_def_601,type,
sK353: $i > $o ).
thf(func_def_604,type,
sK356: $i > ( $i > $o ) > $i ).
thf(func_def_605,type,
sK357: $i > ( $i > $o ) > $i ).
thf(func_def_606,type,
sK358: $i > ( $i > $o ) > $i ).
thf(func_def_607,type,
sK359: $i > $o ).
thf(func_def_612,type,
sK364: $i > $o ).
thf(func_def_625,type,
sK377: $i > $i ).
thf(func_def_626,type,
sK378: ( $i > $i ) > $i > $i > $i ).
thf(func_def_630,type,
sK382: $i > $o ).
thf(func_def_638,type,
sK390: $i > $i > $i ).
thf(func_def_647,type,
sK399: $i > $o ).
thf(func_def_648,type,
sK400: $i > $i ).
thf(func_def_649,type,
sK401: ( $i > $o ) > $i ).
thf(func_def_650,type,
sK402: $i > $i > $i ).
thf(func_def_653,type,
sK405: $i > $i > $i ).
thf(func_def_654,type,
sK406: $i > $i > $i ).
thf(func_def_655,type,
sK407: $i > $i > $i ).
thf(func_def_656,type,
sK408: $i > $i > $i ).
thf(func_def_657,type,
sK409: $i > $i > $i ).
thf(func_def_658,type,
sK410: $i > $i > $i ).
thf(func_def_659,type,
sK411: $i > $i > $i ).
thf(func_def_660,type,
sK412: $i > $i > $i > $i ).
thf(func_def_661,type,
sK413: $i > $i ).
thf(func_def_662,type,
sK414: $i > $i ).
thf(func_def_663,type,
sK415: $i > $i ).
thf(func_def_664,type,
sK416: $i > $i ).
thf(func_def_665,type,
sK417: $i > $i > $i ).
thf(func_def_666,type,
sK418: $i > $i > $i ).
thf(func_def_667,type,
sK419: $i > $i > $i ).
thf(func_def_668,type,
sK420: $i > $i > $i > $i ).
thf(func_def_669,type,
sK421: $i > $i > $i > $i ).
thf(func_def_670,type,
sK422: $i > $i ).
thf(func_def_674,type,
sK426: $i > $i > $o ).
thf(func_def_696,type,
sK448: $i > $i ).
thf(func_def_715,type,
sK467: ( $i > $o ) > $i > $i ).
thf(func_def_717,type,
sK469: $i > $o ).
thf(func_def_720,type,
sK472: $i > $i > $o ).
thf(func_def_725,type,
sK477: $i > $i > $o ).
thf(func_def_732,type,
sK484: $i > $o ).
thf(func_def_734,type,
sK486: ( $i > $o ) > $i > $i ).
thf(func_def_741,type,
sK493: $i > $i ).
thf(func_def_742,type,
sK494: ( $i > $i ) > $i > $i > $i ).
thf(func_def_746,type,
sK498: $i > $i > $i > $i ).
thf(func_def_747,type,
sK499: $i > $i > $i > $i ).
thf(func_def_763,type,
sK515: $i > $o ).
thf(func_def_767,type,
sK519: $i > $i ).
thf(func_def_777,type,
sK529: $i > $o ).
thf(func_def_819,type,
sK571: $i > $i > $i ).
thf(func_def_831,type,
sK583: $i > $i ).
thf(func_def_836,type,
sK588: $o > $i > $i > $i ).
thf(func_def_842,type,
sK594: $i > $i > $i ).
thf(func_def_851,type,
sK603: $i > $o ).
thf(func_def_853,type,
sK605: ( $i > $o ) > $i > $i ).
thf(func_def_854,type,
sK606: $i > ( $i > $i ) > $i > $i > $i ).
thf(func_def_855,type,
sK607: ( $i > $o ) > $i > $i ).
thf(func_def_856,type,
sK608: ( $i > $o ) > $i > $i ).
thf(func_def_857,type,
sK609: ( $i > $o ) > $i > $i ).
thf(func_def_858,type,
sK610: $i > $i > $i > $i ).
thf(func_def_859,type,
sK611: ( $i > $o ) > $i ).
thf(func_def_860,type,
sK612: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_861,type,
sK613: ( $i > $o ) > $i > $i ).
thf(func_def_862,type,
sK614: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_863,type,
sK615: $i > ( $i > $o ) > $i ).
thf(func_def_864,type,
sK616: ( $i > $o ) > $i ).
thf(func_def_865,type,
sK617: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_866,type,
sK618: $i > $i ).
thf(func_def_867,type,
sK619: $i > ( $i > $o ) > $i ).
thf(func_def_868,type,
sK620: ( $i > $o ) > $i ).
thf(func_def_869,type,
sK621: $i > $i > $i > $i ).
thf(func_def_870,type,
sK622: $i > $i > $i > $i ).
thf(func_def_871,type,
sK623: $i > $i > $i > $i ).
thf(func_def_872,type,
sK624: $i > $i ).
thf(func_def_874,type,
sK626: ( $i > $o ) > $i > $i ).
thf(func_def_875,type,
sK627: $i > $i ).
thf(func_def_876,type,
sK628: ( $i > $o ) > $i ).
thf(func_def_877,type,
sK629: ( $i > $o ) > $i ).
thf(func_def_879,type,
sK631: ( $i > $o ) > $i > $i ).
thf(func_def_880,type,
sK632: $i > $i ).
thf(func_def_881,type,
sK633: $i > $i > $i > $i ).
thf(func_def_882,type,
sK634: $i > $i ).
thf(func_def_883,type,
sK635: ( $i > $o ) > $i > $i ).
thf(func_def_884,type,
sK636: ( $i > $o ) > $i > $i ).
thf(func_def_885,type,
sK637: ( $i > $o ) > $i ).
thf(func_def_886,type,
sK638: ( $i > $o ) > $i ).
thf(func_def_887,type,
sK639: ( $i > $o ) > $i ).
thf(func_def_888,type,
sK640: $i > ( $i > $o ) > $i ).
thf(func_def_889,type,
sK641: $i > ( $i > $o ) > $i ).
thf(func_def_890,type,
sK642: ( $i > $o ) > $i ).
thf(func_def_891,type,
sK643: ( $i > $o ) > $i > $i ).
thf(func_def_892,type,
sK644: ( $i > $o ) > $i > $i ).
thf(func_def_893,type,
sK645: ( $i > $o ) > $i ).
thf(func_def_894,type,
sK646: $i > ( $i > $o ) > $i ).
thf(func_def_895,type,
sK647: $i > ( $i > $o ) > $i ).
thf(func_def_896,type,
sK648: $i > ( $i > $o ) > $i ).
thf(func_def_897,type,
sK649: ( $i > $o ) > $i > $i ).
thf(func_def_898,type,
sK650: ( $i > $o ) > $i > $i ).
thf(func_def_899,type,
sK651: $i > ( $i > $o ) > $i ).
thf(func_def_900,type,
sK652: ( $i > $o ) > $i > $i ).
thf(func_def_901,type,
sK653: ( $i > $o ) > $i > $i ).
thf(func_def_903,type,
sK655: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_904,type,
sK656: $i > ( $i > $o ) > $i ).
thf(func_def_905,type,
sK657: ( $i > $o ) > $i ).
thf(func_def_906,type,
sK658: $i > ( $i > $o ) > $i ).
thf(func_def_907,type,
sK659: $i > ( $i > $o ) > $i ).
thf(func_def_909,type,
sK661: $i > $i > $i > $i ).
thf(func_def_910,type,
sK662: ( $i > $o ) > $i ).
thf(func_def_911,type,
sK663: ( $i > $o ) > $i > $i ).
thf(func_def_912,type,
sK664: ( $i > $o ) > $i ).
thf(func_def_913,type,
sK665: ( $i > $o ) > $i > $i ).
thf(func_def_914,type,
sK666: ( $i > $o ) > $i > $i ).
thf(func_def_915,type,
sK667: ( $i > $o ) > $i ).
thf(func_def_916,type,
sK668: $i > ( $i > $o ) > $i ).
thf(func_def_917,type,
sK669: $i > ( $i > $o ) > $i ).
thf(func_def_918,type,
sK670: ( $i > $o ) > $i > $i ).
thf(func_def_919,type,
sK671: $i > ( $i > $o ) > $i ).
thf(func_def_920,type,
ph672:
!>[X0: $tType] : X0 ).
thf(f16150,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f16149,f2434]) ).
thf(f2434,plain,
( $true
= ( in @ sK383 @ sK381 ) ),
inference(cnf_transformation,[status(thm)],[f1498]) ).
thf(f1498,plain,
( ( vacuousDall = $true )
& ( quantDeMorgan3 = $true )
& ( subsetI1 = $true )
& ( cartprodsndin = $true )
& ( setunionsingleton = $true )
& ( emptysetsubset = $true )
& ( symdiffI1 = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoinIR = $true )
& ( setext = $true )
& ( setoftrueEq = $true )
& ( notinsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( subsetE2 = $true )
& ( setminusEL = $true )
& ( setminusSubset2 = $true )
& ( setukpairIL = $true )
& ( subsetTrans = $true )
& ( uniqinunit = $true )
& ( symdiffIneg1 = $true )
& ( dpsetconstrERa = $true )
& ( setextAx = $true )
& ( dpsetconstrEL1 = $true )
& ( kfstpairEq = $true )
& ( binintersectEL = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ( powerset__Cong = $true )
& ( dsetconstrEL = $true )
& ( replAx = $true )
& ( binunionIR = $true )
& ( binintersectRsub = $true )
& ( exuE1 = $true )
& ( notsubsetI = $true )
& ( eqinunit = $true )
& ( subsetI2 = $true )
& ( exuEu = $true )
& ( kfstsingleton = $true )
& ( notequalI1 = $true )
& ( binintersectSubset4 = $true )
& ( setunionE2 = $true )
& ( setminusIRneg = $true )
& ( eqimpsubset1 = $true )
& ( notdallE = $true )
& ( setminusI = $true )
& ( prop2set2propI = $true )
& ( powersetE = $true )
& ( nonemptyImpWitness = $true )
& ( setukpairinjR2 = $true )
& ( secondinupair = $true )
& ( exuI2 = $true )
& ( powersetI = $true )
& ( subsetRefl = $true )
& ( setbeta = $true )
& ( nonemptyE1 = $true )
& ( powersetE1 = $true )
& ( upairsetIR = $true )
& ( notequalI2 = $true )
& ( cartprodpairsurjEq = $true )
& ( exuE3u = $true )
& ( sepInPowerset = $true )
& ( noeltsimpempty = $true )
& ( ap2p = $true )
& ( ubforcartprodlem2 = $true )
& ( app = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinE = $true )
& ( dsetconstrER = $true )
& ( sepSubset = $true )
& ( subset2powerset = $true )
& ( subPowSU = $true )
& ( setminusSubset1 = $true )
& ( subsetE = $true )
& ( singletonsswitch = $true )
& ( setadjoinAx = $true )
& ( setadjoinSub = $true )
& ( cartprodmempair = $true )
& ( ksndpairEq = $true )
& ( omega0Ax = $true )
& ( lamProp = $true )
& ( setminusLsub = $true )
& ( binintersectSubset1 = $true )
& ( ubforcartprodlem3 = $true )
& ( setextsub = $true )
& ( symdiffIneg2 = $true )
& ( binunionLsub = $true )
& ( notdexE = $true )
& ( upairequniteq = $true )
& ( upairset2IR = $true )
& ( nonemptyI = $true )
& ( setminusER = $true )
& ( infuncsetfunc = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinOr = $true )
& ( setminusILneg = $true )
& ( symdiffI2 = $true )
& ( binintersectER = $true )
& ( in__Cong = $true )
& ( singletonprop = $true )
& ( singletonsuniq = $true )
& ( emptyE1 = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrI = $true )
& ( nonemptyI1 = $true )
& ( setukpairinjL2 = $true )
& ( dpsetconstrSub = $true )
& ( exuI3 = $true )
& ( prop2setI = $true )
& ( singletoninpowerset = $true )
& ( emptysetAx = $true )
& ( lam2p = $true )
& ( exu__Cong = $true )
& ( emptyI = $true )
& ( binunionIL = $true )
& ( dsetconstr__Cong = $true )
& ( exuI1 = $true )
& ( powersetI1 = $true )
& ( setadjoin__Cong = $true )
& ( binintersectLsub = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjR12 = $true )
& ( ( breln @ sK379 @ sK380 @ sK381 )
= $true )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK379 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK381 )
!= $true )
| ( ( sK382 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( $true
!= ( in @ X5 @ sK380 ) ) ) )
& ( $true
!= ( sK382 @ sK383 ) )
& ( $true
= ( in @ sK383 @ sK381 ) )
& ( inCongP = $true )
& ( emptysetimpfalse = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairinjR1 = $true )
& ( emptysetE = $true )
& ( setminusELneg = $true )
& ( cartprodmempair1 = $true )
& ( emptyset__Cong = $true )
& ( apProp = $true )
& ( upairsetE = $true )
& ( omega__Cong = $true )
& ( binintersectSubset5 = $true )
& ( kpairiskpair = $true )
& ( omegaIndAx = $true )
& ( theprop = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrER = $true )
& ( eqimpsubset2 = $true )
& ( kpairsurjEq = $true )
& ( upairsubunion = $true )
& ( funcImageSingleton = $true )
& ( exuE3e = $true )
& ( binintersectSubset3 = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL1 = $true )
& ( upairset2E = $true )
& ( notinemptyset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( setunionsingleton2 = $true )
& ( quantDeMorgan1 = $true )
& ( lamp = $true )
& ( setukpairinjR = $true )
& ( setunionI = $true )
& ( setminusERneg = $true )
& ( setOfPairsIsBReln = $true )
& ( upairsetIL = $true )
& ( setunionsingleton1 = $true )
& ( setadjoinSub2 = $true )
& ( cartprodpairin = $true )
& ( ex1I = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( cartprodfstpairEq = $true )
& ( emptyinunitempty = $true )
& ( ex1E1 = $true )
& ( setukpairinjR11 = $true )
& ( prop2setE = $true )
& ( funcinfuncset = $true )
& ( upairinpowunion = $true )
& ( exuE2 = $true )
& ( omegaSAx = $true )
& ( binunionEcases = $true )
& ( emptyinPowerset = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectSubset2 = $true )
& ( singletoninpowunion = $true )
& ( descr__Cong = $true )
& ( ex1I2 = $true )
& ( inPowerset = $true )
& ( cartprodfstin = $true )
& ( binintersectI = $true )
& ( cartprodmempaircEq = $true )
& ( setukpairIR = $true )
& ( symdiffE = $true )
& ( ksndsingleton = $true )
& ( setunion__Cong = $true )
& ( cartprodpairmemEL = $true )
& ( binunionE = $true )
& ( bs114d = $true )
& ( setukpairinjL = $true )
& ( setadjoinIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK379,sK380,sK381,sK382,sK383])],[f761,f1497,f1496,f1495]) ).
thf(f1495,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X2 ) )
& ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ X5 @ X1 )
!= $true ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( $true
= ( in @ X6 @ X2 ) ) ) ) )
=> ( ( ( breln @ sK379 @ sK380 @ sK381 )
= $true )
& ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK379 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK381 )
!= $true )
| ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK380 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( ( in @ X6 @ sK381 )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1496,plain,
( ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK379 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK381 )
!= $true )
| ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ X5 @ sK380 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( ( in @ X6 @ sK381 )
= $true ) ) )
=> ( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK379 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK381 )
!= $true )
| ( ( sK382 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( $true
!= ( in @ X5 @ sK380 ) ) ) )
& ? [X6: $i] :
( ( $true
!= ( sK382 @ X6 ) )
& ( ( in @ X6 @ sK381 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1497,plain,
( ? [X6: $i] :
( ( $true
!= ( sK382 @ X6 ) )
& ( ( in @ X6 @ sK381 )
= $true ) )
=> ( ( $true
!= ( sK382 @ sK383 ) )
& ( $true
= ( in @ sK383 @ sK381 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f761,plain,
( ( vacuousDall = $true )
& ( quantDeMorgan3 = $true )
& ( subsetI1 = $true )
& ( cartprodsndin = $true )
& ( setunionsingleton = $true )
& ( emptysetsubset = $true )
& ( symdiffI1 = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoinIR = $true )
& ( setext = $true )
& ( setoftrueEq = $true )
& ( notinsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( subsetE2 = $true )
& ( setminusEL = $true )
& ( setminusSubset2 = $true )
& ( setukpairIL = $true )
& ( subsetTrans = $true )
& ( uniqinunit = $true )
& ( symdiffIneg1 = $true )
& ( dpsetconstrERa = $true )
& ( setextAx = $true )
& ( dpsetconstrEL1 = $true )
& ( kfstpairEq = $true )
& ( binintersectEL = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ( powerset__Cong = $true )
& ( dsetconstrEL = $true )
& ( replAx = $true )
& ( binunionIR = $true )
& ( binintersectRsub = $true )
& ( exuE1 = $true )
& ( notsubsetI = $true )
& ( eqinunit = $true )
& ( subsetI2 = $true )
& ( exuEu = $true )
& ( kfstsingleton = $true )
& ( notequalI1 = $true )
& ( binintersectSubset4 = $true )
& ( setunionE2 = $true )
& ( setminusIRneg = $true )
& ( eqimpsubset1 = $true )
& ( notdallE = $true )
& ( setminusI = $true )
& ( prop2set2propI = $true )
& ( powersetE = $true )
& ( nonemptyImpWitness = $true )
& ( setukpairinjR2 = $true )
& ( secondinupair = $true )
& ( exuI2 = $true )
& ( powersetI = $true )
& ( subsetRefl = $true )
& ( setbeta = $true )
& ( nonemptyE1 = $true )
& ( powersetE1 = $true )
& ( upairsetIR = $true )
& ( notequalI2 = $true )
& ( cartprodpairsurjEq = $true )
& ( exuE3u = $true )
& ( sepInPowerset = $true )
& ( noeltsimpempty = $true )
& ( ap2p = $true )
& ( ubforcartprodlem2 = $true )
& ( app = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinE = $true )
& ( dsetconstrER = $true )
& ( sepSubset = $true )
& ( subset2powerset = $true )
& ( subPowSU = $true )
& ( setminusSubset1 = $true )
& ( subsetE = $true )
& ( singletonsswitch = $true )
& ( setadjoinAx = $true )
& ( setadjoinSub = $true )
& ( cartprodmempair = $true )
& ( ksndpairEq = $true )
& ( omega0Ax = $true )
& ( lamProp = $true )
& ( setminusLsub = $true )
& ( binintersectSubset1 = $true )
& ( ubforcartprodlem3 = $true )
& ( setextsub = $true )
& ( symdiffIneg2 = $true )
& ( binunionLsub = $true )
& ( notdexE = $true )
& ( upairequniteq = $true )
& ( upairset2IR = $true )
& ( nonemptyI = $true )
& ( setminusER = $true )
& ( infuncsetfunc = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinOr = $true )
& ( setminusILneg = $true )
& ( symdiffI2 = $true )
& ( binintersectER = $true )
& ( in__Cong = $true )
& ( singletonprop = $true )
& ( singletonsuniq = $true )
& ( emptyE1 = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrI = $true )
& ( nonemptyI1 = $true )
& ( setukpairinjL2 = $true )
& ( dpsetconstrSub = $true )
& ( exuI3 = $true )
& ( prop2setI = $true )
& ( singletoninpowerset = $true )
& ( emptysetAx = $true )
& ( lam2p = $true )
& ( exu__Cong = $true )
& ( emptyI = $true )
& ( binunionIL = $true )
& ( dsetconstr__Cong = $true )
& ( exuI1 = $true )
& ( powersetI1 = $true )
& ( setadjoin__Cong = $true )
& ( binintersectLsub = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjR12 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X2 ) )
& ? [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ X5 @ X1 )
!= $true ) ) )
& ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( $true
= ( in @ X6 @ X2 ) ) ) ) )
& ( inCongP = $true )
& ( emptysetimpfalse = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairinjR1 = $true )
& ( emptysetE = $true )
& ( setminusELneg = $true )
& ( cartprodmempair1 = $true )
& ( emptyset__Cong = $true )
& ( apProp = $true )
& ( upairsetE = $true )
& ( omega__Cong = $true )
& ( binintersectSubset5 = $true )
& ( kpairiskpair = $true )
& ( omegaIndAx = $true )
& ( theprop = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrER = $true )
& ( eqimpsubset2 = $true )
& ( kpairsurjEq = $true )
& ( upairsubunion = $true )
& ( funcImageSingleton = $true )
& ( exuE3e = $true )
& ( binintersectSubset3 = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan2 = $true )
& ( setukpairinjL1 = $true )
& ( upairset2E = $true )
& ( notinemptyset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( setunionsingleton2 = $true )
& ( quantDeMorgan1 = $true )
& ( lamp = $true )
& ( setukpairinjR = $true )
& ( setunionI = $true )
& ( setminusERneg = $true )
& ( setOfPairsIsBReln = $true )
& ( upairsetIL = $true )
& ( setunionsingleton1 = $true )
& ( setadjoinSub2 = $true )
& ( cartprodpairin = $true )
& ( ex1I = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( cartprodfstpairEq = $true )
& ( emptyinunitempty = $true )
& ( ex1E1 = $true )
& ( setukpairinjR11 = $true )
& ( prop2setE = $true )
& ( funcinfuncset = $true )
& ( upairinpowunion = $true )
& ( exuE2 = $true )
& ( omegaSAx = $true )
& ( binunionEcases = $true )
& ( emptyinPowerset = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectSubset2 = $true )
& ( singletoninpowunion = $true )
& ( descr__Cong = $true )
& ( ex1I2 = $true )
& ( inPowerset = $true )
& ( cartprodfstin = $true )
& ( binintersectI = $true )
& ( cartprodmempaircEq = $true )
& ( setukpairIR = $true )
& ( symdiffE = $true )
& ( ksndsingleton = $true )
& ( setunion__Cong = $true )
& ( cartprodpairmemEL = $true )
& ( binunionE = $true )
& ( bs114d = $true )
& ( setukpairinjL = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[status(thm)],[f760]) ).
thf(f760,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i > $o] :
( ? [X6: $i] :
( ( $true
!= ( X3 @ X6 ) )
& ( $true
= ( in @ X6 @ X2 ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X4 @ X0 ) ) ) )
& ( $true
= ( breln @ X0 @ X1 @ X2 ) ) )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f234]) ).
thf(f234,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X2 ) )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
=> ( $true
= ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) ) )
=> ! [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
=> ( $true
= ( X3 @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f233]) ).
thf(f233,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( X3 @ ( kpair @ X4 @ X5 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( X3 @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f207]) ).
thf(f207,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ! [X3: $i,X4: $i,X12: $i] :
( ( breln @ X3 @ X4 @ X12 )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X12 )
=> ( X0 @ ( kpair @ X1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X12 )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f206]) ).
thf(f206,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ! [X3: $i,X4: $i,X12: $i] :
( ( breln @ X3 @ X4 @ X12 )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X12 )
=> ( X0 @ ( kpair @ X1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X12 )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',brelnall1) ).
thf(f16149,plain,
( $true
!= ( in @ sK383 @ sK381 ) ),
inference(subsumption_resolution,[status(thm)],[f16148,f2435]) ).
thf(f2435,plain,
( $true
!= ( sK382 @ sK383 ) ),
inference(cnf_transformation,[status(thm)],[f1498]) ).
thf(f16148,plain,
( ( $true
= ( sK382 @ sK383 ) )
| ( $true
!= ( in @ sK383 @ sK381 ) ) ),
inference(subsumption_resolution,[status(thm)],[f16147,f15562]) ).
thf(f15562,plain,
( ( in @ ( ksnd @ sK383 ) @ sK380 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f15518]) ).
thf(f15518,plain,
( ( $true != $true )
| ( ( in @ ( ksnd @ sK383 ) @ sK380 )
= $true ) ),
inference(superposition,[status(thm)],[f4255,f15508]) ).
thf(f15508,plain,
( $true
= ( in @ sK383 @ ( cartprod @ sK379 @ sK380 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f15487]) ).
thf(f15487,plain,
( ( $true
= ( in @ sK383 @ ( cartprod @ sK379 @ sK380 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f5302,f2434]) ).
thf(f5302,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK381 ) )
| ( $true
= ( in @ X0 @ ( cartprod @ sK379 @ sK380 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5287]) ).
thf(f5287,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ sK379 @ sK380 ) ) )
| ( $true
!= ( in @ X0 @ sK381 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3756,f4219]) ).
thf(f4219,plain,
( $true
= ( subset @ sK381 @ ( cartprod @ sK379 @ sK380 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3256]) ).
thf(f3256,plain,
( $true
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK379
@ sK380
@ sK381 ) ),
inference(definition_unfolding,[status(thm)],[f2437,f2662]) ).
thf(f2662,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
thf(f442,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f441]) ).
thf(f441,plain,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f186]) ).
thf(f186,axiom,
( breln
= ( ^ [X3: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',breln) ).
thf(f2437,plain,
( ( breln @ sK379 @ sK380 @ sK381 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1498]) ).
thf(f3756,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3005]) ).
thf(f3005,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f2044,f2528]) ).
thf(f2528,plain,
notsubsetI = $true,
inference(cnf_transformation,[status(thm)],[f1498]) ).
thf(f2044,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( notsubsetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f1131]) ).
thf(f1131,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ( ( $true
= ( subset @ sK165 @ sK166 ) )
& ( $true
= ( in @ sK164 @ sK165 ) )
& ( $true
!= ( in @ sK164 @ sK166 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164,sK165,sK166])],[f1129,f1130]) ).
thf(f1130,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X5 )
= $true )
& ( ( in @ X3 @ X4 )
= $true )
& ( $true
!= ( in @ X3 @ X5 ) ) )
=> ( ( $true
= ( subset @ sK165 @ sK166 ) )
& ( $true
= ( in @ sK164 @ sK165 ) )
& ( $true
!= ( in @ sK164 @ sK166 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1129,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X5 )
= $true )
& ( ( in @ X3 @ X4 )
= $true )
& ( $true
!= ( in @ X3 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f1128]) ).
thf(f1128,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
& ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f662]) ).
thf(f662,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) ) )
<=> ( notsubsetI = $true ) ),
inference(flattening,[status(thm)],[f661]) ).
thf(f661,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f651]) ).
thf(f651,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( $true
!= ( in @ X0 @ X2 ) )
=> ( $true
!= ( subset @ X1 @ X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f598]) ).
thf(f598,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( $true
!= ( in @ X0 @ X2 ) )
=> ( $true
!= ( subset @ X1 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f597]) ).
thf(f597,plain,
( notsubsetI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ~ ( subset @ X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f85]) ).
thf(f85,axiom,
( notsubsetI
= ( ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( subset @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',notsubsetI) ).
thf(f4255,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( $true
= ( in @ ( ksnd @ X1 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3302]) ).
thf(f3302,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( ksnd @ X1 ) @ X0 ) )
| ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f2643,f2558]) ).
thf(f2558,plain,
cartprodsndin = $true,
inference(cnf_transformation,[status(thm)],[f1498]) ).
thf(f2643,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( $true
= ( in @ ( ksnd @ X1 ) @ X0 ) )
| ( cartprodsndin != $true ) ),
inference(cnf_transformation,[status(thm)],[f1589]) ).
thf(f1589,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( $true
= ( in @ ( ksnd @ X1 ) @ X0 ) ) )
| ( cartprodsndin != $true ) )
& ( ( cartprodsndin = $true )
| ( ( $true
= ( in @ sK436 @ ( cartprod @ sK437 @ sK435 ) ) )
& ( $true
!= ( in @ ( ksnd @ sK436 ) @ sK435 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK435,sK436,sK437])],[f1587,f1588]) ).
thf(f1588,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) )
& ( $true
!= ( in @ ( ksnd @ X4 ) @ X3 ) ) )
=> ( ( $true
= ( in @ sK436 @ ( cartprod @ sK437 @ sK435 ) ) )
& ( $true
!= ( in @ ( ksnd @ sK436 ) @ sK435 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1587,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( $true
= ( in @ ( ksnd @ X1 ) @ X0 ) ) )
| ( cartprodsndin != $true ) )
& ( ( cartprodsndin = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) )
& ( $true
!= ( in @ ( ksnd @ X4 ) @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f1586]) ).
thf(f1586,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( $true
= ( in @ ( ksnd @ X1 ) @ X0 ) ) )
| ( cartprodsndin != $true ) )
& ( ( cartprodsndin = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
& ( $true
!= ( in @ ( ksnd @ X1 ) @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f734]) ).
thf(f734,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( $true
= ( in @ ( ksnd @ X1 ) @ X0 ) ) )
<=> ( cartprodsndin = $true ) ),
inference(ennf_transformation,[status(thm)],[f218]) ).
thf(f218,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
=> ( $true
= ( in @ ( ksnd @ X1 ) @ X0 ) ) )
<=> ( cartprodsndin = $true ) ),
inference(fool_elimination,[status(thm)],[f217]) ).
thf(f217,plain,
( cartprodsndin
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
=> ( in @ ( ksnd @ X1 ) @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f179]) ).
thf(f179,axiom,
( cartprodsndin
= ( ! [X4: $i,X10: $i,X3: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( ksnd @ X10 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',cartprodsndin) ).
thf(f16147,plain,
( ( ( in @ ( ksnd @ sK383 ) @ sK380 )
!= $true )
| ( $true
!= ( in @ sK383 @ sK381 ) )
| ( $true
= ( sK382 @ sK383 ) ) ),
inference(subsumption_resolution,[status(thm)],[f16134,f15560]) ).
thf(f15560,plain,
( $true
= ( in @ ( kfst @ sK383 ) @ sK379 ) ),
inference(trivial_inequality_removal,[status(thm)],[f15519]) ).
thf(f15519,plain,
( ( $true
= ( in @ ( kfst @ sK383 ) @ sK379 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f4188,f15508]) ).
thf(f4188,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( ( in @ ( kfst @ X1 ) @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3451]) ).
thf(f3451,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( $true != $true )
| ( ( in @ ( kfst @ X1 ) @ X2 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f2822,f2372]) ).
thf(f2372,plain,
cartprodfstin = $true,
inference(cnf_transformation,[status(thm)],[f1498]) ).
thf(f2822,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( ( in @ ( kfst @ X1 ) @ X2 )
= $true )
| ( cartprodfstin != $true ) ),
inference(cnf_transformation,[status(thm)],[f1807]) ).
thf(f1807,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( ( in @ ( kfst @ X1 ) @ X2 )
= $true ) )
| ( cartprodfstin != $true ) )
& ( ( cartprodfstin = $true )
| ( ( ( in @ sK575 @ ( cartprod @ sK576 @ sK574 ) )
= $true )
& ( $true
!= ( in @ ( kfst @ sK575 ) @ sK576 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK574,sK575,sK576])],[f1805,f1806]) ).
thf(f1806,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) )
& ( $true
!= ( in @ ( kfst @ X4 ) @ X5 ) ) )
=> ( ( ( in @ sK575 @ ( cartprod @ sK576 @ sK574 ) )
= $true )
& ( $true
!= ( in @ ( kfst @ sK575 ) @ sK576 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1805,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( ( in @ ( kfst @ X1 ) @ X2 )
= $true ) )
| ( cartprodfstin != $true ) )
& ( ( cartprodfstin = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( cartprod @ X5 @ X3 ) ) )
& ( $true
!= ( in @ ( kfst @ X4 ) @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f1804]) ).
thf(f1804,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( ( in @ ( kfst @ X1 ) @ X2 )
= $true ) )
| ( cartprodfstin != $true ) )
& ( ( cartprodfstin = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
& ( ( in @ ( kfst @ X1 ) @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f718]) ).
thf(f718,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
| ( ( in @ ( kfst @ X1 ) @ X2 )
= $true ) )
<=> ( cartprodfstin = $true ) ),
inference(ennf_transformation,[status(thm)],[f470]) ).
thf(f470,plain,
( ( cartprodfstin = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( cartprod @ X2 @ X0 ) ) )
=> ( ( in @ ( kfst @ X1 ) @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f469]) ).
thf(f469,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
=> ( in @ ( kfst @ X1 ) @ X2 ) )
= cartprodfstin ),
inference(rectify,[status(thm)],[f167]) ).
thf(f167,axiom,
! [X4: $i,X10: $i,X3: $i] :
( ( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( kfst @ X10 ) @ X3 ) )
= cartprodfstin ),
file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',cartprodfstin) ).
thf(f16134,plain,
( ( $true
!= ( in @ ( kfst @ sK383 ) @ sK379 ) )
| ( $true
!= ( in @ sK383 @ sK381 ) )
| ( ( in @ ( ksnd @ sK383 ) @ sK380 )
!= $true )
| ( $true
= ( sK382 @ sK383 ) ) ),
inference(superposition,[status(thm)],[f2436,f15559]) ).
thf(f15559,plain,
( sK383
= ( kpair @ ( kfst @ sK383 ) @ ( ksnd @ sK383 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f15517]) ).
thf(f15517,plain,
( ( $true != $true )
| ( sK383
= ( kpair @ ( kfst @ sK383 ) @ ( ksnd @ sK383 ) ) ) ),
inference(superposition,[status(thm)],[f3745,f15508]) ).
thf(f3745,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true )
| ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f2952]) ).
thf(f2952,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true )
| ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ),
inference(definition_unfolding,[status(thm)],[f1975,f2503]) ).
thf(f2503,plain,
cartprodpairsurjEq = $true,
inference(cnf_transformation,[status(thm)],[f1498]) ).
thf(f1975,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 )
| ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true )
| ( cartprodpairsurjEq != $true ) ),
inference(cnf_transformation,[status(thm)],[f1048]) ).
thf(f1048,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 )
| ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true ) )
| ( cartprodpairsurjEq != $true ) )
& ( ( cartprodpairsurjEq = $true )
| ( ( ( kpair @ ( kfst @ sK112 ) @ ( ksnd @ sK112 ) )
!= sK112 )
& ( $true
= ( in @ sK112 @ ( cartprod @ sK113 @ sK114 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113,sK114])],[f1046,f1047]) ).
thf(f1047,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
!= X3 )
& ( $true
= ( in @ X3 @ ( cartprod @ X4 @ X5 ) ) ) )
=> ( ( ( kpair @ ( kfst @ sK112 ) @ ( ksnd @ sK112 ) )
!= sK112 )
& ( $true
= ( in @ sK112 @ ( cartprod @ sK113 @ sK114 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1046,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 )
| ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true ) )
| ( cartprodpairsurjEq != $true ) )
& ( ( cartprodpairsurjEq = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
!= X3 )
& ( $true
= ( in @ X3 @ ( cartprod @ X4 @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1045]) ).
thf(f1045,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 )
| ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true ) )
| ( cartprodpairsurjEq != $true ) )
& ( ( cartprodpairsurjEq = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 )
& ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f806]) ).
thf(f806,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 )
| ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
!= $true ) )
<=> ( cartprodpairsurjEq = $true ) ),
inference(ennf_transformation,[status(thm)],[f464]) ).
thf(f464,plain,
( ( cartprodpairsurjEq = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
= $true )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ) ),
inference(fool_elimination,[status(thm)],[f463]) ).
thf(f463,plain,
( cartprodpairsurjEq
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f185]) ).
thf(f185,axiom,
( cartprodpairsurjEq
= ( ! [X10: $i,X3: $i,X4: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( ( kpair @ ( kfst @ X10 ) @ ( ksnd @ X10 ) )
= X10 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',cartprodpairsurjEq) ).
thf(f2436,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ sK381 )
!= $true )
| ( $true
!= ( in @ X4 @ sK379 ) )
| ( $true
!= ( in @ X5 @ sK380 ) )
| ( ( sK382 @ ( kpair @ X4 @ X5 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1498]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU681^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:36:42 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : SEU681^1 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.46 % Domain : Set Theory
% 0.21/0.46 % Problem : Functions - Extensionality and Beta Reduction
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English : (! A:i.! B:i.! R:i.breln A B R -> (! phi:i>o.(! x:i.in x A ->
% 0.21/0.46 % (! y:i.in y B -> in (kpair x y) R -> phi (kpair x y))) ->
% 0.21/0.46 % (! x:i.in x R -> phi x)))
% 0.21/0.46
% 0.21/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.46 % Source : [Bro08]
% 0.21/0.46 % Names : ZFC183g [Bro08]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 1.00 v6.2.0, 0.57 v6.1.0, 0.86 v5.5.0, 1.00 v3.7.0
% 0.21/0.46 % Syntax : Number of formulae : 440 ( 205 unt; 234 typ; 205 def)
% 0.21/0.46 % Number of atoms : 1089 ( 300 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 202 ( 5 avg)
% 0.21/0.46 % Number of connectives : 1991 ( 47 ~; 7 |; 36 &;1405 @)
% 0.21/0.46 % ( 14 <=>; 482 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 213 ( 2 avg)
% 0.21/0.46 % Number of types : 2 ( 0 usr)
% 0.21/0.46 % Number of type conns : 124 ( 124 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 237 ( 234 usr; 201 con; 0-4 aty)
% 0.21/0.46 % Number of variables : 651 ( 77 ^; 538 !; 36 ?; 651 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : http://mathgate.info/detsetitem.php?id=239
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(in_type,type,
% 0.21/0.46 in: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(exu_type,type,
% 0.21/0.46 exu: ( $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(exu,definition,
% 0.21/0.46 ( exu
% 0.21/0.46 = ( ^ [Xphi: $i > $o] :
% 0.21/0.46 ? [Xx: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 & ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setextAx_type,type,
% 0.21/0.46 setextAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setextAx,definition,
% 0.21/0.46 ( setextAx
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 <=> ( in @ Xx @ B ) )
% 0.21/0.46 => ( A = B ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyset_type,type,
% 0.21/0.46 emptyset: $i ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetAx_type,type,
% 0.21/0.46 emptysetAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetAx,definition,
% 0.21/0.46 ( emptysetAx
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoin_type,type,
% 0.21/0.46 setadjoin: $i > $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinAx_type,type,
% 0.21/0.46 setadjoinAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinAx,definition,
% 0.21/0.46 ( setadjoinAx
% 0.21/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.46 <=> ( ( Xy = Xx )
% 0.21/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powerset_type,type,
% 0.21/0.46 powerset: $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(powersetAx_type,type,
% 0.21/0.46 powersetAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powersetAx,definition,
% 0.21/0.46 ( powersetAx
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.46 <=> ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunion_type,type,
% 0.21/0.46 setunion: $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(setunionAx_type,type,
% 0.21/0.46 setunionAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunionAx,definition,
% 0.21/0.46 ( setunionAx
% 0.21/0.46 = ( ! [A: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.46 <=> ? [B: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(omega_type,type,
% 0.21/0.46 omega: $i ).
% 0.21/0.46
% 0.21/0.46 thf(omega0Ax_type,type,
% 0.21/0.46 omega0Ax: $o ).
% 0.21/0.46
% 0.21/0.46 thf(omega0Ax,definition,
% 0.21/0.46 ( omega0Ax
% 0.21/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(omegaSAx_type,type,
% 0.21/0.46 omegaSAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(omegaSAx,definition,
% 0.21/0.46 ( omegaSAx
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ omega )
% 0.21/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(omegaIndAx_type,type,
% 0.21/0.46 omegaIndAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(omegaIndAx,definition,
% 0.21/0.46 ( omegaIndAx
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( ( in @ emptyset @ A )
% 0.21/0.46 & ! [Xx: $i] :
% 0.21/0.46 ( ( ( in @ Xx @ omega )
% 0.21/0.46 & ( in @ Xx @ A ) )
% 0.21/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.21/0.46 => ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ omega )
% 0.21/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(replAx_type,type,
% 0.21/0.46 replAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(replAx,definition,
% 0.21/0.46 ( replAx
% 0.21/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( exu
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.21/0.46 => ? [B: $i] :
% 0.21/0.46 ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 <=> ? [Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ A )
% 0.21/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(foundationAx_type,type,
% 0.21/0.46 foundationAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(foundationAx,definition,
% 0.21/0.46 ( foundationAx
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.21/0.46 => ? [B: $i] :
% 0.21/0.46 ( ( in @ B @ A )
% 0.21/0.46 & ~ ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(wellorderingAx_type,type,
% 0.21/0.46 wellorderingAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(wellorderingAx,definition,
% 0.21/0.46 ( wellorderingAx
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ? [B: $i] :
% 0.21/0.46 ( ! [C: $i] :
% 0.21/0.46 ( ( in @ C @ B )
% 0.21/0.46 => ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ C )
% 0.21/0.46 => ( in @ Xx @ A ) ) )
% 0.21/0.46 & ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( ( in @ Xx @ A )
% 0.21/0.46 & ( in @ Xy @ A ) )
% 0.21/0.46 => ( ! [C: $i] :
% 0.21/0.46 ( ( in @ C @ B )
% 0.21/0.46 => ( ( in @ Xx @ C )
% 0.21/0.46 <=> ( in @ Xy @ C ) ) )
% 0.21/0.46 => ( Xx = Xy ) ) )
% 0.21/0.46 & ! [C: $i,D: $i] :
% 0.21/0.46 ( ( ( in @ C @ B )
% 0.21/0.46 & ( in @ D @ B ) )
% 0.21/0.46 => ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ C )
% 0.21/0.46 => ( in @ Xx @ D ) )
% 0.21/0.46 | ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ D )
% 0.21/0.46 => ( in @ Xx @ C ) ) ) )
% 0.21/0.46 & ! [C: $i] :
% 0.21/0.46 ( ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ C )
% 0.21/0.46 => ( in @ Xx @ A ) )
% 0.21/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.21/0.46 => ? [D: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ D @ B )
% 0.21/0.46 & ( in @ Xx @ C )
% 0.21/0.46 & ~ ? [Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ D )
% 0.21/0.46 & ( in @ Xy @ C ) )
% 0.21/0.46 & ! [E: $i] :
% 0.21/0.46 ( ( in @ E @ B )
% 0.21/0.46 => ( ! [Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ E )
% 0.21/0.46 => ( in @ Xy @ D ) )
% 0.21/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(descr_type,type,
% 0.21/0.46 descr: ( $i > $o ) > $i ).
% 0.21/0.46
% 0.21/0.46 thf(descrp_type,type,
% 0.21/0.46 descrp: $o ).
% 0.21/0.46
% 0.21/0.46 thf(descrp,definition,
% 0.21/0.46 ( descrp
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ( Xphi
% 0.21/0.46 @ ( descr
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstr_type,type,
% 0.21/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrI_type,type,
% 0.21/0.46 dsetconstrI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrI,definition,
% 0.21/0.46 ( dsetconstrI
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( ( Xphi @ Xx )
% 0.21/0.46 => ( in @ Xx
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrEL_type,type,
% 0.21/0.46 dsetconstrEL: $o ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrEL,definition,
% 0.21/0.46 ( dsetconstrEL
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrER_type,type,
% 0.21/0.46 dsetconstrER: $o ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrER,definition,
% 0.21/0.46 ( dsetconstrER
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuE1_type,type,
% 0.21/0.46 exuE1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuE1,definition,
% 0.21/0.46 ( exuE1
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 & ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(prop2set_type,type,
% 0.21/0.46 prop2set: $o > $i ).
