%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU670^1 : 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 : n023.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 09:36:05 AM UTC 2026
% Result : Theorem 13.83s 3.32s
% Output : Refutation 13.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 3263 ( 883 equ; 0 cnn)
% Maximal formula atoms : 188 ( 56 avg)
% Number of connectives : 1961 ( 56 ~; 41 |; 600 &; 493 @)
% ( 5 <=>; 758 =>; 0 <=; 0 <~>)
% Maximal formula depth : 200 ( 27 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 424 ( 420 usr; 200 con; 0-5 aty)
% ( 0 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 210 ( 66 ^; 101 !; 43 ?; 210 :)
% 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_243,type,
sP9: $o > $i > $i > $o ).
thf(func_def_249,type,
sP15: ( $i > $i > $o ) > $i > $o ).
thf(func_def_254,type,
sP20: $i > $o ).
thf(func_def_259,type,
sP25: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_260,type,
sP26: ( $i > $o ) > $i > $o ).
thf(func_def_261,type,
sP27: $i > ( $i > $o ) > $o ).
thf(func_def_262,type,
sP28: ( $i > $o ) > $i > $o ).
thf(func_def_263,type,
sP29: ( $i > $o ) > $i > $o ).
thf(func_def_266,type,
sP32: $i > $i > $o ).
thf(func_def_270,type,
sP36: $i > $i > $i > $o ).
thf(func_def_271,type,
sP37: $i > $i > $o ).
thf(func_def_272,type,
sP38: $i > $o ).
thf(func_def_273,type,
sP39: $i > $i > $o ).
thf(func_def_274,type,
sP40: $i > $i > $o ).
thf(func_def_275,type,
sP41: $i > $i > $o ).
thf(func_def_278,type,
sP44: $o > $i > $i > $i > $o ).
thf(func_def_279,type,
sP45: $i > $i > $i > $o ).
thf(func_def_280,type,
sP46: $i > $i > $o > $o ).
thf(func_def_281,type,
sP47: $i > $i > $i > $o ).
thf(func_def_300,type,
sK66: $i > $i > $i ).
thf(func_def_330,type,
sK96: $i > $i > $o ).
thf(func_def_352,type,
sK118: $i > $i > $i ).
thf(func_def_354,type,
sK120: $i > $o ).
thf(func_def_356,type,
sK122: ( $i > $o ) > $i > $i ).
thf(func_def_360,type,
sK126: $i > $i > $o ).
thf(func_def_378,type,
sK144: $i > $i > $i > $i ).
thf(func_def_379,type,
sK145: $i > $i > $i > $i ).
thf(func_def_380,type,
sK146: $i > $i > $o ).
thf(func_def_385,type,
sK151: $i > $o ).
thf(func_def_386,type,
sK152: $i > $i ).
thf(func_def_387,type,
sK153: ( $i > $o ) > $i ).
thf(func_def_389,type,
sK155: $i > $o ).
thf(func_def_402,type,
sK168: $i > $o ).
thf(func_def_403,type,
sK169: $i > $o ).
thf(func_def_404,type,
sK170: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_405,type,
sK171: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_408,type,
sK174: $i > $o ).
thf(func_def_410,type,
sK176: ( $i > $o ) > $i > $i ).
thf(func_def_415,type,
sK181: $i > $o ).
thf(func_def_417,type,
sK183: $i > ( $i > $o ) > $i ).
thf(func_def_419,type,
sK185: $i > $i ).
thf(func_def_424,type,
sK190: $i > $o ).
thf(func_def_434,type,
sK200: $i > $i > $i ).
thf(func_def_435,type,
sK201: $i > $o ).
thf(func_def_437,type,
sK203: $i > ( $i > $o ) > $i ).
thf(func_def_439,type,
sK205: $i > $o ).
thf(func_def_446,type,
sK212: $i > $o ).
thf(func_def_469,type,
sK235: $i > $o ).
thf(func_def_470,type,
sK236: ( $i > $o ) > $i ).
thf(func_def_475,type,
sK241: $i > $o ).
thf(func_def_476,type,
sK242: $i > $i ).
thf(func_def_477,type,
sK243: ( $i > $o ) > $i ).
thf(func_def_480,type,
sK246: $i > $i > $i ).
thf(func_def_485,type,
sK251: $i > $i > $o ).
thf(func_def_490,type,
sK256: $i > $i > $o ).
thf(func_def_492,type,
sK258: $i > ( $i > $i > $o ) > $i ).
thf(func_def_493,type,
sK259: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_494,type,
sK260: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_495,type,
sK261: ( $i > $i > $o ) > $i > $i ).
thf(func_def_496,type,
sK262: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_498,type,
sK264: $i > $i > $o ).
thf(func_def_508,type,
sK274: $i > $o ).
thf(func_def_510,type,
sK276: ( $i > $o ) > $i ).
thf(func_def_511,type,
sK277: ( $i > $o ) > $i ).
thf(func_def_518,type,
sK284: $i > $o ).
thf(func_def_540,type,
sK306: $i > $i > $i ).
thf(func_def_541,type,
sK307: $i > $o ).
thf(func_def_544,type,
sK310: $i > ( $i > $o ) > $i ).
thf(func_def_564,type,
sK330: $i > $i ).
thf(func_def_567,type,
sK333: $i > $i ).
thf(func_def_568,type,
sK334: $i > $i ).
thf(func_def_570,type,
sK336: $i > $o ).
thf(func_def_573,type,
sK339: $i > $i > ( $i > $o ) > $i ).
thf(func_def_580,type,
sK346: $i > $i ).
thf(func_def_600,type,
sK366: $i > $i > $o ).
thf(func_def_603,type,
sK369: $i > $o ).
thf(func_def_605,type,
sK371: ( $i > $o ) > $i > $i ).
thf(func_def_615,type,
sK381: $i > $o ).
thf(func_def_617,type,
sK383: $i > ( $i > $o ) > $i ).
thf(func_def_618,type,
sK384: $i > $o ).
thf(func_def_621,type,
sK387: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_622,type,
sK388: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_625,type,
sK391: $i > $o ).
thf(func_def_626,type,
sK392: $i > $o ).
thf(func_def_633,type,
sK399: $i > ( $i > $o ) > $i ).
thf(func_def_634,type,
sK400: $i > ( $i > $o ) > $i ).
thf(func_def_635,type,
sK401: ( $i > $o ) > $i > $i ).
thf(func_def_636,type,
sK402: $i > $o ).
thf(func_def_640,type,
sK406: ( $i > $o ) > $i > $i ).
thf(func_def_641,type,
sK407: ( $i > $o ) > $i > $i ).
thf(func_def_642,type,
sK408: ( $i > $o ) > $i > $i ).
thf(func_def_644,type,
sK410: $i > $o ).
thf(func_def_655,type,
sK421: $i > $o ).
thf(func_def_667,type,
sK433: $i > $o ).
thf(func_def_671,type,
sK437: $i > $o ).
thf(func_def_674,type,
sK440: $i > $o ).
thf(func_def_676,type,
sK442: ( $i > $o ) > $i > $i ).
thf(func_def_685,type,
sK451: $i > $o ).
thf(func_def_687,type,
sK453: ( $i > $o ) > $i > $i ).
thf(func_def_692,type,
sK458: $i > $i > $i ).
thf(func_def_693,type,
sK459: $i > $i > $i ).
thf(func_def_699,type,
sK465: $i > $i > $i ).
thf(func_def_704,type,
sK470: $i > $o ).
thf(func_def_705,type,
sK471: $i > $o ).
thf(func_def_706,type,
sK472: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_707,type,
sK473: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_714,type,
sK480: $i > $o ).
thf(func_def_724,type,
sK490: $i > $i > $i ).
thf(func_def_725,type,
sK491: $i > $i > $i ).
thf(func_def_726,type,
sK492: $i > $i > $i ).
thf(func_def_727,type,
sK493: $i > $i > $i ).
thf(func_def_728,type,
sK494: $i > $i > $i ).
thf(func_def_729,type,
sK495: $i > $i > $i ).
thf(func_def_730,type,
sK496: $i > $i > $i ).
thf(func_def_731,type,
sK497: $i > $i > $i > $i ).
thf(func_def_732,type,
sK498: $i > $i ).
thf(func_def_733,type,
sK499: $i > $i ).
thf(func_def_734,type,
sK500: $i > $i ).
thf(func_def_735,type,
sK501: $i > $i ).
thf(func_def_736,type,
sK502: $i > $i > $i ).
thf(func_def_737,type,
sK503: $i > $i > $i ).
thf(func_def_738,type,
sK504: $i > $i > $i ).
thf(func_def_739,type,
sK505: $i > $i > $i > $i ).
thf(func_def_740,type,
sK506: $i > $i > $i > $i ).
thf(func_def_741,type,
sK507: $i > $i ).
thf(func_def_748,type,
sK514: $o > $i > $i > $i ).
thf(func_def_753,type,
sK519: $i > $i > $i ).
thf(func_def_770,type,
sK536: $i > $i > $i > $o ).
thf(func_def_774,type,
sK540: $i > $o ).
thf(func_def_776,type,
sK542: $i > $i > $i ).
thf(func_def_779,type,
sK545: $i > $o ).
thf(func_def_785,type,
sK551: $i > $i > $i > $o ).
thf(func_def_801,type,
sK567: $i > $i ).
thf(func_def_802,type,
sK568: $i > $i ).
thf(func_def_806,type,
sK572: $i > $i ).
thf(func_def_812,type,
sK578: $i > $i ).
thf(func_def_813,type,
sK579: $i > $i ).
thf(func_def_814,type,
sK580: ( $i > $o ) > $i > $i ).
thf(func_def_815,type,
sK581: ( $i > $o ) > $i ).
thf(func_def_816,type,
sK582: ( $i > $o ) > $i > $i ).
thf(func_def_817,type,
sK583: ( $i > $o ) > $i > $i ).
thf(func_def_818,type,
sK584: ( $i > $o ) > $i ).
thf(func_def_819,type,
sK585: ( $i > $o ) > $i > $i ).
thf(func_def_820,type,
sK586: ( $i > $o ) > $i > $i ).
thf(func_def_821,type,
sK587: $i > ( $i > $o ) > $i ).
thf(func_def_822,type,
sK588: ( $i > $o ) > $i > $i ).
thf(func_def_823,type,
sK589: ( $i > $o ) > $i > $i ).
thf(func_def_824,type,
sK590: ( $i > $o ) > $i ).
thf(func_def_825,type,
sK591: ( $i > $o ) > $i > $i ).
thf(func_def_826,type,
sK592: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_827,type,
sK593: ( $i > $o ) > $i ).
thf(func_def_828,type,
sK594: ( $i > $o ) > $i > $i ).
thf(func_def_829,type,
sK595: $i > $i ).
thf(func_def_830,type,
sK596: $i > $i ).
thf(func_def_831,type,
sK597: $i > $i ).
thf(func_def_832,type,
sK598: ( $i > $o ) > $i ).
thf(func_def_833,type,
sK599: $i > ( $i > $o ) > $i ).
thf(func_def_834,type,
sK600: ( $i > $o ) > $i > $i ).