% 0.21/0.46
% 0.21/0.46 thf(prop2setE_type,type,
% 0.21/0.46 prop2setE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(prop2setE,definition,
% 0.21/0.46 ( prop2setE
% 0.21/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.21/0.46 => Xphi ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetE_type,type,
% 0.21/0.46 emptysetE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetE,definition,
% 0.21/0.46 ( emptysetE
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ emptyset )
% 0.21/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetimpfalse_type,type,
% 0.21/0.46 emptysetimpfalse: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetimpfalse,definition,
% 0.21/0.46 ( emptysetimpfalse
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ emptyset )
% 0.21/0.46 => $false ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notinemptyset_type,type,
% 0.21/0.46 notinemptyset: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notinemptyset,definition,
% 0.21/0.46 ( notinemptyset
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuE3e_type,type,
% 0.21/0.46 exuE3e: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuE3e,definition,
% 0.21/0.46 ( exuE3e
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setext_type,type,
% 0.21/0.46 setext: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setext,definition,
% 0.21/0.46 ( setext
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xx @ B ) )
% 0.21/0.46 => ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( in @ Xx @ A ) )
% 0.21/0.46 => ( A = B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyI_type,type,
% 0.21/0.46 emptyI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyI,definition,
% 0.21/0.46 ( emptyI
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ~ ( in @ Xx @ A )
% 0.21/0.46 => ( A = emptyset ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(noeltsimpempty_type,type,
% 0.21/0.46 noeltsimpempty: $o ).
% 0.21/0.46
% 0.21/0.46 thf(noeltsimpempty,definition,
% 0.21/0.46 ( noeltsimpempty
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ~ ( in @ Xx @ A )
% 0.21/0.46 => ( A = emptyset ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setbeta_type,type,
% 0.21/0.46 setbeta: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setbeta,definition,
% 0.21/0.46 ( setbeta
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( ( in @ Xx
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonempty_type,type,
% 0.21/0.46 nonempty: $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonempty,definition,
% 0.21/0.46 ( nonempty
% 0.21/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyE1_type,type,
% 0.21/0.46 nonemptyE1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyE1,definition,
% 0.21/0.46 ( nonemptyE1
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( nonempty @ A )
% 0.21/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyI_type,type,
% 0.21/0.46 nonemptyI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyI,definition,
% 0.21/0.46 ( nonemptyI
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( ( Xphi @ Xx )
% 0.21/0.46 => ( nonempty
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyI1_type,type,
% 0.21/0.46 nonemptyI1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyI1,definition,
% 0.21/0.46 ( nonemptyI1
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.21/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIL_type,type,
% 0.21/0.46 setadjoinIL: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIL,definition,
% 0.21/0.46 ( setadjoinIL
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyinunitempty_type,type,
% 0.21/0.46 emptyinunitempty: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyinunitempty,definition,
% 0.21/0.46 ( emptyinunitempty
% 0.21/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIR_type,type,
% 0.21/0.46 setadjoinIR: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIR,definition,
% 0.21/0.46 ( setadjoinIR
% 0.21/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ A )
% 0.21/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinE_type,type,
% 0.21/0.46 setadjoinE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinE,definition,
% 0.21/0.46 ( setadjoinE
% 0.21/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.46 => ! [Xphi: $o] :
% 0.21/0.46 ( ( ( Xy = Xx )
% 0.21/0.46 => Xphi )
% 0.21/0.46 => ( ( ( in @ Xy @ A )
% 0.21/0.46 => Xphi )
% 0.21/0.46 => Xphi ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinOr_type,type,
% 0.21/0.46 setadjoinOr: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinOr,definition,
% 0.21/0.46 ( setadjoinOr
% 0.21/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.46 => ( ( Xy = Xx )
% 0.21/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setoftrueEq_type,type,
% 0.21/0.46 setoftrueEq: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setoftrueEq,definition,
% 0.21/0.46 ( setoftrueEq
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xx: $i] : $true )
% 0.21/0.46 = A ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powersetI_type,type,
% 0.21/0.46 powersetI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powersetI,definition,
% 0.21/0.46 ( powersetI
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( in @ Xx @ A ) )
% 0.21/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyinPowerset_type,type,
% 0.21/0.46 emptyinPowerset: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyinPowerset,definition,
% 0.21/0.46 ( emptyinPowerset
% 0.21/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyInPowerset_type,type,
% 0.21/0.46 emptyInPowerset: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyInPowerset,definition,
% 0.21/0.46 ( emptyInPowerset
% 0.21/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powersetE_type,type,
% 0.21/0.46 powersetE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powersetE,definition,
% 0.21/0.46 ( powersetE
% 0.21/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.46 => ( ( in @ Xx @ B )
% 0.21/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunionI_type,type,
% 0.21/0.46 setunionI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunionI,definition,
% 0.21/0.46 ( setunionI
% 0.21/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( ( in @ B @ A )
% 0.21/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunionE_type,type,
% 0.21/0.46 setunionE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunionE,definition,
% 0.21/0.46 ( setunionE
% 0.21/0.46 = ( ! [A: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.46 => ! [Xphi: $o] :
% 0.21/0.46 ( ! [B: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( ( in @ B @ A )
% 0.21/0.46 => Xphi ) )
% 0.21/0.46 => Xphi ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subPowSU_type,type,
% 0.21/0.46 subPowSU: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subPowSU,definition,
% 0.21/0.46 ( subPowSU
% 0.21/0.46 = ( ! [A: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuE2_type,type,
% 0.21/0.46 exuE2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuE2,definition,
% 0.21/0.46 ( exuE2
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyImpWitness_type,type,
% 0.21/0.46 nonemptyImpWitness: $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyImpWitness,definition,
% 0.21/0.46 ( nonemptyImpWitness
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( nonempty @ A )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & $true ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(uniqinunit_type,type,
% 0.21/0.46 uniqinunit: $o ).
% 0.21/0.46
% 0.21/0.46 thf(uniqinunit,definition,
% 0.21/0.46 ( uniqinunit
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notinsingleton_type,type,
% 0.21/0.46 notinsingleton: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notinsingleton,definition,
% 0.21/0.46 ( notinsingleton
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx != Xy )
% 0.21/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(eqinunit_type,type,
% 0.21/0.46 eqinunit: $o ).
% 0.21/0.46
% 0.21/0.46 thf(eqinunit,definition,
% 0.21/0.46 ( eqinunit
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(singletonsswitch_type,type,
% 0.21/0.46 singletonsswitch: $o ).
% 0.21/0.46
% 0.21/0.46 thf(singletonsswitch,definition,
% 0.21/0.46 ( singletonsswitch
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetE_type,type,
% 0.21/0.46 upairsetE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetE,definition,
% 0.21/0.46 ( upairsetE
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.21/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.21/0.46 => ( ( Xz = Xx )
% 0.21/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetIL_type,type,
% 0.21/0.46 upairsetIL: $o ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetIL,definition,
% 0.21/0.46 ( upairsetIL
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetIR_type,type,
% 0.21/0.46 upairsetIR: $o ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetIR,definition,
% 0.21/0.46 ( upairsetIR
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyE1_type,type,
% 0.21/0.46 emptyE1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyE1,definition,
% 0.21/0.46 ( emptyE1
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( Xphi @ Xx ) )
% 0.21/0.46 => ( ( ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 = emptyset )
% 0.21/0.46 => $false ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(vacuousDall_type,type,
% 0.21/0.46 vacuousDall: $o ).
% 0.21/0.46
% 0.21/0.46 thf(vacuousDall,definition,
% 0.21/0.46 ( vacuousDall
% 0.21/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ emptyset )
% 0.21/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan1_type,type,
% 0.21/0.46 quantDeMorgan1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan1,definition,
% 0.21/0.46 ( quantDeMorgan1
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ~ ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan2_type,type,
% 0.21/0.46 quantDeMorgan2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan2,definition,
% 0.21/0.46 ( quantDeMorgan2
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ~ ( Xphi @ Xx ) )
% 0.21/0.46 => ~ ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan3_type,type,
% 0.21/0.46 quantDeMorgan3: $o ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan3,definition,
% 0.21/0.46 ( quantDeMorgan3
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ~ ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( Xphi @ Xx ) )
% 0.21/0.46 => ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan4_type,type,
% 0.21/0.46 quantDeMorgan4: $o ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan4,definition,
% 0.21/0.46 ( quantDeMorgan4
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ~ ( Xphi @ Xx ) )
% 0.21/0.46 => ~ ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(prop2setI_type,type,
% 0.21/0.46 prop2setI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(prop2setI,definition,
% 0.21/0.46 ( prop2setI
% 0.21/0.46 = ( ! [Xphi: $o] :
% 0.21/0.46 ( Xphi
% 0.21/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(set2prop_type,type,
% 0.21/0.46 set2prop: $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(prop2set2propI_type,type,
% 0.21/0.46 prop2set2propI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(prop2set2propI,definition,
% 0.21/0.46 ( prop2set2propI
% 0.21/0.46 = ( ! [Xphi: $o] :
% 0.21/0.46 ( Xphi
% 0.21/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notdexE_type,type,
% 0.21/0.46 notdexE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notdexE,definition,
% 0.21/0.46 ( notdexE
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ~ ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( Xphi @ Xx ) )
% 0.21/0.46 => ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notdallE_type,type,
% 0.21/0.46 notdallE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notdallE,definition,
% 0.21/0.46 ( notdallE
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ~ ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuI1_type,type,
% 0.21/0.46 exuI1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuI1,definition,
% 0.21/0.46 ( exuI1
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 & ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) )
% 0.21/0.46 => ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuI3_type,type,
% 0.21/0.46 exuI3: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuI3,definition,
% 0.21/0.46 ( exuI3
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.21/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 => ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) )
% 0.21/0.46 => ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuI2_type,type,
% 0.21/0.46 exuI2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuI2,definition,
% 0.21/0.46 ( exuI2
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] :
% 0.21/0.46 ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 <=> ( Xy = Xx ) )
% 0.21/0.46 => ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(inCongP_type,type,
% 0.21/0.46 inCongP: $o ).
% 0.21/0.46
% 0.21/0.46 thf(inCongP,definition,
% 0.21/0.46 ( inCongP
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(in__Cong_type,type,
% 0.21/0.46 in__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(in__Cong,definition,
% 0.21/0.46 ( in__Cong
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( ( in @ Xx @ A )
% 0.21/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuE3u_type,type,
% 0.21/0.46 exuE3u: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuE3u,definition,
% 0.21/0.46 ( exuE3u
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 => ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exu__Cong_type,type,
% 0.21/0.46 exu__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exu__Cong,definition,
% 0.21/0.46 ( exu__Cong
% 0.21/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( ( Xphi @ Xx )
% 0.21/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.21/0.46 => ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 <=> ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyset__Cong_type,type,
% 0.21/0.46 emptyset__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyset__Cong,definition,
% 0.21/0.46 ( emptyset__Cong
% 0.21/0.46 = ( emptyset = emptyset ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoin__Cong_type,type,
% 0.21/0.46 setadjoin__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoin__Cong,definition,
% 0.21/0.46 ( setadjoin__Cong
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ! [Xz: $i,Xu: $i] :
% 0.21/0.46 ( ( Xz = Xu )
% 0.21/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.21/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powerset__Cong_type,type,
% 0.21/0.46 powerset__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powerset__Cong,definition,
% 0.21/0.46 ( powerset__Cong
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ( ( powerset @ A )
% 0.21/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunion__Cong_type,type,
% 0.21/0.46 setunion__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunion__Cong,definition,
% 0.21/0.46 ( setunion__Cong
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ( ( setunion @ A )
% 0.21/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(omega__Cong_type,type,
% 0.21/0.46 omega__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(omega__Cong,definition,
% 0.21/0.46 ( omega__Cong
% 0.21/0.46 = ( omega = omega ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuEu_type,type,
% 0.21/0.46 exuEu: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuEu,definition,
% 0.21/0.46 ( exuEu
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 => ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(descr__Cong_type,type,
% 0.21/0.46 descr__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(descr__Cong,definition,
% 0.21/0.46 ( descr__Cong
% 0.21/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( ( Xphi @ Xx )
% 0.21/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.21/0.46 => ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.21/0.46 => ( ( descr
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 = ( descr
% 0.21/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstr__Cong_type,type,
% 0.21/0.46 dsetconstr__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstr__Cong,definition,
% 0.21/0.46 ( dsetconstr__Cong
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ! [Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ B )
% 0.21/0.46 => ( ( Xx = Xy )
% 0.21/0.46 => ( ( Xphi @ Xx )
% 0.21/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.21/0.46 => ( ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 = ( dsetconstr @ B
% 0.21/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subset_type,type,
% 0.21/0.46 subset: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(disjoint_type,type,
% 0.21/0.46 disjoint: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(setsmeet_type,type,
% 0.21/0.46 setsmeet: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(subsetI1_type,type,
% 0.21/0.46 subsetI1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subsetI1,definition,
% 0.21/0.46 ( subsetI1
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xx @ B ) )
% 0.21/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(eqimpsubset2_type,type,
% 0.21/0.46 eqimpsubset2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(eqimpsubset2,definition,
% 0.21/0.46 ( eqimpsubset2
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(eqimpsubset1_type,type,
% 0.21/0.46 eqimpsubset1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(eqimpsubset1,definition,
% 0.21/0.46 ( eqimpsubset1
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subsetI2_type,type,
% 0.21/0.46 subsetI2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subsetI2,definition,
% 0.21/0.46 ( subsetI2
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xx @ B ) )
% 0.21/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetsubset_type,type,
% 0.21/0.46 emptysetsubset: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetsubset,definition,
% 0.21/0.46 ( emptysetsubset
% 0.21/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subsetE_type,type,
% 0.21/0.46 subsetE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subsetE,definition,
% 0.21/0.46 ( subsetE
% 0.21/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.46 ( ( subset @ A @ B )
% 0.21/0.46 => ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subsetE2_type,type,
% 0.21/0.46 subsetE2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subsetE2,definition,
% 0.21/0.46 ( subsetE2
% 0.21/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.46 ( ( subset @ A @ B )
% 0.21/0.46 => ( ~ ( in @ Xx @ B )
% 0.21/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notsubsetI_type,type,
% 0.21/0.46 notsubsetI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notsubsetI,definition,
% 0.21/0.46 ( notsubsetI
% 0.21/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( ~ ( in @ Xx @ B )
% 0.21/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notequalI1_type,type,
% 0.21/0.46 notequalI1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notequalI1,definition,
% 0.21/0.46 ( notequalI1
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ~ ( subset @ A @ B )
% 0.21/0.46 => ( A != B ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notequalI2_type,type,
% 0.21/0.46 notequalI2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notequalI2,definition,
% 0.21/0.46 ( notequalI2
% 0.21/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( ~ ( in @ Xx @ B )
% 0.21/0.46 => ( A != B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subsetRefl_type,type,
% 0.21/0.46 subsetRefl: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subsetRefl,definition,
% 0.21/0.46 ( subsetRefl
% 0.21/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subsetTrans_type,type,
% 0.21/0.46 subsetTrans: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subsetTrans,definition,
% 0.21/0.46 ( subsetTrans
% 0.21/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.21/0.46 ( ( subset @ A @ B )
% 0.21/0.46 => ( ( subset @ B @ C )
% 0.21/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinSub_type,type,
% 0.21/0.46 setadjoinSub: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinSub,definition,
% 0.21/0.46 ( setadjoinSub
% 0.21/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinSub2_type,type,
% 0.21/0.46 setadjoinSub2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinSub2,definition,
% 0.21/0.46 ( setadjoinSub2
% 0.21/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.21/0.46 ( ( subset @ A @ B )
% 0.21/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subset2powerset_type,type,
% 0.21/0.46 subset2powerset: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subset2powerset,definition,
% 0.21/0.46 ( subset2powerset
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( subset @ A @ B )
% 0.21/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setextsub_type,type,
% 0.21/0.46 setextsub: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setextsub,definition,
% 0.21/0.46 ( setextsub
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( subset @ A @ B )
% 0.21/0.46 => ( ( subset @ B @ A )
% 0.21/0.46 => ( A = B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subsetemptysetimpeq_type,type,
% 0.21/0.46 subsetemptysetimpeq: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subsetemptysetimpeq,definition,
% 0.21/0.46 ( subsetemptysetimpeq
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( subset @ A @ emptyset )
% 0.21/0.46 => ( A = emptyset ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powersetI1_type,type,
% 0.21/0.46 powersetI1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powersetI1,definition,
% 0.21/0.46 ( powersetI1
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( subset @ B @ A )
% 0.21/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(powersetE1_type,type,
% 0.21/0.47 powersetE1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(powersetE1,definition,
% 0.21/0.47 ( powersetE1
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(inPowerset_type,type,
% 0.21/0.47 inPowerset: $o ).
% 0.21/0.47
% 0.21/0.47 thf(inPowerset,definition,
% 0.21/0.47 ( inPowerset
% 0.21/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(powersetsubset_type,type,
% 0.21/0.47 powersetsubset: $o ).
% 0.21/0.47
% 0.21/0.47 thf(powersetsubset,definition,
% 0.21/0.47 ( powersetsubset
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( subset @ A @ B )
% 0.21/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sepInPowerset_type,type,
% 0.21/0.47 sepInPowerset: $o ).
% 0.21/0.47
% 0.21/0.47 thf(sepInPowerset,definition,
% 0.21/0.47 ( sepInPowerset
% 0.21/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.47 ( in
% 0.21/0.47 @ ( dsetconstr @ A
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sepSubset_type,type,
% 0.21/0.47 sepSubset: $o ).
% 0.21/0.47
% 0.21/0.47 thf(sepSubset,definition,
% 0.21/0.47 ( sepSubset
% 0.21/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.47 ( subset
% 0.21/0.47 @ ( dsetconstr @ A
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.47 @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunion_type,type,
% 0.21/0.47 binunion: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(binunionIL_type,type,
% 0.21/0.47 binunionIL: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binunionIL,definition,
% 0.21/0.47 ( binunionIL
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(upairset2IR_type,type,
% 0.21/0.47 upairset2IR: $o ).
% 0.21/0.47
% 0.21/0.47 thf(upairset2IR,definition,
% 0.21/0.47 ( upairset2IR
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunionIR_type,type,
% 0.21/0.47 binunionIR: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binunionIR,definition,
% 0.21/0.47 ( binunionIR
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ B )
% 0.21/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunionEcases_type,type,
% 0.21/0.47 binunionEcases: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binunionEcases,definition,
% 0.21/0.47 ( binunionEcases
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.21/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.21/0.47 => ( ( ( in @ Xx @ A )
% 0.21/0.47 => Xphi )
% 0.21/0.47 => ( ( ( in @ Xx @ B )
% 0.21/0.47 => Xphi )
% 0.21/0.47 => Xphi ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunionE_type,type,
% 0.21/0.47 binunionE: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binunionE,definition,
% 0.21/0.47 ( binunionE
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.21/0.47 => ( ( in @ Xx @ A )
% 0.21/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunionLsub_type,type,
% 0.21/0.47 binunionLsub: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binunionLsub,definition,
% 0.21/0.47 ( binunionLsub
% 0.21/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binunionRsub_type,type,
% 0.21/0.47 binunionRsub: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binunionRsub,definition,
% 0.21/0.47 ( binunionRsub
% 0.21/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersect_type,type,
% 0.21/0.47 binintersect: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectI_type,type,
% 0.21/0.47 binintersectI: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectI,definition,
% 0.21/0.47 ( binintersectI
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ( in @ Xx @ B )
% 0.21/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset5_type,type,
% 0.21/0.47 binintersectSubset5: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset5,definition,
% 0.21/0.47 ( binintersectSubset5
% 0.21/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.21/0.47 ( ( subset @ C @ A )
% 0.21/0.47 => ( ( subset @ C @ B )
% 0.21/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectEL_type,type,
% 0.21/0.47 binintersectEL: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectEL,definition,
% 0.21/0.47 ( binintersectEL
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.21/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectLsub_type,type,
% 0.21/0.47 binintersectLsub: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectLsub,definition,
% 0.21/0.47 ( binintersectLsub
% 0.21/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset2_type,type,
% 0.21/0.47 binintersectSubset2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset2,definition,
% 0.21/0.47 ( binintersectSubset2
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( subset @ A @ B )
% 0.21/0.47 => ( ( binintersect @ A @ B )
% 0.21/0.47 = A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset3_type,type,
% 0.21/0.47 binintersectSubset3: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset3,definition,
% 0.21/0.47 ( binintersectSubset3
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( ( binintersect @ A @ B )
% 0.21/0.47 = B )
% 0.21/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectER_type,type,
% 0.21/0.47 binintersectER: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectER,definition,
% 0.21/0.47 ( binintersectER
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.21/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(disjointsetsI1_type,type,
% 0.21/0.47 disjointsetsI1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(disjointsetsI1,definition,
% 0.21/0.47 ( disjointsetsI1
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ~ ? [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 & ( in @ Xx @ B ) )
% 0.21/0.47 => ( ( binintersect @ A @ B )
% 0.21/0.47 = emptyset ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectRsub_type,type,
% 0.21/0.47 binintersectRsub: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectRsub,definition,
% 0.21/0.47 ( binintersectRsub
% 0.21/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset4_type,type,
% 0.21/0.47 binintersectSubset4: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset4,definition,
% 0.21/0.47 ( binintersectSubset4
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( subset @ B @ A )
% 0.21/0.47 => ( ( binintersect @ A @ B )
% 0.21/0.47 = B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset1_type,type,
% 0.21/0.47 binintersectSubset1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(binintersectSubset1,definition,
% 0.21/0.47 ( binintersectSubset1
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( ( binintersect @ A @ B )
% 0.21/0.47 = A )
% 0.21/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(bs114d_type,type,
% 0.21/0.47 bs114d: $o ).
% 0.21/0.47
% 0.21/0.47 thf(bs114d,definition,
% 0.21/0.47 ( bs114d
% 0.21/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.21/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.21/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(regular_type,type,
% 0.21/0.47 regular: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminus_type,type,
% 0.21/0.47 setminus: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(setminusI_type,type,
% 0.21/0.47 setminusI: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusI,definition,
% 0.21/0.47 ( setminusI
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ~ ( in @ Xx @ B )
% 0.21/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusEL_type,type,
% 0.21/0.47 setminusEL: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusEL,definition,
% 0.21/0.47 ( setminusEL
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.21/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusER_type,type,
% 0.21/0.47 setminusER: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusER,definition,
% 0.21/0.47 ( setminusER
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.21/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusSubset2_type,type,
% 0.21/0.47 setminusSubset2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusSubset2,definition,
% 0.21/0.47 ( setminusSubset2
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( subset @ A @ B )
% 0.21/0.47 => ( ( setminus @ A @ B )
% 0.21/0.47 = emptyset ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusERneg_type,type,
% 0.21/0.47 setminusERneg: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusERneg,definition,
% 0.21/0.47 ( setminusERneg
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.21/0.47 => ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusELneg_type,type,
% 0.21/0.47 setminusELneg: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusELneg,definition,
% 0.21/0.47 ( setminusELneg
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.21/0.47 => ( ~ ( in @ Xx @ B )
% 0.21/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusILneg_type,type,
% 0.21/0.47 setminusILneg: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusILneg,definition,
% 0.21/0.47 ( setminusILneg
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ~ ( in @ Xx @ A )
% 0.21/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusIRneg_type,type,
% 0.21/0.47 setminusIRneg: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusIRneg,definition,
% 0.21/0.47 ( setminusIRneg
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ B )
% 0.21/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusLsub_type,type,
% 0.21/0.47 setminusLsub: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusLsub,definition,
% 0.21/0.47 ( setminusLsub
% 0.21/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setminusSubset1_type,type,
% 0.21/0.47 setminusSubset1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setminusSubset1,definition,
% 0.21/0.47 ( setminusSubset1
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( ( setminus @ A @ B )
% 0.21/0.47 = emptyset )
% 0.21/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(symdiff_type,type,
% 0.21/0.47 symdiff: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffE_type,type,
% 0.21/0.47 symdiffE: $o ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffE,definition,
% 0.21/0.47 ( symdiffE
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.21/0.47 => ! [Xphi: $o] :
% 0.21/0.47 ( ( ( in @ Xx @ A )
% 0.21/0.47 => ( ~ ( in @ Xx @ B )
% 0.21/0.47 => Xphi ) )
% 0.21/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.21/0.47 => ( ( in @ Xx @ B )
% 0.21/0.47 => Xphi ) )
% 0.21/0.47 => Xphi ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffI1_type,type,
% 0.21/0.47 symdiffI1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffI1,definition,
% 0.21/0.47 ( symdiffI1
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ~ ( in @ Xx @ B )
% 0.21/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffI2_type,type,
% 0.21/0.47 symdiffI2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffI2,definition,
% 0.21/0.47 ( symdiffI2
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ~ ( in @ Xx @ A )
% 0.21/0.47 => ( ( in @ Xx @ B )
% 0.21/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffIneg1_type,type,
% 0.21/0.47 symdiffIneg1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffIneg1,definition,
% 0.21/0.47 ( symdiffIneg1
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ( in @ Xx @ B )
% 0.21/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffIneg2_type,type,
% 0.21/0.47 symdiffIneg2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(symdiffIneg2,definition,
% 0.21/0.47 ( symdiffIneg2
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ~ ( in @ Xx @ A )
% 0.21/0.47 => ( ~ ( in @ Xx @ B )
% 0.21/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(iskpair_type,type,
% 0.21/0.47 iskpair: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(secondinupair_type,type,
% 0.21/0.47 secondinupair: $o ).
% 0.21/0.47
% 0.21/0.47 thf(secondinupair,definition,
% 0.21/0.47 ( secondinupair
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairIL_type,type,
% 0.21/0.47 setukpairIL: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairIL,definition,
% 0.21/0.47 ( setukpairIL
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairIR_type,type,
% 0.21/0.47 setukpairIR: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairIR,definition,
% 0.21/0.47 ( setukpairIR
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(kpairiskpair_type,type,
% 0.21/0.47 kpairiskpair: $o ).
% 0.21/0.47
% 0.21/0.47 thf(kpairiskpair,definition,
% 0.21/0.47 ( kpairiskpair
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(kpair_type,type,
% 0.21/0.47 kpair: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(kpairp_type,type,
% 0.21/0.47 kpairp: $o ).
% 0.21/0.47
% 0.21/0.47 thf(kpairp,definition,
% 0.21/0.47 ( kpairp
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprod_type,type,
% 0.21/0.47 cartprod: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(singletonsubset_type,type,
% 0.21/0.47 singletonsubset: $o ).
% 0.21/0.47
% 0.21/0.47 thf(singletonsubset,definition,
% 0.21/0.47 ( singletonsubset
% 0.21/0.47 = ( ! [A: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(singletoninpowerset_type,type,
% 0.21/0.47 singletoninpowerset: $o ).
% 0.21/0.47
% 0.21/0.47 thf(singletoninpowerset,definition,
% 0.21/0.47 ( singletoninpowerset
% 0.21/0.47 = ( ! [A: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(singletoninpowunion_type,type,
% 0.21/0.47 singletoninpowunion: $o ).
% 0.21/0.47
% 0.21/0.47 thf(singletoninpowunion,definition,
% 0.21/0.47 ( singletoninpowunion
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(upairset2E_type,type,
% 0.21/0.47 upairset2E: $o ).
% 0.21/0.47
% 0.21/0.47 thf(upairset2E,definition,
% 0.21/0.47 ( upairset2E
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.21/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.21/0.47 => ( ( Xz = Xx )
% 0.21/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(upairsubunion_type,type,
% 0.21/0.47 upairsubunion: $o ).
% 0.21/0.47
% 0.21/0.47 thf(upairsubunion,definition,
% 0.21/0.47 ( upairsubunion
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(upairinpowunion_type,type,
% 0.21/0.47 upairinpowunion: $o ).
% 0.21/0.47
% 0.21/0.47 thf(upairinpowunion,definition,
% 0.21/0.47 ( upairinpowunion
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ubforcartprodlem1_type,type,
% 0.21/0.47 ubforcartprodlem1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ubforcartprodlem1,definition,
% 0.21/0.47 ( ubforcartprodlem1
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ubforcartprodlem2_type,type,
% 0.21/0.47 ubforcartprodlem2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ubforcartprodlem2,definition,
% 0.21/0.47 ( ubforcartprodlem2
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ubforcartprodlem3_type,type,
% 0.21/0.47 ubforcartprodlem3: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ubforcartprodlem3,definition,
% 0.21/0.47 ( ubforcartprodlem3
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodpairin_type,type,
% 0.21/0.47 cartprodpairin: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodpairin,definition,
% 0.21/0.47 ( cartprodpairin
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodmempair1_type,type,
% 0.21/0.47 cartprodmempair1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodmempair1,definition,
% 0.21/0.47 ( cartprodmempair1
% 0.21/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.21/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.21/0.47 => ? [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 & ? [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 & ( Xu
% 0.21/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodmempair_type,type,
% 0.21/0.47 cartprodmempair: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodmempair,definition,
% 0.21/0.47 ( cartprodmempair
% 0.21/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.21/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.21/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setunionE2_type,type,
% 0.21/0.47 setunionE2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setunionE2,definition,
% 0.21/0.47 ( setunionE2
% 0.21/0.47 = ( ! [A: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.47 => ? [X: $i] :
% 0.21/0.47 ( ( in @ X @ A )
% 0.21/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setunionsingleton1_type,type,
% 0.21/0.47 setunionsingleton1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setunionsingleton1,definition,
% 0.21/0.47 ( setunionsingleton1
% 0.21/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setunionsingleton2_type,type,
% 0.21/0.47 setunionsingleton2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setunionsingleton2,definition,
% 0.21/0.47 ( setunionsingleton2
% 0.21/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setunionsingleton_type,type,
% 0.21/0.47 setunionsingleton: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setunionsingleton,definition,
% 0.21/0.47 ( setunionsingleton
% 0.21/0.47 = ( ! [Xx: $i] :
% 0.21/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.21/0.47 = Xx ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(singleton_type,type,
% 0.21/0.47 singleton: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(singleton,definition,
% 0.21/0.47 ( singleton
% 0.21/0.47 = ( ^ [A: $i] :
% 0.21/0.47 ? [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 & ( A
% 0.21/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(singletonprop_type,type,
% 0.21/0.47 singletonprop: $o ).
% 0.21/0.47
% 0.21/0.47 thf(singletonprop,definition,
% 0.21/0.47 ( singletonprop
% 0.21/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ A )
% 0.21/0.47 => ( ( Xphi @ Xx )
% 0.21/0.47 => ( ( Xphi @ Xy )
% 0.21/0.47 => ( Xx = Xy ) ) ) ) )
% 0.21/0.47 => ( ? [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 & ( Xphi @ Xx ) )
% 0.21/0.47 => ( singleton
% 0.21/0.47 @ ( dsetconstr @ A
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ex1_type,type,
% 0.21/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(ex1,definition,
% 0.21/0.47 ( ex1
% 0.21/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.21/0.47 ( singleton
% 0.21/0.47 @ ( dsetconstr @ A
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ex1E1_type,type,
% 0.21/0.47 ex1E1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ex1E1,definition,
% 0.21/0.47 ( ex1E1
% 0.21/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.47 ( ( ex1 @ A
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.47 => ? [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ex1I_type,type,
% 0.21/0.47 ex1I: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ex1I,definition,
% 0.21/0.47 ( ex1I
% 0.21/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ( Xphi @ Xx )
% 0.21/0.47 => ( ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ A )
% 0.21/0.47 => ( ( Xphi @ Xy )
% 0.21/0.47 => ( Xy = Xx ) ) )
% 0.21/0.47 => ( ex1 @ A
% 0.21/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ex1I2_type,type,
% 0.21/0.47 ex1I2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ex1I2,definition,
% 0.21/0.47 ( ex1I2
% 0.21/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ A )
% 0.21/0.47 => ( ( Xphi @ Xx )
% 0.21/0.47 => ( ( Xphi @ Xy )
% 0.21/0.47 => ( Xx = Xy ) ) ) ) )
% 0.21/0.47 => ( ? [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 & ( Xphi @ Xx ) )
% 0.21/0.47 => ( ex1 @ A
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(singletonsuniq_type,type,
% 0.21/0.47 singletonsuniq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(singletonsuniq,definition,
% 0.21/0.47 ( singletonsuniq
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.21/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(atmost1p_type,type,
% 0.21/0.47 atmost1p: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(atleast2p_type,type,
% 0.21/0.47 atleast2p: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(atmost2p_type,type,
% 0.21/0.47 atmost2p: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(upairsetp_type,type,
% 0.21/0.47 upairsetp: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjL1_type,type,
% 0.21/0.47 setukpairinjL1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjL1,definition,
% 0.21/0.47 ( setukpairinjL1
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.21/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.21/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(kfstsingleton_type,type,
% 0.21/0.47 kfstsingleton: $o ).
% 0.21/0.47
% 0.21/0.47 thf(kfstsingleton,definition,
% 0.21/0.47 ( kfstsingleton
% 0.21/0.47 = ( ! [Xu: $i] :
% 0.21/0.47 ( ( iskpair @ Xu )
% 0.21/0.47 => ( singleton
% 0.21/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.21/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(theprop_type,type,
% 0.21/0.47 theprop: $o ).
% 0.21/0.47
% 0.21/0.47 thf(theprop,definition,
% 0.21/0.47 ( theprop
% 0.21/0.47 = ( ! [X: $i] :
% 0.21/0.47 ( ( singleton @ X )
% 0.21/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(kfst_type,type,
% 0.21/0.47 kfst: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(kfstpairEq_type,type,
% 0.21/0.47 kfstpairEq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(kfstpairEq,definition,
% 0.21/0.47 ( kfstpairEq
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.21/0.47 = Xx ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodfstin_type,type,
% 0.21/0.47 cartprodfstin: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodfstin,definition,
% 0.21/0.47 ( cartprodfstin
% 0.21/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.21/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.21/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjL2_type,type,
% 0.21/0.47 setukpairinjL2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjL2,definition,
% 0.21/0.47 ( setukpairinjL2
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.21/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.21/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.21/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjL_type,type,
% 0.21/0.47 setukpairinjL: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjL,definition,
% 0.21/0.47 ( setukpairinjL
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.21/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.21/0.47 = ( kpair @ Xz @ Xu ) )
% 0.21/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR11_type,type,
% 0.21/0.47 setukpairinjR11: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR11,definition,
% 0.21/0.47 ( setukpairinjR11
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( Xx = Xy )
% 0.21/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR12_type,type,
% 0.21/0.47 setukpairinjR12: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR12,definition,
% 0.21/0.47 ( setukpairinjR12
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( Xx = Xy )
% 0.21/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.21/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR1_type,type,
% 0.21/0.47 setukpairinjR1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR1,definition,
% 0.21/0.47 ( setukpairinjR1
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.21/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.21/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.21/0.47 => ( ( Xz = Xu )
% 0.21/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(upairequniteq_type,type,
% 0.21/0.47 upairequniteq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(upairequniteq,definition,
% 0.21/0.47 ( upairequniteq
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.21/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.21/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR2_type,type,
% 0.21/0.47 setukpairinjR2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR2,definition,
% 0.21/0.47 ( setukpairinjR2
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.21/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.21/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.21/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR_type,type,
% 0.21/0.47 setukpairinjR: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setukpairinjR,definition,
% 0.21/0.47 ( setukpairinjR
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.21/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.21/0.47 = ( kpair @ Xz @ Xu ) )
% 0.21/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ksndsingleton_type,type,
% 0.21/0.47 ksndsingleton: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ksndsingleton,definition,
% 0.21/0.47 ( ksndsingleton
% 0.21/0.47 = ( ! [Xu: $i] :
% 0.21/0.47 ( ( iskpair @ Xu )
% 0.21/0.47 => ( singleton
% 0.21/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.21/0.47 @ ^ [Xx: $i] :
% 0.21/0.47 ( Xu
% 0.21/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ksnd_type,type,
% 0.21/0.47 ksnd: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(ksndpairEq_type,type,
% 0.21/0.47 ksndpairEq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ksndpairEq,definition,
% 0.21/0.47 ( ksndpairEq
% 0.21/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.21/0.47 = Xy ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(kpairsurjEq_type,type,
% 0.21/0.47 kpairsurjEq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(kpairsurjEq,definition,
% 0.21/0.47 ( kpairsurjEq
% 0.21/0.47 = ( ! [Xu: $i] :
% 0.21/0.47 ( ( iskpair @ Xu )
% 0.21/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.21/0.47 = Xu ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodsndin_type,type,
% 0.21/0.47 cartprodsndin: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodsndin,definition,
% 0.21/0.47 ( cartprodsndin
% 0.21/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.21/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.21/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodpairmemEL_type,type,
% 0.21/0.47 cartprodpairmemEL: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodpairmemEL,definition,
% 0.21/0.47 ( cartprodpairmemEL
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.21/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodpairmemER_type,type,
% 0.21/0.47 cartprodpairmemER: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodpairmemER,definition,
% 0.21/0.47 ( cartprodpairmemER
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.21/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodmempaircEq_type,type,
% 0.21/0.47 cartprodmempaircEq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodmempaircEq,definition,
% 0.21/0.47 ( cartprodmempaircEq
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( ( kpair @ Xx @ Xy )
% 0.21/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodfstpairEq_type,type,
% 0.21/0.47 cartprodfstpairEq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodfstpairEq,definition,
% 0.21/0.47 ( cartprodfstpairEq
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.21/0.47 = Xx ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodsndpairEq_type,type,
% 0.21/0.47 cartprodsndpairEq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodsndpairEq,definition,
% 0.21/0.47 ( cartprodsndpairEq
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.21/0.47 = Xy ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodpairsurjEq_type,type,
% 0.21/0.47 cartprodpairsurjEq: $o ).
% 0.21/0.47
% 0.21/0.47 thf(cartprodpairsurjEq,definition,
% 0.21/0.47 ( cartprodpairsurjEq
% 0.21/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.21/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.21/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.21/0.47 = Xu ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(breln_type,type,
% 0.21/0.47 breln: $i > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(breln,definition,
% 0.21/0.47 ( breln
% 0.21/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstr_type,type,
% 0.21/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrI_type,type,
% 0.21/0.47 dpsetconstrI: $o ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrI,definition,
% 0.21/0.47 ( dpsetconstrI
% 0.21/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.21/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.21/0.47 @ ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrSub_type,type,
% 0.21/0.47 dpsetconstrSub: $o ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrSub,definition,
% 0.21/0.47 ( dpsetconstrSub
% 0.21/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.21/0.47 ( subset
% 0.21/0.47 @ ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.21/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setOfPairsIsBReln_type,type,
% 0.21/0.47 setOfPairsIsBReln: $o ).
% 0.21/0.47
% 0.21/0.47 thf(setOfPairsIsBReln,definition,
% 0.21/0.47 ( setOfPairsIsBReln
% 0.21/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.21/0.47 ( breln @ A @ B
% 0.21/0.47 @ ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrERa_type,type,
% 0.21/0.47 dpsetconstrERa: $o ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrERa,definition,
% 0.21/0.47 ( dpsetconstrERa
% 0.21/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.21/0.47 @ ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.21/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrEL1_type,type,
% 0.21/0.47 dpsetconstrEL1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrEL1,definition,
% 0.21/0.47 ( dpsetconstrEL1
% 0.21/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.21/0.47 @ ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.21/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrEL2_type,type,
% 0.21/0.47 dpsetconstrEL2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrEL2,definition,
% 0.21/0.47 ( dpsetconstrEL2
% 0.21/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.21/0.47 @ ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.21/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrER_type,type,
% 0.21/0.47 dpsetconstrER: $o ).
% 0.21/0.47
% 0.21/0.47 thf(dpsetconstrER,definition,
% 0.21/0.47 ( dpsetconstrER
% 0.21/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.21/0.47 @ ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.21/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(func_type,type,
% 0.21/0.47 func: $i > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(func,definition,
% 0.21/0.47 ( func
% 0.21/0.47 = ( ^ [A: $i,B: $i,R: $i] :
% 0.21/0.47 ( ( breln @ A @ B @ R )
% 0.21/0.47 & ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ex1 @ B
% 0.21/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(funcSet_type,type,
% 0.21/0.47 funcSet: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(funcImageSingleton_type,type,
% 0.21/0.47 funcImageSingleton: $o ).
% 0.21/0.47
% 0.21/0.47 thf(funcImageSingleton,definition,
% 0.21/0.47 ( funcImageSingleton
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.21/0.47 ( ( func @ A @ B @ Xf )
% 0.21/0.47 => ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( singleton
% 0.21/0.47 @ ( dsetconstr @ B
% 0.21/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(apProp_type,type,
% 0.21/0.47 apProp: $o ).
% 0.21/0.47
% 0.21/0.47 thf(apProp,definition,
% 0.21/0.47 ( apProp
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.21/0.47 ( ( func @ A @ B @ Xf )
% 0.21/0.47 => ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in
% 0.21/0.47 @ ( setunion
% 0.21/0.47 @ ( dsetconstr @ B
% 0.21/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.21/0.47 @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ap_type,type,
% 0.21/0.47 ap: $i > $i > $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(ap,definition,
% 0.21/0.47 ( ap
% 0.21/0.47 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 0.21/0.47 ( setunion
% 0.21/0.47 @ ( dsetconstr @ B
% 0.21/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(app_type,type,
% 0.21/0.47 app: $o ).
% 0.21/0.47
% 0.21/0.47 thf(app,definition,
% 0.21/0.47 ( app
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.21/0.47 ( ( func @ A @ B @ Xf )
% 0.21/0.47 => ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(infuncsetfunc_type,type,
% 0.21/0.47 infuncsetfunc: $o ).
% 0.21/0.47
% 0.21/0.47 thf(infuncsetfunc,definition,
% 0.21/0.47 ( infuncsetfunc
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.21/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.21/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ap2p_type,type,
% 0.21/0.47 ap2p: $o ).
% 0.21/0.47
% 0.21/0.47 thf(ap2p,definition,
% 0.21/0.47 ( ap2p
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.21/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.21/0.47 => ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(funcinfuncset_type,type,
% 0.21/0.47 funcinfuncset: $o ).
% 0.21/0.47
% 0.21/0.47 thf(funcinfuncset,definition,
% 0.21/0.47 ( funcinfuncset
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.21/0.47 ( ( func @ A @ B @ Xf )
% 0.21/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(lamProp_type,type,
% 0.21/0.47 lamProp: $o ).
% 0.21/0.47
% 0.21/0.47 thf(lamProp,definition,
% 0.21/0.47 ( lamProp
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.21/0.47 => ( func @ A @ B
% 0.21/0.47 @ ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( Xf @ Xx )
% 0.21/0.47 = Xy ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(lam_type,type,
% 0.21/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(lam,definition,
% 0.21/0.47 ( lam
% 0.21/0.47 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.21/0.47 ( dpsetconstr @ A @ B
% 0.21/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( Xf @ Xx )
% 0.21/0.47 = Xy ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(lamp_type,type,
% 0.21/0.47 lamp: $o ).
% 0.21/0.47
% 0.21/0.47 thf(lamp,definition,
% 0.21/0.47 ( lamp
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.21/0.47 => ( func @ A @ B
% 0.21/0.47 @ ( lam @ A @ B
% 0.21/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(lam2p_type,type,
% 0.21/0.47 lam2p: $o ).