thf(func_def_835,type,
sK601: ( $i > $o ) > $i ).
thf(func_def_836,type,
sK602: $i > $i ).
thf(func_def_837,type,
sK603: $i > $i ).
thf(func_def_838,type,
sK604: $i > $i ).
thf(func_def_842,type,
sK608: ( $i > $o ) > $i > $i ).
thf(func_def_843,type,
sK609: ( $i > $o ) > $i ).
thf(func_def_844,type,
sK610: ( $i > $o ) > $i > $i ).
thf(func_def_845,type,
sK611: $i > ( $i > $o ) > $i ).
thf(func_def_846,type,
sK612: $i > ( $i > $o ) > $i ).
thf(func_def_848,type,
sK614: ( $i > $o ) > $i > $i ).
thf(func_def_849,type,
sK615: $i > ( $i > $o ) > $i ).
thf(func_def_850,type,
sK616: $i > ( $i > $o ) > $i ).
thf(func_def_851,type,
sK617: $i > ( $i > $o ) > $i ).
thf(func_def_852,type,
sK618: $i > ( $i > $o ) > $i ).
thf(func_def_853,type,
sK619: ( $i > $o ) > $i ).
thf(func_def_855,type,
sK621: $i > ( $i > $o ) > $i ).
thf(func_def_857,type,
sK623: ( $i > $o ) > $i ).
thf(func_def_858,type,
sK624: ( $i > $o ) > $i ).
thf(func_def_859,type,
sK625: ( $i > $o ) > $i > $i ).
thf(func_def_860,type,
sK626: ( $i > $o ) > $i > $i ).
thf(func_def_861,type,
sK627: ( $i > $o ) > $i > $i ).
thf(func_def_862,type,
sK628: ( $i > $o ) > $i > $i ).
thf(func_def_863,type,
sK629: ( $i > $o ) > $i ).
thf(func_def_864,type,
sK630: ( $i > $o ) > $i > $i ).
thf(func_def_865,type,
sK631: ( $i > $o ) > $i > $i ).
thf(func_def_866,type,
sK632: ( $i > $o ) > $i ).
thf(func_def_867,type,
sK633: ( $i > $o ) > $i > $i ).
thf(func_def_869,type,
sK635: $i > ( $i > $o ) > $i ).
thf(func_def_870,type,
sK636: ( $i > $o ) > $i > $i ).
thf(func_def_871,type,
sK637: ( $i > $o ) > $i > $i ).
thf(func_def_872,type,
sK638: $i > $i ).
thf(func_def_874,type,
ph639:
!>[X0: $tType] : X0 ).
thf(func_def_877,type,
sK642: $i > $i > $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_878,type,
sK643: $i > $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(f7952,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f7951,f2121]) ).
thf(f2121,plain,
( ( in @ sK250 @ sK249 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1222]) ).
thf(f1222,plain,
( ( singletonsswitch = $true )
& ( disjointsetsI1 = $true )
& ( upairinpowunion = $true )
& ( cartprodfstin = $true )
& ( setbeta = $true )
& ( singletoninpowerset = $true )
& ( kfstsingleton = $true )
& ( singletonprop = $true )
& ( setOfPairsIsBReln = $true )
& ( cartprodpairsurjEq = $true )
& ( subsetTrans = $true )
& ( cartprodsndpairEq = $true )
& ( powersetI = $true )
& ( binunionE = $true )
& ( setminusSubset2 = $true )
& ( ksndpairEq = $true )
& ( setminusIRneg = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( binintersectI = $true )
& ( binintersectEL = $true )
& ( upairequniteq = $true )
& ( wellorderingAx = $true )
& ( emptysetimpfalse = $true )
& ( sepInPowerset = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( ex1I2 = $true )
& ( setukpairinjR12 = $true )
& ( replAx = $true )
& ( secondinupair = $true )
& ( nonemptyI = $true )
& ( setunionE2 = $true )
& ( emptyInPowerset = $true )
& ( dpsetconstrERa = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( setminusLsub = $true )
& ( binintersectLsub = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( setunionsingleton = $true )
& ( exuE1 = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( subsetE2 = $true )
& ( notinsingleton = $true )
& ( setminusI = $true )
& ( setukpairinjL2 = $true )
& ( symdiffIneg1 = $true )
& ( kfstpairEq = $true )
& ( binunionRsub = $true )
& ( cartprodpairin = $true )
& ( ksndsingleton = $true )
& ( prop2setE = $true )
& ( exuI2 = $true )
& ( exuEu = $true )
& ( setukpairIR = $true )
& ( setminusERneg = $true )
& ( upairsetE = $true )
& ( nonemptyI1 = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectSubset1 = $true )
& ( binunionLsub = $true )
& ( exuI1 = $true )
& ( subsetI2 = $true )
& ( cartprodpairmemER = $true )
& ( setukpairinjR2 = $true )
& ( ubforcartprodlem3 = $true )
& ( kpairiskpair = $true )
& ( emptysetE = $true )
& ( symdiffI1 = $true )
& ( cartprodmempair = $true )
& ( setminusSubset1 = $true )
& ( notequalI2 = $true )
& ( subset2powerset = $true )
& ( binunionIR = $true )
& ( notsubsetI = $true )
& ( setadjoinOr = $true )
& ( nonemptyImpWitness = $true )
& ( setunionsingleton1 = $true )
& ( symdiffI2 = $true )
& ( eqinunit = $true )
& ( setunionI = $true )
& ( emptysetAx = $true )
& ( setukpairIL = $true )
& ( binintersectSubset5 = $true )
& ( cartprodfstpairEq = $true )
& ( kpairsurjEq = $true )
& ( kpairp = $true )
& ( powersetI1 = $true )
& ( emptyinPowerset = $true )
& ( prop2set2propI = $true )
& ( dsetconstrEL = $true )
& ( quantDeMorgan4 = $true )
& ( notdexE = $true )
& ( ex1E1 = $true )
& ( omegaSAx = $true )
& ( setminusELneg = $true )
& ( powersetE = $true )
& ( setadjoinSub = $true )
& ( emptyE1 = $true )
& ( setminusER = $true )
& ( theprop = $true )
& ( setunionE = $true )
& ( subsetRefl = $true )
& ( notequalI1 = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem2 = $true )
& ( setukpairinjL = $true )
& ( uniqinunit = $true )
& ( upairsubunion = $true )
& ( setadjoin__Cong = $true )
& ( cartprodpairmemEL = $true )
& ( eqimpsubset1 = $true )
& ( in__Cong = $true )
& ( upairset2E = $true )