% 0.21/0.47
% 0.21/0.47 thf(lam2p,definition,
% 0.21/0.47 ( lam2p
% 0.21/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.21/0.47 => ( in
% 0.21/0.47 @ ( lam @ A @ B
% 0.21/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.21/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(brelnall1,conjecture,
% 0.21/0.47 ( setextAx
% 0.21/0.47 => ( emptysetAx
% 0.21/0.47 => ( setadjoinAx
% 0.21/0.47 => ( powersetAx
% 0.21/0.47 => ( setunionAx
% 0.21/0.47 => ( omega0Ax
% 0.21/0.47 => ( omegaSAx
% 0.21/0.47 => ( omegaIndAx
% 0.21/0.47 => ( replAx
% 0.21/0.47 => ( foundationAx
% 0.21/0.47 => ( wellorderingAx
% 0.21/0.47 => ( descrp
% 0.21/0.47 => ( dsetconstrI
% 0.21/0.47 => ( dsetconstrEL
% 0.21/0.47 => ( dsetconstrER
% 0.21/0.47 => ( exuE1
% 0.21/0.47 => ( prop2setE
% 0.21/0.47 => ( emptysetE
% 0.21/0.47 => ( emptysetimpfalse
% 0.21/0.47 => ( notinemptyset
% 0.21/0.47 => ( exuE3e
% 0.21/0.47 => ( setext
% 0.21/0.47 => ( emptyI
% 0.21/0.47 => ( noeltsimpempty
% 0.21/0.47 => ( setbeta
% 0.21/0.47 => ( nonemptyE1
% 0.21/0.47 => ( nonemptyI
% 0.21/0.47 => ( nonemptyI1
% 0.21/0.47 => ( setadjoinIL
% 0.21/0.47 => ( emptyinunitempty
% 0.21/0.47 => ( setadjoinIR
% 0.21/0.47 => ( setadjoinE
% 0.21/0.47 => ( setadjoinOr
% 0.21/0.47 => ( setoftrueEq
% 0.21/0.47 => ( powersetI
% 0.21/0.47 => ( emptyinPowerset
% 0.21/0.47 => ( emptyInPowerset
% 0.21/0.47 => ( powersetE
% 0.21/0.47 => ( setunionI
% 0.21/0.47 => ( setunionE
% 0.21/0.47 => ( subPowSU
% 0.21/0.47 => ( exuE2
% 0.21/0.47 => ( nonemptyImpWitness
% 0.21/0.47 => ( uniqinunit
% 0.21/0.47 => ( notinsingleton
% 0.21/0.47 => ( eqinunit
% 0.21/0.47 => ( singletonsswitch
% 0.21/0.47 => ( upairsetE
% 0.21/0.47 => ( upairsetIL
% 0.21/0.47 => ( upairsetIR
% 0.21/0.47 => ( emptyE1
% 0.21/0.47 => ( vacuousDall
% 0.21/0.47 => ( quantDeMorgan1
% 0.21/0.47 => ( quantDeMorgan2
% 0.21/0.47 => ( quantDeMorgan3
% 0.21/0.47 => ( quantDeMorgan4
% 0.21/0.47 => ( prop2setI
% 0.21/0.47 => ( prop2set2propI
% 0.21/0.47 => ( notdexE
% 0.21/0.47 => ( notdallE
% 0.21/0.47 => ( exuI1
% 0.21/0.47 => ( exuI3
% 0.21/0.47 => ( exuI2
% 0.21/0.47 => ( inCongP
% 0.21/0.47 => ( in__Cong
% 0.21/0.47 => ( exuE3u
% 0.21/0.47 => ( exu__Cong
% 0.21/0.47 => ( emptyset__Cong
% 0.21/0.47 => ( setadjoin__Cong
% 0.21/0.47 => ( powerset__Cong
% 0.21/0.47 => ( setunion__Cong
% 0.21/0.47 => ( omega__Cong
% 0.21/0.47 => ( exuEu
% 0.21/0.47 => ( descr__Cong
% 0.21/0.47 => ( dsetconstr__Cong
% 0.21/0.47 => ( subsetI1
% 0.21/0.47 => ( eqimpsubset2
% 0.21/0.47 => ( eqimpsubset1
% 0.21/0.47 => ( subsetI2
% 0.21/0.47 => ( emptysetsubset
% 0.21/0.47 => ( subsetE
% 0.21/0.47 => ( subsetE2
% 0.21/0.47 => ( notsubsetI
% 0.21/0.47 => ( notequalI1
% 0.21/0.47 => ( notequalI2
% 0.21/0.47 => ( subsetRefl
% 0.21/0.47 => ( subsetTrans
% 0.21/0.47 => ( setadjoinSub
% 0.21/0.47 => ( setadjoinSub2
% 0.21/0.47 => ( subset2powerset
% 0.21/0.47 => ( setextsub
% 0.21/0.47 => ( subsetemptysetimpeq
% 0.21/0.47 => ( powersetI1
% 0.21/0.47 => ( powersetE1
% 0.21/0.47 => ( inPowerset
% 0.21/0.47 => ( powersetsubset
% 0.21/0.47 => ( sepInPowerset
% 0.21/0.47 => ( sepSubset
% 0.21/0.47 => ( binunionIL
% 0.21/0.47 => ( upairset2IR
% 0.21/0.47 => ( binunionIR
% 0.21/0.47 => ( binunionEcases
% 0.21/0.47 => ( binunionE
% 0.21/0.47 => ( binunionLsub
% 0.21/0.47 => ( binunionRsub
% 0.21/0.47 => ( binintersectI
% 0.21/0.47 => ( binintersectSubset5
% 0.21/0.47 => ( binintersectEL
% 0.21/0.47 => ( binintersectLsub
% 0.21/0.47 => ( binintersectSubset2
% 0.21/0.47 => ( binintersectSubset3
% 0.21/0.47 => ( binintersectER
% 0.21/0.47 => ( disjointsetsI1
% 0.21/0.47 => ( binintersectRsub
% 0.21/0.47 => ( binintersectSubset4
% 0.21/0.47 => ( binintersectSubset1
% 0.21/0.47 => ( bs114d
% 0.21/0.47 => ( setminusI
% 0.21/0.47 => ( setminusEL
% 0.21/0.47 => ( setminusER
% 0.21/0.47 => ( setminusSubset2
% 0.21/0.47 => ( setminusERneg
% 0.21/0.47 => ( setminusELneg
% 0.21/0.47 => ( setminusILneg
% 0.21/0.47 => ( setminusIRneg
% 0.21/0.47 => ( setminusLsub
% 0.21/0.47 => ( setminusSubset1
% 0.21/0.47 => ( symdiffE
% 0.21/0.47 => ( symdiffI1
% 0.21/0.47 => ( symdiffI2
% 0.21/0.47 => ( symdiffIneg1
% 0.21/0.47 => ( symdiffIneg2
% 0.21/0.47 => ( secondinupair
% 0.21/0.47 => ( setukpairIL
% 0.21/0.47 => ( setukpairIR
% 0.21/0.47 => ( kpairiskpair
% 0.21/0.47 => ( kpairp
% 0.21/0.47 => ( singletonsubset
% 0.21/0.47 => ( singletoninpowerset
% 0.21/0.47 => ( singletoninpowunion
% 0.21/0.47 => ( upairset2E
% 0.21/0.47 => ( upairsubunion
% 0.21/0.47 => ( upairinpowunion
% 0.21/0.47 => ( ubforcartprodlem1
% 0.21/0.47 => ( ubforcartprodlem2
% 0.21/0.47 => ( ubforcartprodlem3
% 0.21/0.47 => ( cartprodpairin
% 0.21/0.47 => ( cartprodmempair1
% 0.21/0.47 => ( cartprodmempair
% 0.21/0.47 => ( setunionE2
% 0.21/0.47 => ( setunionsingleton1
% 0.21/0.47 => ( setunionsingleton2
% 0.21/0.47 => ( setunionsingleton
% 0.21/0.47 => ( singletonprop
% 0.21/0.47 => ( ex1E1
% 0.21/0.47 => ( ex1I
% 0.21/0.47 => ( ex1I2
% 0.21/0.47 => ( singletonsuniq
% 0.21/0.47 => ( setukpairinjL1
% 0.21/0.47 => ( kfstsingleton
% 0.21/0.47 => ( theprop
% 0.21/0.47 => ( kfstpairEq
% 0.21/0.47 => ( cartprodfstin
% 0.21/0.47 => ( setukpairinjL2
% 0.21/0.47 => ( setukpairinjL
% 0.21/0.47 => ( setukpairinjR11
% 0.21/0.47 => ( setukpairinjR12
% 0.21/0.47 => ( setukpairinjR1
% 0.21/0.47 => ( upairequniteq
% 0.21/0.47 => ( setukpairinjR2
% 0.21/0.47 => ( setukpairinjR
% 0.21/0.47 => ( ksndsingleton
% 0.21/0.47 => ( ksndpairEq
% 0.21/0.47 => ( kpairsurjEq
% 0.21/0.47 => ( cartprodsndin
% 0.21/0.47 => ( cartprodpairmemEL
% 0.21/0.47 => ( cartprodpairmemER
% 0.21/0.47 => ( cartprodmempaircEq
% 0.21/0.47 => ( cartprodfstpairEq
% 0.21/0.47 => ( cartprodsndpairEq
% 0.21/0.47 => ( cartprodpairsurjEq
% 0.21/0.47 => ( dpsetconstrI
% 0.21/0.47 => ( dpsetconstrSub
% 0.21/0.47 => ( setOfPairsIsBReln
% 0.21/0.47 => ( dpsetconstrERa
% 0.21/0.47 => ( dpsetconstrEL1
% 0.21/0.47 => ( dpsetconstrEL2
% 0.21/0.47 => ( dpsetconstrER
% 0.21/0.47 => ( funcImageSingleton
% 0.21/0.47 => ( apProp
% 0.21/0.47 => ( app
% 0.21/0.47 => ( infuncsetfunc
% 0.21/0.47 => ( ap2p
% 0.21/0.47 => ( funcinfuncset
% 0.21/0.47 => ( lamProp
% 0.21/0.47 => ( lamp
% 0.21/0.47 => ( lam2p
% 0.21/0.47 => ! [A: $i,B: $i,R: $i] :
% 0.21/0.47 ( ( breln @ A @ B @ R )
% 0.21/0.47 => ! [Xphi: $i > $o] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.21/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.21/0.47 => ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ R )
% 0.21/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 2.47/1.50 ---- Embedded in THF ---
% 2.76/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.76/1.50 %%% Generated on Tue Feb 24 12:36:43 EST 2026
% 2.76/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 2.76/1.50 %%% Logic specification used:
% 2.76/1.50 %%% thf(spec, logic, $$dhol).
% 2.76/1.50
% 2.76/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2DTF26535.p
% See solution above
% 2.76/1.50 ------------------------
% 2.76/1.53 ---- Cleaned THF ---
% 2.76/1.53 thf(in_type,type,
% 2.76/1.53 in: $i > $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(exu_type,type,
% 2.76/1.53 exu: ( $i > $o ) > $o ).
% 2.76/1.53
% 2.76/1.53 thf(exu,definition,
% 2.76/1.53 ( exu
% 2.76/1.53 = ( ^ [Xphi: $i > $o] :
% 2.76/1.53 ? [Xx: $i] :
% 2.76/1.53 ( ( Xphi @ Xx )
% 2.76/1.53 & ! [Xy: $i] :
% 2.76/1.53 ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xx = Xy ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setextAx_type,type,
% 2.76/1.53 setextAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setextAx,definition,
% 2.76/1.53 ( setextAx
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 <=> ( in @ Xx @ B ) )
% 2.76/1.53 => ( A = B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptyset_type,type,
% 2.76/1.53 emptyset: $i ).
% 2.76/1.53
% 2.76/1.53 thf(emptysetAx_type,type,
% 2.76/1.53 emptysetAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptysetAx,definition,
% 2.76/1.53 ( emptysetAx
% 2.76/1.53 = ( ! [Xx: $i] :
% 2.76/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoin_type,type,
% 2.76/1.53 setadjoin: $i > $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinAx_type,type,
% 2.76/1.53 setadjoinAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinAx,definition,
% 2.76/1.53 ( setadjoinAx
% 2.76/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.76/1.53 <=> ( ( Xy = Xx )
% 2.76/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(powerset_type,type,
% 2.76/1.53 powerset: $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(powersetAx_type,type,
% 2.76/1.53 powersetAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(powersetAx,definition,
% 2.76/1.53 ( powersetAx
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.76/1.53 <=> ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setunion_type,type,
% 2.76/1.53 setunion: $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(setunionAx_type,type,
% 2.76/1.53 setunionAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setunionAx,definition,
% 2.76/1.53 ( setunionAx
% 2.76/1.53 = ( ! [A: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.76/1.53 <=> ? [B: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 & ( in @ B @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(omega_type,type,
% 2.76/1.53 omega: $i ).
% 2.76/1.53
% 2.76/1.53 thf(omega0Ax_type,type,
% 2.76/1.53 omega0Ax: $o ).
% 2.76/1.53
% 2.76/1.53 thf(omega0Ax,definition,
% 2.76/1.53 ( omega0Ax
% 2.76/1.53 = ( in @ emptyset @ omega ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(omegaSAx_type,type,
% 2.76/1.53 omegaSAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(omegaSAx,definition,
% 2.76/1.53 ( omegaSAx
% 2.76/1.53 = ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ omega )
% 2.76/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(omegaIndAx_type,type,
% 2.76/1.53 omegaIndAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(omegaIndAx,definition,
% 2.76/1.53 ( omegaIndAx
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ( ( in @ emptyset @ A )
% 2.76/1.53 & ! [Xx: $i] :
% 2.76/1.53 ( ( ( in @ Xx @ omega )
% 2.76/1.53 & ( in @ Xx @ A ) )
% 2.76/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.76/1.53 => ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ omega )
% 2.76/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(replAx_type,type,
% 2.76/1.53 replAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(replAx,definition,
% 2.76/1.53 ( replAx
% 2.76/1.53 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( exu
% 2.76/1.53 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.76/1.53 => ? [B: $i] :
% 2.76/1.53 ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 <=> ? [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ A )
% 2.76/1.53 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(foundationAx_type,type,
% 2.76/1.53 foundationAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(foundationAx,definition,
% 2.76/1.53 ( foundationAx
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.76/1.53 => ? [B: $i] :
% 2.76/1.53 ( ( in @ B @ A )
% 2.76/1.53 & ~ ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(wellorderingAx_type,type,
% 2.76/1.53 wellorderingAx: $o ).
% 2.76/1.53
% 2.76/1.53 thf(wellorderingAx,definition,
% 2.76/1.53 ( wellorderingAx
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ? [B: $i] :
% 2.76/1.53 ( ! [C: $i] :
% 2.76/1.53 ( ( in @ C @ B )
% 2.76/1.53 => ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ C )
% 2.76/1.53 => ( in @ Xx @ A ) ) )
% 2.76/1.53 & ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( ( in @ Xx @ A )
% 2.76/1.53 & ( in @ Xy @ A ) )
% 2.76/1.53 => ( ! [C: $i] :
% 2.76/1.53 ( ( in @ C @ B )
% 2.76/1.53 => ( ( in @ Xx @ C )
% 2.76/1.53 <=> ( in @ Xy @ C ) ) )
% 2.76/1.53 => ( Xx = Xy ) ) )
% 2.76/1.53 & ! [C: $i,D: $i] :
% 2.76/1.53 ( ( ( in @ C @ B )
% 2.76/1.53 & ( in @ D @ B ) )
% 2.76/1.53 => ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ C )
% 2.76/1.53 => ( in @ Xx @ D ) )
% 2.76/1.53 | ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ D )
% 2.76/1.53 => ( in @ Xx @ C ) ) ) )
% 2.76/1.53 & ! [C: $i] :
% 2.76/1.53 ( ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ C )
% 2.76/1.53 => ( in @ Xx @ A ) )
% 2.76/1.53 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.76/1.53 => ? [D: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ D @ B )
% 2.76/1.53 & ( in @ Xx @ C )
% 2.76/1.53 & ~ ? [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ D )
% 2.76/1.53 & ( in @ Xy @ C ) )
% 2.76/1.53 & ! [E: $i] :
% 2.76/1.53 ( ( in @ E @ B )
% 2.76/1.53 => ( ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ E )
% 2.76/1.53 => ( in @ Xy @ D ) )
% 2.76/1.53 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(descr_type,type,
% 2.76/1.53 descr: ( $i > $o ) > $i ).
% 2.76/1.53
% 2.76/1.53 thf(descrp_type,type,
% 2.76/1.53 descrp: $o ).
% 2.76/1.53
% 2.76/1.53 thf(descrp,definition,
% 2.76/1.53 ( descrp
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 => ( Xphi
% 2.76/1.53 @ ( descr
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstr_type,type,
% 2.76/1.53 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstrI_type,type,
% 2.76/1.53 dsetconstrI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstrI,definition,
% 2.76/1.53 ( dsetconstrI
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ( Xphi @ Xx )
% 2.76/1.53 => ( in @ Xx
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstrEL_type,type,
% 2.76/1.53 dsetconstrEL: $o ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstrEL,definition,
% 2.76/1.53 ( dsetconstrEL
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.76/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstrER_type,type,
% 2.76/1.53 dsetconstrER: $o ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstrER,definition,
% 2.76/1.53 ( dsetconstrER
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.76/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exuE1_type,type,
% 2.76/1.53 exuE1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exuE1,definition,
% 2.76/1.53 ( exuE1
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 => ? [Xx: $i] :
% 2.76/1.53 ( ( Xphi @ Xx )
% 2.76/1.53 & ! [Xy: $i] :
% 2.76/1.53 ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(prop2set_type,type,
% 2.76/1.53 prop2set: $o > $i ).
% 2.76/1.53
% 2.76/1.53 thf(prop2setE_type,type,
% 2.76/1.53 prop2setE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(prop2setE,definition,
% 2.76/1.53 ( prop2setE
% 2.76/1.53 = ( ! [Xphi: $o,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.76/1.53 => Xphi ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptysetE_type,type,
% 2.76/1.53 emptysetE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptysetE,definition,
% 2.76/1.53 ( emptysetE
% 2.76/1.53 = ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ emptyset )
% 2.76/1.53 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptysetimpfalse_type,type,
% 2.76/1.53 emptysetimpfalse: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptysetimpfalse,definition,
% 2.76/1.53 ( emptysetimpfalse
% 2.76/1.53 = ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ emptyset )
% 2.76/1.53 => $false ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(notinemptyset_type,type,
% 2.76/1.53 notinemptyset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(notinemptyset,definition,
% 2.76/1.53 ( notinemptyset
% 2.76/1.53 = ( ! [Xx: $i] :
% 2.76/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exuE3e_type,type,
% 2.76/1.53 exuE3e: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exuE3e,definition,
% 2.76/1.53 ( exuE3e
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setext_type,type,
% 2.76/1.53 setext: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setext,definition,
% 2.76/1.53 ( setext
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ Xx @ B ) )
% 2.76/1.53 => ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ A ) )
% 2.76/1.53 => ( A = B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptyI_type,type,
% 2.76/1.53 emptyI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptyI,definition,
% 2.76/1.53 ( emptyI
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ~ ( in @ Xx @ A )
% 2.76/1.53 => ( A = emptyset ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(noeltsimpempty_type,type,
% 2.76/1.53 noeltsimpempty: $o ).
% 2.76/1.53
% 2.76/1.53 thf(noeltsimpempty,definition,
% 2.76/1.53 ( noeltsimpempty
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ~ ( in @ Xx @ A )
% 2.76/1.53 => ( A = emptyset ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setbeta_type,type,
% 2.76/1.53 setbeta: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setbeta,definition,
% 2.76/1.53 ( setbeta
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ( in @ Xx
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.76/1.53 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(nonempty_type,type,
% 2.76/1.53 nonempty: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(nonempty,definition,
% 2.76/1.53 ( nonempty
% 2.76/1.53 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(nonemptyE1_type,type,
% 2.76/1.53 nonemptyE1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(nonemptyE1,definition,
% 2.76/1.53 ( nonemptyE1
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ( nonempty @ A )
% 2.76/1.53 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(nonemptyI_type,type,
% 2.76/1.53 nonemptyI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(nonemptyI,definition,
% 2.76/1.53 ( nonemptyI
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ( Xphi @ Xx )
% 2.76/1.53 => ( nonempty
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(nonemptyI1_type,type,
% 2.76/1.53 nonemptyI1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(nonemptyI1,definition,
% 2.76/1.53 ( nonemptyI1
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.76/1.53 => ( nonempty @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinIL_type,type,
% 2.76/1.53 setadjoinIL: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinIL,definition,
% 2.76/1.53 ( setadjoinIL
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptyinunitempty_type,type,
% 2.76/1.53 emptyinunitempty: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptyinunitempty,definition,
% 2.76/1.53 ( emptyinunitempty
% 2.76/1.53 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinIR_type,type,
% 2.76/1.53 setadjoinIR: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinIR,definition,
% 2.76/1.53 ( setadjoinIR
% 2.76/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ A )
% 2.76/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinE_type,type,
% 2.76/1.53 setadjoinE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinE,definition,
% 2.76/1.53 ( setadjoinE
% 2.76/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.76/1.53 => ! [Xphi: $o] :
% 2.76/1.53 ( ( ( Xy = Xx )
% 2.76/1.53 => Xphi )
% 2.76/1.53 => ( ( ( in @ Xy @ A )
% 2.76/1.53 => Xphi )
% 2.76/1.53 => Xphi ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinOr_type,type,
% 2.76/1.53 setadjoinOr: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinOr,definition,
% 2.76/1.53 ( setadjoinOr
% 2.76/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.76/1.53 => ( ( Xy = Xx )
% 2.76/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setoftrueEq_type,type,
% 2.76/1.53 setoftrueEq: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setoftrueEq,definition,
% 2.76/1.53 ( setoftrueEq
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xx: $i] : $true )
% 2.76/1.53 = A ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(powersetI_type,type,
% 2.76/1.53 powersetI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(powersetI,definition,
% 2.76/1.53 ( powersetI
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ A ) )
% 2.76/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptyinPowerset_type,type,
% 2.76/1.53 emptyinPowerset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptyinPowerset,definition,
% 2.76/1.53 ( emptyinPowerset
% 2.76/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptyInPowerset_type,type,
% 2.76/1.53 emptyInPowerset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptyInPowerset,definition,
% 2.76/1.53 ( emptyInPowerset
% 2.76/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(powersetE_type,type,
% 2.76/1.53 powersetE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(powersetE,definition,
% 2.76/1.53 ( powersetE
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.76/1.53 => ( ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setunionI_type,type,
% 2.76/1.53 setunionI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setunionI,definition,
% 2.76/1.53 ( setunionI
% 2.76/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 => ( ( in @ B @ A )
% 2.76/1.53 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setunionE_type,type,
% 2.76/1.53 setunionE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setunionE,definition,
% 2.76/1.53 ( setunionE
% 2.76/1.53 = ( ! [A: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.76/1.53 => ! [Xphi: $o] :
% 2.76/1.53 ( ! [B: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 => ( ( in @ B @ A )
% 2.76/1.53 => Xphi ) )
% 2.76/1.53 => Xphi ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subPowSU_type,type,
% 2.76/1.53 subPowSU: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subPowSU,definition,
% 2.76/1.53 ( subPowSU
% 2.76/1.53 = ( ! [A: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exuE2_type,type,
% 2.76/1.53 exuE2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exuE2,definition,
% 2.76/1.53 ( exuE2
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 => ? [Xx: $i] :
% 2.76/1.53 ! [Xy: $i] :
% 2.76/1.53 ( ( Xphi @ Xy )
% 2.76/1.53 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(nonemptyImpWitness_type,type,
% 2.76/1.53 nonemptyImpWitness: $o ).
% 2.76/1.53
% 2.76/1.53 thf(nonemptyImpWitness,definition,
% 2.76/1.53 ( nonemptyImpWitness
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ( nonempty @ A )
% 2.76/1.53 => ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & $true ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(uniqinunit_type,type,
% 2.76/1.53 uniqinunit: $o ).
% 2.76/1.53
% 2.76/1.53 thf(uniqinunit,definition,
% 2.76/1.53 ( uniqinunit
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.76/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(notinsingleton_type,type,
% 2.76/1.53 notinsingleton: $o ).
% 2.76/1.53
% 2.76/1.53 thf(notinsingleton,definition,
% 2.76/1.53 ( notinsingleton
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xx != Xy )
% 2.76/1.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(eqinunit_type,type,
% 2.76/1.53 eqinunit: $o ).
% 2.76/1.53
% 2.76/1.53 thf(eqinunit,definition,
% 2.76/1.53 ( eqinunit
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xx = Xy )
% 2.76/1.53 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(singletonsswitch_type,type,
% 2.76/1.53 singletonsswitch: $o ).
% 2.76/1.53
% 2.76/1.53 thf(singletonsswitch,definition,
% 2.76/1.53 ( singletonsswitch
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.76/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(upairsetE_type,type,
% 2.76/1.53 upairsetE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(upairsetE,definition,
% 2.76/1.53 ( upairsetE
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.76/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.76/1.53 => ( ( Xz = Xx )
% 2.76/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(upairsetIL_type,type,
% 2.76/1.53 upairsetIL: $o ).
% 2.76/1.53
% 2.76/1.53 thf(upairsetIL,definition,
% 2.76/1.53 ( upairsetIL
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(upairsetIR_type,type,
% 2.76/1.53 upairsetIR: $o ).
% 2.76/1.53
% 2.76/1.53 thf(upairsetIR,definition,
% 2.76/1.53 ( upairsetIR
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptyE1_type,type,
% 2.76/1.53 emptyE1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptyE1,definition,
% 2.76/1.53 ( emptyE1
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( Xphi @ Xx ) )
% 2.76/1.53 => ( ( ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 = emptyset )
% 2.76/1.53 => $false ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(vacuousDall_type,type,
% 2.76/1.53 vacuousDall: $o ).
% 2.76/1.53
% 2.76/1.53 thf(vacuousDall,definition,
% 2.76/1.53 ( vacuousDall
% 2.76/1.53 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ emptyset )
% 2.76/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(quantDeMorgan1_type,type,
% 2.76/1.53 quantDeMorgan1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(quantDeMorgan1,definition,
% 2.76/1.53 ( quantDeMorgan1
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ~ ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( Xphi @ Xx ) )
% 2.76/1.53 => ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(quantDeMorgan2_type,type,
% 2.76/1.53 quantDeMorgan2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(quantDeMorgan2,definition,
% 2.76/1.53 ( quantDeMorgan2
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ~ ( Xphi @ Xx ) )
% 2.76/1.53 => ~ ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(quantDeMorgan3_type,type,
% 2.76/1.53 quantDeMorgan3: $o ).
% 2.76/1.53
% 2.76/1.53 thf(quantDeMorgan3,definition,
% 2.76/1.53 ( quantDeMorgan3
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ~ ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( Xphi @ Xx ) )
% 2.76/1.53 => ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(quantDeMorgan4_type,type,
% 2.76/1.53 quantDeMorgan4: $o ).
% 2.76/1.53
% 2.76/1.53 thf(quantDeMorgan4,definition,
% 2.76/1.53 ( quantDeMorgan4
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ~ ( Xphi @ Xx ) )
% 2.76/1.53 => ~ ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(prop2setI_type,type,
% 2.76/1.53 prop2setI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(prop2setI,definition,
% 2.76/1.53 ( prop2setI
% 2.76/1.53 = ( ! [Xphi: $o] :
% 2.76/1.53 ( Xphi
% 2.76/1.53 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(set2prop_type,type,
% 2.76/1.53 set2prop: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(prop2set2propI_type,type,
% 2.76/1.53 prop2set2propI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(prop2set2propI,definition,
% 2.76/1.53 ( prop2set2propI
% 2.76/1.53 = ( ! [Xphi: $o] :
% 2.76/1.53 ( Xphi
% 2.76/1.53 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(notdexE_type,type,
% 2.76/1.53 notdexE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(notdexE,definition,
% 2.76/1.53 ( notdexE
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ~ ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( Xphi @ Xx ) )
% 2.76/1.53 => ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(notdallE_type,type,
% 2.76/1.53 notdallE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(notdallE,definition,
% 2.76/1.53 ( notdallE
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ~ ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( Xphi @ Xx ) )
% 2.76/1.53 => ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exuI1_type,type,
% 2.76/1.53 exuI1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exuI1,definition,
% 2.76/1.53 ( exuI1
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ? [Xx: $i] :
% 2.76/1.53 ( ( Xphi @ Xx )
% 2.76/1.53 & ! [Xy: $i] :
% 2.76/1.53 ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xx = Xy ) ) )
% 2.76/1.53 => ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exuI3_type,type,
% 2.76/1.53 exuI3: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exuI3,definition,
% 2.76/1.53 ( exuI3
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.76/1.53 => ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xphi @ Xx )
% 2.76/1.53 => ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xx = Xy ) ) )
% 2.76/1.53 => ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exuI2_type,type,
% 2.76/1.53 exuI2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exuI2,definition,
% 2.76/1.53 ( exuI2
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ? [Xx: $i] :
% 2.76/1.53 ! [Xy: $i] :
% 2.76/1.53 ( ( Xphi @ Xy )
% 2.76/1.53 <=> ( Xy = Xx ) )
% 2.76/1.53 => ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(inCongP_type,type,
% 2.76/1.53 inCongP: $o ).
% 2.76/1.53
% 2.76/1.53 thf(inCongP,definition,
% 2.76/1.53 ( inCongP
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( A = B )
% 2.76/1.53 => ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xx = Xy )
% 2.76/1.53 => ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(in__Cong_type,type,
% 2.76/1.53 in__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(in__Cong,definition,
% 2.76/1.53 ( in__Cong
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( A = B )
% 2.76/1.53 => ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xx = Xy )
% 2.76/1.53 => ( ( in @ Xx @ A )
% 2.76/1.53 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exuE3u_type,type,
% 2.76/1.53 exuE3u: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exuE3u,definition,
% 2.76/1.53 ( exuE3u
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 => ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xphi @ Xx )
% 2.76/1.53 => ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exu__Cong_type,type,
% 2.76/1.53 exu__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exu__Cong,definition,
% 2.76/1.53 ( exu__Cong
% 2.76/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.76/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xx = Xy )
% 2.76/1.53 => ( ( Xphi @ Xx )
% 2.76/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.76/1.53 => ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 <=> ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptyset__Cong_type,type,
% 2.76/1.53 emptyset__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptyset__Cong,definition,
% 2.76/1.53 ( emptyset__Cong
% 2.76/1.53 = ( emptyset = emptyset ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoin__Cong_type,type,
% 2.76/1.53 setadjoin__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoin__Cong,definition,
% 2.76/1.53 ( setadjoin__Cong
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xx = Xy )
% 2.76/1.53 => ! [Xz: $i,Xu: $i] :
% 2.76/1.53 ( ( Xz = Xu )
% 2.76/1.53 => ( ( setadjoin @ Xx @ Xz )
% 2.76/1.53 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(powerset__Cong_type,type,
% 2.76/1.53 powerset__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(powerset__Cong,definition,
% 2.76/1.53 ( powerset__Cong
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( A = B )
% 2.76/1.53 => ( ( powerset @ A )
% 2.76/1.53 = ( powerset @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setunion__Cong_type,type,
% 2.76/1.53 setunion__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setunion__Cong,definition,
% 2.76/1.53 ( setunion__Cong
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( A = B )
% 2.76/1.53 => ( ( setunion @ A )
% 2.76/1.53 = ( setunion @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(omega__Cong_type,type,
% 2.76/1.53 omega__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(omega__Cong,definition,
% 2.76/1.53 ( omega__Cong
% 2.76/1.53 = ( omega = omega ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(exuEu_type,type,
% 2.76/1.53 exuEu: $o ).
% 2.76/1.53
% 2.76/1.53 thf(exuEu,definition,
% 2.76/1.53 ( exuEu
% 2.76/1.53 = ( ! [Xphi: $i > $o] :
% 2.76/1.53 ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 => ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xphi @ Xx )
% 2.76/1.53 => ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(descr__Cong_type,type,
% 2.76/1.53 descr__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(descr__Cong,definition,
% 2.76/1.53 ( descr__Cong
% 2.76/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.76/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xx = Xy )
% 2.76/1.53 => ( ( Xphi @ Xx )
% 2.76/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.76/1.53 => ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 => ( ( exu
% 2.76/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.76/1.53 => ( ( descr
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 = ( descr
% 2.76/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstr__Cong_type,type,
% 2.76/1.53 dsetconstr__Cong: $o ).
% 2.76/1.53
% 2.76/1.53 thf(dsetconstr__Cong,definition,
% 2.76/1.53 ( dsetconstr__Cong
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( A = B )
% 2.76/1.53 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ B )
% 2.76/1.53 => ( ( Xx = Xy )
% 2.76/1.53 => ( ( Xphi @ Xx )
% 2.76/1.53 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.76/1.53 => ( ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 = ( dsetconstr @ B
% 2.76/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subset_type,type,
% 2.76/1.53 subset: $i > $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(disjoint_type,type,
% 2.76/1.53 disjoint: $i > $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(setsmeet_type,type,
% 2.76/1.53 setsmeet: $i > $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(subsetI1_type,type,
% 2.76/1.53 subsetI1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subsetI1,definition,
% 2.76/1.53 ( subsetI1
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ Xx @ B ) )
% 2.76/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(eqimpsubset2_type,type,
% 2.76/1.53 eqimpsubset2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(eqimpsubset2,definition,
% 2.76/1.53 ( eqimpsubset2
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( A = B )
% 2.76/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(eqimpsubset1_type,type,
% 2.76/1.53 eqimpsubset1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(eqimpsubset1,definition,
% 2.76/1.53 ( eqimpsubset1
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( A = B )
% 2.76/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subsetI2_type,type,
% 2.76/1.53 subsetI2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subsetI2,definition,
% 2.76/1.53 ( subsetI2
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ Xx @ B ) )
% 2.76/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(emptysetsubset_type,type,
% 2.76/1.53 emptysetsubset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(emptysetsubset,definition,
% 2.76/1.53 ( emptysetsubset
% 2.76/1.53 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subsetE_type,type,
% 2.76/1.53 subsetE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subsetE,definition,
% 2.76/1.53 ( subsetE
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subsetE2_type,type,
% 2.76/1.53 subsetE2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subsetE2,definition,
% 2.76/1.53 ( subsetE2
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( ~ ( in @ Xx @ B )
% 2.76/1.53 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(notsubsetI_type,type,
% 2.76/1.53 notsubsetI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(notsubsetI,definition,
% 2.76/1.53 ( notsubsetI
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ~ ( in @ Xx @ B )
% 2.76/1.53 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(notequalI1_type,type,
% 2.76/1.53 notequalI1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(notequalI1,definition,
% 2.76/1.53 ( notequalI1
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ~ ( subset @ A @ B )
% 2.76/1.53 => ( A != B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(notequalI2_type,type,
% 2.76/1.53 notequalI2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(notequalI2,definition,
% 2.76/1.53 ( notequalI2
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ~ ( in @ Xx @ B )
% 2.76/1.53 => ( A != B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subsetRefl_type,type,
% 2.76/1.53 subsetRefl: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subsetRefl,definition,
% 2.76/1.53 ( subsetRefl
% 2.76/1.53 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subsetTrans_type,type,
% 2.76/1.53 subsetTrans: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subsetTrans,definition,
% 2.76/1.53 ( subsetTrans
% 2.76/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( ( subset @ B @ C )
% 2.76/1.53 => ( subset @ A @ C ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinSub_type,type,
% 2.76/1.53 setadjoinSub: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinSub,definition,
% 2.76/1.53 ( setadjoinSub
% 2.76/1.53 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinSub2_type,type,
% 2.76/1.53 setadjoinSub2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setadjoinSub2,definition,
% 2.76/1.53 ( setadjoinSub2
% 2.76/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subset2powerset_type,type,
% 2.76/1.53 subset2powerset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subset2powerset,definition,
% 2.76/1.53 ( subset2powerset
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setextsub_type,type,
% 2.76/1.53 setextsub: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setextsub,definition,
% 2.76/1.53 ( setextsub
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( ( subset @ B @ A )
% 2.76/1.53 => ( A = B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(subsetemptysetimpeq_type,type,
% 2.76/1.53 subsetemptysetimpeq: $o ).
% 2.76/1.53
% 2.76/1.53 thf(subsetemptysetimpeq,definition,
% 2.76/1.53 ( subsetemptysetimpeq
% 2.76/1.53 = ( ! [A: $i] :
% 2.76/1.53 ( ( subset @ A @ emptyset )
% 2.76/1.53 => ( A = emptyset ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(powersetI1_type,type,
% 2.76/1.53 powersetI1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(powersetI1,definition,
% 2.76/1.53 ( powersetI1
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( subset @ B @ A )
% 2.76/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(powersetE1_type,type,
% 2.76/1.53 powersetE1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(powersetE1,definition,
% 2.76/1.53 ( powersetE1
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.76/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(inPowerset_type,type,
% 2.76/1.53 inPowerset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(inPowerset,definition,
% 2.76/1.53 ( inPowerset
% 2.76/1.53 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(powersetsubset_type,type,
% 2.76/1.53 powersetsubset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(powersetsubset,definition,
% 2.76/1.53 ( powersetsubset
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(sepInPowerset_type,type,
% 2.76/1.53 sepInPowerset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(sepInPowerset,definition,
% 2.76/1.53 ( sepInPowerset
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( in
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 @ ( powerset @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(sepSubset_type,type,
% 2.76/1.53 sepSubset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(sepSubset,definition,
% 2.76/1.53 ( sepSubset
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( subset
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 @ A ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binunion_type,type,
% 2.76/1.53 binunion: $i > $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(binunionIL_type,type,
% 2.76/1.53 binunionIL: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binunionIL,definition,
% 2.76/1.53 ( binunionIL
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(upairset2IR_type,type,
% 2.76/1.53 upairset2IR: $o ).
% 2.76/1.53
% 2.76/1.53 thf(upairset2IR,definition,
% 2.76/1.53 ( upairset2IR
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binunionIR_type,type,
% 2.76/1.53 binunionIR: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binunionIR,definition,
% 2.76/1.53 ( binunionIR
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binunionEcases_type,type,
% 2.76/1.53 binunionEcases: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binunionEcases,definition,
% 2.76/1.53 ( binunionEcases
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.76/1.53 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.76/1.53 => ( ( ( in @ Xx @ A )
% 2.76/1.53 => Xphi )
% 2.76/1.53 => ( ( ( in @ Xx @ B )
% 2.76/1.53 => Xphi )
% 2.76/1.53 => Xphi ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binunionE_type,type,
% 2.76/1.53 binunionE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binunionE,definition,
% 2.76/1.53 ( binunionE
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.76/1.53 => ( ( in @ Xx @ A )
% 2.76/1.53 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binunionLsub_type,type,
% 2.76/1.53 binunionLsub: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binunionLsub,definition,
% 2.76/1.53 ( binunionLsub
% 2.76/1.53 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binunionRsub_type,type,
% 2.76/1.53 binunionRsub: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binunionRsub,definition,
% 2.76/1.53 ( binunionRsub
% 2.76/1.53 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersect_type,type,
% 2.76/1.53 binintersect: $i > $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectI_type,type,
% 2.76/1.53 binintersectI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectI,definition,
% 2.76/1.53 ( binintersectI
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset5_type,type,
% 2.76/1.53 binintersectSubset5: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset5,definition,
% 2.76/1.53 ( binintersectSubset5
% 2.76/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.76/1.53 ( ( subset @ C @ A )
% 2.76/1.53 => ( ( subset @ C @ B )
% 2.76/1.53 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectEL_type,type,
% 2.76/1.53 binintersectEL: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectEL,definition,
% 2.76/1.53 ( binintersectEL
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.76/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectLsub_type,type,
% 2.76/1.53 binintersectLsub: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectLsub,definition,
% 2.76/1.53 ( binintersectLsub
% 2.76/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset2_type,type,
% 2.76/1.53 binintersectSubset2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset2,definition,
% 2.76/1.53 ( binintersectSubset2
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( ( binintersect @ A @ B )
% 2.76/1.53 = A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset3_type,type,
% 2.76/1.53 binintersectSubset3: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset3,definition,
% 2.76/1.53 ( binintersectSubset3
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( ( binintersect @ A @ B )
% 2.76/1.53 = B )
% 2.76/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectER_type,type,
% 2.76/1.53 binintersectER: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectER,definition,
% 2.76/1.53 ( binintersectER
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.76/1.53 => ( in @ Xx @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(disjointsetsI1_type,type,
% 2.76/1.53 disjointsetsI1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(disjointsetsI1,definition,
% 2.76/1.53 ( disjointsetsI1
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ~ ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( in @ Xx @ B ) )
% 2.76/1.53 => ( ( binintersect @ A @ B )
% 2.76/1.53 = emptyset ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectRsub_type,type,
% 2.76/1.53 binintersectRsub: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectRsub,definition,
% 2.76/1.53 ( binintersectRsub
% 2.76/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset4_type,type,
% 2.76/1.53 binintersectSubset4: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset4,definition,
% 2.76/1.53 ( binintersectSubset4
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( subset @ B @ A )
% 2.76/1.53 => ( ( binintersect @ A @ B )
% 2.76/1.53 = B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset1_type,type,
% 2.76/1.53 binintersectSubset1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(binintersectSubset1,definition,
% 2.76/1.53 ( binintersectSubset1
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( ( binintersect @ A @ B )
% 2.76/1.53 = A )
% 2.76/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(bs114d_type,type,
% 2.76/1.53 bs114d: $o ).