& ( setadjoinIL = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( inPowerset = $true )
& ( cartprodmempair1 = $true )
& ( prop2setI = $true )
& ( symdiffE = $true )
& ( setukpairinjL1 = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg2 = $true )
& ( upairset2IR = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR1 = $true )
& ( emptyI = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodsndin = $true )
& ( exuI3 = $true )
& ( setadjoinAx = $true )
& ( setadjoinIR = $true )
& ( dsetconstrI = $true )
& ( noeltsimpempty = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjR = $true )
& ( singletonsuniq = $true )
& ( inCongP = $true )
& ( cartprodmempaircEq = $true )
& ( exuE3u = $true )
& ( setextAx = $true )
& ( subsetE = $true )
& ( descr__Cong = $true )
& ( binintersectSubset2 = $true )
& ( setextsub = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true )
& ( ( in @ sK250 @ sK249 )
!= $true )
& ( ( in @ ( kpair @ sK252 @ sK250 )
@ ( dpsetconstr @ sK253 @ sK249
@ ^ [Y0: $i,Y1: $i] : ( sK251 @ Y0 @ Y1 ) ) )
= $true )
& ( sepSubset = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR11 = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( setadjoinE = $true )
& ( setunionsingleton2 = $true )
& ( emptyinunitempty = $true )
& ( notdallE = $true )
& ( ubforcartprodlem1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( dpsetconstrSub = $true )
& ( singletoninpowunion = $true )
& ( setext = $true )
& ( setminusILneg = $true )
& ( exu__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( descrp = $true )
& ( powersetE1 = $true )
& ( binintersectSubset4 = $true )
& ( dpsetconstrEL1 = $true )
& ( setunionAx = $true )
& ( binunionEcases = $true )
& ( singletonsubset = $true )
& ( ex1I = $true )
& ( bs114d = $true )
& ( exuE2 = $true )
& ( eqimpsubset2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK249,sK250,sK251,sK252,sK253])],[f687,f1221]) ).
thf(f1221,plain,
( ? [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X1 )
@ ( dpsetconstr @ X4 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( in @ sK250 @ sK249 )
!= $true )
& ( ( in @ ( kpair @ sK252 @ sK250 )
@ ( dpsetconstr @ sK253 @ sK249
@ ^ [Y0: $i,Y1: $i] : ( sK251 @ Y0 @ Y1 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f687,plain,
( ( singletonsswitch = $true )
& ( disjointsetsI1 = $true )
& ( upairinpowunion = $true )
& ( cartprodfstin = $true )
& ( setbeta = $true )
& ( singletoninpowerset = $true )
& ( kfstsingleton = $true )
& ( singletonprop = $true )
& ( setOfPairsIsBReln = $true )
& ( cartprodpairsurjEq = $true )
& ( subsetTrans = $true )
& ( cartprodsndpairEq = $true )
& ( powersetI = $true )
& ( binunionE = $true )
& ( setminusSubset2 = $true )
& ( ksndpairEq = $true )
& ( setminusIRneg = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( binintersectI = $true )
& ( binintersectEL = $true )
& ( upairequniteq = $true )
& ( wellorderingAx = $true )
& ( emptysetimpfalse = $true )
& ( sepInPowerset = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( ex1I2 = $true )
& ( setukpairinjR12 = $true )
& ( replAx = $true )
& ( secondinupair = $true )
& ( nonemptyI = $true )
& ( setunionE2 = $true )
& ( emptyInPowerset = $true )
& ( dpsetconstrERa = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( setminusLsub = $true )
& ( binintersectLsub = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( setunionsingleton = $true )
& ( exuE1 = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( subsetE2 = $true )
& ( notinsingleton = $true )
& ( setminusI = $true )
& ( setukpairinjL2 = $true )
& ( symdiffIneg1 = $true )
& ( kfstpairEq = $true )
& ( binunionRsub = $true )
& ( cartprodpairin = $true )
& ( ksndsingleton = $true )
& ( prop2setE = $true )
& ( exuI2 = $true )
& ( exuEu = $true )
& ( setukpairIR = $true )
& ( setminusERneg = $true )
& ( upairsetE = $true )
& ( nonemptyI1 = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectSubset1 = $true )
& ( binunionLsub = $true )
& ( exuI1 = $true )
& ( subsetI2 = $true )
& ( cartprodpairmemER = $true )
& ( setukpairinjR2 = $true )
& ( ubforcartprodlem3 = $true )
& ( kpairiskpair = $true )
& ( emptysetE = $true )
& ( symdiffI1 = $true )
& ( cartprodmempair = $true )
& ( setminusSubset1 = $true )
& ( notequalI2 = $true )
& ( subset2powerset = $true )
& ( binunionIR = $true )
& ( notsubsetI = $true )
& ( setadjoinOr = $true )
& ( nonemptyImpWitness = $true )
& ( setunionsingleton1 = $true )
& ( symdiffI2 = $true )
& ( eqinunit = $true )
& ( setunionI = $true )
& ( emptysetAx = $true )
& ( setukpairIL = $true )
& ( binintersectSubset5 = $true )
& ( cartprodfstpairEq = $true )
& ( kpairsurjEq = $true )
& ( kpairp = $true )
& ( powersetI1 = $true )
& ( emptyinPowerset = $true )
& ( prop2set2propI = $true )
& ( dsetconstrEL = $true )
& ( quantDeMorgan4 = $true )
& ( notdexE = $true )
& ( ex1E1 = $true )
& ( omegaSAx = $true )
& ( setminusELneg = $true )
& ( powersetE = $true )
& ( setadjoinSub = $true )
& ( emptyE1 = $true )
& ( setminusER = $true )
& ( theprop = $true )
& ( setunionE = $true )
& ( subsetRefl = $true )
& ( notequalI1 = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem2 = $true )