% 2.76/1.53
% 2.76/1.53 thf(bs114d,definition,
% 2.76/1.53 ( bs114d
% 2.76/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.76/1.53 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.76/1.53 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(regular_type,type,
% 2.76/1.53 regular: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminus_type,type,
% 2.76/1.53 setminus: $i > $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(setminusI_type,type,
% 2.76/1.53 setminusI: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusI,definition,
% 2.76/1.53 ( setminusI
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ~ ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusEL_type,type,
% 2.76/1.53 setminusEL: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusEL,definition,
% 2.76/1.53 ( setminusEL
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.76/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusER_type,type,
% 2.76/1.53 setminusER: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusER,definition,
% 2.76/1.53 ( setminusER
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.76/1.53 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusSubset2_type,type,
% 2.76/1.53 setminusSubset2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusSubset2,definition,
% 2.76/1.53 ( setminusSubset2
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( subset @ A @ B )
% 2.76/1.53 => ( ( setminus @ A @ B )
% 2.76/1.53 = emptyset ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusERneg_type,type,
% 2.76/1.53 setminusERneg: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusERneg,definition,
% 2.76/1.53 ( setminusERneg
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.76/1.53 => ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusELneg_type,type,
% 2.76/1.53 setminusELneg: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusELneg,definition,
% 2.76/1.53 ( setminusELneg
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.76/1.53 => ( ~ ( in @ Xx @ B )
% 2.76/1.53 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusILneg_type,type,
% 2.76/1.53 setminusILneg: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusILneg,definition,
% 2.76/1.53 ( setminusILneg
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ~ ( in @ Xx @ A )
% 2.76/1.53 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusIRneg_type,type,
% 2.76/1.53 setminusIRneg: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusIRneg,definition,
% 2.76/1.53 ( setminusIRneg
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ B )
% 2.76/1.53 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusLsub_type,type,
% 2.76/1.53 setminusLsub: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusLsub,definition,
% 2.76/1.53 ( setminusLsub
% 2.76/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setminusSubset1_type,type,
% 2.76/1.53 setminusSubset1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setminusSubset1,definition,
% 2.76/1.53 ( setminusSubset1
% 2.76/1.53 = ( ! [A: $i,B: $i] :
% 2.76/1.53 ( ( ( setminus @ A @ B )
% 2.76/1.53 = emptyset )
% 2.76/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(symdiff_type,type,
% 2.76/1.53 symdiff: $i > $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffE_type,type,
% 2.76/1.53 symdiffE: $o ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffE,definition,
% 2.76/1.53 ( symdiffE
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.76/1.53 => ! [Xphi: $o] :
% 2.76/1.53 ( ( ( in @ Xx @ A )
% 2.76/1.53 => ( ~ ( in @ Xx @ B )
% 2.76/1.53 => Xphi ) )
% 2.76/1.53 => ( ( ~ ( in @ Xx @ A )
% 2.76/1.53 => ( ( in @ Xx @ B )
% 2.76/1.53 => Xphi ) )
% 2.76/1.53 => Xphi ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffI1_type,type,
% 2.76/1.53 symdiffI1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffI1,definition,
% 2.76/1.53 ( symdiffI1
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ~ ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffI2_type,type,
% 2.76/1.53 symdiffI2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffI2,definition,
% 2.76/1.53 ( symdiffI2
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ~ ( in @ Xx @ A )
% 2.76/1.53 => ( ( in @ Xx @ B )
% 2.76/1.53 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffIneg1_type,type,
% 2.76/1.53 symdiffIneg1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffIneg1,definition,
% 2.76/1.53 ( symdiffIneg1
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ( in @ Xx @ B )
% 2.76/1.53 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffIneg2_type,type,
% 2.76/1.53 symdiffIneg2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(symdiffIneg2,definition,
% 2.76/1.53 ( symdiffIneg2
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ~ ( in @ Xx @ A )
% 2.76/1.53 => ( ~ ( in @ Xx @ B )
% 2.76/1.53 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(iskpair_type,type,
% 2.76/1.53 iskpair: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(secondinupair_type,type,
% 2.76/1.53 secondinupair: $o ).
% 2.76/1.53
% 2.76/1.53 thf(secondinupair,definition,
% 2.76/1.53 ( secondinupair
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairIL_type,type,
% 2.76/1.53 setukpairIL: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairIL,definition,
% 2.76/1.53 ( setukpairIL
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairIR_type,type,
% 2.76/1.53 setukpairIR: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairIR,definition,
% 2.76/1.53 ( setukpairIR
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(kpairiskpair_type,type,
% 2.76/1.53 kpairiskpair: $o ).
% 2.76/1.53
% 2.76/1.53 thf(kpairiskpair,definition,
% 2.76/1.53 ( kpairiskpair
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(kpair_type,type,
% 2.76/1.53 kpair: $i > $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(kpairp_type,type,
% 2.76/1.53 kpairp: $o ).
% 2.76/1.53
% 2.76/1.53 thf(kpairp,definition,
% 2.76/1.53 ( kpairp
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(cartprod_type,type,
% 2.76/1.53 cartprod: $i > $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(singletonsubset_type,type,
% 2.76/1.53 singletonsubset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(singletonsubset,definition,
% 2.76/1.53 ( singletonsubset
% 2.76/1.53 = ( ! [A: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(singletoninpowerset_type,type,
% 2.76/1.53 singletoninpowerset: $o ).
% 2.76/1.53
% 2.76/1.53 thf(singletoninpowerset,definition,
% 2.76/1.53 ( singletoninpowerset
% 2.76/1.53 = ( ! [A: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(singletoninpowunion_type,type,
% 2.76/1.53 singletoninpowunion: $o ).
% 2.76/1.53
% 2.76/1.53 thf(singletoninpowunion,definition,
% 2.76/1.53 ( singletoninpowunion
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(upairset2E_type,type,
% 2.76/1.53 upairset2E: $o ).
% 2.76/1.53
% 2.76/1.53 thf(upairset2E,definition,
% 2.76/1.53 ( upairset2E
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.76/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.76/1.53 => ( ( Xz = Xx )
% 2.76/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(upairsubunion_type,type,
% 2.76/1.53 upairsubunion: $o ).
% 2.76/1.53
% 2.76/1.53 thf(upairsubunion,definition,
% 2.76/1.53 ( upairsubunion
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ B )
% 2.76/1.53 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(upairinpowunion_type,type,
% 2.76/1.53 upairinpowunion: $o ).
% 2.76/1.53
% 2.76/1.53 thf(upairinpowunion,definition,
% 2.76/1.53 ( upairinpowunion
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ B )
% 2.76/1.53 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(ubforcartprodlem1_type,type,
% 2.76/1.53 ubforcartprodlem1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(ubforcartprodlem1,definition,
% 2.76/1.53 ( ubforcartprodlem1
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ B )
% 2.76/1.53 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(ubforcartprodlem2_type,type,
% 2.76/1.53 ubforcartprodlem2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(ubforcartprodlem2,definition,
% 2.76/1.53 ( ubforcartprodlem2
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ B )
% 2.76/1.53 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(ubforcartprodlem3_type,type,
% 2.76/1.53 ubforcartprodlem3: $o ).
% 2.76/1.53
% 2.76/1.53 thf(ubforcartprodlem3,definition,
% 2.76/1.53 ( ubforcartprodlem3
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ B )
% 2.76/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(cartprodpairin_type,type,
% 2.76/1.53 cartprodpairin: $o ).
% 2.76/1.53
% 2.76/1.53 thf(cartprodpairin,definition,
% 2.76/1.53 ( cartprodpairin
% 2.76/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ B )
% 2.76/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(cartprodmempair1_type,type,
% 2.76/1.53 cartprodmempair1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(cartprodmempair1,definition,
% 2.76/1.53 ( cartprodmempair1
% 2.76/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.76/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.76/1.53 => ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ? [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ B )
% 2.76/1.53 & ( Xu
% 2.76/1.53 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(cartprodmempair_type,type,
% 2.76/1.53 cartprodmempair: $o ).
% 2.76/1.53
% 2.76/1.53 thf(cartprodmempair,definition,
% 2.76/1.53 ( cartprodmempair
% 2.76/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.76/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.76/1.53 => ( iskpair @ Xu ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setunionE2_type,type,
% 2.76/1.53 setunionE2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setunionE2,definition,
% 2.76/1.53 ( setunionE2
% 2.76/1.53 = ( ! [A: $i,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.76/1.53 => ? [X: $i] :
% 2.76/1.53 ( ( in @ X @ A )
% 2.76/1.53 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setunionsingleton1_type,type,
% 2.76/1.53 setunionsingleton1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setunionsingleton1,definition,
% 2.76/1.53 ( setunionsingleton1
% 2.76/1.53 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setunionsingleton2_type,type,
% 2.76/1.53 setunionsingleton2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setunionsingleton2,definition,
% 2.76/1.53 ( setunionsingleton2
% 2.76/1.53 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setunionsingleton_type,type,
% 2.76/1.53 setunionsingleton: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setunionsingleton,definition,
% 2.76/1.53 ( setunionsingleton
% 2.76/1.53 = ( ! [Xx: $i] :
% 2.76/1.53 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.76/1.53 = Xx ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(singleton_type,type,
% 2.76/1.53 singleton: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(singleton,definition,
% 2.76/1.53 ( singleton
% 2.76/1.53 = ( ^ [A: $i] :
% 2.76/1.53 ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( A
% 2.76/1.53 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(singletonprop_type,type,
% 2.76/1.53 singletonprop: $o ).
% 2.76/1.53
% 2.76/1.53 thf(singletonprop,definition,
% 2.76/1.53 ( singletonprop
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ A )
% 2.76/1.53 => ( ( Xphi @ Xx )
% 2.76/1.53 => ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xx = Xy ) ) ) ) )
% 2.76/1.53 => ( ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( Xphi @ Xx ) )
% 2.76/1.53 => ( singleton
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(ex1_type,type,
% 2.76/1.53 ex1: $i > ( $i > $o ) > $o ).
% 2.76/1.53
% 2.76/1.53 thf(ex1,definition,
% 2.76/1.53 ( ex1
% 2.76/1.53 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( singleton
% 2.76/1.53 @ ( dsetconstr @ A
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(ex1E1_type,type,
% 2.76/1.53 ex1E1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(ex1E1,definition,
% 2.76/1.53 ( ex1E1
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ( ex1 @ A
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.76/1.53 => ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(ex1I_type,type,
% 2.76/1.53 ex1I: $o ).
% 2.76/1.53
% 2.76/1.53 thf(ex1I,definition,
% 2.76/1.53 ( ex1I
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ( ( Xphi @ Xx )
% 2.76/1.53 => ( ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ A )
% 2.76/1.53 => ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xy = Xx ) ) )
% 2.76/1.53 => ( ex1 @ A
% 2.76/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(ex1I2_type,type,
% 2.76/1.53 ex1I2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(ex1I2,definition,
% 2.76/1.53 ( ex1I2
% 2.76/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.76/1.53 ( ! [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 => ! [Xy: $i] :
% 2.76/1.53 ( ( in @ Xy @ A )
% 2.76/1.53 => ( ( Xphi @ Xx )
% 2.76/1.53 => ( ( Xphi @ Xy )
% 2.76/1.53 => ( Xx = Xy ) ) ) ) )
% 2.76/1.53 => ( ? [Xx: $i] :
% 2.76/1.53 ( ( in @ Xx @ A )
% 2.76/1.53 & ( Xphi @ Xx ) )
% 2.76/1.53 => ( ex1 @ A
% 2.76/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(singletonsuniq_type,type,
% 2.76/1.53 singletonsuniq: $o ).
% 2.76/1.53
% 2.76/1.53 thf(singletonsuniq,definition,
% 2.76/1.53 ( singletonsuniq
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( ( setadjoin @ Xx @ emptyset )
% 2.76/1.53 = ( setadjoin @ Xy @ emptyset ) )
% 2.76/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(atmost1p_type,type,
% 2.76/1.53 atmost1p: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(atleast2p_type,type,
% 2.76/1.53 atleast2p: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(atmost2p_type,type,
% 2.76/1.53 atmost2p: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(upairsetp_type,type,
% 2.76/1.53 upairsetp: $i > $o ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjL1_type,type,
% 2.76/1.53 setukpairinjL1: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjL1,definition,
% 2.76/1.53 ( setukpairinjL1
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.76/1.53 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.76/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(kfstsingleton_type,type,
% 2.76/1.53 kfstsingleton: $o ).
% 2.76/1.53
% 2.76/1.53 thf(kfstsingleton,definition,
% 2.76/1.53 ( kfstsingleton
% 2.76/1.53 = ( ! [Xu: $i] :
% 2.76/1.53 ( ( iskpair @ Xu )
% 2.76/1.53 => ( singleton
% 2.76/1.53 @ ( dsetconstr @ ( setunion @ Xu )
% 2.76/1.53 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(theprop_type,type,
% 2.76/1.53 theprop: $o ).
% 2.76/1.53
% 2.76/1.53 thf(theprop,definition,
% 2.76/1.53 ( theprop
% 2.76/1.53 = ( ! [X: $i] :
% 2.76/1.53 ( ( singleton @ X )
% 2.76/1.53 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(kfst_type,type,
% 2.76/1.53 kfst: $i > $i ).
% 2.76/1.53
% 2.76/1.53 thf(kfstpairEq_type,type,
% 2.76/1.53 kfstpairEq: $o ).
% 2.76/1.53
% 2.76/1.53 thf(kfstpairEq,definition,
% 2.76/1.53 ( kfstpairEq
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.76/1.53 = Xx ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(cartprodfstin_type,type,
% 2.76/1.53 cartprodfstin: $o ).
% 2.76/1.53
% 2.76/1.53 thf(cartprodfstin,definition,
% 2.76/1.53 ( cartprodfstin
% 2.76/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.76/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.76/1.53 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjL2_type,type,
% 2.76/1.53 setukpairinjL2: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjL2,definition,
% 2.76/1.53 ( setukpairinjL2
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.76/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.76/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.76/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjL_type,type,
% 2.76/1.53 setukpairinjL: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjL,definition,
% 2.76/1.53 ( setukpairinjL
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.76/1.53 ( ( ( kpair @ Xx @ Xy )
% 2.76/1.53 = ( kpair @ Xz @ Xu ) )
% 2.76/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjR11_type,type,
% 2.76/1.53 setukpairinjR11: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjR11,definition,
% 2.76/1.53 ( setukpairinjR11
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.53 ( ( Xx = Xy )
% 2.76/1.53 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.76/1.53 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjR12_type,type,
% 2.76/1.53 setukpairinjR12: $o ).
% 2.76/1.53
% 2.76/1.53 thf(setukpairinjR12,definition,
% 2.76/1.53 ( setukpairinjR12
% 2.76/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( Xx = Xy )
% 2.76/1.54 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.76/1.54 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(setukpairinjR1_type,type,
% 2.76/1.54 setukpairinjR1: $o ).
% 2.76/1.54
% 2.76/1.54 thf(setukpairinjR1,definition,
% 2.76/1.54 ( setukpairinjR1
% 2.76/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.76/1.54 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.76/1.54 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.76/1.54 => ( ( Xz = Xu )
% 2.76/1.54 => ( Xy = Xu ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(upairequniteq_type,type,
% 2.76/1.54 upairequniteq: $o ).
% 2.76/1.54
% 2.76/1.54 thf(upairequniteq,definition,
% 2.76/1.54 ( upairequniteq
% 2.76/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.76/1.54 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.76/1.54 = ( setadjoin @ Xz @ emptyset ) )
% 2.76/1.54 => ( Xx = Xy ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(setukpairinjR2_type,type,
% 2.76/1.54 setukpairinjR2: $o ).
% 2.76/1.54
% 2.76/1.54 thf(setukpairinjR2,definition,
% 2.76/1.54 ( setukpairinjR2
% 2.76/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.76/1.54 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.76/1.54 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.76/1.54 => ( Xy = Xu ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(setukpairinjR_type,type,
% 2.76/1.54 setukpairinjR: $o ).
% 2.76/1.54
% 2.76/1.54 thf(setukpairinjR,definition,
% 2.76/1.54 ( setukpairinjR
% 2.76/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.76/1.54 ( ( ( kpair @ Xx @ Xy )
% 2.76/1.54 = ( kpair @ Xz @ Xu ) )
% 2.76/1.54 => ( Xy = Xu ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(ksndsingleton_type,type,
% 2.76/1.54 ksndsingleton: $o ).
% 2.76/1.54
% 2.76/1.54 thf(ksndsingleton,definition,
% 2.76/1.54 ( ksndsingleton
% 2.76/1.54 = ( ! [Xu: $i] :
% 2.76/1.54 ( ( iskpair @ Xu )
% 2.76/1.54 => ( singleton
% 2.76/1.54 @ ( dsetconstr @ ( setunion @ Xu )
% 2.76/1.54 @ ^ [Xx: $i] :
% 2.76/1.54 ( Xu
% 2.76/1.54 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(ksnd_type,type,
% 2.76/1.54 ksnd: $i > $i ).
% 2.76/1.54
% 2.76/1.54 thf(ksndpairEq_type,type,
% 2.76/1.54 ksndpairEq: $o ).
% 2.76/1.54
% 2.76/1.54 thf(ksndpairEq,definition,
% 2.76/1.54 ( ksndpairEq
% 2.76/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.76/1.54 = Xy ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(kpairsurjEq_type,type,
% 2.76/1.54 kpairsurjEq: $o ).
% 2.76/1.54
% 2.76/1.54 thf(kpairsurjEq,definition,
% 2.76/1.54 ( kpairsurjEq
% 2.76/1.54 = ( ! [Xu: $i] :
% 2.76/1.54 ( ( iskpair @ Xu )
% 2.76/1.54 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.76/1.54 = Xu ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodsndin_type,type,
% 2.76/1.54 cartprodsndin: $o ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodsndin,definition,
% 2.76/1.54 ( cartprodsndin
% 2.76/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.76/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.76/1.54 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodpairmemEL_type,type,
% 2.76/1.54 cartprodpairmemEL: $o ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodpairmemEL,definition,
% 2.76/1.54 ( cartprodpairmemEL
% 2.76/1.54 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.76/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodpairmemER_type,type,
% 2.76/1.54 cartprodpairmemER: $o ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodpairmemER,definition,
% 2.76/1.54 ( cartprodpairmemER
% 2.76/1.54 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.76/1.54 => ( in @ Xy @ B ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodmempaircEq_type,type,
% 2.76/1.54 cartprodmempaircEq: $o ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodmempaircEq,definition,
% 2.76/1.54 ( cartprodmempaircEq
% 2.76/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ! [Xy: $i] :
% 2.76/1.54 ( ( in @ Xy @ B )
% 2.76/1.54 => ( ( kpair @ Xx @ Xy )
% 2.76/1.54 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodfstpairEq_type,type,
% 2.76/1.54 cartprodfstpairEq: $o ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodfstpairEq,definition,
% 2.76/1.54 ( cartprodfstpairEq
% 2.76/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ! [Xy: $i] :
% 2.76/1.54 ( ( in @ Xy @ B )
% 2.76/1.54 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.76/1.54 = Xx ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodsndpairEq_type,type,
% 2.76/1.54 cartprodsndpairEq: $o ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodsndpairEq,definition,
% 2.76/1.54 ( cartprodsndpairEq
% 2.76/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ! [Xy: $i] :
% 2.76/1.54 ( ( in @ Xy @ B )
% 2.76/1.54 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.76/1.54 = Xy ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodpairsurjEq_type,type,
% 2.76/1.54 cartprodpairsurjEq: $o ).
% 2.76/1.54
% 2.76/1.54 thf(cartprodpairsurjEq,definition,
% 2.76/1.54 ( cartprodpairsurjEq
% 2.76/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.76/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.76/1.54 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.76/1.54 = Xu ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(breln_type,type,
% 2.76/1.54 breln: $i > $i > $i > $o ).
% 2.76/1.54
% 2.76/1.54 thf(breln,definition,
% 2.76/1.54 ( breln
% 2.76/1.54 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstr_type,type,
% 2.76/1.54 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrI_type,type,
% 2.76/1.54 dpsetconstrI: $o ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrI,definition,
% 2.76/1.54 ( dpsetconstrI
% 2.76/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ! [Xy: $i] :
% 2.76/1.54 ( ( in @ Xy @ B )
% 2.76/1.54 => ( ( Xphi @ Xx @ Xy )
% 2.76/1.54 => ( in @ ( kpair @ Xx @ Xy )
% 2.76/1.54 @ ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrSub_type,type,
% 2.76/1.54 dpsetconstrSub: $o ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrSub,definition,
% 2.76/1.54 ( dpsetconstrSub
% 2.76/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.76/1.54 ( subset
% 2.76/1.54 @ ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.76/1.54 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(setOfPairsIsBReln_type,type,
% 2.76/1.54 setOfPairsIsBReln: $o ).
% 2.76/1.54
% 2.76/1.54 thf(setOfPairsIsBReln,definition,
% 2.76/1.54 ( setOfPairsIsBReln
% 2.76/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.76/1.54 ( breln @ A @ B
% 2.76/1.54 @ ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrERa_type,type,
% 2.76/1.54 dpsetconstrERa: $o ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrERa,definition,
% 2.76/1.54 ( dpsetconstrERa
% 2.76/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ! [Xy: $i] :
% 2.76/1.54 ( ( in @ Xy @ B )
% 2.76/1.54 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.76/1.54 @ ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.76/1.54 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrEL1_type,type,
% 2.76/1.54 dpsetconstrEL1: $o ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrEL1,definition,
% 2.76/1.54 ( dpsetconstrEL1
% 2.76/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( in @ ( kpair @ Xx @ Xy )
% 2.76/1.54 @ ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.76/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrEL2_type,type,
% 2.76/1.54 dpsetconstrEL2: $o ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrEL2,definition,
% 2.76/1.54 ( dpsetconstrEL2
% 2.76/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( in @ ( kpair @ Xx @ Xy )
% 2.76/1.54 @ ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.76/1.54 => ( in @ Xy @ B ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrER_type,type,
% 2.76/1.54 dpsetconstrER: $o ).
% 2.76/1.54
% 2.76/1.54 thf(dpsetconstrER,definition,
% 2.76/1.54 ( dpsetconstrER
% 2.76/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( in @ ( kpair @ Xx @ Xy )
% 2.76/1.54 @ ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.76/1.54 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(func_type,type,
% 2.76/1.54 func: $i > $i > $i > $o ).
% 2.76/1.54
% 2.76/1.54 thf(func,definition,
% 2.76/1.54 ( func
% 2.76/1.54 = ( ^ [A: $i,B: $i,R: $i] :
% 2.76/1.54 ( ( breln @ A @ B @ R )
% 2.76/1.54 & ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ( ex1 @ B
% 2.76/1.54 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(funcSet_type,type,
% 2.76/1.54 funcSet: $i > $i > $i ).
% 2.76/1.54
% 2.76/1.54 thf(funcImageSingleton_type,type,
% 2.76/1.54 funcImageSingleton: $o ).
% 2.76/1.54
% 2.76/1.54 thf(funcImageSingleton,definition,
% 2.76/1.54 ( funcImageSingleton
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.76/1.54 ( ( func @ A @ B @ Xf )
% 2.76/1.54 => ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ( singleton
% 2.76/1.54 @ ( dsetconstr @ B
% 2.76/1.54 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(apProp_type,type,
% 2.76/1.54 apProp: $o ).
% 2.76/1.54
% 2.76/1.54 thf(apProp,definition,
% 2.76/1.54 ( apProp
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.76/1.54 ( ( func @ A @ B @ Xf )
% 2.76/1.54 => ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ( in
% 2.76/1.54 @ ( setunion
% 2.76/1.54 @ ( dsetconstr @ B
% 2.76/1.54 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.76/1.54 @ B ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(ap_type,type,
% 2.76/1.54 ap: $i > $i > $i > $i > $i ).
% 2.76/1.54
% 2.76/1.54 thf(ap,definition,
% 2.76/1.54 ( ap
% 2.76/1.54 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 2.76/1.54 ( setunion
% 2.76/1.54 @ ( dsetconstr @ B
% 2.76/1.54 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(app_type,type,
% 2.76/1.54 app: $o ).
% 2.76/1.54
% 2.76/1.54 thf(app,definition,
% 2.76/1.54 ( app
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.76/1.54 ( ( func @ A @ B @ Xf )
% 2.76/1.54 => ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(infuncsetfunc_type,type,
% 2.76/1.54 infuncsetfunc: $o ).
% 2.76/1.54
% 2.76/1.54 thf(infuncsetfunc,definition,
% 2.76/1.54 ( infuncsetfunc
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.76/1.54 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.76/1.54 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(ap2p_type,type,
% 2.76/1.54 ap2p: $o ).
% 2.76/1.54
% 2.76/1.54 thf(ap2p,definition,
% 2.76/1.54 ( ap2p
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.76/1.54 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.76/1.54 => ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(funcinfuncset_type,type,
% 2.76/1.54 funcinfuncset: $o ).
% 2.76/1.54
% 2.76/1.54 thf(funcinfuncset,definition,
% 2.76/1.54 ( funcinfuncset
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.76/1.54 ( ( func @ A @ B @ Xf )
% 2.76/1.54 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(lamProp_type,type,
% 2.76/1.54 lamProp: $o ).
% 2.76/1.54
% 2.76/1.54 thf(lamProp,definition,
% 2.76/1.54 ( lamProp
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.76/1.54 ( ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.76/1.54 => ( func @ A @ B
% 2.76/1.54 @ ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( Xf @ Xx )
% 2.76/1.54 = Xy ) ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(lam_type,type,
% 2.76/1.54 lam: $i > $i > ( $i > $i ) > $i ).
% 2.76/1.54
% 2.76/1.54 thf(lam,definition,
% 2.76/1.54 ( lam
% 2.76/1.54 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 2.76/1.54 ( dpsetconstr @ A @ B
% 2.76/1.54 @ ^ [Xx: $i,Xy: $i] :
% 2.76/1.54 ( ( Xf @ Xx )
% 2.76/1.54 = Xy ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(lamp_type,type,
% 2.76/1.54 lamp: $o ).
% 2.76/1.54
% 2.76/1.54 thf(lamp,definition,
% 2.76/1.54 ( lamp
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.76/1.54 ( ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.76/1.54 => ( func @ A @ B
% 2.76/1.54 @ ( lam @ A @ B
% 2.76/1.54 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(lam2p_type,type,
% 2.76/1.54 lam2p: $o ).
% 2.76/1.54
% 2.76/1.54 thf(lam2p,definition,
% 2.76/1.54 ( lam2p
% 2.76/1.54 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.76/1.54 ( ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.76/1.54 => ( in
% 2.76/1.54 @ ( lam @ A @ B
% 2.76/1.54 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.76/1.54 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.76/1.54
% 2.76/1.54 thf(brelnall1,conjecture,
% 2.76/1.54 ( setextAx
% 2.76/1.54 => ( emptysetAx
% 2.76/1.54 => ( setadjoinAx
% 2.76/1.54 => ( powersetAx
% 2.76/1.54 => ( setunionAx
% 2.76/1.54 => ( omega0Ax
% 2.76/1.54 => ( omegaSAx
% 2.76/1.54 => ( omegaIndAx
% 2.76/1.54 => ( replAx
% 2.76/1.54 => ( foundationAx
% 2.76/1.54 => ( wellorderingAx
% 2.76/1.54 => ( descrp
% 2.76/1.54 => ( dsetconstrI
% 2.76/1.54 => ( dsetconstrEL
% 2.76/1.54 => ( dsetconstrER
% 2.76/1.54 => ( exuE1
% 2.76/1.54 => ( prop2setE
% 2.76/1.54 => ( emptysetE
% 2.76/1.54 => ( emptysetimpfalse
% 2.76/1.54 => ( notinemptyset
% 2.76/1.54 => ( exuE3e
% 2.76/1.54 => ( setext
% 2.76/1.54 => ( emptyI
% 2.76/1.54 => ( noeltsimpempty
% 2.76/1.54 => ( setbeta
% 2.76/1.54 => ( nonemptyE1
% 2.76/1.54 => ( nonemptyI
% 2.76/1.54 => ( nonemptyI1
% 2.76/1.54 => ( setadjoinIL
% 2.76/1.54 => ( emptyinunitempty
% 2.76/1.54 => ( setadjoinIR
% 2.76/1.54 => ( setadjoinE
% 2.76/1.54 => ( setadjoinOr
% 2.76/1.54 => ( setoftrueEq
% 2.76/1.54 => ( powersetI
% 2.76/1.54 => ( emptyinPowerset
% 2.76/1.54 => ( emptyInPowerset
% 2.76/1.54 => ( powersetE
% 2.76/1.54 => ( setunionI
% 2.76/1.54 => ( setunionE
% 2.76/1.54 => ( subPowSU
% 2.76/1.54 => ( exuE2
% 2.76/1.54 => ( nonemptyImpWitness
% 2.76/1.54 => ( uniqinunit
% 2.76/1.54 => ( notinsingleton
% 2.76/1.54 => ( eqinunit
% 2.76/1.54 => ( singletonsswitch
% 2.76/1.54 => ( upairsetE
% 2.76/1.54 => ( upairsetIL
% 2.76/1.54 => ( upairsetIR
% 2.76/1.54 => ( emptyE1
% 2.76/1.54 => ( vacuousDall
% 2.76/1.54 => ( quantDeMorgan1
% 2.76/1.54 => ( quantDeMorgan2
% 2.76/1.54 => ( quantDeMorgan3
% 2.76/1.54 => ( quantDeMorgan4
% 2.76/1.54 => ( prop2setI
% 2.76/1.54 => ( prop2set2propI
% 2.76/1.54 => ( notdexE
% 2.76/1.54 => ( notdallE
% 2.76/1.54 => ( exuI1
% 2.76/1.54 => ( exuI3
% 2.76/1.54 => ( exuI2
% 2.76/1.54 => ( inCongP
% 2.76/1.54 => ( in__Cong
% 2.76/1.54 => ( exuE3u
% 2.76/1.54 => ( exu__Cong
% 2.76/1.54 => ( emptyset__Cong
% 2.76/1.54 => ( setadjoin__Cong
% 2.76/1.54 => ( powerset__Cong
% 2.76/1.54 => ( setunion__Cong
% 2.76/1.54 => ( omega__Cong
% 2.76/1.54 => ( exuEu
% 2.76/1.54 => ( descr__Cong
% 2.76/1.54 => ( dsetconstr__Cong
% 2.76/1.54 => ( subsetI1
% 2.76/1.54 => ( eqimpsubset2
% 2.76/1.54 => ( eqimpsubset1
% 2.76/1.54 => ( subsetI2
% 2.76/1.54 => ( emptysetsubset
% 2.76/1.54 => ( subsetE
% 2.76/1.54 => ( subsetE2
% 2.76/1.54 => ( notsubsetI
% 2.76/1.54 => ( notequalI1
% 2.76/1.54 => ( notequalI2
% 2.76/1.54 => ( subsetRefl
% 2.76/1.54 => ( subsetTrans
% 2.76/1.54 => ( setadjoinSub
% 2.76/1.54 => ( setadjoinSub2
% 2.76/1.54 => ( subset2powerset
% 2.76/1.54 => ( setextsub
% 2.76/1.54 => ( subsetemptysetimpeq
% 2.76/1.54 => ( powersetI1
% 2.76/1.54 => ( powersetE1
% 2.76/1.54 => ( inPowerset
% 2.76/1.54 => ( powersetsubset
% 2.76/1.54 => ( sepInPowerset
% 2.76/1.54 => ( sepSubset
% 2.76/1.54 => ( binunionIL
% 2.76/1.54 => ( upairset2IR
% 2.76/1.54 => ( binunionIR
% 2.76/1.54 => ( binunionEcases
% 2.76/1.54 => ( binunionE
% 2.76/1.54 => ( binunionLsub
% 2.76/1.54 => ( binunionRsub
% 2.76/1.54 => ( binintersectI
% 2.76/1.54 => ( binintersectSubset5
% 2.76/1.54 => ( binintersectEL
% 2.76/1.54 => ( binintersectLsub
% 2.76/1.54 => ( binintersectSubset2
% 2.76/1.54 => ( binintersectSubset3
% 2.76/1.54 => ( binintersectER
% 2.76/1.54 => ( disjointsetsI1
% 2.76/1.54 => ( binintersectRsub
% 2.76/1.54 => ( binintersectSubset4
% 2.76/1.54 => ( binintersectSubset1
% 2.76/1.54 => ( bs114d
% 2.76/1.54 => ( setminusI
% 2.76/1.54 => ( setminusEL
% 2.76/1.54 => ( setminusER
% 2.76/1.54 => ( setminusSubset2
% 2.76/1.54 => ( setminusERneg
% 2.76/1.54 => ( setminusELneg
% 2.76/1.54 => ( setminusILneg
% 2.76/1.54 => ( setminusIRneg
% 2.76/1.54 => ( setminusLsub
% 2.76/1.54 => ( setminusSubset1
% 2.76/1.54 => ( symdiffE
% 2.76/1.54 => ( symdiffI1
% 2.76/1.54 => ( symdiffI2
% 2.76/1.54 => ( symdiffIneg1
% 2.76/1.54 => ( symdiffIneg2
% 2.76/1.54 => ( secondinupair
% 2.76/1.54 => ( setukpairIL
% 2.76/1.54 => ( setukpairIR
% 2.76/1.54 => ( kpairiskpair
% 2.76/1.54 => ( kpairp
% 2.76/1.54 => ( singletonsubset
% 2.76/1.54 => ( singletoninpowerset
% 2.76/1.54 => ( singletoninpowunion
% 2.76/1.54 => ( upairset2E
% 2.76/1.54 => ( upairsubunion
% 2.76/1.54 => ( upairinpowunion
% 2.76/1.54 => ( ubforcartprodlem1
% 2.76/1.54 => ( ubforcartprodlem2
% 2.76/1.54 => ( ubforcartprodlem3
% 2.76/1.54 => ( cartprodpairin
% 2.76/1.54 => ( cartprodmempair1
% 2.76/1.54 => ( cartprodmempair
% 2.76/1.54 => ( setunionE2
% 2.76/1.54 => ( setunionsingleton1
% 2.76/1.54 => ( setunionsingleton2
% 2.76/1.54 => ( setunionsingleton
% 2.76/1.54 => ( singletonprop
% 2.76/1.54 => ( ex1E1
% 2.76/1.54 => ( ex1I
% 2.76/1.54 => ( ex1I2
% 2.76/1.54 => ( singletonsuniq
% 2.76/1.54 => ( setukpairinjL1
% 2.76/1.54 => ( kfstsingleton
% 2.76/1.54 => ( theprop
% 2.76/1.54 => ( kfstpairEq
% 2.76/1.54 => ( cartprodfstin
% 2.76/1.54 => ( setukpairinjL2
% 2.76/1.54 => ( setukpairinjL
% 2.76/1.54 => ( setukpairinjR11
% 2.76/1.54 => ( setukpairinjR12
% 2.76/1.54 => ( setukpairinjR1
% 2.76/1.54 => ( upairequniteq
% 2.76/1.54 => ( setukpairinjR2
% 2.76/1.54 => ( setukpairinjR
% 2.76/1.54 => ( ksndsingleton
% 2.76/1.54 => ( ksndpairEq
% 2.76/1.54 => ( kpairsurjEq
% 2.76/1.54 => ( cartprodsndin
% 2.76/1.54 => ( cartprodpairmemEL
% 2.76/1.54 => ( cartprodpairmemER
% 2.76/1.54 => ( cartprodmempaircEq
% 2.76/1.54 => ( cartprodfstpairEq
% 2.76/1.54 => ( cartprodsndpairEq
% 2.76/1.54 => ( cartprodpairsurjEq
% 2.76/1.54 => ( dpsetconstrI
% 2.76/1.54 => ( dpsetconstrSub
% 2.76/1.54 => ( setOfPairsIsBReln
% 2.76/1.54 => ( dpsetconstrERa
% 2.76/1.54 => ( dpsetconstrEL1
% 2.76/1.54 => ( dpsetconstrEL2
% 2.76/1.54 => ( dpsetconstrER
% 2.76/1.54 => ( funcImageSingleton
% 2.76/1.54 => ( apProp
% 2.76/1.54 => ( app
% 2.76/1.54 => ( infuncsetfunc
% 2.76/1.54 => ( ap2p
% 2.76/1.54 => ( funcinfuncset
% 2.76/1.54 => ( lamProp
% 2.76/1.54 => ( lamp
% 2.76/1.54 => ( lam2p
% 2.76/1.54 => ! [A: $i,B: $i,R: $i] :
% 2.76/1.54 ( ( breln @ A @ B @ R )
% 2.76/1.54 => ! [Xphi: $i > $o] :
% 2.76/1.54 ( ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ A )
% 2.76/1.54 => ! [Xy: $i] :
% 2.76/1.54 ( ( in @ Xy @ B )
% 2.76/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.76/1.54 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.76/1.54 => ! [Xx: $i] :
% 2.76/1.54 ( ( in @ Xx @ R )
% 2.76/1.54 => ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.76/1.54 ------------------------
% 2.76/1.55 % (26777)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/183Mi)
% 2.76/1.55 % (26778)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_26535 for (2999ds/4Mi)
% 2.76/1.55 % (26780)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/2Mi)
% 2.76/1.55 % (26779)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_26535 for (2999ds/27Mi)
% 2.76/1.55 % (26780)Instruction limit reached!
% 2.76/1.55 % (26780)------------------------------
% 2.76/1.55 % (26780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.55 % (26780)Termination reason: Unknown
% 2.76/1.56 % (26780)Termination phase: shuffling
% 2.76/1.56
% 2.76/1.56 % (26780)Memory used [KB]: 1407
% 2.76/1.56 % (26780)Time elapsed: 0.002 s
% 2.76/1.56 % (26780)Instructions burned: 3 (million)
% 2.76/1.56 % (26780)------------------------------
% 2.76/1.56 % (26780)------------------------------
% 2.76/1.56 % (26778)Instruction limit reached!
% 2.76/1.56 % (26778)------------------------------
% 2.76/1.56 % (26778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.56 % (26778)Termination reason: Unknown
% 2.76/1.56 % (26778)Termination phase: shuffling
% 2.76/1.56
% 2.76/1.56 % (26778)Memory used [KB]: 1407
% 2.76/1.56 % (26778)Time elapsed: 0.003 s
% 2.76/1.56 % (26778)Instructions burned: 6 (million)
% 2.76/1.56 % (26778)------------------------------
% 2.76/1.56 % (26778)------------------------------
% 2.76/1.56 % (26781)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_26535 for (2999ds/2Mi)
% 2.76/1.56 % (26782)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_26535 for (2999ds/275Mi)
% 2.76/1.56 % (26783)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/18Mi)
% 2.76/1.56 % (26781)Instruction limit reached!
% 2.76/1.56 % (26781)------------------------------
% 2.76/1.56 % (26781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.56 % (26781)Termination reason: Unknown
% 2.76/1.56 % (26781)Termination phase: shuffling
% 2.76/1.56
% 2.76/1.56 % (26781)Memory used [KB]: 1407
% 2.76/1.56 % (26781)Time elapsed: 0.004 s
% 2.76/1.56 % (26781)Instructions burned: 3 (million)
% 2.76/1.56 % (26781)------------------------------
% 2.76/1.56 % (26781)------------------------------
% 2.76/1.57 % (26789)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/3Mi)
% 2.76/1.57 % (26790)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_26535 for (2999ds/37Mi)
% 2.76/1.57 % (26789)Instruction limit reached!
% 2.76/1.57 % (26789)------------------------------
% 2.76/1.57 % (26789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.57 % (26789)Termination reason: Unknown
% 2.76/1.57 % (26789)Termination phase: shuffling
% 2.76/1.57
% 2.76/1.57 % (26789)Memory used [KB]: 1407
% 2.76/1.57 % (26789)Time elapsed: 0.003 s
% 2.76/1.57 % (26789)Instructions burned: 4 (million)
% 2.76/1.57 % (26789)------------------------------
% 2.76/1.57 % (26789)------------------------------
% 2.76/1.57 % (26779)Instruction limit reached!
% 2.76/1.57 % (26779)------------------------------
% 2.76/1.57 % (26779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.57 % (26779)Termination reason: Unknown
% 2.76/1.57 % (26779)Termination phase: shuffling
% 2.76/1.57
% 2.76/1.57 % (26779)Memory used [KB]: 1918
% 2.76/1.57 % (26779)Time elapsed: 0.014 s
% 2.76/1.57 % (26779)Instructions burned: 29 (million)
% 2.76/1.57 % (26779)------------------------------
% 2.76/1.57 % (26779)------------------------------
% 2.76/1.57 % (26783)Instruction limit reached!
% 2.76/1.57 % (26783)------------------------------
% 2.76/1.57 % (26783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.57 % (26783)Termination reason: Unknown
% 2.76/1.57 % (26783)Termination phase: shuffling
% 2.76/1.57
% 2.76/1.57 % (26783)Memory used [KB]: 1663
% 2.76/1.57 % (26783)Time elapsed: 0.013 s
% 2.76/1.57 % (26783)Instructions burned: 18 (million)
% 2.76/1.57 % (26783)------------------------------
% 2.76/1.57 % (26783)------------------------------
% 2.76/1.58 % (26794)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_26535 for (2999ds/3Mi)
% 2.76/1.58 % (26790)Instruction limit reached!
% 2.76/1.58 % (26790)------------------------------
% 2.76/1.58 % (26790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.58 % (26790)Termination reason: Unknown
% 2.76/1.58 % (26790)Termination phase: Property scanning
% 2.76/1.58
% 2.76/1.58 % (26790)Memory used [KB]: 2174
% 2.76/1.58 % (26790)Time elapsed: 0.013 s
% 2.76/1.58 % (26790)Instructions burned: 40 (million)
% 2.76/1.58 % (26790)------------------------------
% 2.76/1.58 % (26790)------------------------------
% 2.76/1.58 % (26794)Instruction limit reached!
% 2.76/1.58 % (26794)------------------------------
% 2.76/1.58 % (26794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.58 % (26794)Termination reason: Unknown
% 2.76/1.58 % (26794)Termination phase: shuffling
% 2.76/1.58
% 2.76/1.58 % (26794)Memory used [KB]: 1407
% 2.76/1.58 % (26794)Time elapsed: 0.002 s
% 2.76/1.58 % (26794)Instructions burned: 4 (million)
% 2.76/1.58 % (26794)------------------------------
% 2.76/1.58 % (26794)------------------------------
% 2.76/1.58 % (26795)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_26535 for (2999ds/1041Mi)
% 2.76/1.58 % (26792)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_26535 for (2999ds/15Mi)
% 2.76/1.59 % (26802)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/16Mi)
% 2.76/1.59 % (26803)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_26535 for (2999ds/3Mi)
% 2.76/1.59 % (26803)Instruction limit reached!
% 2.76/1.59 % (26803)------------------------------
% 2.76/1.59 % (26803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.59 % (26803)Termination reason: Unknown
% 2.76/1.59 % (26803)Termination phase: shuffling
% 2.76/1.59
% 2.76/1.59 % (26803)Memory used [KB]: 1407
% 2.76/1.59 % (26803)Time elapsed: 0.002 s
% 2.76/1.59 % (26803)Instructions burned: 3 (million)
% 2.76/1.59 % (26803)------------------------------
% 2.76/1.59 % (26803)------------------------------
% 2.76/1.59 % (26792)Instruction limit reached!
% 2.76/1.59 % (26792)------------------------------
% 2.76/1.59 % (26792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.59 % (26792)Termination reason: Unknown
% 2.76/1.59 % (26792)Termination phase: shuffling
% 2.76/1.59
% 2.76/1.59 % (26792)Memory used [KB]: 1663
% 2.76/1.59 % (26792)Time elapsed: 0.011 s
% 2.76/1.59 % (26792)Instructions burned: 15 (million)
% 2.76/1.59 % (26792)------------------------------
% 2.76/1.59 % (26792)------------------------------
% 2.76/1.59 % (26798)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/7Mi)
% 2.76/1.59 % (26802)Instruction limit reached!
% 2.76/1.59 % (26802)------------------------------
% 2.76/1.59 % (26802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.59 % (26802)Termination reason: Unknown
% 2.76/1.59 % (26802)Termination phase: shuffling
% 2.76/1.59
% 2.76/1.59 % (26802)Memory used [KB]: 1663
% 2.76/1.59 % (26802)Time elapsed: 0.007 s
% 2.76/1.59 % (26802)Instructions burned: 17 (million)
% 2.76/1.59 % (26802)------------------------------
% 2.76/1.59 % (26802)------------------------------
% 2.76/1.59 % (26798)Instruction limit reached!
% 2.76/1.59 % (26798)------------------------------
% 2.76/1.59 % (26798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.59 % (26798)Termination reason: Unknown
% 2.76/1.59 % (26798)Termination phase: shuffling
% 2.76/1.59
% 2.76/1.59 % (26798)Memory used [KB]: 1535
% 2.76/1.59 % (26798)Time elapsed: 0.006 s
% 2.76/1.59 % (26798)Instructions burned: 8 (million)
% 2.76/1.59 % (26798)------------------------------
% 2.76/1.59 % (26798)------------------------------
% 2.80/1.60 % (26810)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/7Mi)
% 2.80/1.60 % (26809)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_26535 for (2999ds/3Mi)
% 2.80/1.60 % (26809)Instruction limit reached!
% 2.80/1.60 % (26809)------------------------------
% 2.80/1.60 % (26809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.60 % (26809)Termination reason: Unknown
% 2.80/1.60 % (26809)Termination phase: shuffling
% 2.80/1.60
% 2.80/1.60 % (26809)Memory used [KB]: 1407
% 2.80/1.60 % (26809)Time elapsed: 0.002 s
% 2.80/1.60 % (26809)Instructions burned: 3 (million)
% 2.80/1.60 % (26809)------------------------------
% 2.80/1.60 % (26809)------------------------------
% 2.80/1.60 % (26810)Instruction limit reached!
% 2.80/1.60 % (26810)------------------------------
% 2.80/1.60 % (26810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.60 % (26810)Termination reason: Unknown
% 2.80/1.60 % (26810)Termination phase: shuffling
% 2.80/1.60
% 2.80/1.60 % (26810)Memory used [KB]: 1407
% 2.80/1.60 % (26810)Time elapsed: 0.003 s
% 2.80/1.60 % (26810)Instructions burned: 7 (million)
% 2.80/1.60 % (26810)------------------------------
% 2.80/1.60 % (26810)------------------------------
% 2.80/1.60 % (26812)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/3Mi)
% 2.80/1.60 % (26812)Instruction limit reached!
% 2.80/1.60 % (26812)------------------------------
% 2.80/1.60 % (26812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.60 % (26812)Termination reason: Unknown
% 2.80/1.60 % (26812)Termination phase: shuffling
% 2.80/1.60
% 2.80/1.60 % (26812)Memory used [KB]: 1407
% 2.80/1.60 % (26812)Time elapsed: 0.002 s
% 2.80/1.60 % (26812)Instructions burned: 4 (million)
% 2.80/1.60 % (26812)------------------------------
% 2.80/1.60 % (26812)------------------------------
% 2.80/1.61 % (26777)Instruction limit reached!
% 2.80/1.61 % (26777)------------------------------
% 2.80/1.61 % (26777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.61 % (26777)Termination reason: Unknown
% 2.80/1.61 % (26777)Termination phase: Saturation
% 2.80/1.61
% 2.80/1.61 % (26777)Memory used [KB]: 7547
% 2.80/1.61 % (26777)Time elapsed: 0.054 s
% 2.80/1.61 % (26777)Instructions burned: 185 (million)
% 2.80/1.61 % (26777)------------------------------
% 2.80/1.61 % (26777)------------------------------
% 2.80/1.61 % (26818)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/710Mi)
% 2.80/1.61 % (26817)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/18Mi)
% 2.80/1.61 % (26813)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/4Mi)
% 2.80/1.61 % (26813)Instruction limit reached!
% 2.80/1.61 % (26813)------------------------------
% 2.80/1.61 % (26813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.61 % (26813)Termination reason: Unknown
% 2.80/1.61 % (26813)Termination phase: shuffling
% 2.80/1.61
% 2.80/1.61 % (26813)Memory used [KB]: 1407
% 2.80/1.61 % (26813)Time elapsed: 0.004 s
% 2.80/1.61 % (26813)Instructions burned: 4 (million)
% 2.80/1.61 % (26813)------------------------------
% 2.80/1.61 % (26813)------------------------------
% 2.80/1.61 % (26820)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/6Mi)
% 2.80/1.62 % (26820)Instruction limit reached!
% 2.80/1.62 % (26820)------------------------------
% 2.80/1.62 % (26820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.62 % (26820)Termination reason: Unknown
% 2.80/1.62 % (26820)Termination phase: shuffling
% 2.80/1.62
% 2.80/1.62 % (26820)Memory used [KB]: 1407
% 2.80/1.62 % (26820)Time elapsed: 0.003 s
% 2.80/1.62 % (26820)Instructions burned: 7 (million)
% 2.80/1.62 % (26820)------------------------------
% 2.80/1.62 % (26820)------------------------------
% 2.80/1.62 % (26817)Instruction limit reached!
% 2.80/1.62 % (26817)------------------------------
% 2.80/1.62 % (26817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.62 % (26817)Termination reason: Unknown
% 2.80/1.62 % (26817)Termination phase: shuffling
% 2.80/1.62
% 2.80/1.62 % (26817)Memory used [KB]: 1791
% 2.80/1.62 % (26817)Time elapsed: 0.007 s
% 2.80/1.62 % (26817)Instructions burned: 21 (million)
% 2.80/1.62 % (26817)------------------------------
% 2.80/1.62 % (26817)------------------------------
% 2.80/1.62 % (26822)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_26535 for (2999ds/902Mi)
% 2.80/1.63 % (26825)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/5Mi)
% 2.80/1.63 % (26826)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_26535 for (2999ds/6Mi)
% 2.80/1.63 % (26825)Instruction limit reached!
% 2.80/1.63 % (26825)------------------------------
% 2.80/1.63 % (26825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.63 % (26825)Termination reason: Unknown
% 2.80/1.63 % (26825)Termination phase: shuffling
% 2.80/1.63
% 2.80/1.63 % (26825)Memory used [KB]: 1407
% 2.80/1.63 % (26825)Time elapsed: 0.004 s
% 2.80/1.63 % (26825)Instructions burned: 7 (million)
% 2.80/1.63 % (26825)------------------------------
% 2.80/1.63 % (26825)------------------------------
% 2.80/1.63 % (26826)Instruction limit reached!
% 2.80/1.63 % (26826)------------------------------
% 2.80/1.63 % (26826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.63 % (26826)Termination reason: Unknown
% 2.80/1.63 % (26826)Termination phase: shuffling
% 2.80/1.63
% 2.80/1.63 % (26826)Memory used [KB]: 1407
% 2.80/1.63 % (26826)Time elapsed: 0.003 s
% 2.80/1.63 % (26826)Instructions burned: 7 (million)
% 2.80/1.63 % (26826)------------------------------
% 2.80/1.63 % (26826)------------------------------
% 2.80/1.63 % (26823)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_26535 for (2999ds/21Mi)
% 2.80/1.64 % (26835)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26535 for (2999ds/377Mi)
% 2.80/1.64 % (26836)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_26535 for (2999ds/779Mi)
% 2.80/1.64 % (26823)Instruction limit reached!
% 2.80/1.64 % (26823)------------------------------
% 2.80/1.64 % (26823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.64 % (26823)Termination reason: Unknown
% 2.80/1.64 % (26823)Termination phase: shuffling
% 2.80/1.64
% 2.80/1.64 % (26823)Memory used [KB]: 1791
% 2.80/1.64 % (26823)Time elapsed: 0.013 s
% 2.80/1.64 % (26823)Instructions burned: 21 (million)
% 2.80/1.64 % (26823)------------------------------
% 2.80/1.64 % (26823)------------------------------
% 2.80/1.66 % (26837)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_26535 for (2999ds/19Mi)
% 2.80/1.67 % (26837)Instruction limit reached!
% 2.80/1.67 % (26837)------------------------------
% 2.80/1.67 % (26837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.67 % (26837)Termination reason: Unknown
% 2.80/1.67 % (26837)Termination phase: shuffling
% 2.80/1.67
% 2.80/1.67 % (26837)Memory used [KB]: 1791
% 2.80/1.67 % (26837)Time elapsed: 0.011 s
% 2.80/1.67 % (26837)Instructions burned: 19 (million)
% 2.80/1.67 % (26837)------------------------------
% 2.80/1.67 % (26837)------------------------------
% 2.80/1.68 % (26856)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26535 for (2998ds/879Mi)
% 2.80/1.69 % (26782)Instruction limit reached!
% 2.80/1.69 % (26782)------------------------------
% 2.80/1.69 % (26782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.69 % (26782)Termination reason: Unknown
% 2.80/1.69 % (26782)Termination phase: Saturation
% 2.80/1.69
% 2.80/1.69 % (26782)Memory used [KB]: 8571
% 2.80/1.69 % (26782)Time elapsed: 0.130 s
% 2.80/1.69 % (26782)Instructions burned: 277 (million)
% 2.80/1.69 % (26782)------------------------------
% 2.80/1.69 % (26782)------------------------------
% 2.80/1.70 % (26860)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26535 for (2998ds/17Mi)
% 2.80/1.70 % (26860)Instruction limit reached!
% 2.80/1.70 % (26860)------------------------------
% 2.80/1.70 % (26860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.70 % (26860)Termination reason: Unknown
% 2.80/1.70 % (26860)Termination phase: shuffling
% 2.80/1.70
% 2.80/1.70 % (26860)Memory used [KB]: 1791
% 2.80/1.70 % (26860)Time elapsed: 0.006 s
% 2.80/1.70 % (26860)Instructions burned: 17 (million)
% 2.80/1.70 % (26860)------------------------------
% 2.80/1.70 % (26860)------------------------------
% 2.80/1.72 % (26875)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26535 for (2998ds/3Mi)
% 2.80/1.72 % (26875)Instruction limit reached!
% 2.80/1.72 % (26875)------------------------------
% 2.80/1.72 % (26875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.72 % (26875)Termination reason: Unknown
% 2.80/1.72 % (26875)Termination phase: shuffling
% 2.80/1.72
% 2.80/1.72 % (26875)Memory used [KB]: 1407
% 2.80/1.72 % (26875)Time elapsed: 0.003 s
% 2.80/1.72 % (26875)Instructions burned: 4 (million)
% 2.80/1.72 % (26875)------------------------------
% 2.80/1.72 % (26875)------------------------------
% 2.80/1.73 % (26883)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26535 for (2998ds/30Mi)
% 2.80/1.74 % (26883)Instruction limit reached!
% 2.80/1.74 % (26883)------------------------------
% 2.80/1.74 % (26883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.74 % (26883)Termination reason: Unknown
% 2.80/1.74 % (26883)Termination phase: shuffling
% 2.80/1.74
% 2.80/1.74 % (26883)Memory used [KB]: 1918
% 2.80/1.74 % (26883)Time elapsed: 0.010 s
% 2.80/1.74 % (26883)Instructions burned: 31 (million)
% 2.80/1.74 % (26883)------------------------------
% 2.80/1.74 % (26883)------------------------------
% 2.80/1.75 % (26886)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26535 for (2998ds/127Mi)
% 2.80/1.75 % (26835)Instruction limit reached!
% 2.80/1.75 % (26835)------------------------------
% 2.80/1.75 % (26835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.75 % (26835)Termination reason: Unknown
% 2.80/1.75 % (26835)Termination phase: Saturation
% 2.80/1.75
% 2.80/1.75 % (26835)Memory used [KB]: 8443
% 2.80/1.75 % (26835)Time elapsed: 0.113 s
% 2.80/1.75 % (26835)Instructions burned: 377 (million)
% 2.80/1.75 % (26835)------------------------------
% 2.80/1.75 % (26835)------------------------------
% 2.80/1.76 % (26901)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26535 for (2998ds/100Mi)
% 2.80/1.78 % (26886)Instruction limit reached!
% 2.80/1.78 % (26886)------------------------------
% 2.80/1.78 % (26886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.78 % (26886)Termination reason: Unknown
% 2.80/1.78 % (26886)Termination phase: Saturation
% 2.80/1.78
% 2.80/1.78 % (26886)Memory used [KB]: 6908
% 2.80/1.78 % (26886)Time elapsed: 0.036 s
% 2.80/1.78 % (26886)Instructions burned: 127 (million)
% 2.80/1.78 % (26886)------------------------------
% 2.80/1.78 % (26886)------------------------------
% 2.80/1.79 % (26901)Instruction limit reached!
% 2.80/1.79 % (26901)------------------------------
% 2.80/1.79 % (26901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.79 % (26901)Termination reason: Unknown
% 2.80/1.79 % (26901)Termination phase: Saturation
% 2.80/1.79
% 2.80/1.79 % (26901)Memory used [KB]: 6780
% 2.80/1.79 % (26901)Time elapsed: 0.027 s
% 2.80/1.79 % (26901)Instructions burned: 102 (million)
% 2.80/1.79 % (26901)------------------------------
% 2.80/1.79 % (26901)------------------------------
% 2.80/1.79 % (26913)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_26535 for (2997ds/3Mi)
% 2.80/1.79 % (26913)Instruction limit reached!
% 2.80/1.79 % (26913)------------------------------
% 2.80/1.79 % (26913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.79 % (26913)Termination reason: Unknown
% 2.80/1.79 % (26913)Termination phase: shuffling
% 2.80/1.79
% 2.80/1.79 % (26913)Memory used [KB]: 1407
% 2.80/1.79 % (26913)Time elapsed: 0.002 s
% 2.80/1.79 % (26913)Instructions burned: 4 (million)
% 2.80/1.79 % (26913)------------------------------
% 2.80/1.79 % (26913)------------------------------
% 2.80/1.80 % (26917)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_26535 for (2997ds/20Mi)
% 2.80/1.80 % (26920)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_26535 for (2997ds/86Mi)
% 2.80/1.80 % (26917)Instruction limit reached!
% 2.80/1.80 % (26917)------------------------------
% 2.80/1.80 % (26917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.80 % (26917)Termination reason: Unknown
% 2.80/1.80 % (26917)Termination phase: Property scanning
% 2.80/1.80
% 2.80/1.80 % (26917)Memory used [KB]: 1791
% 2.80/1.80 % (26917)Time elapsed: 0.008 s
% 2.80/1.80 % (26917)Instructions burned: 21 (million)
% 2.80/1.80 % (26917)------------------------------
% 2.80/1.80 % (26917)------------------------------
% 2.80/1.81 % (26924)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_26535 for (2997ds/107Mi)
% 2.80/1.83 % (26920)Instruction limit reached!
% 2.80/1.83 % (26920)------------------------------
% 2.80/1.83 % (26920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.83 % (26920)Termination reason: Unknown
% 2.80/1.83 % (26920)Termination phase: Property scanning
% 2.80/1.83
% 2.80/1.83 % (26920)Memory used [KB]: 2302
% 2.80/1.83 % (26920)Time elapsed: 0.026 s
% 2.80/1.83 % (26920)Instructions burned: 88 (million)
% 2.80/1.83 % (26920)------------------------------
% 2.80/1.83 % (26920)------------------------------
% 2.80/1.83 % (26818)Instruction limit reached!
% 2.80/1.83 % (26818)------------------------------
% 2.80/1.83 % (26818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.83 % (26818)Termination reason: Unknown
% 2.80/1.83 % (26818)Termination phase: Saturation
% 2.80/1.83
% 2.80/1.83 % (26818)Memory used [KB]: 9850
% 2.80/1.83 % (26818)Time elapsed: 0.223 s
% 2.80/1.83 % (26818)Instructions burned: 712 (million)
% 2.80/1.83 % (26818)------------------------------
% 2.80/1.83 % (26818)------------------------------
% 2.80/1.84 % (26933)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_26535 for (2997ds/39Mi)
% 2.80/1.84 % (26795)Instruction limit reached!
% 2.80/1.84 % (26795)------------------------------
% 2.80/1.84 % (26795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.84 % (26795)Termination reason: Unknown
% 2.80/1.84 % (26795)Termination phase: Saturation
% 2.80/1.84
% 2.80/1.84 % (26795)Memory used [KB]: 11513
% 2.80/1.84 % (26795)Time elapsed: 0.261 s
% 2.80/1.84 % (26795)Instructions burned: 1043 (million)
% 2.80/1.84 % (26795)------------------------------
% 2.80/1.84 % (26795)------------------------------
% 2.80/1.84 % (26836)Instruction limit reached!
% 2.80/1.84 % (26836)------------------------------
% 2.80/1.84 % (26836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.84 % (26836)Termination reason: Unknown
% 2.80/1.84 % (26836)Termination phase: Saturation
% 2.80/1.84
% 2.80/1.84 % (26836)Memory used [KB]: 7291
% 2.80/1.84 % (26836)Time elapsed: 0.200 s
% 2.80/1.84 % (26836)Instructions burned: 780 (million)
% 2.80/1.84 % (26836)------------------------------
% 2.80/1.84 % (26836)------------------------------
% 2.80/1.84 % (26924)Instruction limit reached!
% 2.80/1.84 % (26924)------------------------------
% 2.80/1.84 % (26924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.84 % (26924)Termination reason: Unknown
% 2.80/1.84 % (26924)Termination phase: Property scanning
% 2.80/1.84
% 2.80/1.84 % (26924)Memory used [KB]: 2430
% 2.80/1.84 % (26924)Time elapsed: 0.029 s
% 2.80/1.84 % (26924)Instructions burned: 107 (million)
% 2.80/1.84 % (26924)------------------------------
% 2.80/1.84 % (26924)------------------------------
% 2.80/1.84 % (26937)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_26535 for (2997ds/448Mi)
% 2.80/1.85 % (26939)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_26535 for (2997ds/46Mi)
% 2.80/1.85 % (26940)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_26535 for (2997ds/98Mi)
% 2.80/1.85 % (26933)Instruction limit reached!
% 2.80/1.85 % (26933)------------------------------
% 2.80/1.85 % (26933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.85 % (26933)Termination reason: Unknown
% 2.80/1.85 % (26933)Termination phase: Property scanning
% 2.80/1.85
% 2.80/1.85 % (26933)Memory used [KB]: 2174
% 2.80/1.85 % (26933)Time elapsed: 0.012 s
% 2.80/1.85 % (26933)Instructions burned: 39 (million)
% 2.80/1.85 % (26933)------------------------------
% 2.80/1.85 % (26933)------------------------------
% 2.80/1.85 % (26942)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_26535 for (2997ds/507Mi)
% 2.80/1.86 % (26948)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_26535 for (2996ds/149Mi)
% 2.80/1.86 % (26939)Instruction limit reached!
% 2.80/1.86 % (26939)------------------------------
% 2.80/1.86 % (26939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.86 % (26939)Termination reason: Unknown
% 2.80/1.86 % (26939)Termination phase: Property scanning
% 2.80/1.86
% 2.80/1.86 % (26939)Memory used [KB]: 1918
% 2.80/1.86 % (26939)Time elapsed: 0.014 s
% 2.80/1.86 % (26939)Instructions burned: 49 (million)
% 2.80/1.86 % (26939)------------------------------
% 2.80/1.86 % (26939)------------------------------
% 2.80/1.87 % (26955)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26535 for (2996ds/39Mi)
% 2.80/1.87 % (26940)Instruction limit reached!
% 2.80/1.87 % (26940)------------------------------
% 2.80/1.87 % (26940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.87 % (26940)Termination reason: Unknown
% 2.80/1.87 % (26940)Termination phase: Property scanning
% 2.80/1.87
% 2.80/1.87 % (26940)Memory used [KB]: 2302
% 2.80/1.87 % (26940)Time elapsed: 0.026 s
% 2.80/1.87 % (26940)Instructions burned: 99 (million)
% 2.80/1.87 % (26940)------------------------------
% 2.80/1.87 % (26940)------------------------------
% 2.80/1.88 % (26955)Instruction limit reached!
% 2.80/1.88 % (26955)------------------------------
% 2.80/1.88 % (26955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.88 % (26955)Termination reason: Unknown
% 2.80/1.88 % (26955)Termination phase: Property scanning
% 2.80/1.88
% 2.80/1.88 % (26955)Memory used [KB]: 1918
% 2.80/1.88 % (26955)Time elapsed: 0.012 s
% 2.80/1.88 % (26955)Instructions burned: 42 (million)
% 2.80/1.88 % (26955)------------------------------
% 2.80/1.88 % (26955)------------------------------
% 2.80/1.88 % (26959)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_26535 for (2996ds/6Mi)
% 2.80/1.89 % (26959)Instruction limit reached!
% 2.80/1.89 % (26959)------------------------------
% 2.80/1.89 % (26959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.89 % (26959)Termination reason: Unknown
% 2.80/1.89 % (26959)Termination phase: shuffling
% 2.80/1.89
% 2.80/1.89 % (26959)Memory used [KB]: 1407
% 2.80/1.89 % (26959)Time elapsed: 0.003 s
% 2.80/1.89 % (26959)Instructions burned: 7 (million)
% 2.80/1.89 % (26959)------------------------------
% 2.80/1.89 % (26959)------------------------------
% 2.80/1.89 % (26962)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_26535 for (2996ds/1087Mi)
% 2.80/1.89 % (26964)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26535 for (2996ds/47Mi)
% 2.80/1.90 % (26822)Instruction limit reached!
% 2.80/1.90 % (26822)------------------------------
% 2.80/1.90 % (26822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.90 % (26822)Termination reason: Unknown
% 2.80/1.90 % (26822)Termination phase: Saturation
% 2.80/1.90
% 2.80/1.90 % (26822)Memory used [KB]: 10362
% 2.80/1.90 % (26822)Time elapsed: 0.285 s
% 2.80/1.90 % (26822)Instructions burned: 903 (million)
% 2.80/1.90 % (26822)------------------------------
% 2.80/1.90 % (26822)------------------------------
% 2.80/1.90 % (26948)Instruction limit reached!
% 2.80/1.90 % (26948)------------------------------
% 2.80/1.90 % (26948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.90 % (26948)Termination reason: Unknown
% 2.80/1.90 % (26948)Termination phase: Saturation
% 2.80/1.90
% 2.80/1.90 % (26948)Memory used [KB]: 7419
% 2.80/1.90 % (26948)Time elapsed: 0.044 s
% 2.80/1.90 % (26948)Instructions burned: 150 (million)
% 2.80/1.90 % (26948)------------------------------
% 2.80/1.90 % (26948)------------------------------
% 2.80/1.91 % (26964)Instruction limit reached!
% 2.80/1.91 % (26964)------------------------------
% 2.80/1.91 % (26964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.91 % (26964)Termination reason: Unknown
% 2.80/1.91 % (26964)Termination phase: Property scanning
% 2.80/1.91
% 2.80/1.91 % (26964)Memory used [KB]: 1918
% 2.80/1.91 % (26964)Time elapsed: 0.014 s
% 2.80/1.91 % (26964)Instructions burned: 49 (million)
% 2.80/1.91 % (26964)------------------------------
% 2.80/1.91 % (26964)------------------------------
% 2.80/1.91 % (26968)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_26535 for (2996ds/44Mi)
% 2.80/1.91 % (26969)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_26535 for (2996ds/432Mi)
% 2.80/1.92 % (26974)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26535 for (2996ds/62Mi)
% 2.80/1.92 % (26968)Instruction limit reached!
% 2.80/1.92 % (26968)------------------------------
% 2.80/1.92 % (26968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.92 % (26968)Termination reason: Unknown
% 2.80/1.92 % (26968)Termination phase: Property scanning
% 2.80/1.92
% 2.80/1.92 % (26968)Memory used [KB]: 2174
% 2.80/1.92 % (26968)Time elapsed: 0.013 s
% 2.80/1.92 % (26968)Instructions burned: 44 (million)
% 2.80/1.92 % (26968)------------------------------
% 2.80/1.92 % (26968)------------------------------
% 2.80/1.93 % (26981)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_26535 for (2996ds/31Mi)
% 2.80/1.93 % (26974)Instruction limit reached!
% 2.80/1.93 % (26974)------------------------------
% 2.80/1.93 % (26974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.93 % (26974)Termination reason: Unknown
% 2.80/1.93 % (26974)Termination phase: Property scanning
% 2.80/1.93
% 2.80/1.93 % (26974)Memory used [KB]: 2174
% 2.80/1.93 % (26974)Time elapsed: 0.018 s
% 2.80/1.93 % (26974)Instructions burned: 65 (million)
% 2.80/1.93 % (26974)------------------------------
% 2.80/1.93 % (26974)------------------------------
% 2.80/1.94 % (26981)Instruction limit reached!
% 2.80/1.94 % (26981)------------------------------
% 2.80/1.94 % (26981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.94 % (26981)Termination reason: Unknown
% 2.80/1.94 % (26981)Termination phase: Property scanning
% 2.80/1.94
% 2.80/1.94 % (26981)Memory used [KB]: 1918
% 2.80/1.94 % (26981)Time elapsed: 0.010 s
% 2.80/1.94 % (26981)Instructions burned: 34 (million)
% 2.80/1.94 % (26981)------------------------------
% 2.80/1.94 % (26981)------------------------------
% 2.80/1.94 % (26985)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26535 for (2996ds/96Mi)
% 2.80/1.95 % (26987)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_26535 for (2996ds/453Mi)
% 2.80/1.95 % (26937)Instruction limit reached!
% 2.80/1.95 % (26937)------------------------------
% 2.80/1.95 % (26937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.95 % (26937)Termination reason: Unknown
% 2.80/1.95 % (26937)Termination phase: Saturation
% 2.80/1.95
% 2.80/1.95 % (26937)Memory used [KB]: 7036
% 2.80/1.95 % (26937)Time elapsed: 0.112 s
% 2.80/1.95 % (26937)Instructions burned: 451 (million)
% 2.80/1.95 % (26937)------------------------------
% 2.80/1.95 % (26937)------------------------------
% 2.80/1.96 % (26990)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_26535 for (2995ds/71Mi)
% 2.80/1.97 % (26856)Refutation not found, non-redundant clauses discarded% (26856)------------------------------
% 2.80/1.97 % (26856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.97 % (26856)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.80/1.97
% 2.80/1.97 % (26856)Memory used [KB]: 8571
% 2.80/1.97 % (26856)Time elapsed: 0.287 s
% 2.80/1.97 % (26856)Instructions burned: 865 (million)
% 2.80/1.97 % (26856)------------------------------
% 2.80/1.97 % (26856)------------------------------
% 2.80/1.97 % (26985)Instruction limit reached!
% 2.80/1.97 % (26985)------------------------------
% 2.80/1.97 % (26985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.97 % (26985)Termination reason: Unknown
% 2.80/1.97 % (26985)Termination phase: Property scanning
% 2.80/1.97
% 2.80/1.97 % (26985)Memory used [KB]: 2302
% 2.80/1.97 % (26985)Time elapsed: 0.026 s
% 2.80/1.97 % (26985)Instructions burned: 98 (million)
% 2.80/1.97 % (26985)------------------------------
% 2.80/1.97 % (26985)------------------------------
% 2.80/1.98 % (26999)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26535 for (2995ds/83Mi)
% 2.80/1.98 % (27000)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26535 for (2995ds/11Mi)
% 2.80/1.98 % (26990)Instruction limit reached!
% 2.80/1.98 % (26990)------------------------------
% 2.80/1.98 % (26990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.98 % (26990)Termination reason: Unknown
% 2.80/1.98 % (26990)Termination phase: Function definition elimination
% 2.80/1.98
% 2.80/1.98 % (26990)Memory used [KB]: 2174
% 2.80/1.98 % (26990)Time elapsed: 0.020 s
% 2.80/1.98 % (26990)Instructions burned: 73 (million)
% 2.80/1.98 % (26990)------------------------------
% 2.80/1.98 % (26990)------------------------------
% 2.80/1.98 % (27000)Instruction limit reached!
% 2.80/1.98 % (27000)------------------------------
% 2.80/1.98 % (27000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.98 % (27000)Termination reason: Unknown
% 2.80/1.98 % (27000)Termination phase: shuffling
% 2.80/1.98
% 2.80/1.98 % (27000)Memory used [KB]: 1535
% 2.80/1.98 % (27000)Time elapsed: 0.004 s
% 2.80/1.98 % (27000)Instructions burned: 11 (million)
% 2.80/1.98 % (27000)------------------------------
% 2.80/1.98 % (27000)------------------------------
% 2.80/1.99 % (27010)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_26535 for (2995ds/41Mi)
% 2.80/1.99 % (27011)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26535 for (2995ds/6Mi)
% 2.80/1.99 % (27011)Instruction limit reached!
% 2.80/1.99 % (27011)------------------------------
% 2.80/1.99 % (27011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.99 % (27011)Termination reason: Unknown
% 2.80/1.99 % (27011)Termination phase: shuffling
% 2.80/1.99
% 2.80/1.99 % (27011)Memory used [KB]: 1407
% 2.80/1.99 % (27011)Time elapsed: 0.004 s
% 2.80/1.99 % (27011)Instructions burned: 8 (million)
% 2.80/1.99 % (27011)------------------------------
% 2.80/1.99 % (27011)------------------------------
% 2.80/2.00 % (26942)Instruction limit reached!
% 2.80/2.00 % (26942)------------------------------
% 2.80/2.00 % (26942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/2.00 % (26942)Termination reason: Unknown
% 2.80/2.00 % (26942)Termination phase: Saturation
% 2.80/2.00
% 2.80/2.00 % (26942)Memory used [KB]: 7931
% 2.80/2.00 % (26942)Time elapsed: 0.173 s
% 2.80/2.00 % (26942)Instructions burned: 510 (million)
% 2.80/2.00 % (26942)------------------------------
% 2.80/2.00 % (26942)------------------------------
% 2.80/2.00 % (27010)Instruction limit reached!
% 2.80/2.00 % (27010)------------------------------
% 2.80/2.00 % (27010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/2.00 % (27010)Termination reason: Unknown
% 2.80/2.00 % (27010)Termination phase: Property scanning
% 2.80/2.00
% 2.80/2.00 % (27010)Memory used [KB]: 2174
% 2.80/2.00 % (27010)Time elapsed: 0.012 s
% 2.80/2.00 % (27010)Instructions burned: 42 (million)
% 2.80/2.00 % (27010)------------------------------
% 2.80/2.00 % (27010)------------------------------
% 2.80/2.00 % (26999)Instruction limit reached!
% 2.80/2.00 % (26999)------------------------------
% 2.80/2.00 % (26999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/2.00 % (26999)Termination reason: Unknown
% 2.80/2.00 % (26999)Termination phase: Property scanning
% 2.80/2.00
% 2.80/2.00 % (26999)Memory used [KB]: 2174
% 2.80/2.00 % (26999)Time elapsed: 0.026 s
% 2.80/2.00 % (26999)Instructions burned: 83 (million)
% 2.80/2.00 % (26999)------------------------------
% 2.80/2.00 % (26999)------------------------------
% 2.80/2.00 % (27020)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26535 for (2995ds/150Mi)
% 2.80/2.01 % (27024)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26535 for (2995ds/343Mi)
% 2.80/2.01 % (27026)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_26535 for (2995ds/109Mi)
% 6.01/2.02 % (27028)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_26535 for (2995ds/253Mi)
% 6.01/2.02 % (26969)Instruction limit reached!
% 6.01/2.02 % (26969)------------------------------
% 6.01/2.02 % (26969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.02 % (26969)Termination reason: Unknown
% 6.01/2.02 % (26969)Termination phase: Saturation
% 6.01/2.02
% 6.01/2.02 % (26969)Memory used [KB]: 3326
% 6.01/2.02 % (26969)Time elapsed: 0.113 s
% 6.01/2.02 % (26969)Instructions burned: 432 (million)
% 6.01/2.02 % (26969)------------------------------
% 6.01/2.02 % (26969)------------------------------
% 6.01/2.03 % (27035)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26535 for (2995ds/140Mi)
% 6.01/2.04 % (27026)Instruction limit reached!
% 6.01/2.04 % (27026)------------------------------
% 6.01/2.04 % (27026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.04 % (27026)Termination reason: Unknown
% 6.01/2.04 % (27026)Termination phase: Property scanning
% 6.01/2.04
% 6.01/2.04 % (27026)Memory used [KB]: 2302
% 6.01/2.04 % (27026)Time elapsed: 0.029 s
% 6.01/2.04 % (27026)Instructions burned: 109 (million)
% 6.01/2.04 % (27026)------------------------------
% 6.01/2.04 % (27026)------------------------------
% 6.01/2.05 % (27020)Instruction limit reached!
% 6.01/2.05 % (27020)------------------------------
% 6.01/2.05 % (27020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.05 % (27020)Termination reason: Unknown
% 6.01/2.05 % (27020)Termination phase: Saturation
% 6.01/2.05
% 6.01/2.05 % (27020)Memory used [KB]: 8315
% 6.01/2.05 % (27020)Time elapsed: 0.044 s
% 6.01/2.05 % (27020)Instructions burned: 150 (million)
% 6.01/2.05 % (27020)------------------------------
% 6.01/2.05 % (27020)------------------------------
% 6.01/2.05 % (27040)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_26535 for (2995ds/614Mi)
% 6.01/2.06 % (27041)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_26535 for (2995ds/202Mi)
% 6.01/2.06 % (26987)Instruction limit reached!
% 6.01/2.06 % (26987)------------------------------
% 6.01/2.06 % (26987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.06 % (26987)Termination reason: Unknown
% 6.01/2.06 % (26987)Termination phase: Saturation
% 6.01/2.06
% 6.01/2.06 % (26987)Memory used [KB]: 7036
% 6.01/2.06 % (26987)Time elapsed: 0.112 s
% 6.01/2.06 % (26987)Instructions burned: 453 (million)
% 6.01/2.06 % (26987)------------------------------
% 6.01/2.06 % (26987)------------------------------
% 6.01/2.07 % (27035)Instruction limit reached!
% 6.01/2.07 % (27035)------------------------------
% 6.01/2.07 % (27035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.07 % (27035)Termination reason: Unknown
% 6.01/2.07 % (27035)Termination phase: Saturation
% 6.01/2.07
% 6.01/2.07 % (27035)Memory used [KB]: 7036
% 6.01/2.07 % (27035)Time elapsed: 0.038 s
% 6.01/2.07 % (27035)Instructions burned: 140 (million)
% 6.01/2.07 % (27035)------------------------------
% 6.01/2.07 % (27035)------------------------------
% 6.01/2.07 % (27042)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_26535 for (2994ds/339Mi)
% 6.01/2.08 % (27043)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_26535 for (2994ds/283Mi)
% 6.01/2.10 % (27024)Instruction limit reached!
% 6.01/2.10 % (27024)------------------------------
% 6.01/2.10 % (27024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.10 % (27024)Termination reason: Unknown
% 6.01/2.10 % (27024)Termination phase: Saturation
% 6.01/2.10
% 6.01/2.10 % (27024)Memory used [KB]: 8059
% 6.01/2.10 % (27024)Time elapsed: 0.095 s
% 6.01/2.10 % (27024)Instructions burned: 346 (million)
% 6.01/2.10 % (27024)------------------------------
% 6.01/2.10 % (27024)------------------------------
% 6.42/2.11 % (27044)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_26535 for (2994ds/134Mi)
% 6.42/2.11 % (27041)Instruction limit reached!
% 6.42/2.11 % (27041)------------------------------
% 6.42/2.11 % (27041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.11 % (27041)Termination reason: Unknown
% 6.42/2.11 % (27041)Termination phase: Saturation
% 6.42/2.11
% 6.42/2.11 % (27041)Memory used [KB]: 4733
% 6.42/2.11 % (27041)Time elapsed: 0.059 s
% 6.42/2.11 % (27041)Instructions burned: 202 (million)
% 6.42/2.11 % (27041)------------------------------
% 6.42/2.11 % (27041)------------------------------
% 6.42/2.12 % (27045)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_26535 for (2994ds/298Mi)
% 6.42/2.14 % (27028)Instruction limit reached!
% 6.42/2.14 % (27028)------------------------------
% 6.42/2.14 % (27028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.14 % (27028)Termination reason: Unknown
% 6.42/2.14 % (27028)Termination phase: Saturation
% 6.42/2.14
% 6.42/2.14 % (27028)Memory used [KB]: 8571
% 6.42/2.14 % (27028)Time elapsed: 0.123 s
% 6.42/2.14 % (27028)Instructions burned: 253 (million)
% 6.42/2.14 % (27028)------------------------------
% 6.42/2.14 % (27028)------------------------------
% 6.42/2.15 % (27044)Instruction limit reached!
% 6.42/2.15 % (27044)------------------------------
% 6.42/2.15 % (27044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.15 % (27044)Termination reason: Unknown
% 6.42/2.15 % (27044)Termination phase: Saturation
% 6.42/2.15
% 6.42/2.15 % (27044)Memory used [KB]: 7036
% 6.42/2.15 % (27044)Time elapsed: 0.036 s
% 6.42/2.15 % (27044)Instructions burned: 136 (million)
% 6.42/2.15 % (27044)------------------------------
% 6.42/2.15 % (27044)------------------------------
% 6.42/2.15 % (27043)Instruction limit reached!
% 6.42/2.15 % (27043)------------------------------
% 6.42/2.15 % (27043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.15 % (27043)Termination reason: Unknown
% 6.42/2.15 % (27043)Termination phase: Saturation
% 6.42/2.15
% 6.42/2.15 % (27043)Memory used [KB]: 6908
% 6.42/2.15 % (27043)Time elapsed: 0.072 s
% 6.42/2.15 % (27043)Instructions burned: 285 (million)
% 6.42/2.15 % (27043)------------------------------
% 6.42/2.15 % (27043)------------------------------
% 6.42/2.15 % (27046)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_26535 for (2994ds/192Mi)
% 6.42/2.16 % (27047)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_26535 for (2994ds/258Mi)
% 6.42/2.16 % (27048)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_26535 for (2994ds/90Mi)
% 6.42/2.16 % (27042)Instruction limit reached!
% 6.42/2.16 % (27042)------------------------------
% 6.42/2.16 % (27042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.16 % (27042)Termination reason: Unknown
% 6.42/2.16 % (27042)Termination phase: Saturation
% 6.42/2.16
% 6.42/2.16 % (27042)Memory used [KB]: 7419
% 6.42/2.16 % (27042)Time elapsed: 0.091 s
% 6.42/2.16 % (27042)Instructions burned: 341 (million)
% 6.42/2.16 % (27042)------------------------------
% 6.42/2.16 % (27042)------------------------------
% 6.42/2.17 % (27049)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_26535 for (2993ds/231Mi)
% 6.42/2.19 % (27048)Instruction limit reached!
% 6.42/2.19 % (27048)------------------------------
% 6.42/2.19 % (27048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.19 % (27048)Termination reason: Unknown
% 6.42/2.19 % (27048)Termination phase: Twee Goal Transformation
% 6.42/2.19
% 6.42/2.19 % (27048)Memory used [KB]: 2558
% 6.42/2.19 % (27048)Time elapsed: 0.026 s
% 6.42/2.19 % (27048)Instructions burned: 93 (million)
% 6.42/2.19 % (27048)------------------------------
% 6.42/2.19 % (27048)------------------------------
% 6.42/2.20 % (27050)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_26535 for (2993ds/458Mi)
% 6.96/2.20 % (27045)Instruction limit reached!
% 6.96/2.20 % (27045)------------------------------
% 6.96/2.20 % (27045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.20 % (27045)Termination reason: Unknown
% 6.96/2.20 % (27045)Termination phase: Saturation
% 6.96/2.20
% 6.96/2.20 % (27045)Memory used [KB]: 6908
% 6.96/2.20 % (27045)Time elapsed: 0.076 s
% 6.96/2.20 % (27045)Instructions burned: 300 (million)
% 6.96/2.20 % (27045)------------------------------
% 6.96/2.20 % (27045)------------------------------
% 6.96/2.21 % (27046)Instruction limit reached!
% 6.96/2.21 % (27046)------------------------------
% 6.96/2.21 % (27046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.21 % (27046)Termination reason: Unknown
% 6.96/2.21 % (27046)Termination phase: Saturation
% 6.96/2.21
% 6.96/2.21 % (27046)Memory used [KB]: 7547
% 6.96/2.21 % (27046)Time elapsed: 0.056 s
% 6.96/2.21 % (27046)Instructions burned: 195 (million)
% 6.96/2.21 % (27046)------------------------------
% 6.96/2.21 % (27046)------------------------------
% 6.96/2.21 % (27051)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_26535 for (2993ds/31Mi)
% 6.96/2.22 % (27051)Instruction limit reached!
% 6.96/2.22 % (27051)------------------------------
% 6.96/2.22 % (27051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.22 % (27051)Termination reason: Unknown
% 6.96/2.22 % (27051)Termination phase: shuffling
% 6.96/2.22
% 6.96/2.22 % (27051)Memory used [KB]: 1918
% 6.96/2.22 % (27051)Time elapsed: 0.010 s
% 6.96/2.22 % (27051)Instructions burned: 32 (million)
% 6.96/2.22 % (27051)------------------------------
% 6.96/2.22 % (27051)------------------------------
% 6.96/2.22 % (27052)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_26535 for (2993ds/297Mi)
% 6.96/2.23 % (27053)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_26535 for (2993ds/987Mi)
% 6.96/2.23 % (27047)Instruction limit reached!
% 6.96/2.23 % (27047)------------------------------
% 6.96/2.23 % (27047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.23 % (27047)Termination reason: Unknown
% 6.96/2.23 % (27047)Termination phase: Saturation
% 6.96/2.23
% 6.96/2.23 % (27047)Memory used [KB]: 7803
% 6.96/2.23 % (27047)Time elapsed: 0.071 s
% 6.96/2.23 % (27047)Instructions burned: 258 (million)
% 6.96/2.23 % (27047)------------------------------
% 6.96/2.23 % (27047)------------------------------
% 6.96/2.23 % (27040)Instruction limit reached!
% 6.96/2.23 % (27040)------------------------------
% 6.96/2.23 % (27040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.23 % (27040)Termination reason: Unknown
% 6.96/2.23 % (27040)Termination phase: Saturation
% 6.96/2.23
% 6.96/2.23 % (27040)Memory used [KB]: 8955
% 6.96/2.23 % (27040)Time elapsed: 0.183 s
% 6.96/2.23 % (27040)Instructions burned: 616 (million)
% 6.96/2.23 % (27040)------------------------------
% 6.96/2.23 % (27040)------------------------------
% 6.96/2.24 % (26962)Instruction limit reached!
% 6.96/2.24 % (26962)------------------------------
% 6.96/2.24 % (26962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.24 % (26962)Termination reason: Unknown
% 6.96/2.24 % (26962)Termination phase: Saturation
% 6.96/2.24
% 6.96/2.24 % (26962)Memory used [KB]: 10490
% 6.96/2.24 % (26962)Time elapsed: 0.346 s
% 6.96/2.24 % (26962)Instructions burned: 1089 (million)
% 6.96/2.24 % (26962)------------------------------
% 6.96/2.24 % (26962)------------------------------
% 6.96/2.24 % (27049)Instruction limit reached!
% 6.96/2.24 % (27049)------------------------------
% 6.96/2.24 % (27049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.24 % (27049)Termination reason: Unknown
% 6.96/2.24 % (27049)Termination phase: Saturation
% 6.96/2.24
% 6.96/2.24 % (27049)Memory used [KB]: 12281
% 6.96/2.24 % (27049)Time elapsed: 0.090 s
% 6.96/2.24 % (27049)Instructions burned: 234 (million)
% 6.96/2.24 % (27049)------------------------------
% 6.96/2.24 % (27049)------------------------------
% 6.96/2.24 % (27054)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_26535 for (2993ds/182Mi)
% 6.96/2.24 % (27055)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_26535 for (2993ds/182Mi)
% 6.96/2.25 % (27056)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_26535 for (2993ds/154Mi)
% 6.96/2.25 % (27057)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_26535 for (2993ds/79Mi)
% 6.96/2.27 % (27057)Instruction limit reached!