& ( setukpairinjL = $true )
& ( uniqinunit = $true )
& ( upairsubunion = $true )
& ( setadjoin__Cong = $true )
& ( cartprodpairmemEL = $true )
& ( eqimpsubset1 = $true )
& ( in__Cong = $true )
& ( upairset2E = $true )
& ( setadjoinIL = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( inPowerset = $true )
& ( cartprodmempair1 = $true )
& ( prop2setI = $true )
& ( symdiffE = $true )
& ( setukpairinjL1 = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg2 = $true )
& ( upairset2IR = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR1 = $true )
& ( emptyI = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodsndin = $true )
& ( exuI3 = $true )
& ( setadjoinAx = $true )
& ( setadjoinIR = $true )
& ( dsetconstrI = $true )
& ( noeltsimpempty = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjR = $true )
& ( singletonsuniq = $true )
& ( inCongP = $true )
& ( cartprodmempaircEq = $true )
& ( exuE3u = $true )
& ( setextAx = $true )
& ( subsetE = $true )
& ( descr__Cong = $true )
& ( binintersectSubset2 = $true )
& ( setextsub = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true )
& ? [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X1 )
@ ( dpsetconstr @ X4 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) )
& ( sepSubset = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR11 = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( setadjoinE = $true )
& ( setunionsingleton2 = $true )
& ( emptyinunitempty = $true )
& ( notdallE = $true )
& ( ubforcartprodlem1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( dpsetconstrSub = $true )
& ( singletoninpowunion = $true )
& ( setext = $true )
& ( setminusILneg = $true )
& ( exu__Cong = $true )
& ( dsetconstr__Cong = $true )
& ( descrp = $true )
& ( powersetE1 = $true )
& ( binintersectSubset4 = $true )
& ( dpsetconstrEL1 = $true )
& ( setunionAx = $true )
& ( binunionEcases = $true )
& ( singletonsubset = $true )
& ( ex1I = $true )
& ( bs114d = $true )
& ( exuE2 = $true )
& ( eqimpsubset2 = $true ) ),
inference(flattening,[status(thm)],[f686]) ).
thf(f686,plain,
( ? [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X1 )
@ ( dpsetconstr @ X4 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) )
& ( 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)],[f282]) ).
thf(f282,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 )
=> ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ X1 )
@ ( dpsetconstr @ X4 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) )
=> ( $true
= ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f281]) ).
thf(f281,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
=> ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X1 )
@ ( dpsetconstr @ X4 @ X0
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) )
=> ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f194]) ).
thf(f194,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
=> ! [X4: $i,X2: $i,X0: $i > $i > $o,X1: $i,X3: $i] :
( ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X3 @ X4
@ ^ [X8: $i,X10: $i] : ( X0 @ X8 @ X10 ) ) )
=> ( in @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f193]) ).
thf(f193,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
=> ! [X4: $i,X2: $i,X0: $i > $i > $o,X1: $i,X3: $i] :
( ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X3 @ X4
@ ^ [X8: $i,X10: $i] : ( X0 @ X8 @ X10 ) ) )
=> ( in @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',dpsetconstrEL2) ).
thf(f7951,plain,
( ( in @ sK250 @ sK249 )
= $true ),
inference(forward_demodulation,[status(thm)],[f7934,f4141]) ).
thf(f4141,plain,
! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ),
inference(trivial_inequality_removal,[status(thm)],[f3005]) ).
thf(f3005,plain,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f2090,f2263]) ).
thf(f2263,plain,
ksndpairEq = $true,
inference(cnf_transformation,[status(thm)],[f1222]) ).
thf(f2090,plain,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
| ( ksndpairEq != $true ) ),
inference(cnf_transformation,[status(thm)],[f1220]) ).
thf(f1220,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ( ( ksnd @ ( kpair @ sK247 @ sK248 ) )
!= sK248 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK247,sK248])],[f1218,f1219]) ).
thf(f1219,plain,
( ? [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
!= X3 )
=> ( ( ksnd @ ( kpair @ sK247 @ sK248 ) )
!= sK248 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1218,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ? [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
!= X3 ) ) ),
inference(rectify,[status(thm)],[f1217]) ).
thf(f1217,plain,
( ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
| ( ksndpairEq != $true ) )
& ( ( ksndpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 ) ) ),
inference(nnf_transformation,[status(thm)],[f199]) ).
thf(f199,plain,
( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
<=> ( ksndpairEq = $true ) ),
inference(fool_elimination,[status(thm)],[f198]) ).
thf(f198,plain,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
= ksndpairEq ),
inference(rectify,[status(thm)],[f177]) ).
thf(f177,axiom,
! [X1: $i,X2: $i] :
( ( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 )
= ksndpairEq ),
file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',ksndpairEq) ).
thf(f7934,plain,
( $true
= ( in @ ( ksnd @ ( kpair @ sK252 @ sK250 ) ) @ sK249 ) ),
inference(trivial_inequality_removal,[status(thm)],[f7922]) ).
thf(f7922,plain,
( ( $true
= ( in @ ( ksnd @ ( kpair @ sK252 @ sK250 ) ) @ sK249 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3751,f6576]) ).
thf(f6576,plain,
( ( in @ ( kpair @ sK252 @ sK250 ) @ ( cartprod @ sK253 @ sK249 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f6572]) ).
thf(f6572,plain,
( ( ( in @ ( kpair @ sK252 @ sK250 ) @ ( cartprod @ sK253 @ sK249 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3487,f3642]) ).
thf(f3642,plain,
( $true
= ( in @ ( kpair @ sK252 @ sK250 )
@ ( dsetconstr @ ( cartprod @ sK253 @ sK249 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK253 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK249 )
& ( sK251 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3007]) ).
thf(f3007,plain,
( ( in @ ( kpair @ sK252 @ sK250 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) )
@ sK253
@ sK249
@ ^ [Y0: $i,Y1: $i] : ( sK251 @ Y0 @ Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f2120,f1879]) ).
thf(f1879,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
thf(f221,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f220]) ).
thf(f220,plain,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( ( kpair @ X4 @ X5 )
= X3 )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) )
& ( in @ X4 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f187]) ).
thf(f187,axiom,
( dpsetconstr
= ( ^ [X3: $i,X4: $i,X0: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X3 @ X4 )
@ ^ [X10: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( ( kpair @ X1 @ X2 )
= X10 )
& ( X0 @ X1 @ X2 )
& ( in @ X2 @ X4 ) )
& ( in @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',dpsetconstr) ).
thf(f2120,plain,
( ( in @ ( kpair @ sK252 @ sK250 )
@ ( dpsetconstr @ sK253 @ sK249
@ ^ [Y0: $i,Y1: $i] : ( sK251 @ Y0 @ Y1 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1222]) ).
thf(f3487,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) ) )
| ( $true
= ( in @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3486]) ).
thf(f3486,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
| ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2934]) ).
thf(f2934,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f2006,f2181]) ).
thf(f2181,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f1222]) ).
thf(f2006,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f1117]) ).
thf(f1117,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ( ( ( in @ sK191
@ ( dsetconstr @ sK192
@ ^ [Y0: $i] : ( sK190 @ Y0 ) ) )
= $true )
& ( $true
!= ( in @ sK191 @ sK192 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190,sK191,sK192])],[f1115,f1116]) ).
thf(f1116,plain,
( ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
& ( $true
!= ( in @ X4 @ X5 ) ) )
=> ( ( ( in @ sK191
@ ( dsetconstr @ sK192
@ ^ [Y0: $i] : ( sK190 @ Y0 ) ) )
= $true )
& ( $true
!= ( in @ sK191 @ sK192 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1115,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
& ( $true
!= ( in @ X4 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f1114]) ).
thf(f1114,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
& ( $true
!= ( in @ X1 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f619]) ).
thf(f619,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( $true
= ( in @ X1 @ X2 ) ) )
<=> ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f431]) ).
thf(f431,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
=> ( $true
= ( in @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f430]) ).
thf(f430,plain,
( dsetconstrEL
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
( dsetconstrEL
= ( ! [X0: $i > $o,X1: $i,X3: $i] :
( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( in @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',dsetconstrEL) ).
thf(f3751,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( cartprod @ X4 @ X5 ) )
!= $true )
| ( ( in @ ( ksnd @ X3 ) @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3275]) ).
thf(f3275,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ ( ksnd @ X3 ) @ X5 )
= $true )
| ( ( in @ X3 @ ( cartprod @ X4 @ X5 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2632,f2140]) ).
thf(f2140,plain,
cartprodsndin = $true,
inference(cnf_transformation,[status(thm)],[f1222]) ).
thf(f2632,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( cartprod @ X4 @ X5 ) )
!= $true )
| ( ( in @ ( ksnd @ X3 ) @ X5 )
= $true )
| ( cartprodsndin != $true ) ),
inference(cnf_transformation,[status(thm)],[f1642]) ).
thf(f1642,plain,
( ( ( cartprodsndin = $true )
| ( ( ( in @ sK484 @ ( cartprod @ sK485 @ sK486 ) )
= $true )
& ( $true
!= ( in @ ( ksnd @ sK484 ) @ sK486 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( cartprod @ X4 @ X5 ) )
!= $true )
| ( ( in @ ( ksnd @ X3 ) @ X5 )
= $true ) )
| ( cartprodsndin != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK484,sK485,sK486])],[f1640,f1641]) ).
thf(f1641,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
& ( ( in @ ( ksnd @ X0 ) @ X2 )
!= $true ) )
=> ( ( ( in @ sK484 @ ( cartprod @ sK485 @ sK486 ) )
= $true )
& ( $true
!= ( in @ ( ksnd @ sK484 ) @ sK486 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1640,plain,
( ( ( cartprodsndin = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
& ( ( in @ ( ksnd @ X0 ) @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( cartprod @ X4 @ X5 ) )
!= $true )
| ( ( in @ ( ksnd @ X3 ) @ X5 )
= $true ) )
| ( cartprodsndin != $true ) ) ),
inference(rectify,[status(thm)],[f1639]) ).
thf(f1639,plain,
( ( ( cartprodsndin = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
& ( ( in @ ( ksnd @ X0 ) @ X2 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( in @ ( ksnd @ X0 ) @ X2 )
= $true ) )
| ( cartprodsndin != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f673]) ).
thf(f673,plain,
( ( cartprodsndin = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
| ( ( in @ ( ksnd @ X0 ) @ X2 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f382]) ).
thf(f382,plain,
( ( cartprodsndin = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
=> ( ( in @ ( ksnd @ X0 ) @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f381]) ).
thf(f381,plain,
( cartprodsndin
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
=> ( in @ ( ksnd @ X0 ) @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f179]) ).
thf(f179,axiom,
( cartprodsndin
= ( ! [X10: $i,X3: $i,X4: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( ksnd @ X10 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',cartprodsndin) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU670^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n023.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:31:04 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.38 thf(spec,logic,$$dhol).