% 6.96/2.27 % (27057)------------------------------
% 6.96/2.27 % (27057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.27 % (27057)Termination reason: Unknown
% 6.96/2.27 % (27057)Termination phase: Property scanning
% 6.96/2.27
% 6.96/2.27 % (27057)Memory used [KB]: 2302
% 6.96/2.27 % (27057)Time elapsed: 0.022 s
% 6.96/2.27 % (27057)Instructions burned: 81 (million)
% 6.96/2.27 % (27057)------------------------------
% 6.96/2.27 % (27057)------------------------------
% 6.96/2.28 % (27058)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_26535 for (2992ds/216Mi)
% 6.96/2.28 % (27056)Instruction limit reached!
% 6.96/2.28 % (27056)------------------------------
% 6.96/2.28 % (27056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.28 % (27056)Termination reason: Unknown
% 6.96/2.28 % (27056)Termination phase: Saturation
% 6.96/2.28
% 6.96/2.28 % (27056)Memory used [KB]: 6908
% 6.96/2.28 % (27056)Time elapsed: 0.040 s
% 6.96/2.28 % (27056)Instructions burned: 155 (million)
% 6.96/2.28 % (27056)------------------------------
% 6.96/2.28 % (27056)------------------------------
% 6.96/2.29 % (27054)Instruction limit reached!
% 6.96/2.29 % (27054)------------------------------
% 6.96/2.29 % (27054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.29 % (27054)Termination reason: Unknown
% 6.96/2.29 % (27054)Termination phase: Saturation
% 6.96/2.29
% 6.96/2.29 % (27054)Memory used [KB]: 7419
% 6.96/2.29 % (27054)Time elapsed: 0.049 s
% 6.96/2.29 % (27054)Instructions burned: 182 (million)
% 6.96/2.29 % (27054)------------------------------
% 6.96/2.29 % (27054)------------------------------
% 6.96/2.29 % (27059)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_26535 for (2992ds/114Mi)
% 6.96/2.29 % (27055)Instruction limit reached!
% 6.96/2.29 % (27055)------------------------------
% 6.96/2.29 % (27055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.29 % (27055)Termination reason: Unknown
% 6.96/2.29 % (27055)Termination phase: Saturation
% 6.96/2.29
% 6.96/2.29 % (27055)Memory used [KB]: 10106
% 6.96/2.29 % (27055)Time elapsed: 0.054 s
% 6.96/2.29 % (27055)Instructions burned: 183 (million)
% 6.96/2.29 % (27055)------------------------------
% 6.96/2.29 % (27055)------------------------------
% 6.96/2.29 % (27060)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_26535 for (2992ds/922Mi)
% 7.74/2.30 % (27052)Instruction limit reached!
% 7.74/2.30 % (27052)------------------------------
% 7.74/2.30 % (27052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.30 % (27052)Termination reason: Unknown
% 7.74/2.30 % (27052)Termination phase: Saturation
% 7.74/2.30
% 7.74/2.30 % (27052)Memory used [KB]: 7164
% 7.74/2.30 % (27052)Time elapsed: 0.081 s
% 7.74/2.30 % (27052)Instructions burned: 299 (million)
% 7.74/2.30 % (27052)------------------------------
% 7.74/2.30 % (27052)------------------------------
% 7.74/2.30 % (27061)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_26535 for (2992ds/182Mi)
% 7.74/2.31 % (27062)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_26535 for (2992ds/164Mi)
% 7.74/2.32 % (27059)Instruction limit reached!
% 7.74/2.32 % (27059)------------------------------
% 7.74/2.32 % (27059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.32 % (27059)Termination reason: Unknown
% 7.74/2.32 % (27059)Termination phase: Saturation
% 7.74/2.32
% 7.74/2.32 % (27059)Memory used [KB]: 6908
% 7.74/2.32 % (27059)Time elapsed: 0.030 s
% 7.74/2.32 % (27059)Instructions burned: 114 (million)
% 7.74/2.32 % (27059)------------------------------
% 7.74/2.32 % (27059)------------------------------
% 7.74/2.33 % (27050)Instruction limit reached!
% 7.74/2.33 % (27050)------------------------------
% 7.74/2.33 % (27050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.33 % (27050)Termination reason: Unknown
% 7.74/2.33 % (27050)Termination phase: Saturation
% 7.74/2.33
% 7.74/2.33 % (27050)Memory used [KB]: 8571
% 7.74/2.33 % (27050)Time elapsed: 0.132 s
% 7.74/2.33 % (27050)Instructions burned: 459 (million)
% 7.74/2.33 % (27050)------------------------------
% 7.74/2.33 % (27050)------------------------------
% 7.74/2.33 % (27058)Instruction limit reached!
% 7.74/2.33 % (27058)------------------------------
% 7.74/2.33 % (27058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.33 % (27058)Termination reason: Unknown
% 7.74/2.33 % (27058)Termination phase: Saturation
% 7.74/2.33
% 7.74/2.33 % (27058)Memory used [KB]: 6908
% 7.74/2.33 % (27058)Time elapsed: 0.055 s
% 7.74/2.33 % (27058)Instructions burned: 218 (million)
% 7.74/2.33 % (27058)------------------------------
% 7.74/2.33 % (27058)------------------------------
% 7.74/2.33 % (27063)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_26535 for (2992ds/50Mi)
% 7.74/2.34 % (27064)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_26535 for (2992ds/368Mi)
% 7.74/2.34 % (27065)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_26535 for (2992ds/1021Mi)
% 7.74/2.35 % (27063)Instruction limit reached!
% 7.74/2.35 % (27063)------------------------------
% 7.74/2.35 % (27063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.35 % (27063)Termination reason: Unknown
% 7.74/2.35 % (27063)Termination phase: shuffling
% 7.74/2.35
% 7.74/2.35 % (27063)Memory used [KB]: 2174
% 7.74/2.35 % (27063)Time elapsed: 0.015 s
% 7.74/2.35 % (27063)Instructions burned: 53 (million)
% 7.74/2.35 % (27063)------------------------------
% 7.74/2.35 % (27063)------------------------------
% 7.74/2.35 % (27061)Instruction limit reached!
% 7.74/2.35 % (27061)------------------------------
% 7.74/2.35 % (27061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.35 % (27061)Termination reason: Unknown
% 7.74/2.35 % (27061)Termination phase: Saturation
% 7.74/2.35
% 7.74/2.35 % (27061)Memory used [KB]: 6908
% 7.74/2.35 % (27061)Time elapsed: 0.047 s
% 7.74/2.35 % (27061)Instructions burned: 185 (million)
% 7.74/2.35 % (27061)------------------------------
% 7.74/2.35 % (27061)------------------------------
% 7.74/2.35 % (27062)Instruction limit reached!
% 7.74/2.35 % (27062)------------------------------
% 7.74/2.35 % (27062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.35 % (27062)Termination reason: Unknown
% 7.74/2.35 % (27062)Termination phase: Saturation
% 7.74/2.35
% 7.74/2.35 % (27062)Memory used [KB]: 2558
% 7.74/2.35 % (27062)Time elapsed: 0.047 s
% 7.74/2.35 % (27062)Instructions burned: 166 (million)
% 7.74/2.35 % (27062)------------------------------
% 7.74/2.35 % (27062)------------------------------
% 7.74/2.36 % (27066)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_26535 for (2991ds/267Mi)
% 7.74/2.36 % (27067)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_26535 for (2991ds/204Mi)
% 7.74/2.37 % (27068)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_26535 for (2991ds/26Mi)
% 7.74/2.37 % (27068)Instruction limit reached!
% 7.74/2.37 % (27068)------------------------------
% 7.74/2.37 % (27068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.74/2.37 % (27068)Termination reason: Unknown
% 7.74/2.37 % (27068)Termination phase: shuffling
% 7.74/2.37
% 7.74/2.37 % (27068)Memory used [KB]: 1918
% 7.74/2.37 % (27068)Time elapsed: 0.009 s
% 7.74/2.37 % (27068)Instructions burned: 28 (million)
% 7.74/2.37 % (27068)------------------------------
% 7.74/2.37 % (27068)------------------------------
% 7.74/2.38 % (27069)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_26535 for (2991ds/53Mi)
% 8.24/2.40 % (27069)Instruction limit reached!
% 8.24/2.40 % (27069)------------------------------
% 8.24/2.40 % (27069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.40 % (27069)Termination reason: Unknown
% 8.24/2.40 % (27069)Termination phase: Clausification
% 8.24/2.40
% 8.24/2.40 % (27069)Memory used [KB]: 2174
% 8.24/2.40 % (27069)Time elapsed: 0.017 s
% 8.24/2.40 % (27069)Instructions burned: 54 (million)
% 8.24/2.40 % (27069)------------------------------
% 8.24/2.40 % (27069)------------------------------
% 8.24/2.41 % (27070)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_26535 for (2991ds/4436Mi)
% 8.24/2.41 % (27067)Instruction limit reached!
% 8.24/2.41 % (27067)------------------------------
% 8.24/2.41 % (27067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.41 % (27067)Termination reason: Unknown
% 8.24/2.41 % (27067)Termination phase: Saturation
% 8.24/2.41
% 8.24/2.41 % (27067)Memory used [KB]: 7547
% 8.24/2.41 % (27067)Time elapsed: 0.055 s
% 8.24/2.41 % (27067)Instructions burned: 205 (million)
% 8.24/2.41 % (27067)------------------------------
% 8.24/2.41 % (27067)------------------------------
% 8.24/2.42 % (27071)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_26535 for (2991ds/1539Mi)
% 8.24/2.42 % (27066)Instruction limit reached!
% 8.24/2.42 % (27066)------------------------------
% 8.24/2.42 % (27066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.42 % (27066)Termination reason: Unknown
% 8.24/2.42 % (27066)Termination phase: Saturation
% 8.24/2.42
% 8.24/2.42 % (27066)Memory used [KB]: 6908
% 8.24/2.42 % (27066)Time elapsed: 0.069 s
% 8.24/2.42 % (27066)Instructions burned: 270 (million)
% 8.24/2.42 % (27066)------------------------------
% 8.24/2.42 % (27066)------------------------------
% 8.24/2.43 % (27072)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_26535 for (2991ds/408Mi)
% 8.24/2.44 % (27064)Instruction limit reached!
% 8.24/2.44 % (27064)------------------------------
% 8.24/2.44 % (27064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.44 % (27064)Termination reason: Unknown
% 8.24/2.44 % (27064)Termination phase: Saturation
% 8.24/2.44
% 8.24/2.44 % (27064)Memory used [KB]: 8315
% 8.24/2.44 % (27064)Time elapsed: 0.108 s
% 8.24/2.44 % (27064)Instructions burned: 369 (million)
% 8.24/2.44 % (27064)------------------------------
% 8.24/2.44 % (27064)------------------------------
% 8.24/2.45 % (27073)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_26535 for (2991ds/5205Mi)
% 8.24/2.47 % (27053)Instruction limit reached!
% 8.24/2.47 % (27053)------------------------------
% 8.24/2.47 % (27053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.47 % (27053)Termination reason: Unknown
% 8.24/2.47 % (27053)Termination phase: Saturation
% 8.24/2.47
% 8.24/2.47 % (27053)Memory used [KB]: 11641
% 8.24/2.47 % (27053)Time elapsed: 0.247 s
% 8.24/2.47 % (27053)Instructions burned: 988 (million)
% 8.24/2.47 % (27053)------------------------------
% 8.24/2.47 % (27053)------------------------------
% 8.24/2.48 % (27074)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_26535 for (2990ds/1913Mi)
% 8.77/2.56 % (27072)Instruction limit reached!
% 8.77/2.56 % (27072)------------------------------
% 8.77/2.56 % (27072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.56 % (27072)Termination reason: Unknown
% 8.77/2.56 % (27072)Termination phase: Saturation
% 8.77/2.56
% 8.77/2.56 % (27072)Memory used [KB]: 9850
% 8.77/2.56 % (27072)Time elapsed: 0.128 s
% 8.77/2.56 % (27072)Instructions burned: 409 (million)
% 8.77/2.56 % (27072)------------------------------
% 8.77/2.56 % (27072)------------------------------
% 8.77/2.57 % (27075)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_26535 for (2989ds/4350Mi)
% 8.77/2.58 % (27060)Instruction limit reached!
% 8.77/2.58 % (27060)------------------------------
% 8.77/2.58 % (27060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.58 % (27060)Termination reason: Unknown
% 8.77/2.58 % (27060)Termination phase: Saturation
% 8.77/2.58
% 8.77/2.58 % (27060)Memory used [KB]: 10362
% 8.77/2.58 % (27060)Time elapsed: 0.287 s
% 8.77/2.58 % (27060)Instructions burned: 923 (million)
% 8.77/2.58 % (27060)------------------------------
% 8.77/2.58 % (27060)------------------------------
% 8.77/2.59 % (27076)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_26535 for (2989ds/68Mi)
% 9.21/2.61 % (27076)Instruction limit reached!
% 9.21/2.61 % (27076)------------------------------
% 9.21/2.61 % (27076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.61 % (27076)Termination reason: Unknown
% 9.21/2.61 % (27076)Termination phase: Property scanning
% 9.21/2.61
% 9.21/2.61 % (27076)Memory used [KB]: 2174
% 9.21/2.61 % (27076)Time elapsed: 0.019 s
% 9.21/2.61 % (27076)Instructions burned: 70 (million)
% 9.21/2.61 % (27076)------------------------------
% 9.21/2.61 % (27076)------------------------------
% 9.21/2.62 % (27077)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_26535 for (2989ds/358Mi)
% 9.21/2.66 % (27065)Instruction limit reached!
% 9.21/2.66 % (27065)------------------------------
% 9.21/2.66 % (27065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.66 % (27065)Termination reason: Unknown
% 9.21/2.66 % (27065)Termination phase: Saturation
% 9.21/2.66
% 9.21/2.66 % (27065)Memory used [KB]: 10874
% 9.21/2.66 % (27065)Time elapsed: 0.322 s
% 9.21/2.66 % (27065)Instructions burned: 1023 (million)
% 9.21/2.66 % (27065)------------------------------
% 9.21/2.66 % (27065)------------------------------
% 9.21/2.67 % (27078)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_26535 for (2988ds/31Mi)
% 9.21/2.68 % (27078)Instruction limit reached!
% 9.21/2.68 % (27078)------------------------------
% 9.21/2.68 % (27078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.68 % (27078)Termination reason: Unknown
% 9.21/2.68 % (27078)Termination phase: Property scanning
% 9.21/2.68
% 9.21/2.68 % (27078)Memory used [KB]: 2046
% 9.21/2.68 % (27078)Time elapsed: 0.010 s
% 9.21/2.68 % (27078)Instructions burned: 33 (million)
% 9.21/2.68 % (27078)------------------------------
% 9.21/2.68 % (27078)------------------------------
% 9.21/2.69 % (27079)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_26535 for (2988ds/279Mi)
% 9.59/2.72 % (27077)Instruction limit reached!
% 9.59/2.72 % (27077)------------------------------
% 9.59/2.72 % (27077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.72 % (27077)Termination reason: Unknown
% 9.59/2.72 % (27077)Termination phase: Saturation
% 9.59/2.72
% 9.59/2.72 % (27077)Memory used [KB]: 8187
% 9.59/2.72 % (27077)Time elapsed: 0.103 s
% 9.59/2.72 % (27077)Instructions burned: 358 (million)
% 9.59/2.72 % (27077)------------------------------
% 9.59/2.72 % (27077)------------------------------
% 9.59/2.73 % (27080)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_26535 for (2988ds/258Mi)
% 9.59/2.76 % (27079)Instruction limit reached!
% 9.59/2.76 % (27079)------------------------------
% 9.59/2.76 % (27079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.76 % (27079)Termination reason: Unknown
% 9.59/2.76 % (27079)Termination phase: Saturation
% 9.59/2.76
% 9.59/2.76 % (27079)Memory used [KB]: 6908
% 9.59/2.76 % (27079)Time elapsed: 0.072 s
% 9.59/2.76 % (27079)Instructions burned: 282 (million)
% 9.59/2.76 % (27079)------------------------------
% 9.59/2.76 % (27079)------------------------------
% 9.59/2.77 % (27081)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_26535 for (2987ds/26Mi)
% 9.59/2.78 % (27081)Instruction limit reached!
% 9.59/2.78 % (27081)------------------------------
% 9.59/2.78 % (27081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.78 % (27081)Termination reason: Unknown
% 9.59/2.78 % (27081)Termination phase: shuffling
% 9.59/2.78
% 9.59/2.78 % (27081)Memory used [KB]: 1918
% 9.59/2.78 % (27081)Time elapsed: 0.008 s
% 9.59/2.78 % (27081)Instructions burned: 27 (million)
% 9.59/2.78 % (27081)------------------------------
% 9.59/2.78 % (27081)------------------------------
% 9.59/2.79 % (27082)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_26535 for (2987ds/995Mi)
% 9.80/2.80 % (27080)Instruction limit reached!
% 9.80/2.80 % (27080)------------------------------
% 9.80/2.80 % (27080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.80 % (27080)Termination reason: Unknown
% 9.80/2.80 % (27080)Termination phase: Saturation
% 9.80/2.80
% 9.80/2.80 % (27080)Memory used [KB]: 8187
% 9.80/2.80 % (27080)Time elapsed: 0.070 s
% 9.80/2.80 % (27080)Instructions burned: 259 (million)
% 9.80/2.80 % (27080)------------------------------
% 9.80/2.80 % (27080)------------------------------
% 9.80/2.81 % (27083)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_26535 for (2987ds/373Mi)
% 9.87/2.90 % (27071)Instruction limit reached!
% 9.87/2.90 % (27071)------------------------------
% 9.87/2.90 % (27071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.90 % (27071)Termination reason: Unknown
% 9.87/2.90 % (27071)Termination phase: Saturation
% 9.87/2.90
% 9.87/2.90 % (27071)Memory used [KB]: 10106
% 9.87/2.90 % (27071)Time elapsed: 0.480 s
% 9.87/2.90 % (27071)Instructions burned: 1541 (million)
% 9.87/2.90 % (27071)------------------------------
% 9.87/2.90 % (27071)------------------------------
% 9.87/2.91 % (27084)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_26535 for (2986ds/253Mi)
% 9.87/2.92 % (27083)Instruction limit reached!
% 9.87/2.92 % (27083)------------------------------
% 9.87/2.92 % (27083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.92 % (27083)Termination reason: Unknown
% 9.87/2.92 % (27083)Termination phase: Saturation
% 9.87/2.92
% 9.87/2.92 % (27083)Memory used [KB]: 8187
% 9.87/2.92 % (27083)Time elapsed: 0.109 s
% 9.87/2.92 % (27083)Instructions burned: 374 (million)
% 9.87/2.92 % (27083)------------------------------
% 9.87/2.92 % (27083)------------------------------
% 9.87/2.93 % (27085)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_26535 for (2986ds/832Mi)
% 9.87/2.98 % (27084)Instruction limit reached!
% 9.87/2.98 % (27084)------------------------------
% 9.87/2.98 % (27084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.98 % (27084)Termination reason: Unknown
% 9.87/2.98 % (27084)Termination phase: Saturation
% 9.87/2.98
% 9.87/2.98 % (27084)Memory used [KB]: 7164
% 9.87/2.98 % (27084)Time elapsed: 0.066 s
% 9.87/2.98 % (27084)Instructions burned: 253 (million)
% 9.87/2.98 % (27084)------------------------------
% 9.87/2.98 % (27084)------------------------------
% 9.87/2.99 % (27086)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_26535 for (2985ds/668Mi)
% 13.11/3.03 % (27082)Instruction limit reached!
% 13.11/3.03 % (27082)------------------------------
% 13.11/3.03 % (27082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.03 % (27082)Termination reason: Unknown
% 13.11/3.03 % (27082)Termination phase: Saturation
% 13.11/3.03
% 13.11/3.03 % (27082)Memory used [KB]: 11129
% 13.11/3.03 % (27082)Time elapsed: 0.245 s
% 13.11/3.03 % (27082)Instructions burned: 998 (million)
% 13.11/3.03 % (27082)------------------------------
% 13.11/3.03 % (27082)------------------------------
% 13.11/3.04 % (27087)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_26535 for (2985ds/40Mi)
% 13.11/3.05 % (27087)Instruction limit reached!
% 13.11/3.05 % (27087)------------------------------
% 13.11/3.05 % (27087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.05 % (27087)Termination reason: Unknown
% 13.11/3.05 % (27087)Termination phase: Property scanning
% 13.11/3.05
% 13.11/3.05 % (27087)Memory used [KB]: 2046
% 13.11/3.05 % (27087)Time elapsed: 0.012 s
% 13.11/3.05 % (27087)Instructions burned: 40 (million)
% 13.11/3.05 % (27087)------------------------------
% 13.11/3.05 % (27087)------------------------------
% 13.11/3.06 % (27088)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_26535 for (2984ds/294Mi)
% 13.11/3.08 % (27074)Instruction limit reached!
% 13.11/3.08 % (27074)------------------------------
% 13.11/3.08 % (27074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.08 % (27074)Termination reason: Unknown
% 13.11/3.08 % (27074)Termination phase: Saturation
% 13.11/3.08
% 13.11/3.08 % (27074)Memory used [KB]: 4861
% 13.11/3.08 % (27074)Time elapsed: 0.593 s
% 13.11/3.08 % (27074)Instructions burned: 1916 (million)
% 13.11/3.08 % (27074)------------------------------
% 13.11/3.08 % (27074)------------------------------
% 13.11/3.09 % (27089)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_26535 for (2984ds/187Mi)
% 13.72/3.14 % (27088)Instruction limit reached!
% 13.72/3.14 % (27088)------------------------------
% 13.72/3.14 % (27088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.14 % (27088)Termination reason: Unknown
% 13.72/3.14 % (27088)Termination phase: Saturation
% 13.72/3.14
% 13.72/3.14 % (27088)Memory used [KB]: 6908
% 13.72/3.14 % (27088)Time elapsed: 0.076 s
% 13.72/3.14 % (27088)Instructions burned: 294 (million)
% 13.72/3.14 % (27088)------------------------------
% 13.72/3.14 % (27088)------------------------------
% 13.72/3.14 % (27089)Instruction limit reached!
% 13.72/3.14 % (27089)------------------------------
% 13.72/3.14 % (27089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.14 % (27089)Termination reason: Unknown
% 13.72/3.14 % (27089)Termination phase: Saturation
% 13.72/3.14
% 13.72/3.14 % (27089)Memory used [KB]: 7547
% 13.72/3.14 % (27089)Time elapsed: 0.053 s
% 13.72/3.14 % (27089)Instructions burned: 190 (million)
% 13.72/3.14 % (27089)------------------------------
% 13.72/3.14 % (27089)------------------------------
% 13.72/3.15 % (27090)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_26535 for (2984ds/371Mi)
% 13.72/3.15 % (27091)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_26535 for (2984ds/1827Mi)
% 13.72/3.16 % (27086)Instruction limit reached!
% 13.72/3.16 % (27086)------------------------------
% 13.72/3.16 % (27086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.16 % (27086)Termination reason: Unknown
% 13.72/3.16 % (27086)Termination phase: Saturation
% 13.72/3.16
% 13.72/3.16 % (27086)Memory used [KB]: 15991
% 13.72/3.16 % (27086)Time elapsed: 0.173 s
% 13.72/3.16 % (27086)Instructions burned: 669 (million)
% 13.72/3.16 % (27086)------------------------------
% 13.72/3.16 % (27086)------------------------------
% 13.72/3.17 % (27092)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_26535 for (2983ds/70Mi)
% 13.72/3.18 % (27085)Instruction limit reached!
% 13.72/3.18 % (27085)------------------------------
% 13.72/3.18 % (27085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.18 % (27085)Termination reason: Unknown
% 13.72/3.18 % (27085)Termination phase: Saturation
% 13.72/3.18
% 13.72/3.18 % (27085)Memory used [KB]: 9722
% 13.72/3.18 % (27085)Time elapsed: 0.252 s
% 13.72/3.18 % (27085)Instructions burned: 834 (million)
% 13.72/3.18 % (27085)------------------------------
% 13.72/3.18 % (27085)------------------------------
% 13.72/3.19 % (27093)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_26535 for (2983ds/316Mi)
% 13.72/3.19 % (27092)Instruction limit reached!
% 13.72/3.19 % (27092)------------------------------
% 13.72/3.19 % (27092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.19 % (27092)Termination reason: Unknown
% 13.72/3.19 % (27092)Termination phase: Property scanning
% 13.72/3.19
% 13.72/3.19 % (27092)Memory used [KB]: 2174
% 13.72/3.19 % (27092)Time elapsed: 0.020 s
% 13.72/3.19 % (27092)Instructions burned: 72 (million)
% 13.72/3.19 % (27092)------------------------------
% 13.72/3.19 % (27092)------------------------------
% 13.72/3.20 % (27094)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_26535 for (2983ds/932Mi)
% 14.22/3.25 % (27090)Instruction limit reached!
% 14.22/3.25 % (27090)------------------------------
% 14.22/3.25 % (27090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.22/3.25 % (27090)Termination reason: Unknown
% 14.22/3.25 % (27090)Termination phase: Saturation
% 14.22/3.25
% 14.22/3.25 % (27090)Memory used [KB]: 8571
% 14.22/3.25 % (27090)Time elapsed: 0.106 s
% 14.22/3.25 % (27090)Instructions burned: 373 (million)
% 14.22/3.25 % (27090)------------------------------
% 14.22/3.25 % (27090)------------------------------
% 14.22/3.26 % (27095)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_26535 for (2982ds/4714Mi)
% 14.22/3.27 % (27093)Instruction limit reached!
% 14.22/3.27 % (27093)------------------------------
% 14.22/3.27 % (27093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.22/3.27 % (27093)Termination reason: Unknown
% 14.22/3.27 % (27093)Termination phase: Saturation
% 14.22/3.27
% 14.22/3.27 % (27093)Memory used [KB]: 7164
% 14.22/3.27 % (27093)Time elapsed: 0.080 s
% 14.22/3.27 % (27093)Instructions burned: 319 (million)
% 14.22/3.27 % (27093)------------------------------
% 14.22/3.27 % (27093)------------------------------
% 14.22/3.28 % (27096)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_26535 for (2982ds/8250Mi)
% 15.02/3.43 % (27094)Instruction limit reached!
% 15.02/3.43 % (27094)------------------------------
% 15.02/3.43 % (27094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.43 % (27094)Termination reason: Unknown
% 15.02/3.43 % (27094)Termination phase: Saturation
% 15.02/3.43
% 15.02/3.43 % (27094)Memory used [KB]: 12792
% 15.02/3.43 % (27094)Time elapsed: 0.236 s
% 15.02/3.43 % (27094)Instructions burned: 934 (million)
% 15.02/3.43 % (27094)------------------------------
% 15.02/3.43 % (27094)------------------------------
% 15.02/3.44 % (27097)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_26535 for (2981ds/770Mi)
% 15.87/3.65 % (27097)Instruction limit reached!
% 15.87/3.65 % (27097)------------------------------
% 15.87/3.65 % (27097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.87/3.65 % (27097)Termination reason: Unknown
% 15.87/3.65 % (27097)Termination phase: Saturation
% 15.87/3.65
% 15.87/3.65 % (27097)Memory used [KB]: 7164
% 15.87/3.65 % (27097)Time elapsed: 0.210 s
% 15.87/3.65 % (27097)Instructions burned: 770 (million)
% 15.87/3.65 % (27097)------------------------------
% 15.87/3.65 % (27097)------------------------------
% 15.87/3.66 % (27098)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_26535 for (2978ds/794Mi)
% 15.87/3.68 % (27091)Instruction limit reached!
% 15.87/3.68 % (27091)------------------------------
% 15.87/3.68 % (27091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.87/3.68 % (27091)Termination reason: Unknown
% 15.87/3.68 % (27091)Termination phase: Saturation
% 15.87/3.68
% 15.87/3.68 % (27091)Memory used [KB]: 17782
% 15.87/3.68 % (27091)Time elapsed: 0.534 s
% 15.87/3.68 % (27091)Instructions burned: 1827 (million)
% 15.87/3.68 % (27091)------------------------------
% 15.87/3.68 % (27091)------------------------------
% 15.87/3.69 % (27099)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_26535 for (2978ds/464Mi)
% 16.93/3.73 % (27073)Instruction limit reached!
% 16.93/3.73 % (27073)------------------------------
% 16.93/3.73 % (27073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.93/3.73 % (27073)Termination reason: Unknown
% 16.93/3.73 % (27073)Termination phase: Saturation
% 16.93/3.73
% 16.93/3.73 % (27073)Memory used [KB]: 12025
% 16.93/3.73 % (27073)Time elapsed: 1.277 s
% 16.93/3.73 % (27073)Instructions burned: 5207 (million)
% 16.93/3.73 % (27073)------------------------------
% 16.93/3.73 % (27073)------------------------------
% 16.93/3.74 % (27100)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_26535 for (2978ds/1376Mi)
% 17.17/3.81 % (27070)Instruction limit reached!
% 17.17/3.81 % (27070)------------------------------
% 17.17/3.81 % (27070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.17/3.81 % (27070)Termination reason: Unknown
% 17.17/3.81 % (27070)Termination phase: Saturation
% 17.17/3.81
% 17.17/3.81 % (27070)Memory used [KB]: 17398
% 17.17/3.81 % (27070)Time elapsed: 1.406 s
% 17.17/3.81 % (27070)Instructions burned: 4437 (million)
% 17.17/3.81 % (27070)------------------------------
% 17.17/3.81 % (27070)------------------------------
% 17.17/3.82 % (27101)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_26535 for (2977ds/906Mi)
% 17.17/3.83 % (27099)Instruction limit reached!
% 17.17/3.83 % (27099)------------------------------
% 17.17/3.83 % (27099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.17/3.83 % (27099)Termination reason: Unknown
% 17.17/3.83 % (27099)Termination phase: Saturation
% 17.17/3.83
% 17.17/3.83 % (27099)Memory used [KB]: 8443
% 17.17/3.83 % (27099)Time elapsed: 0.138 s
% 17.17/3.83 % (27099)Instructions burned: 464 (million)
% 17.17/3.83 % (27099)------------------------------
% 17.17/3.83 % (27099)------------------------------
% 17.17/3.84 % (27102)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_26535 for (2977ds/434Mi)
% 17.47/3.90 % (27098)Instruction limit reached!
% 17.47/3.90 % (27098)------------------------------
% 17.47/3.90 % (27098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/3.90 % (27098)Termination reason: Unknown
% 17.47/3.90 % (27098)Termination phase: Saturation
% 17.47/3.90
% 17.47/3.90 % (27098)Memory used [KB]: 5117
% 17.47/3.90 % (27098)Time elapsed: 0.241 s
% 17.47/3.90 % (27098)Instructions burned: 797 (million)
% 17.47/3.90 % (27098)------------------------------
% 17.47/3.90 % (27098)------------------------------
% 17.47/3.90 % (27075)Instruction limit reached!
% 17.47/3.90 % (27075)------------------------------
% 17.47/3.90 % (27075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/3.90 % (27075)Termination reason: Unknown
% 17.47/3.90 % (27075)Termination phase: Saturation
% 17.47/3.90
% 17.47/3.90 % (27075)Memory used [KB]: 11769
% 17.47/3.90 % (27075)Time elapsed: 1.334 s
% 17.47/3.90 % (27075)Instructions burned: 4352 (million)
% 17.47/3.90 % (27075)------------------------------
% 17.47/3.90 % (27075)------------------------------
% 17.47/3.91 % (27103)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_26535 for (2976ds/865Mi)
% 17.47/3.91 % (27104)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_26535 for (2976ds/593Mi)
% 17.47/3.96 % (27102)Refutation not found, non-redundant clauses discarded% (27102)------------------------------
% 17.47/3.96 % (27102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.47/3.96 % (27102)Termination reason: Refutation not found, non-redundant clauses discarded
% 17.47/3.96
% 17.47/3.96 % (27102)Memory used [KB]: 9594
% 17.47/3.96 % (27102)Time elapsed: 0.123 s
% 17.47/3.96 % (27102)Instructions burned: 416 (million)
% 17.47/3.96 % (27102)------------------------------
% 17.47/3.96 % (27102)------------------------------
% 17.47/3.97 % (27105)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_26535 for (2975ds/443Mi)
% 20.14/4.06 % (27104)Instruction limit reached!
% 20.14/4.06 % (27104)------------------------------
% 20.14/4.06 % (27104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.14/4.06 % (27104)Termination reason: Unknown
% 20.14/4.06 % (27104)Termination phase: Saturation
% 20.14/4.06
% 20.14/4.06 % (27104)Memory used [KB]: 7291
% 20.14/4.06 % (27104)Time elapsed: 0.146 s
% 20.14/4.06 % (27104)Instructions burned: 594 (million)
% 20.14/4.06 % (27104)------------------------------
% 20.14/4.06 % (27104)------------------------------
% 20.14/4.07 % (27106)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_26535 for (2974ds/594Mi)
% 20.14/4.08 % (27100)Instruction limit reached!
% 20.14/4.08 % (27100)------------------------------
% 20.14/4.08 % (27100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.14/4.08 % (27100)Termination reason: Unknown
% 20.14/4.08 % (27100)Termination phase: Saturation
% 20.14/4.08
% 20.14/4.08 % (27100)Memory used [KB]: 9083
% 20.14/4.08 % (27100)Time elapsed: 0.346 s
% 20.14/4.08 % (27100)Instructions burned: 1377 (million)
% 20.14/4.08 % (27100)------------------------------
% 20.14/4.08 % (27100)------------------------------
% 20.14/4.09 % (27107)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_26535 for (2974ds/327Mi)
% 20.14/4.10 % (27105)Instruction limit reached!
% 20.14/4.10 % (27105)------------------------------
% 20.14/4.10 % (27105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.14/4.10 % (27105)Termination reason: Unknown
% 20.14/4.10 % (27105)Termination phase: Saturation
% 20.14/4.10
% 20.14/4.10 % (27105)Memory used [KB]: 8443
% 20.14/4.10 % (27105)Time elapsed: 0.131 s
% 20.14/4.10 % (27105)Instructions burned: 443 (million)
% 20.14/4.10 % (27105)------------------------------
% 20.14/4.10 % (27105)------------------------------
% 20.14/4.10 % (27101)Instruction limit reached!
% 20.14/4.10 % (27101)------------------------------
% 20.14/4.10 % (27101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.14/4.10 % (27101)Termination reason: Unknown
% 20.14/4.10 % (27101)Termination phase: Saturation
% 20.14/4.10
% 20.14/4.10 % (27101)Memory used [KB]: 10490
% 20.14/4.10 % (27101)Time elapsed: 0.279 s
% 20.14/4.10 % (27101)Instructions burned: 906 (million)
% 20.14/4.10 % (27101)------------------------------
% 20.14/4.10 % (27101)------------------------------
% 20.14/4.11 % (27108)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_26535 for (2974ds/5411Mi)
% 20.14/4.11 % (27109)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_26535 for (2974ds/1762Mi)
% 20.74/4.17 % (27103)Instruction limit reached!
% 20.74/4.17 % (27103)------------------------------
% 20.74/4.17 % (27103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.17 % (27103)Termination reason: Unknown
% 20.74/4.17 % (27103)Termination phase: Saturation
% 20.74/4.17
% 20.74/4.17 % (27103)Memory used [KB]: 9338
% 20.74/4.17 % (27103)Time elapsed: 0.259 s
% 20.74/4.17 % (27103)Instructions burned: 865 (million)
% 20.74/4.17 % (27103)------------------------------
% 20.74/4.17 % (27103)------------------------------
% 20.74/4.18 % (27110)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_26535 for (2973ds/96Mi)
% 20.74/4.19 % (27107)Instruction limit reached!
% 20.74/4.19 % (27107)------------------------------
% 20.74/4.19 % (27107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.19 % (27107)Termination reason: Unknown
% 20.74/4.19 % (27107)Termination phase: Saturation
% 20.74/4.19
% 20.74/4.19 % (27107)Memory used [KB]: 10106
% 20.74/4.19 % (27107)Time elapsed: 0.102 s
% 20.74/4.19 % (27107)Instructions burned: 327 (million)
% 20.74/4.19 % (27107)------------------------------
% 20.74/4.19 % (27107)------------------------------
% 21.04/4.20 % (27110)Instruction limit reached!
% 21.04/4.20 % (27110)------------------------------
% 21.04/4.20 % (27110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.04/4.20 % (27110)Termination reason: Unknown
% 21.04/4.20 % (27110)Termination phase: Property scanning
% 21.04/4.20
% 21.04/4.20 % (27110)Memory used [KB]: 2302
% 21.04/4.20 % (27110)Time elapsed: 0.026 s
% 21.04/4.20 % (27110)Instructions burned: 99 (million)
% 21.04/4.20 % (27110)------------------------------
% 21.04/4.20 % (27110)------------------------------
% 21.04/4.20 % (27111)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_26535 for (2973ds/503Mi)
% 21.04/4.21 % (27112)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_26535 for (2973ds/90Mi)
% 21.04/4.24 % (27112)Instruction limit reached!
% 21.04/4.24 % (27112)------------------------------
% 21.04/4.24 % (27112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.04/4.24 % (27112)Termination reason: Unknown
% 21.04/4.24 % (27112)Termination phase: Twee Goal Transformation
% 21.04/4.24
% 21.04/4.24 % (27112)Memory used [KB]: 2558
% 21.04/4.24 % (27112)Time elapsed: 0.025 s
% 21.04/4.24 % (27112)Instructions burned: 92 (million)
% 21.04/4.24 % (27112)------------------------------
% 21.04/4.24 % (27112)------------------------------
% 21.04/4.24 % (27106)Instruction limit reached!
% 21.04/4.24 % (27106)------------------------------
% 21.04/4.24 % (27106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.04/4.24 % (27106)Termination reason: Unknown
% 21.04/4.24 % (27106)Termination phase: Saturation
% 21.04/4.24
% 21.04/4.24 % (27106)Memory used [KB]: 8571
% 21.04/4.24 % (27106)Time elapsed: 0.177 s
% 21.04/4.24 % (27106)Instructions burned: 594 (million)
% 21.04/4.24 % (27106)------------------------------
% 21.04/4.24 % (27106)------------------------------
% 21.04/4.25 % (27113)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_26535 for (2973ds/593Mi)
% 21.04/4.25 % (27114)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_26535 for (2972ds/1512Mi)
% 21.50/4.35 % (27111)Instruction limit reached!
% 21.50/4.35 % (27111)------------------------------
% 21.50/4.35 % (27111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.50/4.35 % (27111)Termination reason: Unknown
% 21.50/4.35 % (27111)Termination phase: Saturation
% 21.50/4.35
% 21.50/4.35 % (27111)Memory used [KB]: 8699
% 21.50/4.35 % (27111)Time elapsed: 0.148 s
% 21.50/4.35 % (27111)Instructions burned: 504 (million)
% 21.50/4.35 % (27111)------------------------------
% 21.50/4.35 % (27111)------------------------------
% 21.50/4.36 % (27115)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_26535 for (2971ds/569Mi)
% 21.50/4.39 % (27095)Instruction limit reached!
% 21.50/4.39 % (27095)------------------------------
% 21.50/4.39 % (27095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.50/4.39 % (27095)Termination reason: Unknown
% 21.50/4.39 % (27095)Termination phase: Saturation
% 21.50/4.39
% 21.50/4.39 % (27095)Memory used [KB]: 7419
% 21.50/4.39 % (27095)Time elapsed: 1.130 s
% 21.50/4.39 % (27095)Instructions burned: 4714 (million)
% 21.50/4.39 % (27095)------------------------------
% 21.50/4.39 % (27095)------------------------------
% 21.87/4.40 % (27116)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_26535 for (2971ds/501Mi)
% 21.87/4.42 % (27113)Instruction limit reached!
% 21.87/4.42 % (27113)------------------------------
% 21.87/4.42 % (27113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.87/4.42 % (27113)Termination reason: Unknown
% 21.87/4.42 % (27113)Termination phase: Saturation
% 21.87/4.42
% 21.87/4.42 % (27113)Memory used [KB]: 8571
% 21.87/4.42 % (27113)Time elapsed: 0.178 s
% 21.87/4.42 % (27113)Instructions burned: 595 (million)
% 21.87/4.42 % (27113)------------------------------
% 21.87/4.42 % (27113)------------------------------
% 21.87/4.43 % (27117)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_26535 for (2971ds/562Mi)
% 22.14/4.50 % (27115)Instruction limit reached!
% 22.14/4.50 % (27115)------------------------------
% 22.14/4.50 % (27115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.14/4.50 % (27115)Termination reason: Unknown
% 22.14/4.50 % (27115)Termination phase: Saturation
% 22.14/4.50
% 22.14/4.50 % (27115)Memory used [KB]: 11001
% 22.14/4.50 % (27115)Time elapsed: 0.145 s
% 22.14/4.50 % (27115)Instructions burned: 572 (million)
% 22.14/4.50 % (27115)------------------------------
% 22.14/4.50 % (27115)------------------------------
% 22.14/4.52 % (27118)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_26535 for (2970ds/406Mi)
% 22.14/4.55 % (27109)Instruction limit reached!
% 22.14/4.55 % (27109)------------------------------
% 22.14/4.55 % (27109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.14/4.55 % (27109)Termination reason: Unknown
% 22.14/4.55 % (27109)Termination phase: Saturation
% 22.14/4.55
% 22.14/4.55 % (27109)Memory used [KB]: 15607
% 22.14/4.55 % (27109)Time elapsed: 0.435 s
% 22.14/4.55 % (27109)Instructions burned: 1763 (million)
% 22.14/4.55 % (27109)------------------------------
% 22.14/4.55 % (27109)------------------------------
% 22.14/4.55 % (27116)Instruction limit reached!
% 22.14/4.55 % (27116)------------------------------
% 22.14/4.55 % (27116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.14/4.55 % (27116)Termination reason: Unknown
% 22.14/4.55 % (27116)Termination phase: Saturation
% 22.14/4.55
% 22.14/4.55 % (27116)Memory used [KB]: 9338
% 22.14/4.55 % (27116)Time elapsed: 0.153 s
% 22.14/4.55 % (27116)Instructions burned: 503 (million)
% 22.14/4.55 % (27116)------------------------------
% 22.14/4.55 % (27116)------------------------------
% 22.14/4.56 % (27119)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_26535 for (2969ds/582Mi)
% 22.14/4.56 % (27120)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_26535 for (2969ds/456Mi)
% 23.00/4.60 % (27117)Instruction limit reached!
% 23.00/4.60 % (27117)------------------------------
% 23.00/4.60 % (27117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.00/4.60 % (27117)Termination reason: Unknown
% 23.00/4.60 % (27117)Termination phase: Saturation
% 23.00/4.60
% 23.00/4.60 % (27117)Memory used [KB]: 8187
% 23.00/4.60 % (27117)Time elapsed: 0.166 s
% 23.00/4.60 % (27117)Instructions burned: 564 (million)
% 23.00/4.60 % (27117)------------------------------
% 23.00/4.60 % (27117)------------------------------
% 23.00/4.61 % (27121)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_26535 for (2969ds/393Mi)
% 23.00/4.63 % (27118)Instruction limit reached!