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 % File : SEU670^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.38 % Domain : Set Theory
% 0.16/0.38 % Problem : Ordered Pairs - Sets of Pairs
% 0.16/0.38 % Version : Especial.
% 0.16/0.38 % English : (! A:i.! B:i.! phi:i>(i>o).! x:i.! y:i.in (kpair x y)
% 0.16/0.38 % (dpsetconstr A B (^ z,u:i.phi z u)) -> in y B)
% 0.16/0.38
% 0.16/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.38 % Source : [Bro08]
% 0.16/0.38 % Names : ZFC172g [Bro08]
% 0.16/0.38
% 0.16/0.38 % Status : Theorem
% 0.16/0.38 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v5.0.0, 1.00 v3.7.0
% 0.16/0.38 % Syntax : Number of formulae : 412 ( 192 unt; 219 typ; 192 def)
% 0.16/0.38 % Number of atoms : 1016 ( 286 equ; 0 cnn)
% 0.16/0.38 % Maximal formula atoms : 188 ( 5 avg)
% 0.16/0.38 % Number of connectives : 1820 ( 47 ~; 7 |; 38 &;1267 @)
% 0.16/0.38 % ( 14 <=>; 447 =>; 0 <=; 0 <~>)
% 0.16/0.38 % Maximal formula depth : 199 ( 2 avg)
% 0.16/0.38 % Number of types : 2 ( 0 usr)
% 0.16/0.38 % Number of type conns : 106 ( 106 >; 0 *; 0 +; 0 <<)
% 0.16/0.38 % Number of symbols : 222 ( 219 usr; 190 con; 0-3 aty)
% 0.16/0.38 % Number of variables : 588 ( 59 ^; 491 !; 38 ?; 588 :)
% 0.16/0.38 % SPC : TH0_THM_EQU_NAR
% 0.16/0.38
% 0.16/0.38 % Comments : http://mathgate.info/detsetitem.php?id=340
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 thf(in_type,type,
% 0.16/0.38 in: $i > $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(exu_type,type,
% 0.16/0.38 exu: ( $i > $o ) > $o ).
% 0.16/0.38
% 0.16/0.38 thf(exu,definition,
% 0.16/0.38 ( exu
% 0.16/0.38 = ( ^ [Xphi: $i > $o] :
% 0.16/0.38 ? [Xx: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 & ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setextAx_type,type,
% 0.16/0.38 setextAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setextAx,definition,
% 0.16/0.38 ( setextAx
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 <=> ( in @ Xx @ B ) )
% 0.16/0.38 => ( A = B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyset_type,type,
% 0.16/0.38 emptyset: $i ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetAx_type,type,
% 0.16/0.38 emptysetAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetAx,definition,
% 0.16/0.38 ( emptysetAx
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoin_type,type,
% 0.16/0.38 setadjoin: $i > $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinAx_type,type,
% 0.16/0.38 setadjoinAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinAx,definition,
% 0.16/0.38 ( setadjoinAx
% 0.16/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.38 <=> ( ( Xy = Xx )
% 0.16/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powerset_type,type,
% 0.16/0.38 powerset: $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(powersetAx_type,type,
% 0.16/0.38 powersetAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetAx,definition,
% 0.16/0.38 ( powersetAx
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.38 <=> ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setunion_type,type,
% 0.16/0.38 setunion: $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(setunionAx_type,type,
% 0.16/0.38 setunionAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setunionAx,definition,
% 0.16/0.38 ( setunionAx
% 0.16/0.38 = ( ! [A: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.38 <=> ? [B: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(omega_type,type,
% 0.16/0.38 omega: $i ).
% 0.16/0.38
% 0.16/0.38 thf(omega0Ax_type,type,
% 0.16/0.38 omega0Ax: $o ).
% 0.16/0.38
% 0.16/0.38 thf(omega0Ax,definition,
% 0.16/0.38 ( omega0Ax
% 0.16/0.38 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(omegaSAx_type,type,
% 0.16/0.38 omegaSAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(omegaSAx,definition,
% 0.16/0.38 ( omegaSAx
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ omega )
% 0.16/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(omegaIndAx_type,type,
% 0.16/0.38 omegaIndAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(omegaIndAx,definition,
% 0.16/0.38 ( omegaIndAx
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( ( in @ emptyset @ A )
% 0.16/0.38 & ! [Xx: $i] :
% 0.16/0.38 ( ( ( in @ Xx @ omega )
% 0.16/0.38 & ( in @ Xx @ A ) )
% 0.16/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.38 => ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ omega )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(replAx_type,type,
% 0.16/0.38 replAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(replAx,definition,
% 0.16/0.38 ( replAx
% 0.16/0.38 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( exu
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.38 => ? [B: $i] :
% 0.16/0.38 ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 <=> ? [Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ A )
% 0.16/0.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(foundationAx_type,type,
% 0.16/0.38 foundationAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(foundationAx,definition,
% 0.16/0.38 ( foundationAx
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.38 => ? [B: $i] :
% 0.16/0.38 ( ( in @ B @ A )
% 0.16/0.38 & ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(wellorderingAx_type,type,
% 0.16/0.38 wellorderingAx: $o ).