% 23.00/4.63 % (27118)------------------------------
% 23.00/4.63 % (27118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.00/4.63 % (27118)Termination reason: Unknown
% 23.00/4.63 % (27118)Termination phase: Saturation
% 23.00/4.63
% 23.00/4.63 % (27118)Memory used [KB]: 7291
% 23.00/4.63 % (27118)Time elapsed: 0.114 s
% 23.00/4.63 % (27118)Instructions burned: 409 (million)
% 23.00/4.63 % (27118)------------------------------
% 23.00/4.63 % (27118)------------------------------
% 23.00/4.64 % (27122)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_26535 for (2969ds/1335Mi)
% 23.00/4.69 % (27120)Instruction limit reached!
% 23.00/4.69 % (27120)------------------------------
% 23.00/4.69 % (27120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.00/4.69 % (27120)Termination reason: Unknown
% 23.00/4.69 % (27120)Termination phase: Saturation
% 23.00/4.69
% 23.00/4.69 % (27120)Memory used [KB]: 8571
% 23.00/4.69 % (27120)Time elapsed: 0.133 s
% 23.00/4.69 % (27120)Instructions burned: 457 (million)
% 23.00/4.69 % (27120)------------------------------
% 23.00/4.69 % (27120)------------------------------
% 23.55/4.70 % (27123)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_26535 for (2968ds/3373Mi)
% 23.55/4.72 % (27114)Instruction limit reached!
% 23.55/4.72 % (27114)------------------------------
% 23.55/4.72 % (27114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.55/4.72 % (27114)Termination reason: Unknown
% 23.55/4.72 % (27114)Termination phase: Saturation
% 23.55/4.72
% 23.55/4.72 % (27114)Memory used [KB]: 10746
% 23.55/4.72 % (27114)Time elapsed: 0.469 s
% 23.55/4.72 % (27114)Instructions burned: 1513 (million)
% 23.55/4.72 % (27114)------------------------------
% 23.55/4.72 % (27114)------------------------------
% 23.55/4.72 % (27121)Instruction limit reached!
% 23.55/4.72 % (27121)------------------------------
% 23.55/4.72 % (27121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.55/4.72 % (27121)Termination reason: Unknown
% 23.55/4.72 % (27121)Termination phase: Saturation
% 23.55/4.72
% 23.55/4.72 % (27121)Memory used [KB]: 8827
% 23.55/4.72 % (27121)Time elapsed: 0.118 s
% 23.55/4.72 % (27121)Instructions burned: 395 (million)
% 23.55/4.72 % (27121)------------------------------
% 23.55/4.72 % (27121)------------------------------
% 23.55/4.73 % (27124)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_26535 for (2968ds/474Mi)
% 23.55/4.73 % (27119)Instruction limit reached!
% 23.55/4.73 % (27119)------------------------------
% 23.55/4.73 % (27119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.55/4.73 % (27119)Termination reason: Unknown
% 23.55/4.73 % (27119)Termination phase: Saturation
% 23.55/4.73
% 23.55/4.73 % (27119)Memory used [KB]: 9594
% 23.55/4.73 % (27119)Time elapsed: 0.178 s
% 23.55/4.73 % (27119)Instructions burned: 582 (million)
% 23.55/4.73 % (27119)------------------------------
% 23.55/4.73 % (27119)------------------------------
% 23.55/4.73 % (27125)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_26535 for (2968ds/157Mi)
% 23.55/4.74 % (27126)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_26535 for (2968ds/590Mi)
% 23.55/4.77 % (27125)Instruction limit reached!
% 23.55/4.77 % (27125)------------------------------
% 23.55/4.77 % (27125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.55/4.77 % (27125)Termination reason: Unknown
% 23.55/4.77 % (27125)Termination phase: Saturation
% 23.55/4.77
% 23.55/4.77 % (27125)Memory used [KB]: 6908
% 23.55/4.77 % (27125)Time elapsed: 0.040 s
% 23.55/4.77 % (27125)Instructions burned: 157 (million)
% 23.55/4.77 % (27125)------------------------------
% 23.55/4.77 % (27125)------------------------------
% 23.55/4.78 % (27127)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_26535 for (2967ds/104Mi)
% 24.49/4.81 % (27127)Instruction limit reached!
% 24.49/4.81 % (27127)------------------------------
% 24.49/4.81 % (27127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.49/4.81 % (27127)Termination reason: Unknown
% 24.49/4.81 % (27127)Termination phase: Saturation
% 24.49/4.81
% 24.49/4.81 % (27127)Memory used [KB]: 6908
% 24.49/4.81 % (27127)Time elapsed: 0.029 s
% 24.49/4.81 % (27127)Instructions burned: 106 (million)
% 24.49/4.81 % (27127)------------------------------
% 24.49/4.81 % (27127)------------------------------
% 24.49/4.82 % (27128)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_26535 for (2967ds/414Mi)
% 24.49/4.85 % (27124)Instruction limit reached!
% 24.49/4.85 % (27124)------------------------------
% 24.49/4.85 % (27124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.49/4.85 % (27124)Termination reason: Unknown
% 24.49/4.85 % (27124)Termination phase: Saturation
% 24.49/4.85
% 24.49/4.85 % (27124)Memory used [KB]: 11001
% 24.49/4.85 % (27124)Time elapsed: 0.119 s
% 24.49/4.85 % (27124)Instructions burned: 475 (million)
% 24.49/4.85 % (27124)------------------------------
% 24.49/4.85 % (27124)------------------------------
% 24.49/4.86 % (27129)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_26535 for (2967ds/715Mi)
% 24.75/4.90 % (27126)Instruction limit reached!
% 24.75/4.90 % (27126)------------------------------
% 24.75/4.90 % (27126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.75/4.90 % (27126)Termination reason: Unknown
% 24.75/4.90 % (27126)Termination phase: Saturation
% 24.75/4.90
% 24.75/4.90 % (27126)Memory used [KB]: 8571
% 24.75/4.90 % (27126)Time elapsed: 0.160 s
% 24.75/4.90 % (27126)Instructions burned: 591 (million)
% 24.75/4.90 % (27126)------------------------------
% 24.75/4.90 % (27126)------------------------------
% 24.75/4.91 % (27130)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_26535 for (2966ds/961Mi)
% 24.75/4.92 % (27128)Instruction limit reached!
% 24.75/4.92 % (27128)------------------------------
% 24.75/4.92 % (27128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.75/4.92 % (27128)Termination reason: Unknown
% 24.75/4.92 % (27128)Termination phase: Saturation
% 24.75/4.92
% 24.75/4.92 % (27128)Memory used [KB]: 7164
% 24.75/4.92 % (27128)Time elapsed: 0.103 s
% 24.75/4.92 % (27128)Instructions burned: 416 (million)
% 24.75/4.92 % (27128)------------------------------
% 24.75/4.92 % (27128)------------------------------
% 24.75/4.93 % (27131)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_26535 for (2966ds/1213Mi)
% 24.75/5.01 % (27122)Instruction limit reached!
% 24.75/5.01 % (27122)------------------------------
% 24.75/5.01 % (27122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.75/5.01 % (27122)Termination reason: Unknown
% 24.75/5.01 % (27122)Termination phase: Saturation
% 24.75/5.01
% 24.75/5.01 % (27122)Memory used [KB]: 9083
% 24.75/5.01 % (27122)Time elapsed: 0.373 s
% 24.75/5.01 % (27122)Instructions burned: 1337 (million)
% 24.75/5.01 % (27122)------------------------------
% 24.75/5.01 % (27122)------------------------------
% 24.75/5.02 % (27132)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_26535 for (2965ds/1979Mi)
% 27.17/5.08 % (27129)Instruction limit reached!
% 27.17/5.08 % (27129)------------------------------
% 27.17/5.08 % (27129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.17/5.08 % (27129)Termination reason: Unknown
% 27.17/5.08 % (27129)Termination phase: Saturation
% 27.17/5.08
% 27.17/5.08 % (27129)Memory used [KB]: 4221
% 27.17/5.08 % (27129)Time elapsed: 0.219 s
% 27.17/5.08 % (27129)Instructions burned: 715 (million)
% 27.17/5.08 % (27129)------------------------------
% 27.17/5.08 % (27129)------------------------------
% 27.17/5.09 % (27133)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_26535 for (2964ds/481Mi)
% 28.10/5.21 % (27133)Instruction limit reached!
% 28.10/5.21 % (27133)------------------------------
% 28.10/5.21 % (27133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.10/5.21 % (27133)Termination reason: Unknown
% 28.10/5.21 % (27133)Termination phase: Saturation
% 28.10/5.21
% 28.10/5.21 % (27133)Memory used [KB]: 11001
% 28.10/5.21 % (27133)Time elapsed: 0.121 s
% 28.10/5.21 % (27133)Instructions burned: 482 (million)
% 28.10/5.21 % (27133)------------------------------
% 28.10/5.21 % (27133)------------------------------
% 28.10/5.21 % (27130)Instruction limit reached!
% 28.10/5.21 % (27130)------------------------------
% 28.10/5.21 % (27130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.10/5.21 % (27130)Termination reason: Unknown
% 28.10/5.21 % (27130)Termination phase: Saturation
% 28.10/5.21
% 28.10/5.21 % (27130)Memory used [KB]: 8955
% 28.10/5.21 % (27130)Time elapsed: 0.298 s
% 28.10/5.21 % (27130)Instructions burned: 961 (million)
% 28.10/5.21 % (27130)------------------------------
% 28.10/5.21 % (27130)------------------------------
% 28.10/5.22 % (27134)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_26535 for (2963ds/783Mi)
% 28.10/5.22 % (27135)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_26535 for (2963ds/432Mi)
% 28.65/5.31 % (27131)Instruction limit reached!
% 28.65/5.31 % (27131)------------------------------
% 28.65/5.31 % (27131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.65/5.31 % (27131)Termination reason: Unknown
% 28.65/5.31 % (27131)Termination phase: Saturation
% 28.65/5.31
% 28.65/5.31 % (27131)Memory used [KB]: 12792
% 28.65/5.31 % (27131)Time elapsed: 0.379 s
% 28.65/5.31 % (27131)Instructions burned: 1215 (million)
% 28.65/5.31 % (27131)------------------------------
% 28.65/5.31 % (27131)------------------------------
% 28.65/5.32 % (27136)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_26535 for (2962ds/1670Mi)
% 28.65/5.35 % (27135)Instruction limit reached!
% 28.65/5.35 % (27135)------------------------------
% 28.65/5.35 % (27135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.65/5.35 % (27135)Termination reason: Unknown
% 28.65/5.35 % (27135)Termination phase: Saturation
% 28.65/5.35
% 28.65/5.35 % (27135)Memory used [KB]: 8187
% 28.65/5.35 % (27135)Time elapsed: 0.128 s
% 28.65/5.35 % (27135)Instructions burned: 433 (million)
% 28.65/5.35 % (27135)------------------------------
% 28.65/5.35 % (27135)------------------------------
% 28.65/5.36 % (27137)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_26535 for (2961ds/90Mi)
% 28.65/5.38 % (27137)Instruction limit reached!
% 28.65/5.38 % (27137)------------------------------
% 28.65/5.38 % (27137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.65/5.38 % (27137)Termination reason: Unknown
% 28.65/5.38 % (27137)Termination phase: Property scanning
% 28.65/5.38
% 28.65/5.38 % (27137)Memory used [KB]: 2302
% 28.65/5.38 % (27137)Time elapsed: 0.024 s
% 28.65/5.38 % (27137)Instructions burned: 90 (million)
% 28.65/5.38 % (27137)------------------------------
% 28.65/5.38 % (27137)------------------------------
% 28.65/5.39 % (27138)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_26535 for (2961ds/346Mi)
% 29.13/5.46 % (27134)Instruction limit reached!
% 29.13/5.46 % (27134)------------------------------
% 29.13/5.46 % (27134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.13/5.46 % (27134)Termination reason: Unknown
% 29.13/5.46 % (27134)Termination phase: Saturation
% 29.13/5.46
% 29.13/5.46 % (27134)Memory used [KB]: 10618
% 29.13/5.46 % (27134)Time elapsed: 0.244 s
% 29.13/5.46 % (27134)Instructions burned: 783 (million)
% 29.13/5.46 % (27134)------------------------------
% 29.13/5.46 % (27134)------------------------------
% 29.13/5.47 % (27139)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_26535 for (2960ds/401Mi)
% 29.13/5.47 % (27138)Instruction limit reached!
% 29.13/5.47 % (27138)------------------------------
% 29.13/5.47 % (27138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.13/5.47 % (27138)Termination reason: Unknown
% 29.13/5.47 % (27138)Termination phase: Saturation
% 29.13/5.47
% 29.13/5.47 % (27138)Memory used [KB]: 7547
% 29.13/5.47 % (27138)Time elapsed: 0.087 s
% 29.13/5.47 % (27138)Instructions burned: 347 (million)
% 29.13/5.47 % (27138)------------------------------
% 29.13/5.47 % (27138)------------------------------
% 29.13/5.48 % (27140)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_26535 for (2960ds/6454Mi)
% 29.78/5.57 % (27139)Instruction limit reached!
% 29.78/5.57 % (27139)------------------------------
% 29.78/5.57 % (27139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.78/5.57 % (27139)Termination reason: Unknown
% 29.78/5.57 % (27139)Termination phase: Saturation
% 29.78/5.57
% 29.78/5.57 % (27139)Memory used [KB]: 7164
% 29.78/5.57 % (27139)Time elapsed: 0.099 s
% 29.78/5.57 % (27139)Instructions burned: 401 (million)
% 29.78/5.57 % (27139)------------------------------
% 29.78/5.57 % (27139)------------------------------
% 29.78/5.58 % (27141)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_26535 for (2959ds/283Mi)
% 30.21/5.62 % (27132)Instruction limit reached!
% 30.21/5.62 % (27132)------------------------------
% 30.21/5.62 % (27132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.21/5.62 % (27132)Termination reason: Unknown
% 30.21/5.62 % (27132)Termination phase: Saturation
% 30.21/5.62
% 30.21/5.62 % (27132)Memory used [KB]: 9466
% 30.21/5.62 % (27132)Time elapsed: 0.604 s
% 30.21/5.62 % (27132)Instructions burned: 1981 (million)
% 30.21/5.62 % (27132)------------------------------
% 30.21/5.62 % (27132)------------------------------
% 30.21/5.63 % (27142)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_26535 for (2959ds/865Mi)
% 30.21/5.65 % (27141)Instruction limit reached!
% 30.21/5.65 % (27141)------------------------------
% 30.21/5.65 % (27141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.21/5.65 % (27141)Termination reason: Unknown
% 30.21/5.65 % (27141)Termination phase: Saturation
% 30.21/5.65
% 30.21/5.65 % (27141)Memory used [KB]: 8059
% 30.21/5.65 % (27141)Time elapsed: 0.079 s
% 30.21/5.65 % (27141)Instructions burned: 283 (million)
% 30.21/5.65 % (27141)------------------------------
% 30.21/5.65 % (27141)------------------------------
% 30.21/5.66 % (27143)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_26535 for (2958ds/4528Mi)
% 31.19/5.73 % (27123)Instruction limit reached!
% 31.19/5.73 % (27123)------------------------------
% 31.19/5.73 % (27123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.19/5.73 % (27123)Termination reason: Unknown
% 31.19/5.73 % (27123)Termination phase: Saturation
% 31.19/5.73
% 31.19/5.73 % (27123)Memory used [KB]: 12153
% 31.19/5.73 % (27123)Time elapsed: 1.030 s
% 31.19/5.73 % (27123)Instructions burned: 3374 (million)
% 31.19/5.73 % (27123)------------------------------
% 31.19/5.73 % (27123)------------------------------
% 31.19/5.74 % (27136)Instruction limit reached!
% 31.19/5.74 % (27136)------------------------------
% 31.19/5.74 % (27136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.19/5.74 % (27136)Termination reason: Unknown
% 31.19/5.74 % (27136)Termination phase: Saturation
% 31.19/5.74
% 31.19/5.74 % (27136)Memory used [KB]: 12153
% 31.19/5.74 % (27136)Time elapsed: 0.418 s
% 31.19/5.74 % (27136)Instructions burned: 1673 (million)
% 31.19/5.74 % (27136)------------------------------
% 31.19/5.74 % (27136)------------------------------
% 31.19/5.74 % (27144)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_26535 for (2958ds/1001Mi)
% 31.19/5.75 % (27145)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_26535 for (2958ds/102Mi)
% 31.19/5.76 % (27143)Refutation not found, incomplete strategy
% 31.19/5.76 % (27143)------------------------------
% 31.19/5.76 % (27143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.19/5.76 % (27143)Termination reason: Refutation not found, incomplete strategy
% 31.19/5.76
% 31.19/5.76
% 31.19/5.76 % (27143)Memory used [KB]: 2558
% 31.19/5.76 % (27143)Time elapsed: 0.099 s
% 31.19/5.76 % (27143)Instructions burned: 377 (million)
% 31.19/5.76 % (27143)------------------------------
% 31.19/5.76 % (27143)------------------------------
% 31.19/5.77 % (27146)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_26535 for (2957ds/952Mi)
% 31.19/5.77 % (27145)Instruction limit reached!
% 31.19/5.77 % (27145)------------------------------
% 31.19/5.77 % (27145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.19/5.77 % (27145)Termination reason: Unknown
% 31.19/5.77 % (27145)Termination phase: Saturation
% 31.19/5.77
% 31.19/5.77 % (27145)Memory used [KB]: 6780
% 31.19/5.77 % (27145)Time elapsed: 0.028 s
% 31.19/5.77 % (27145)Instructions burned: 103 (million)
% 31.19/5.77 % (27145)------------------------------
% 31.19/5.77 % (27145)------------------------------
% 31.19/5.78 % (27147)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_26535 for (2957ds/578Mi)
% 32.02/5.80 % (27108)Instruction limit reached!
% 32.02/5.80 % (27108)------------------------------
% 32.02/5.80 % (27108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.02/5.80 % (27108)Termination reason: Unknown
% 32.02/5.80 % (27108)Termination phase: Saturation
% 32.02/5.80
% 32.02/5.80 % (27108)Memory used [KB]: 15863
% 32.02/5.80 % (27108)Time elapsed: 1.697 s
% 32.02/5.80 % (27108)Instructions burned: 5414 (million)
% 32.02/5.80 % (27108)------------------------------
% 32.02/5.80 % (27108)------------------------------
% 32.02/5.82 % (27148)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_26535 for (2957ds/643Mi)
% 32.02/5.87 % (27142)Instruction limit reached!
% 32.02/5.87 % (27142)------------------------------
% 32.02/5.87 % (27142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.02/5.87 % (27142)Termination reason: Unknown
% 32.02/5.87 % (27142)Termination phase: Saturation
% 32.02/5.87
% 32.02/5.87 % (27142)Memory used [KB]: 8315
% 32.02/5.87 % (27142)Time elapsed: 0.242 s
% 32.02/5.87 % (27142)Instructions burned: 865 (million)
% 32.02/5.87 % (27142)------------------------------
% 32.02/5.87 % (27142)------------------------------
% 32.02/5.88 % (27149)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_26535 for (2956ds/865Mi)
% 32.38/5.91 % (27147)Instruction limit reached!
% 32.38/5.91 % (27147)------------------------------
% 32.38/5.91 % (27147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.38/5.91 % (27147)Termination reason: Unknown
% 32.38/5.91 % (27147)Termination phase: Saturation
% 32.38/5.91
% 32.38/5.91 % (27147)Memory used [KB]: 8571
% 32.38/5.91 % (27147)Time elapsed: 0.133 s
% 32.38/5.91 % (27147)Instructions burned: 580 (million)
% 32.38/5.91 % (27147)------------------------------
% 32.38/5.91 % (27147)------------------------------
% 32.38/5.92 % (27096)Instruction limit reached!
% 32.38/5.92 % (27096)------------------------------
% 32.38/5.92 % (27096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.38/5.92 % (27096)Termination reason: Unknown
% 32.38/5.92 % (27096)Termination phase: Saturation
% 32.38/5.92
% 32.38/5.92 % (27096)Memory used [KB]: 27888
% 32.38/5.92 % (27096)Time elapsed: 2.649 s
% 32.38/5.92 % (27096)Instructions burned: 8251 (million)
% 32.38/5.92 % (27096)------------------------------
% 32.38/5.92 % (27096)------------------------------
% 32.38/5.92 % (27150)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_26535 for (2956ds/1174Mi)
% 32.38/5.93 % (27151)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_26535 for (2956ds/644Mi)
% 32.38/5.98 % (27148)Instruction limit reached!
% 32.38/5.98 % (27148)------------------------------
% 32.38/5.98 % (27148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.38/5.98 % (27148)Termination reason: Unknown
% 32.38/5.98 % (27148)Termination phase: Saturation
% 32.38/5.98
% 32.38/5.98 % (27148)Memory used [KB]: 11257
% 32.38/5.98 % (27148)Time elapsed: 0.162 s
% 32.38/5.98 % (27148)Instructions burned: 645 (million)
% 32.38/5.98 % (27148)------------------------------
% 32.38/5.98 % (27148)------------------------------
% 32.38/5.98 % (27144)Instruction limit reached!
% 32.38/5.98 % (27144)------------------------------
% 32.38/5.98 % (27144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.38/5.98 % (27144)Termination reason: Unknown
% 32.38/5.98 % (27144)Termination phase: Saturation
% 32.38/5.98
% 32.38/5.98 % (27144)Memory used [KB]: 9083
% 32.38/5.98 % (27144)Time elapsed: 0.240 s
% 32.38/5.98 % (27144)Instructions burned: 1005 (million)
% 32.38/5.98 % (27144)------------------------------
% 32.38/5.98 % (27144)------------------------------
% 32.38/5.99 % (27152)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_26535 for (2955ds/1201Mi)
% 32.38/5.99 % (27153)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_26535 for (2955ds/1046Mi)
% 34.18/6.06 % (27146)Instruction limit reached!
% 34.18/6.06 % (27146)------------------------------
% 34.18/6.06 % (27146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.18/6.06 % (27146)Termination reason: Unknown
% 34.18/6.06 % (27146)Termination phase: Saturation
% 34.18/6.06
% 34.18/6.06 % (27146)Memory used [KB]: 9850
% 34.18/6.06 % (27146)Time elapsed: 0.290 s
% 34.18/6.06 % (27146)Instructions burned: 952 (million)
% 34.18/6.06 % (27146)------------------------------
% 34.18/6.06 % (27146)------------------------------
% 34.18/6.07 % (27154)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_26535 for (2955ds/222Mi)
% 34.18/6.12 % (27149)Instruction limit reached!
% 34.18/6.12 % (27149)------------------------------
% 34.18/6.12 % (27149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.18/6.12 % (27149)Termination reason: Unknown
% 34.18/6.12 % (27149)Termination phase: Saturation
% 34.18/6.12
% 34.18/6.12 % (27149)Memory used [KB]: 7419
% 34.18/6.12 % (27149)Time elapsed: 0.236 s
% 34.18/6.12 % (27149)Instructions burned: 865 (million)
% 34.18/6.12 % (27149)------------------------------
% 34.18/6.12 % (27149)------------------------------
% 34.18/6.12 % (27151)Instruction limit reached!
% 34.18/6.12 % (27151)------------------------------
% 34.18/6.12 % (27151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.18/6.12 % (27151)Termination reason: Unknown
% 34.18/6.12 % (27151)Termination phase: Saturation
% 34.18/6.12
% 34.18/6.12 % (27151)Memory used [KB]: 7675
% 34.18/6.12 % (27151)Time elapsed: 0.190 s
% 34.18/6.12 % (27151)Instructions burned: 645 (million)
% 34.18/6.12 % (27151)------------------------------
% 34.18/6.12 % (27151)------------------------------
% 34.85/6.13 % (27155)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_26535 for (2954ds/68Mi)
% 34.85/6.13 % (27154)Instruction limit reached!
% 34.85/6.13 % (27154)------------------------------
% 34.85/6.13 % (27154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.85/6.13 % (27154)Termination reason: Unknown
% 34.85/6.13 % (27154)Termination phase: Saturation
% 34.85/6.13
% 34.85/6.13 % (27154)Memory used [KB]: 7164
% 34.85/6.13 % (27154)Time elapsed: 0.057 s
% 34.85/6.13 % (27154)Instructions burned: 224 (million)
% 34.85/6.13 % (27154)------------------------------
% 34.85/6.13 % (27154)------------------------------
% 34.85/6.13 % (27156)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_26535 for (2954ds/454Mi)
% 34.85/6.14 % (27157)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_26535 for (2954ds/360Mi)
% 34.85/6.15 % (27155)Instruction limit reached!
% 34.85/6.15 % (27155)------------------------------
% 34.85/6.15 % (27155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.85/6.15 % (27155)Termination reason: Unknown
% 34.85/6.15 % (27155)Termination phase: Property scanning
% 34.85/6.15
% 34.85/6.15 % (27155)Memory used [KB]: 2046
% 34.85/6.15 % (27155)Time elapsed: 0.019 s
% 34.85/6.15 % (27155)Instructions burned: 69 (million)
% 34.85/6.15 % (27155)------------------------------
% 34.85/6.15 % (27155)------------------------------
% 34.85/6.15 % (27158)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_26535 for (2953ds/157Mi)
% 34.85/6.19 % (27158)Instruction limit reached!
% 34.85/6.19 % (27158)------------------------------
% 34.85/6.19 % (27158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.85/6.19 % (27158)Termination reason: Unknown
% 34.85/6.19 % (27158)Termination phase: Saturation
% 34.85/6.19
% 34.85/6.19 % (27158)Memory used [KB]: 6908
% 34.85/6.19 % (27158)Time elapsed: 0.040 s
% 34.85/6.19 % (27158)Instructions burned: 159 (million)
% 34.85/6.19 % (27158)------------------------------
% 34.85/6.19 % (27158)------------------------------
% 35.30/6.20 % (27159)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_26535 for (2953ds/5061Mi)
% 35.30/6.23 % (27157)Instruction limit reached!
% 35.30/6.23 % (27157)------------------------------
% 35.30/6.23 % (27157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.30/6.23 % (27157)Termination reason: Unknown
% 35.30/6.23 % (27157)Termination phase: Saturation
% 35.30/6.23
% 35.30/6.23 % (27157)Memory used [KB]: 7036
% 35.30/6.23 % (27157)Time elapsed: 0.090 s
% 35.30/6.23 % (27157)Instructions burned: 360 (million)
% 35.30/6.23 % (27157)------------------------------
% 35.30/6.23 % (27157)------------------------------
% 35.30/6.24 % (27160)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_26535 for (2953ds/2401Mi)
% 35.30/6.24 % (27153)Instruction limit reached!
% 35.30/6.24 % (27153)------------------------------
% 35.30/6.24 % (27153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.30/6.24 % (27153)Termination reason: Unknown
% 35.30/6.24 % (27153)Termination phase: Saturation
% 35.30/6.24
% 35.30/6.24 % (27153)Memory used [KB]: 7164
% 35.30/6.24 % (27153)Time elapsed: 0.252 s
% 35.30/6.24 % (27153)Instructions burned: 1049 (million)
% 35.30/6.24 % (27153)------------------------------
% 35.30/6.24 % (27153)------------------------------
% 35.30/6.25 % (27156)Instruction limit reached!
% 35.30/6.25 % (27156)------------------------------
% 35.30/6.25 % (27156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.30/6.25 % (27156)Termination reason: Unknown
% 35.30/6.25 % (27156)Termination phase: Saturation
% 35.30/6.25
% 35.30/6.25 % (27156)Memory used [KB]: 15735
% 35.30/6.25 % (27156)Time elapsed: 0.116 s
% 35.30/6.25 % (27156)Instructions burned: 456 (million)
% 35.30/6.25 % (27156)------------------------------
% 35.30/6.25 % (27156)------------------------------
% 35.30/6.25 % (27161)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_26535 for (2953ds/5798Mi)
% 35.30/6.26 % (27162)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_26535 for (2952ds/346Mi)
% 35.30/6.29 % (27150)Instruction limit reached!
% 35.30/6.29 % (27150)------------------------------
% 35.30/6.29 % (27150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.30/6.29 % (27150)Termination reason: Unknown
% 35.30/6.29 % (27150)Termination phase: Saturation
% 35.30/6.29
% 35.30/6.29 % (27150)Memory used [KB]: 8827
% 35.30/6.29 % (27150)Time elapsed: 0.362 s
% 35.30/6.29 % (27150)Instructions burned: 1176 (million)
% 35.30/6.29 % (27150)------------------------------
% 35.30/6.29 % (27150)------------------------------
% 35.30/6.30 % (27163)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_26535 for (2952ds/1321Mi)
% 35.85/6.32 % (27152)Instruction limit reached!
% 35.85/6.32 % (27152)------------------------------
% 35.85/6.32 % (27152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.85/6.32 % (27152)Termination reason: Unknown
% 35.85/6.32 % (27152)Termination phase: Saturation
% 35.85/6.32
% 35.85/6.32 % (27152)Memory used [KB]: 9850
% 35.85/6.32 % (27152)Time elapsed: 0.332 s
% 35.85/6.32 % (27152)Instructions burned: 1202 (million)
% 35.85/6.32 % (27152)------------------------------
% 35.85/6.32 % (27152)------------------------------
% 35.85/6.33 % (27164)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_26535 for (2952ds/1312Mi)
% 35.85/6.35 % (27162)Instruction limit reached!
% 35.85/6.35 % (27162)------------------------------
% 35.85/6.35 % (27162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.85/6.35 % (27162)Termination reason: Unknown
% 35.85/6.35 % (27162)Termination phase: Saturation
% 35.85/6.35
% 35.85/6.35 % (27162)Memory used [KB]: 8187
% 35.85/6.35 % (27162)Time elapsed: 0.089 s
% 35.85/6.35 % (27162)Instructions burned: 347 (million)
% 35.85/6.35 % (27162)------------------------------
% 35.85/6.35 % (27162)------------------------------
% 35.85/6.36 % (27165)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_26535 for (2951ds/672Mi)
% 36.18/6.56 % (27165)Instruction limit reached!
% 36.18/6.56 % (27165)------------------------------
% 36.18/6.56 % (27165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.18/6.56 % (27165)Termination reason: Unknown
% 36.18/6.56 % (27165)Termination phase: Saturation
% 36.18/6.56
% 36.18/6.56 % (27165)Memory used [KB]: 9722
% 36.18/6.56 % (27165)Time elapsed: 0.203 s
% 36.18/6.56 % (27165)Instructions burned: 673 (million)
% 36.18/6.56 % (27165)------------------------------
% 36.18/6.56 % (27165)------------------------------
% 36.18/6.57 % (27166)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_26535 for (2949ds/1897Mi)
% 36.50/6.66 % (27164)Instruction limit reached!
% 36.50/6.66 % (27164)------------------------------
% 36.50/6.66 % (27164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.50/6.66 % (27164)Termination reason: Unknown
% 36.50/6.66 % (27164)Termination phase: Saturation
% 36.50/6.66
% 36.50/6.66 % (27164)Memory used [KB]: 11897
% 36.50/6.66 % (27164)Time elapsed: 0.336 s
% 36.50/6.66 % (27164)Instructions burned: 1315 (million)
% 36.50/6.66 % (27164)------------------------------
% 36.50/6.66 % (27164)------------------------------
% 36.50/6.67 % (27167)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_26535 for (2948ds/1202Mi)
% 36.50/6.68 % (27163)Instruction limit reached!
% 36.50/6.68 % (27163)------------------------------
% 36.50/6.68 % (27163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.50/6.68 % (27163)Termination reason: Unknown
% 36.50/6.68 % (27163)Termination phase: Saturation
% 36.50/6.68
% 36.50/6.68 % (27163)Memory used [KB]: 7036
% 36.50/6.68 % (27163)Time elapsed: 0.386 s
% 36.50/6.68 % (27163)Instructions burned: 1322 (million)
% 36.50/6.68 % (27163)------------------------------
% 36.50/6.68 % (27163)------------------------------
% 36.50/6.69 % (27168)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_26535 for (2948ds/1493Mi)
% 37.55/6.97 % (27160)Instruction limit reached!
% 37.55/6.97 % (27160)------------------------------
% 37.55/6.97 % (27160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/6.97 % (27160)Termination reason: Unknown
% 37.55/6.97 % (27160)Termination phase: Saturation
% 37.55/6.97
% 37.55/6.97 % (27160)Memory used [KB]: 8827
% 37.55/6.97 % (27160)Time elapsed: 0.736 s
% 37.55/6.97 % (27160)Instructions burned: 2403 (million)
% 37.55/6.97 % (27160)------------------------------
% 37.55/6.97 % (27160)------------------------------
% 37.55/6.98 % (27169)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_26535 for (2945ds/7679Mi)
% 37.55/7.02 % (27167)Instruction limit reached!
% 37.55/7.02 % (27167)------------------------------
% 37.55/7.02 % (27167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/7.02 % (27167)Termination reason: Unknown
% 37.55/7.02 % (27167)Termination phase: Saturation
% 37.55/7.02
% 37.55/7.02 % (27167)Memory used [KB]: 7419
% 37.55/7.02 % (27167)Time elapsed: 0.353 s
% 37.55/7.02 % (27167)Instructions burned: 1202 (million)
% 37.55/7.02 % (27167)------------------------------
% 37.55/7.02 % (27167)------------------------------
% 41.19/7.03 % (27170)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_26535 for (2945ds/340Mi)
% 41.19/7.06 % (27168)Instruction limit reached!
% 41.19/7.06 % (27168)------------------------------
% 41.19/7.06 % (27168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.19/7.06 % (27168)Termination reason: Unknown
% 41.19/7.06 % (27168)Termination phase: Saturation
% 41.19/7.06
% 41.19/7.06 % (27168)Memory used [KB]: 7291
% 41.19/7.06 % (27168)Time elapsed: 0.366 s
% 41.19/7.06 % (27168)Instructions burned: 1496 (million)
% 41.19/7.06 % (27168)------------------------------
% 41.19/7.06 % (27168)------------------------------
% 41.19/7.06 % (27171)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_26535 for (2945ds/3672Mi)
% 41.75/7.13 % (27170)Instruction limit reached!
% 41.75/7.13 % (27170)------------------------------
% 41.75/7.13 % (27170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.75/7.13 % (27170)Termination reason: Unknown
% 41.75/7.13 % (27170)Termination phase: Saturation
% 41.75/7.13
% 41.75/7.13 % (27170)Memory used [KB]: 9594
% 41.75/7.13 % (27170)Time elapsed: 0.101 s
% 41.75/7.13 % (27170)Instructions burned: 343 (million)
% 41.75/7.13 % (27170)------------------------------
% 41.75/7.13 % (27170)------------------------------
% 41.75/7.14 % (27172)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_26535 for (2944ds/1535Mi)
% 41.75/7.16 % (27166)Instruction limit reached!
% 41.75/7.16 % (27166)------------------------------
% 41.75/7.16 % (27166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.75/7.16 % (27166)Termination reason: Unknown
% 41.75/7.16 % (27166)Termination phase: Saturation
% 41.75/7.16
% 41.75/7.16 % (27166)Memory used [KB]: 12409
% 41.75/7.16 % (27166)Time elapsed: 0.596 s
% 41.75/7.16 % (27166)Instructions burned: 1898 (million)
% 41.75/7.16 % (27166)------------------------------
% 41.75/7.16 % (27166)------------------------------
% 41.75/7.17 % (27173)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_26535 for (2943ds/4637Mi)
% 42.99/7.44 % (27159)Instruction limit reached!
% 42.99/7.44 % (27159)------------------------------
% 42.99/7.44 % (27159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.99/7.44 % (27159)Termination reason: Unknown
% 42.99/7.44 % (27159)Termination phase: Saturation
% 42.99/7.44
% 42.99/7.44 % (27159)Memory used [KB]: 9083
% 42.99/7.44 % (27159)Time elapsed: 1.236 s
% 42.99/7.44 % (27159)Instructions burned: 5061 (million)
% 42.99/7.44 % (27159)------------------------------
% 42.99/7.44 % (27159)------------------------------
% 42.99/7.45 % (27174)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_26535 for (2941ds/3174Mi)
% 43.35/7.50 % (27140)Instruction limit reached!
% 43.35/7.50 % (27140)------------------------------
% 43.35/7.50 % (27140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.35/7.50 % (27140)Termination reason: Unknown
% 43.35/7.50 % (27140)Termination phase: Saturation
% 43.35/7.50
% 43.35/7.50 % (27140)Memory used [KB]: 12920
% 43.35/7.50 % (27140)Time elapsed: 2.022 s
% 43.35/7.50 % (27140)Instructions burned: 6455 (million)
% 43.35/7.50 % (27140)------------------------------
% 43.35/7.50 % (27140)------------------------------
% 43.35/7.51 % (27161)First to succeed.
% 43.35/7.51 % (27175)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_26535 for (2940ds/307Mi)
% 43.35/7.52 % (27161)Refutation found. Thanks to Tanya!
% 43.35/7.52 % SZS status Theorem for DTF2THF_26535
% 43.35/7.52 % SZS output start Proof for DTF2THF_26535
% 43.35/7.52 thf(func_def_0, type, in: $i > $i > $o).
% 43.35/7.52 thf(func_def_1, type, exu: ($i > $o) > $o).
% 43.35/7.52 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 43.35/7.52 thf(func_def_8, type, powerset: $i > $i).
% 43.35/7.52 thf(func_def_10, type, setunion: $i > $i).
% 43.35/7.52 thf(func_def_19, type, descr: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_26, type, prop2set: $o > $i).
% 43.35/7.52 thf(func_def_36, type, nonempty: $i > $o).
% 43.35/7.52 thf(func_def_69, type, set2prop: $i > $o).
% 43.35/7.52 thf(func_def_88, type, subset: $i > $i > $o).
% 43.35/7.52 thf(func_def_89, type, disjoint: $i > $i > $o).
% 43.35/7.52 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 43.35/7.52 thf(func_def_114, type, binunion: $i > $i > $i).
% 43.35/7.52 thf(func_def_122, type, binintersect: $i > $i > $i).
% 43.35/7.52 thf(func_def_135, type, regular: $i > $o).
% 43.35/7.52 thf(func_def_136, type, setminus: $i > $i > $i).
% 43.35/7.52 thf(func_def_147, type, symdiff: $i > $i > $i).
% 43.35/7.52 thf(func_def_153, type, iskpair: $i > $o).
% 43.35/7.52 thf(func_def_158, type, kpair: $i > $i > $i).
% 43.35/7.52 thf(func_def_160, type, cartprod: $i > $i > $i).
% 43.35/7.52 thf(func_def_177, type, singleton: $i > $o).
% 43.35/7.52 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 43.35/7.52 thf(func_def_184, type, atmost1p: $i > $o).
% 43.35/7.52 thf(func_def_185, type, atleast2p: $i > $o).
% 43.35/7.52 thf(func_def_186, type, atmost2p: $i > $o).
% 43.35/7.52 thf(func_def_187, type, upairsetp: $i > $o).
% 43.35/7.52 thf(func_def_191, type, kfst: $i > $i).
% 43.35/7.52 thf(func_def_203, type, ksnd: $i > $i).
% 43.35/7.52 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 43.35/7.52 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 43.35/7.52 thf(func_def_222, type, func: $i > $i > $i > $o).
% 43.35/7.52 thf(func_def_223, type, funcSet: $i > $i > $i).
% 43.35/7.52 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 43.35/7.52 thf(func_def_249, type, sP1: $i > ($i > $i > $o) > $o).
% 43.35/7.52 thf(func_def_260, type, sP12: ($i > $o) > $i > $o).
% 43.35/7.52 thf(func_def_268, type, sP20: $i > ($i > $o) > $o).
% 43.35/7.52 thf(func_def_270, type, sP22: $i > $i > $i > $o).
% 43.35/7.52 thf(func_def_271, type, sP23: $i > $i > $o).
% 43.35/7.52 thf(func_def_272, type, sP24: $i > $o).
% 43.35/7.52 thf(func_def_273, type, sP25: $i > $i > $o).
% 43.35/7.52 thf(func_def_274, type, sP26: $i > $i > $o).
% 43.35/7.52 thf(func_def_275, type, sP27: $i > $i > $o).
% 43.35/7.52 thf(func_def_278, type, sP30: $i > $i > $i > $o > $o).
% 43.35/7.52 thf(func_def_287, type, sK39: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_288, type, sK40: $i > $o).
% 43.35/7.52 thf(func_def_289, type, sK41: $i > $i > $o).
% 43.35/7.52 thf(func_def_301, type, sK53: $i > $o).
% 43.35/7.52 thf(func_def_307, type, sK59: $i > $i > ($i > $i > $o) > $i).
% 43.35/7.52 thf(func_def_308, type, sK60: $i > $i > ($i > $i > $o) > $i).
% 43.35/7.52 thf(func_def_309, type, sK61: $i > ($i > $i > $o) > $i).
% 43.35/7.52 thf(func_def_310, type, sK62: $i > $i > ($i > $i > $o) > $i).
% 43.35/7.52 thf(func_def_311, type, sK63: $i > ($i > $i > $o) > $i).
% 43.35/7.52 thf(func_def_312, type, sK64: $i > $i > $o).
% 43.35/7.52 thf(func_def_347, type, sK99: $i > $i > $o).
% 43.35/7.52 thf(func_def_348, type, sK100: $i > $o).
% 43.35/7.52 thf(func_def_349, type, sK101: $i > $i).
% 43.35/7.52 thf(func_def_350, type, sK102: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_352, type, sK104: $i > $i > $o).
% 43.35/7.52 thf(func_def_370, type, sK122: $i > $i > $i).
% 43.35/7.52 thf(func_def_380, type, sK132: $i > $o).
% 43.35/7.52 thf(func_def_381, type, sK133: $i > $o).
% 43.35/7.52 thf(func_def_382, type, sK134: ($i > $o) > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_383, type, sK135: ($i > $o) > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_398, type, sK150: $i > $o).
% 43.35/7.52 thf(func_def_399, type, sK151: $i > $o).
% 43.35/7.52 thf(func_def_400, type, sK152: ($i > $o) > ($i > $o) > $i > $i > $i).
% 43.35/7.52 thf(func_def_401, type, sK153: ($i > $o) > ($i > $o) > $i > $i > $i).
% 43.35/7.52 thf(func_def_402, type, sK154: ($i > $i) > $i > $i > $i).
% 43.35/7.52 thf(func_def_405, type, sK157: $i > $i).
% 43.35/7.52 thf(func_def_421, type, sK173: $i > $i > $o).
% 43.35/7.52 thf(func_def_428, type, sK180: $i > $o).
% 43.35/7.52 thf(func_def_432, type, sK184: $i > $o).
% 43.35/7.52 thf(func_def_446, type, sK198: $i > $o).
% 43.35/7.52 thf(func_def_448, type, sK200: $i > $o).
% 43.35/7.52 thf(func_def_450, type, sK202: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_457, type, sK209: $i > $o).
% 43.35/7.52 thf(func_def_459, type, sK211: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_460, type, sK212: $i > $o).
% 43.35/7.52 thf(func_def_464, type, sK216: $i > $i > $i).
% 43.35/7.52 thf(func_def_465, type, sK217: $i > $i > $i).
% 43.35/7.52 thf(func_def_469, type, sK221: ($i > $o) > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_470, type, sK222: ($i > $o) > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_471, type, sK223: $i > $o).
% 43.35/7.52 thf(func_def_472, type, sK224: $i > $o).
% 43.35/7.52 thf(func_def_477, type, sK229: $i > $o).
% 43.35/7.52 thf(func_def_479, type, sK231: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_487, type, sK239: $i > $o).
% 43.35/7.52 thf(func_def_489, type, sK241: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_498, type, sK250: $i > $i > $i).
% 43.35/7.52 thf(func_def_499, type, sK251: $i > $o).
% 43.35/7.52 thf(func_def_501, type, sK253: $i > $o).
% 43.35/7.52 thf(func_def_504, type, sK256: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_505, type, sK257: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_507, type, sK259: $i > $o).
% 43.35/7.52 thf(func_def_544, type, sK296: $i > $i).
% 43.35/7.52 thf(func_def_545, type, sK297: $i > $i).
% 43.35/7.52 thf(func_def_547, type, sK299: $i > $o).
% 43.35/7.52 thf(func_def_555, type, sK307: $i > $o).
% 43.35/7.52 thf(func_def_557, type, sK309: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_558, type, sK310: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_567, type, sK319: $i > $o).
% 43.35/7.52 thf(func_def_570, type, sK322: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_575, type, sK327: $i > $i).
% 43.35/7.52 thf(func_def_581, type, sK333: $i > $i).
% 43.35/7.52 thf(func_def_586, type, sK338: $i > $o).
% 43.35/7.52 thf(func_def_589, type, sK341: $i > $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_590, type, sK342: $i > $o).
% 43.35/7.52 thf(func_def_595, type, sK347: $i > $i > $i).
% 43.35/7.52 thf(func_def_600, type, sK352: $i > $i > $i).
% 43.35/7.52 thf(func_def_601, type, sK353: $i > $o).
% 43.35/7.52 thf(func_def_604, type, sK356: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_605, type, sK357: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_606, type, sK358: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_607, type, sK359: $i > $o).
% 43.35/7.52 thf(func_def_612, type, sK364: $i > $o).
% 43.35/7.52 thf(func_def_625, type, sK377: $i > $i).
% 43.35/7.52 thf(func_def_626, type, sK378: ($i > $i) > $i > $i > $i).
% 43.35/7.52 thf(func_def_630, type, sK382: $i > $o).
% 43.35/7.52 thf(func_def_638, type, sK390: $i > $i > $i).
% 43.35/7.52 thf(func_def_647, type, sK399: $i > $o).
% 43.35/7.52 thf(func_def_648, type, sK400: $i > $i).
% 43.35/7.52 thf(func_def_649, type, sK401: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_650, type, sK402: $i > $i > $i).
% 43.35/7.52 thf(func_def_653, type, sK405: $i > $i > $i).
% 43.35/7.52 thf(func_def_654, type, sK406: $i > $i > $i).
% 43.35/7.52 thf(func_def_655, type, sK407: $i > $i > $i).
% 43.35/7.52 thf(func_def_656, type, sK408: $i > $i > $i).
% 43.35/7.52 thf(func_def_657, type, sK409: $i > $i > $i).
% 43.35/7.52 thf(func_def_658, type, sK410: $i > $i > $i).
% 43.35/7.52 thf(func_def_659, type, sK411: $i > $i > $i).
% 43.35/7.52 thf(func_def_660, type, sK412: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_661, type, sK413: $i > $i).
% 43.35/7.52 thf(func_def_662, type, sK414: $i > $i).
% 43.35/7.52 thf(func_def_663, type, sK415: $i > $i).
% 43.35/7.52 thf(func_def_664, type, sK416: $i > $i).
% 43.35/7.52 thf(func_def_665, type, sK417: $i > $i > $i).
% 43.35/7.52 thf(func_def_666, type, sK418: $i > $i > $i).
% 43.35/7.52 thf(func_def_667, type, sK419: $i > $i > $i).
% 43.35/7.52 thf(func_def_668, type, sK420: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_669, type, sK421: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_670, type, sK422: $i > $i).
% 43.35/7.52 thf(func_def_674, type, sK426: $i > $i > $o).
% 43.35/7.52 thf(func_def_696, type, sK448: $i > $i).
% 43.35/7.52 thf(func_def_715, type, sK467: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_717, type, sK469: $i > $o).
% 43.35/7.52 thf(func_def_720, type, sK472: $i > $i > $o).
% 43.35/7.52 thf(func_def_725, type, sK477: $i > $i > $o).
% 43.35/7.52 thf(func_def_732, type, sK484: $i > $o).
% 43.35/7.52 thf(func_def_734, type, sK486: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_741, type, sK493: $i > $i).
% 43.35/7.52 thf(func_def_742, type, sK494: ($i > $i) > $i > $i > $i).
% 43.35/7.52 thf(func_def_746, type, sK498: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_747, type, sK499: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_763, type, sK515: $i > $o).
% 43.35/7.52 thf(func_def_767, type, sK519: $i > $i).
% 43.35/7.52 thf(func_def_777, type, sK529: $i > $o).
% 43.35/7.52 thf(func_def_819, type, sK571: $i > $i > $i).
% 43.35/7.52 thf(func_def_831, type, sK583: $i > $i).
% 43.35/7.52 thf(func_def_836, type, sK588: $o > $i > $i > $i).
% 43.35/7.52 thf(func_def_842, type, sK594: $i > $i > $i).
% 43.35/7.52 thf(func_def_851, type, sK603: $i > $o).
% 43.35/7.52 thf(func_def_853, type, sK605: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_854, type, sK606: $i > ($i > $i) > $i > $i > $i).
% 43.35/7.52 thf(func_def_855, type, sK607: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_856, type, sK608: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_857, type, sK609: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_858, type, sK610: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_859, type, sK611: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_860, type, sK612: $i > $i > $i > ($i > $i) > $i).
% 43.35/7.52 thf(func_def_861, type, sK613: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_862, type, sK614: $i > $i > $i > ($i > $i) > $i).
% 43.35/7.52 thf(func_def_863, type, sK615: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_864, type, sK616: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_865, type, sK617: $i > $i > $i > ($i > $i) > $i).
% 43.35/7.52 thf(func_def_866, type, sK618: $i > $i).
% 43.35/7.52 thf(func_def_867, type, sK619: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_868, type, sK620: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_869, type, sK621: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_870, type, sK622: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_871, type, sK623: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_872, type, sK624: $i > $i).
% 43.35/7.52 thf(func_def_874, type, sK626: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_875, type, sK627: $i > $i).
% 43.35/7.52 thf(func_def_876, type, sK628: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_877, type, sK629: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_879, type, sK631: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_880, type, sK632: $i > $i).
% 43.35/7.52 thf(func_def_881, type, sK633: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_882, type, sK634: $i > $i).
% 43.35/7.52 thf(func_def_883, type, sK635: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_884, type, sK636: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_885, type, sK637: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_886, type, sK638: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_887, type, sK639: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_888, type, sK640: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_889, type, sK641: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_890, type, sK642: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_891, type, sK643: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_892, type, sK644: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_893, type, sK645: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_894, type, sK646: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_895, type, sK647: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_896, type, sK648: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_897, type, sK649: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_898, type, sK650: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_899, type, sK651: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_900, type, sK652: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_901, type, sK653: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_903, type, sK655: $i > ($i > $i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_904, type, sK656: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_905, type, sK657: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_906, type, sK658: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_907, type, sK659: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_909, type, sK661: $i > $i > $i > $i).
% 43.35/7.52 thf(func_def_910, type, sK662: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_911, type, sK663: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_912, type, sK664: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_913, type, sK665: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_914, type, sK666: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_915, type, sK667: ($i > $o) > $i).
% 43.35/7.52 thf(func_def_916, type, sK668: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_917, type, sK669: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_918, type, sK670: ($i > $o) > $i > $i).
% 43.35/7.52 thf(func_def_919, type, sK671: $i > ($i > $o) > $i).
% 43.35/7.52 thf(func_def_920, type, ph672: !>[X0: $tType]:(X0)).
% 43.35/7.52 thf(f16150,plain,(
% 43.35/7.52 $false),
% 43.35/7.52 inference(subsumption_resolution,[status(thm)],[f16149,f2434])).
% 43.35/7.52 thf(f2434,plain,(
% 43.35/7.52 ($true = (in @ sK383 @ sK381))),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1498])).
% 43.35/7.52 thf(f1498,plain,(
% 43.35/7.52 (vacuousDall = $true) & (quantDeMorgan3 = $true) & (subsetI1 = $true) & (cartprodsndin = $true) & (setunionsingleton = $true) & (emptysetsubset = $true) & (symdiffI1 = $true) & (dpsetconstrEL2 = $true) & (setadjoinIR = $true) & (setext = $true) & (setoftrueEq = $true) & (notinsingleton = $true) & (ubforcartprodlem1 = $true) & (subsetE2 = $true) & (setminusEL = $true) & (setminusSubset2 = $true) & (setukpairIL = $true) & (subsetTrans = $true) & (uniqinunit = $true) & (symdiffIneg1 = $true) & (dpsetconstrERa = $true) & (setextAx = $true) & (dpsetconstrEL1 = $true) & (kfstpairEq = $true) & (binintersectEL = $true) & (dsetconstrI = $true) & (foundationAx = $true) & (powerset__Cong = $true) & (dsetconstrEL = $true) & (replAx = $true) & (binunionIR = $true) & (binintersectRsub = $true) & (exuE1 = $true) & (notsubsetI = $true) & (eqinunit = $true) & (subsetI2 = $true) & (exuEu = $true) & (kfstsingleton = $true) & (notequalI1 = $true) & (binintersectSubset4 = $true) & (setunionE2 = $true) & (setminusIRneg = $true) & (eqimpsubset1 = $true) & (notdallE = $true) & (setminusI = $true) & (prop2set2propI = $true) & (powersetE = $true) & (nonemptyImpWitness = $true) & (setukpairinjR2 = $true) & (secondinupair = $true) & (exuI2 = $true) & (powersetI = $true) & (subsetRefl = $true) & (setbeta = $true) & (nonemptyE1 = $true) & (powersetE1 = $true) & (upairsetIR = $true) & (notequalI2 = $true) & (cartprodpairsurjEq = $true) & (exuE3u = $true) & (sepInPowerset = $true) & (noeltsimpempty = $true) & (ap2p = $true) & (ubforcartprodlem2 = $true) & (app = $true) & (quantDeMorgan4 = $true) & (setadjoinE = $true) & (dsetconstrER = $true) & (sepSubset = $true) & (subset2powerset = $true) & (subPowSU = $true) & (setminusSubset1 = $true) & (subsetE = $true) & (singletonsswitch = $true) & (setadjoinAx = $true) & (setadjoinSub = $true) & (cartprodmempair = $true) & (ksndpairEq = $true) & (omega0Ax = $true) & (lamProp = $true) & (setminusLsub = $true) & (binintersectSubset1 = $true) & (ubforcartprodlem3 = $true) & (setextsub = $true) & (symdiffIneg2 = $true) & (binunionLsub = $true) & (notdexE = $true) & (upairequniteq = $true) & (upairset2IR = $true) & (nonemptyI = $true) & (setminusER = $true) & (infuncsetfunc = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinOr = $true) & (setminusILneg = $true) & (symdiffI2 = $true) & (binintersectER = $true) & (in__Cong = $true) & (singletonprop = $true) & (singletonsuniq = $true) & (emptyE1 = $true) & (disjointsetsI1 = $true) & (dpsetconstrI = $true) & (nonemptyI1 = $true) & (setukpairinjL2 = $true) & (dpsetconstrSub = $true) & (exuI3 = $true) & (prop2setI = $true) & (singletoninpowerset = $true) & (emptysetAx = $true) & (lam2p = $true) & (exu__Cong = $true) & (emptyI = $true) & (binunionIL = $true) & (dsetconstr__Cong = $true) & (exuI1 = $true) & (powersetI1 = $true) & (setadjoin__Cong = $true) & (binintersectLsub = $true) & (powersetsubset = $true) & (wellorderingAx = $true) & (emptyInPowerset = $true) & (setukpairinjR12 = $true) & (((breln @ sK379 @ sK380 @ sK381) = $true) & (! [X4 : $i] : (($true != (in @ X4 @ sK379)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK381) != $true) | ((sK382 @ (kpair @ X4 @ X5)) = $true) | ($true != (in @ X5 @ sK380)))) & (($true != (sK382 @ sK383)) & ($true = (in @ sK383 @ sK381))))) & (inCongP = $true) & (emptysetimpfalse = $true) & (subsetemptysetimpeq = $true) & (setukpairinjR1 = $true) & (emptysetE = $true) & (setminusELneg = $true) & (cartprodmempair1 = $true) & (emptyset__Cong = $true) & (apProp = $true) & (upairsetE = $true) & (omega__Cong = $true) & (binintersectSubset5 = $true) & (kpairiskpair = $true) & (omegaIndAx = $true) & (theprop = $true) & (cartprodpairmemER = $true) & (dpsetconstrER = $true) & (eqimpsubset2 = $true) & (kpairsurjEq = $true) & (upairsubunion = $true) & (funcImageSingleton = $true) & (exuE3e = $true) & (binintersectSubset3 = $true) & (binunionRsub = $true) & (quantDeMorgan2 = $true) & (setukpairinjL1 = $true) & (upairset2E = $true) & (notinemptyset = $true) & (singletonsubset = $true) & (kpairp = $true) & (setunionsingleton2 = $true) & (quantDeMorgan1 = $true) & (lamp = $true) & (setukpairinjR = $true) & (setunionI = $true) & (setminusERneg = $true) & (setOfPairsIsBReln = $true) & (upairsetIL = $true) & (setunionsingleton1 = $true) & (setadjoinSub2 = $true) & (cartprodpairin = $true) & (ex1I = $true) & (descrp = $true) & (setunionE = $true) & (cartprodfstpairEq = $true) & (emptyinunitempty = $true) & (ex1E1 = $true) & (setukpairinjR11 = $true) & (prop2setE = $true) & (funcinfuncset = $true) & (upairinpowunion = $true) & (exuE2 = $true) & (omegaSAx = $true) & (binunionEcases = $true) & (emptyinPowerset = $true) & (cartprodsndpairEq = $true) & (binintersectSubset2 = $true) & (singletoninpowunion = $true) & (descr__Cong = $true) & (ex1I2 = $true) & (inPowerset = $true) & (cartprodfstin = $true) & (binintersectI = $true) & (cartprodmempaircEq = $true) & (setukpairIR = $true) & (symdiffE = $true) & (ksndsingleton = $true) & (setunion__Cong = $true) & (cartprodpairmemEL = $true) & (binunionE = $true) & (bs114d = $true) & (setukpairinjL = $true) & (setadjoinIL = $true)),
% 43.35/7.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK379,sK380,sK381,sK382,sK383])],[f761,f1497,f1496,f1495])).
% 43.35/7.52 thf(f1495,plain,(
% 43.35/7.52 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X0 @ X1 @ X2)) & ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ X2) != $true) | ($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ X5 @ X1) != $true))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ X2))))) => (((breln @ sK379 @ sK380 @ sK381) = $true) & ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ sK379)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK381) != $true) | ($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK380)))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ((in @ X6 @ sK381) = $true))))),
% 43.35/7.52 introduced(definition,[],[choice_axiom])).
% 43.35/7.52 thf(f1496,plain,(
% 43.35/7.52 ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ sK379)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK381) != $true) | ($true = (X3 @ (kpair @ X4 @ X5))) | ($true != (in @ X5 @ sK380)))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ((in @ X6 @ sK381) = $true))) => (! [X4 : $i] : (($true != (in @ X4 @ sK379)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK381) != $true) | ((sK382 @ (kpair @ X4 @ X5)) = $true) | ($true != (in @ X5 @ sK380)))) & ? [X6 : $i] : (($true != (sK382 @ X6)) & ((in @ X6 @ sK381) = $true)))),
% 43.35/7.52 introduced(definition,[],[choice_axiom])).
% 43.35/7.52 thf(f1497,plain,(
% 43.35/7.52 ? [X6 : $i] : (($true != (sK382 @ X6)) & ((in @ X6 @ sK381) = $true)) => (($true != (sK382 @ sK383)) & ($true = (in @ sK383 @ sK381)))),
% 43.35/7.52 introduced(definition,[],[choice_axiom])).
% 43.35/7.52 thf(f761,plain,(
% 43.35/7.52 (vacuousDall = $true) & (quantDeMorgan3 = $true) & (subsetI1 = $true) & (cartprodsndin = $true) & (setunionsingleton = $true) & (emptysetsubset = $true) & (symdiffI1 = $true) & (dpsetconstrEL2 = $true) & (setadjoinIR = $true) & (setext = $true) & (setoftrueEq = $true) & (notinsingleton = $true) & (ubforcartprodlem1 = $true) & (subsetE2 = $true) & (setminusEL = $true) & (setminusSubset2 = $true) & (setukpairIL = $true) & (subsetTrans = $true) & (uniqinunit = $true) & (symdiffIneg1 = $true) & (dpsetconstrERa = $true) & (setextAx = $true) & (dpsetconstrEL1 = $true) & (kfstpairEq = $true) & (binintersectEL = $true) & (dsetconstrI = $true) & (foundationAx = $true) & (powerset__Cong = $true) & (dsetconstrEL = $true) & (replAx = $true) & (binunionIR = $true) & (binintersectRsub = $true) & (exuE1 = $true) & (notsubsetI = $true) & (eqinunit = $true) & (subsetI2 = $true) & (exuEu = $true) & (kfstsingleton = $true) & (notequalI1 = $true) & (binintersectSubset4 = $true) & (setunionE2 = $true) & (setminusIRneg = $true) & (eqimpsubset1 = $true) & (notdallE = $true) & (setminusI = $true) & (prop2set2propI = $true) & (powersetE = $true) & (nonemptyImpWitness = $true) & (setukpairinjR2 = $true) & (secondinupair = $true) & (exuI2 = $true) & (powersetI = $true) & (subsetRefl = $true) & (setbeta = $true) & (nonemptyE1 = $true) & (powersetE1 = $true) & (upairsetIR = $true) & (notequalI2 = $true) & (cartprodpairsurjEq = $true) & (exuE3u = $true) & (sepInPowerset = $true) & (noeltsimpempty = $true) & (ap2p = $true) & (ubforcartprodlem2 = $true) & (app = $true) & (quantDeMorgan4 = $true) & (setadjoinE = $true) & (dsetconstrER = $true) & (sepSubset = $true) & (subset2powerset = $true) & (subPowSU = $true) & (setminusSubset1 = $true) & (subsetE = $true) & (singletonsswitch = $true) & (setadjoinAx = $true) & (setadjoinSub = $true) & (cartprodmempair = $true) & (ksndpairEq = $true) & (omega0Ax = $true) & (lamProp = $true) & (setminusLsub = $true) & (binintersectSubset1 = $true) & (ubforcartprodlem3 = $true) & (setextsub = $true) & (symdiffIneg2 = $true) & (binunionLsub = $true) & (notdexE = $true) & (upairequniteq = $true) & (upairset2IR = $true) & (nonemptyI = $true) & (setminusER = $true) & (infuncsetfunc = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinOr = $true) & (setminusILneg = $true) & (symdiffI2 = $true) & (binintersectER = $true) & (in__Cong = $true) & (singletonprop = $true) & (singletonsuniq = $true) & (emptyE1 = $true) & (disjointsetsI1 = $true) & (dpsetconstrI = $true) & (nonemptyI1 = $true) & (setukpairinjL2 = $true) & (dpsetconstrSub = $true) & (exuI3 = $true) & (prop2setI = $true) & (singletoninpowerset = $true) & (emptysetAx = $true) & (lam2p = $true) & (exu__Cong = $true) & (emptyI = $true) & (binunionIL = $true) & (dsetconstr__Cong = $true) & (exuI1 = $true) & (powersetI1 = $true) & (setadjoin__Cong = $true) & (binintersectLsub = $true) & (powersetsubset = $true) & (wellorderingAx = $true) & (emptyInPowerset = $true) & (setukpairinjR12 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X0 @ X1 @ X2)) & ? [X3 : $i > $o] : (! [X4 : $i] : (($true != (in @ X4 @ X0)) | ! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ X2) != $true) | ($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ X5 @ X1) != $true))) & ? [X6 : $i] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ X2))))) & (inCongP = $true) & (emptysetimpfalse = $true) & (subsetemptysetimpeq = $true) & (setukpairinjR1 = $true) & (emptysetE = $true) & (setminusELneg = $true) & (cartprodmempair1 = $true) & (emptyset__Cong = $true) & (apProp = $true) & (upairsetE = $true) & (omega__Cong = $true) & (binintersectSubset5 = $true) & (kpairiskpair = $true) & (omegaIndAx = $true) & (theprop = $true) & (cartprodpairmemER = $true) & (dpsetconstrER = $true) & (eqimpsubset2 = $true) & (kpairsurjEq = $true) & (upairsubunion = $true) & (funcImageSingleton = $true) & (exuE3e = $true) & (binintersectSubset3 = $true) & (binunionRsub = $true) & (quantDeMorgan2 = $true) & (setukpairinjL1 = $true) & (upairset2E = $true) & (notinemptyset = $true) & (singletonsubset = $true) & (kpairp = $true) & (setunionsingleton2 = $true) & (quantDeMorgan1 = $true) & (lamp = $true) & (setukpairinjR = $true) & (setunionI = $true) & (setminusERneg = $true) & (setOfPairsIsBReln = $true) & (upairsetIL = $true) & (setunionsingleton1 = $true) & (setadjoinSub2 = $true) & (cartprodpairin = $true) & (ex1I = $true) & (descrp = $true) & (setunionE = $true) & (cartprodfstpairEq = $true) & (emptyinunitempty = $true) & (ex1E1 = $true) & (setukpairinjR11 = $true) & (prop2setE = $true) & (funcinfuncset = $true) & (upairinpowunion = $true) & (exuE2 = $true) & (omegaSAx = $true) & (binunionEcases = $true) & (emptyinPowerset = $true) & (cartprodsndpairEq = $true) & (binintersectSubset2 = $true) & (singletoninpowunion = $true) & (descr__Cong = $true) & (ex1I2 = $true) & (inPowerset = $true) & (cartprodfstin = $true) & (binintersectI = $true) & (cartprodmempaircEq = $true) & (setukpairIR = $true) & (symdiffE = $true) & (ksndsingleton = $true) & (setunion__Cong = $true) & (cartprodpairmemEL = $true) & (binunionE = $true) & (bs114d = $true) & (setukpairinjL = $true) & (setadjoinIL = $true)),
% 43.35/7.52 inference(flattening,[status(thm)],[f760])).
% 43.35/7.52 thf(f760,plain,(
% 43.35/7.52 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i > $o] : (? [X6 : $i] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ X2))) & ! [X4 : $i] : (! [X5 : $i] : ((($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X2) != $true)) | ((in @ X5 @ X1) != $true)) | ($true != (in @ X4 @ X0)))) & ($true = (breln @ X0 @ X1 @ X2))) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 43.35/7.52 inference(ennf_transformation,[status(thm)],[f234])).
% 43.35/7.52 thf(f234,plain,(
% 43.35/7.52 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X0 @ X1 @ X2)) => ! [X3 : $i > $o] : (! [X4 : $i] : (($true = (in @ X4 @ X0)) => ! [X5 : $i] : (((in @ X5 @ X1) = $true) => (((in @ (kpair @ X4 @ X5) @ X2) = $true) => ($true = (X3 @ (kpair @ X4 @ X5)))))) => ! [X6 : $i] : (($true = (in @ X6 @ X2)) => ($true = (X3 @ X6))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 43.35/7.52 inference(fool_elimination,[status(thm)],[f233])).
% 43.35/7.52 thf(f233,plain,(
% 43.35/7.52 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i > $o] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X2) => (X3 @ X6)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 43.35/7.52 inference(rectify,[status(thm)],[f207])).
% 43.35/7.52 thf(f207,negated_conjecture,(
% 43.35/7.52 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => ! [X3 : $i,X4 : $i,X12 : $i] : ((breln @ X3 @ X4 @ X12) => ! [X0 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X12) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1 : $i] : ((in @ X1 @ X12) => (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 43.35/7.52 inference(negated_conjecture,[status(cth)],[f206])).
% 43.35/7.52 thf(f206,conjecture,(
% 43.35/7.52 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => ! [X3 : $i,X4 : $i,X12 : $i] : ((breln @ X3 @ X4 @ X12) => ! [X0 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X12) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1 : $i] : ((in @ X1 @ X12) => (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 43.35/7.52 file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',brelnall1)).
% 43.35/7.52 thf(f16149,plain,(
% 43.35/7.52 ($true != (in @ sK383 @ sK381))),
% 43.35/7.52 inference(subsumption_resolution,[status(thm)],[f16148,f2435])).
% 43.35/7.52 thf(f2435,plain,(
% 43.35/7.52 ($true != (sK382 @ sK383))),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1498])).
% 43.35/7.52 thf(f16148,plain,(
% 43.35/7.52 ($true = (sK382 @ sK383)) | ($true != (in @ sK383 @ sK381))),
% 43.35/7.52 inference(subsumption_resolution,[status(thm)],[f16147,f15562])).
% 43.35/7.52 thf(f15562,plain,(
% 43.35/7.52 ((in @ (ksnd @ sK383) @ sK380) = $true)),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f15518])).
% 43.35/7.52 thf(f15518,plain,(
% 43.35/7.52 ($true != $true) | ((in @ (ksnd @ sK383) @ sK380) = $true)),
% 43.35/7.52 inference(superposition,[status(thm)],[f4255,f15508])).
% 43.35/7.52 thf(f15508,plain,(
% 43.35/7.52 ($true = (in @ sK383 @ (cartprod @ sK379 @ sK380)))),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f15487])).
% 43.35/7.52 thf(f15487,plain,(
% 43.35/7.52 ($true = (in @ sK383 @ (cartprod @ sK379 @ sK380))) | ($true != $true)),
% 43.35/7.52 inference(superposition,[status(thm)],[f5302,f2434])).
% 43.35/7.52 thf(f5302,plain,(
% 43.35/7.52 ( ! [X0 : $i] : (($true != (in @ X0 @ sK381)) | ($true = (in @ X0 @ (cartprod @ sK379 @ sK380)))) )),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f5287])).
% 43.35/7.52 thf(f5287,plain,(
% 43.35/7.52 ( ! [X0 : $i] : (($true = (in @ X0 @ (cartprod @ sK379 @ sK380))) | ($true != (in @ X0 @ sK381)) | ($true != $true)) )),
% 43.35/7.52 inference(superposition,[status(thm)],[f3756,f4219])).
% 43.35/7.52 thf(f4219,plain,(
% 43.35/7.52 ($true = (subset @ sK381 @ (cartprod @ sK379 @ sK380)))),
% 43.35/7.52 inference(beta_eta_normalization,[status(thm)],[f3256])).
% 43.35/7.52 thf(f3256,plain,(
% 43.35/7.52 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK379 @ sK380 @ sK381))),
% 43.35/7.52 inference(definition_unfolding,[status(thm)],[f2437,f2662])).
% 43.35/7.52 thf(f2662,plain,(
% 43.35/7.52 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f442])).
% 43.35/7.52 thf(f442,plain,(
% 43.35/7.52 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 43.35/7.52 inference(fool_elimination,[status(thm)],[f441])).
% 43.35/7.52 thf(f441,plain,(
% 43.35/7.52 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 43.35/7.52 inference(rectify,[status(thm)],[f186])).
% 43.35/7.52 thf(f186,axiom,(
% 43.35/7.52 (breln = (^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))))),
% 43.35/7.52 file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',breln)).
% 43.35/7.52 thf(f2437,plain,(
% 43.35/7.52 ((breln @ sK379 @ sK380 @ sK381) = $true)),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1498])).
% 43.35/7.52 thf(f3756,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2))) )),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f3005])).
% 43.35/7.52 thf(f3005,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2))) )),
% 43.35/7.52 inference(definition_unfolding,[status(thm)],[f2044,f2528])).
% 43.35/7.52 thf(f2528,plain,(
% 43.35/7.52 (notsubsetI = $true)),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1498])).
% 43.35/7.52 thf(f2044,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2)) | (notsubsetI != $true)) )),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1131])).
% 43.35/7.52 thf(f1131,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2))) | (notsubsetI != $true)) & ((notsubsetI = $true) | (($true = (subset @ sK165 @ sK166)) & ($true = (in @ sK164 @ sK165)) & ($true != (in @ sK164 @ sK166))))),
% 43.35/7.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK164,sK165,sK166])],[f1129,f1130])).
% 43.35/7.52 thf(f1130,plain,(
% 43.35/7.52 ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X5) = $true) & ((in @ X3 @ X4) = $true) & ($true != (in @ X3 @ X5))) => (($true = (subset @ sK165 @ sK166)) & ($true = (in @ sK164 @ sK165)) & ($true != (in @ sK164 @ sK166)))),
% 43.35/7.52 introduced(definition,[],[choice_axiom])).
% 43.35/7.52 thf(f1129,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2))) | (notsubsetI != $true)) & ((notsubsetI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X5) = $true) & ((in @ X3 @ X4) = $true) & ($true != (in @ X3 @ X5))))),
% 43.35/7.52 inference(rectify,[status(thm)],[f1128])).
% 43.35/7.52 thf(f1128,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2))) | (notsubsetI != $true)) & ((notsubsetI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X2)) & ($true = (in @ X0 @ X1)) & ($true != (in @ X0 @ X2))))),
% 43.35/7.52 inference(nnf_transformation,[status(thm)],[f662])).
% 43.35/7.52 thf(f662,plain,(
% 43.35/7.52 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2))) <=> (notsubsetI = $true)),
% 43.35/7.52 inference(flattening,[status(thm)],[f661])).
% 43.35/7.52 thf(f661,plain,(
% 43.35/7.52 (notsubsetI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((($true != (subset @ X1 @ X2)) | ($true = (in @ X0 @ X2))) | ($true != (in @ X0 @ X1)))),
% 43.35/7.52 inference(ennf_transformation,[status(thm)],[f651])).
% 43.35/7.52 thf(f651,plain,(
% 43.35/7.52 (notsubsetI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) => (($true != (in @ X0 @ X2)) => ($true != (subset @ X1 @ X2))))),
% 43.35/7.52 inference(flattening,[status(thm)],[f598])).
% 43.35/7.52 thf(f598,plain,(
% 43.35/7.52 (notsubsetI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) => (~($true = (in @ X0 @ X2)) => ~($true = (subset @ X1 @ X2))))),
% 43.35/7.52 inference(fool_elimination,[status(thm)],[f597])).
% 43.35/7.52 thf(f597,plain,(
% 43.35/7.52 (notsubsetI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => ~(subset @ X1 @ X2))))),
% 43.35/7.52 inference(rectify,[status(thm)],[f85])).
% 43.35/7.52 thf(f85,axiom,(
% 43.35/7.52 (notsubsetI = ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(subset @ X3 @ X4))))),
% 43.35/7.52 file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',notsubsetI)).
% 43.35/7.52 thf(f4255,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ($true = (in @ (ksnd @ X1) @ X0))) )),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f3302])).
% 43.35/7.52 thf(f3302,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = (in @ (ksnd @ X1) @ X0)) | ($true != (in @ X1 @ (cartprod @ X2 @ X0)))) )),
% 43.35/7.52 inference(definition_unfolding,[status(thm)],[f2643,f2558])).
% 43.35/7.52 thf(f2558,plain,(
% 43.35/7.52 (cartprodsndin = $true)),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1498])).
% 43.35/7.52 thf(f2643,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ($true = (in @ (ksnd @ X1) @ X0)) | (cartprodsndin != $true)) )),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1589])).
% 43.35/7.52 thf(f1589,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ($true = (in @ (ksnd @ X1) @ X0))) | (cartprodsndin != $true)) & ((cartprodsndin = $true) | (($true = (in @ sK436 @ (cartprod @ sK437 @ sK435))) & ($true != (in @ (ksnd @ sK436) @ sK435))))),
% 43.35/7.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK435,sK436,sK437])],[f1587,f1588])).
% 43.35/7.52 thf(f1588,plain,(
% 43.35/7.52 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (cartprod @ X5 @ X3))) & ($true != (in @ (ksnd @ X4) @ X3))) => (($true = (in @ sK436 @ (cartprod @ sK437 @ sK435))) & ($true != (in @ (ksnd @ sK436) @ sK435)))),
% 43.35/7.52 introduced(definition,[],[choice_axiom])).
% 43.35/7.52 thf(f1587,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ($true = (in @ (ksnd @ X1) @ X0))) | (cartprodsndin != $true)) & ((cartprodsndin = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (cartprod @ X5 @ X3))) & ($true != (in @ (ksnd @ X4) @ X3))))),
% 43.35/7.52 inference(rectify,[status(thm)],[f1586])).
% 43.35/7.52 thf(f1586,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ($true = (in @ (ksnd @ X1) @ X0))) | (cartprodsndin != $true)) & ((cartprodsndin = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (cartprod @ X2 @ X0))) & ($true != (in @ (ksnd @ X1) @ X0))))),
% 43.35/7.52 inference(nnf_transformation,[status(thm)],[f734])).
% 43.35/7.52 thf(f734,plain,(
% 43.35/7.52 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ($true = (in @ (ksnd @ X1) @ X0))) <=> (cartprodsndin = $true)),
% 43.35/7.52 inference(ennf_transformation,[status(thm)],[f218])).
% 43.35/7.52 thf(f218,plain,(
% 43.35/7.52 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (cartprod @ X2 @ X0))) => ($true = (in @ (ksnd @ X1) @ X0))) <=> (cartprodsndin = $true)),
% 43.35/7.52 inference(fool_elimination,[status(thm)],[f217])).
% 43.35/7.52 thf(f217,plain,(
% 43.35/7.52 (cartprodsndin = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (in @ (ksnd @ X1) @ X0)))),
% 43.35/7.52 inference(rectify,[status(thm)],[f179])).
% 43.35/7.52 thf(f179,axiom,(
% 43.35/7.52 (cartprodsndin = ! [X4 : $i,X10 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4)))),
% 43.35/7.52 file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',cartprodsndin)).
% 43.35/7.52 thf(f16147,plain,(
% 43.35/7.52 ((in @ (ksnd @ sK383) @ sK380) != $true) | ($true != (in @ sK383 @ sK381)) | ($true = (sK382 @ sK383))),
% 43.35/7.52 inference(subsumption_resolution,[status(thm)],[f16134,f15560])).
% 43.35/7.52 thf(f15560,plain,(
% 43.35/7.52 ($true = (in @ (kfst @ sK383) @ sK379))),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f15519])).
% 43.35/7.52 thf(f15519,plain,(
% 43.35/7.52 ($true = (in @ (kfst @ sK383) @ sK379)) | ($true != $true)),
% 43.35/7.52 inference(superposition,[status(thm)],[f4188,f15508])).
% 43.35/7.52 thf(f4188,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ((in @ (kfst @ X1) @ X2) = $true)) )),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f3451])).
% 43.35/7.52 thf(f3451,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ($true != $true) | ((in @ (kfst @ X1) @ X2) = $true)) )),
% 43.35/7.52 inference(definition_unfolding,[status(thm)],[f2822,f2372])).
% 43.35/7.52 thf(f2372,plain,(
% 43.35/7.52 (cartprodfstin = $true)),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1498])).
% 43.35/7.52 thf(f2822,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ((in @ (kfst @ X1) @ X2) = $true) | (cartprodfstin != $true)) )),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1807])).
% 43.35/7.52 thf(f1807,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ((in @ (kfst @ X1) @ X2) = $true)) | (cartprodfstin != $true)) & ((cartprodfstin = $true) | (((in @ sK575 @ (cartprod @ sK576 @ sK574)) = $true) & ($true != (in @ (kfst @ sK575) @ sK576))))),
% 43.35/7.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK574,sK575,sK576])],[f1805,f1806])).
% 43.35/7.52 thf(f1806,plain,(
% 43.35/7.52 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (cartprod @ X5 @ X3))) & ($true != (in @ (kfst @ X4) @ X5))) => (((in @ sK575 @ (cartprod @ sK576 @ sK574)) = $true) & ($true != (in @ (kfst @ sK575) @ sK576)))),
% 43.35/7.52 introduced(definition,[],[choice_axiom])).
% 43.35/7.52 thf(f1805,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ((in @ (kfst @ X1) @ X2) = $true)) | (cartprodfstin != $true)) & ((cartprodfstin = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (cartprod @ X5 @ X3))) & ($true != (in @ (kfst @ X4) @ X5))))),
% 43.35/7.52 inference(rectify,[status(thm)],[f1804])).
% 43.35/7.52 thf(f1804,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ((in @ (kfst @ X1) @ X2) = $true)) | (cartprodfstin != $true)) & ((cartprodfstin = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (cartprod @ X2 @ X0))) & ((in @ (kfst @ X1) @ X2) != $true)))),
% 43.35/7.52 inference(nnf_transformation,[status(thm)],[f718])).
% 43.35/7.52 thf(f718,plain,(
% 43.35/7.52 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (cartprod @ X2 @ X0))) | ((in @ (kfst @ X1) @ X2) = $true)) <=> (cartprodfstin = $true)),
% 43.35/7.52 inference(ennf_transformation,[status(thm)],[f470])).
% 43.35/7.52 thf(f470,plain,(
% 43.35/7.52 (cartprodfstin = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (cartprod @ X2 @ X0))) => ((in @ (kfst @ X1) @ X2) = $true))),
% 43.35/7.52 inference(fool_elimination,[status(thm)],[f469])).
% 43.35/7.52 thf(f469,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (in @ (kfst @ X1) @ X2)) = cartprodfstin)),
% 43.35/7.52 inference(rectify,[status(thm)],[f167])).
% 43.35/7.52 thf(f167,axiom,(
% 43.35/7.52 (! [X4 : $i,X10 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (kfst @ X10) @ X3)) = cartprodfstin)),
% 43.35/7.52 file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',cartprodfstin)).
% 43.35/7.52 thf(f16134,plain,(
% 43.35/7.52 ($true != (in @ (kfst @ sK383) @ sK379)) | ($true != (in @ sK383 @ sK381)) | ((in @ (ksnd @ sK383) @ sK380) != $true) | ($true = (sK382 @ sK383))),
% 43.35/7.52 inference(superposition,[status(thm)],[f2436,f15559])).
% 43.35/7.52 thf(f15559,plain,(
% 43.35/7.52 (sK383 = (kpair @ (kfst @ sK383) @ (ksnd @ sK383)))),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f15517])).
% 43.35/7.52 thf(f15517,plain,(
% 43.35/7.52 ($true != $true) | (sK383 = (kpair @ (kfst @ sK383) @ (ksnd @ sK383)))),
% 43.35/7.52 inference(superposition,[status(thm)],[f3745,f15508])).
% 43.35/7.52 thf(f3745,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (cartprod @ X1 @ X2)) != $true) | ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)) )),
% 43.35/7.52 inference(trivial_inequality_removal,[status(thm)],[f2952])).
% 43.35/7.52 thf(f2952,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X0 @ (cartprod @ X1 @ X2)) != $true) | ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)) )),
% 43.35/7.52 inference(definition_unfolding,[status(thm)],[f1975,f2503])).
% 43.35/7.52 thf(f2503,plain,(
% 43.35/7.52 (cartprodpairsurjEq = $true)),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1498])).
% 43.35/7.52 thf(f1975,plain,(
% 43.35/7.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0) | ((in @ X0 @ (cartprod @ X1 @ X2)) != $true) | (cartprodpairsurjEq != $true)) )),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1048])).
% 43.35/7.52 thf(f1048,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0) | ((in @ X0 @ (cartprod @ X1 @ X2)) != $true)) | (cartprodpairsurjEq != $true)) & ((cartprodpairsurjEq = $true) | (((kpair @ (kfst @ sK112) @ (ksnd @ sK112)) != sK112) & ($true = (in @ sK112 @ (cartprod @ sK113 @ sK114)))))),
% 43.35/7.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113,sK114])],[f1046,f1047])).
% 43.35/7.52 thf(f1047,plain,(
% 43.35/7.52 ? [X3 : $i,X4 : $i,X5 : $i] : (((kpair @ (kfst @ X3) @ (ksnd @ X3)) != X3) & ($true = (in @ X3 @ (cartprod @ X4 @ X5)))) => (((kpair @ (kfst @ sK112) @ (ksnd @ sK112)) != sK112) & ($true = (in @ sK112 @ (cartprod @ sK113 @ sK114))))),
% 43.35/7.52 introduced(definition,[],[choice_axiom])).
% 43.35/7.52 thf(f1046,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0) | ((in @ X0 @ (cartprod @ X1 @ X2)) != $true)) | (cartprodpairsurjEq != $true)) & ((cartprodpairsurjEq = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((kpair @ (kfst @ X3) @ (ksnd @ X3)) != X3) & ($true = (in @ X3 @ (cartprod @ X4 @ X5)))))),
% 43.35/7.52 inference(rectify,[status(thm)],[f1045])).
% 43.35/7.52 thf(f1045,plain,(
% 43.35/7.52 (! [X0 : $i,X1 : $i,X2 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0) | ((in @ X0 @ (cartprod @ X1 @ X2)) != $true)) | (cartprodpairsurjEq != $true)) & ((cartprodpairsurjEq = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ((in @ X0 @ (cartprod @ X1 @ X2)) = $true)))),
% 43.35/7.52 inference(nnf_transformation,[status(thm)],[f806])).
% 43.35/7.52 thf(f806,plain,(
% 43.35/7.52 ! [X0 : $i,X1 : $i,X2 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0) | ((in @ X0 @ (cartprod @ X1 @ X2)) != $true)) <=> (cartprodpairsurjEq = $true)),
% 43.35/7.52 inference(ennf_transformation,[status(thm)],[f464])).
% 43.35/7.52 thf(f464,plain,(
% 43.35/7.52 (cartprodpairsurjEq = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (cartprod @ X1 @ X2)) = $true) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0))),
% 43.35/7.52 inference(fool_elimination,[status(thm)],[f463])).
% 43.35/7.52 thf(f463,plain,(
% 43.35/7.52 (cartprodpairsurjEq = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X1 @ X2)) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)))),
% 43.35/7.52 inference(rectify,[status(thm)],[f185])).
% 43.35/7.52 thf(f185,axiom,(
% 43.35/7.52 (cartprodpairsurjEq = ! [X10 : $i,X3 : $i,X4 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)))),
% 43.35/7.52 file('/export/starexec/sandbox/tmp/tmp.g6SN7tFXrT/DTF2THF_26535.p',cartprodpairsurjEq)).
% 43.35/7.52 thf(f2436,plain,(
% 43.35/7.52 ( ! [X4 : $i,X5 : $i] : (((in @ (kpair @ X4 @ X5) @ sK381) != $true) | ($true != (in @ X4 @ sK379)) | ($true != (in @ X5 @ sK380)) | ((sK382 @ (kpair @ X4 @ X5)) = $true)) )),
% 43.35/7.52 inference(cnf_transformation,[status(thm)],[f1498])).
% 43.35/7.52 % SZS output end Proof for DTF2THF_26535
% 43.35/7.52 % (27161)------------------------------
% 43.35/7.52 % (27161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.35/7.52 % (27161)Termination reason: Refutation
% 43.35/7.52
% 43.35/7.52 % (27161)Memory used [KB]: 11129
% 43.35/7.52 % (27161)Time elapsed: 1.266 s
% 43.35/7.52 % (27161)Instructions burned: 4014 (million)
% 43.35/7.52 % (27161)------------------------------
% 43.35/7.52 % (27161)------------------------------
% 43.35/7.52 % (26770)Success in time 5.978 s
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