% 0.16/0.38
% 0.16/0.38 thf(wellorderingAx,definition,
% 0.16/0.38 ( wellorderingAx
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ? [B: $i] :
% 0.16/0.38 ( ! [C: $i] :
% 0.16/0.38 ( ( in @ C @ B )
% 0.16/0.38 => ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ C )
% 0.16/0.38 => ( in @ Xx @ A ) ) )
% 0.16/0.38 & ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( ( in @ Xx @ A )
% 0.16/0.38 & ( in @ Xy @ A ) )
% 0.16/0.38 => ( ! [C: $i] :
% 0.16/0.38 ( ( in @ C @ B )
% 0.16/0.38 => ( ( in @ Xx @ C )
% 0.16/0.38 <=> ( in @ Xy @ C ) ) )
% 0.16/0.38 => ( Xx = Xy ) ) )
% 0.16/0.38 & ! [C: $i,D: $i] :
% 0.16/0.38 ( ( ( in @ C @ B )
% 0.16/0.38 & ( in @ D @ B ) )
% 0.16/0.38 => ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ C )
% 0.16/0.38 => ( in @ Xx @ D ) )
% 0.16/0.38 | ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ D )
% 0.16/0.38 => ( in @ Xx @ C ) ) ) )
% 0.16/0.38 & ! [C: $i] :
% 0.16/0.38 ( ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ C )
% 0.16/0.38 => ( in @ Xx @ A ) )
% 0.16/0.38 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.38 => ? [D: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ D @ B )
% 0.16/0.38 & ( in @ Xx @ C )
% 0.16/0.38 & ~ ? [Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ D )
% 0.16/0.38 & ( in @ Xy @ C ) )
% 0.16/0.38 & ! [E: $i] :
% 0.16/0.38 ( ( in @ E @ B )
% 0.16/0.38 => ( ! [Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ E )
% 0.16/0.38 => ( in @ Xy @ D ) )
% 0.16/0.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(descr_type,type,
% 0.16/0.38 descr: ( $i > $o ) > $i ).
% 0.16/0.38
% 0.16/0.38 thf(descrp_type,type,
% 0.16/0.38 descrp: $o ).
% 0.16/0.38
% 0.16/0.38 thf(descrp,definition,
% 0.16/0.38 ( descrp
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ( Xphi
% 0.16/0.38 @ ( descr
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstr_type,type,
% 0.16/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrI_type,type,
% 0.16/0.38 dsetconstrI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrI,definition,
% 0.16/0.38 ( dsetconstrI
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 => ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrEL_type,type,
% 0.16/0.38 dsetconstrEL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrEL,definition,
% 0.16/0.38 ( dsetconstrEL
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrER_type,type,
% 0.16/0.38 dsetconstrER: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstrER,definition,
% 0.16/0.38 ( dsetconstrER
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuE1_type,type,
% 0.16/0.38 exuE1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuE1,definition,
% 0.16/0.38 ( exuE1
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 & ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(prop2set_type,type,
% 0.16/0.38 prop2set: $o > $i ).
% 0.16/0.38
% 0.16/0.38 thf(prop2setE_type,type,
% 0.16/0.38 prop2setE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(prop2setE,definition,
% 0.16/0.38 ( prop2setE
% 0.16/0.38 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.38 => Xphi ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetE_type,type,
% 0.16/0.38 emptysetE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetE,definition,
% 0.16/0.38 ( emptysetE
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ emptyset )
% 0.16/0.38 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetimpfalse_type,type,
% 0.16/0.38 emptysetimpfalse: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetimpfalse,definition,
% 0.16/0.38 ( emptysetimpfalse
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ emptyset )
% 0.16/0.38 => $false ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notinemptyset_type,type,
% 0.16/0.38 notinemptyset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notinemptyset,definition,
% 0.16/0.38 ( notinemptyset
% 0.16/0.38 = ( ! [Xx: $i] :
% 0.16/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuE3e_type,type,
% 0.16/0.38 exuE3e: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuE3e,definition,
% 0.16/0.38 ( exuE3e
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setext_type,type,
% 0.16/0.38 setext: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setext,definition,
% 0.16/0.38 ( setext
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ B ) )
% 0.16/0.38 => ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) )
% 0.16/0.38 => ( A = B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyI_type,type,
% 0.16/0.38 emptyI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyI,definition,
% 0.16/0.38 ( emptyI
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ~ ( in @ Xx @ A )
% 0.16/0.38 => ( A = emptyset ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(noeltsimpempty_type,type,
% 0.16/0.38 noeltsimpempty: $o ).
% 0.16/0.38
% 0.16/0.38 thf(noeltsimpempty,definition,
% 0.16/0.38 ( noeltsimpempty
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ~ ( in @ Xx @ A )
% 0.16/0.38 => ( A = emptyset ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setbeta_type,type,
% 0.16/0.38 setbeta: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setbeta,definition,
% 0.16/0.38 ( setbeta
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ( in @ Xx
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.38 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonempty_type,type,
% 0.16/0.38 nonempty: $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonempty,definition,
% 0.16/0.38 ( nonempty
% 0.16/0.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyE1_type,type,
% 0.16/0.38 nonemptyE1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyE1,definition,
% 0.16/0.38 ( nonemptyE1
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( nonempty @ A )
% 0.16/0.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyI_type,type,
% 0.16/0.38 nonemptyI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyI,definition,
% 0.16/0.38 ( nonemptyI
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 => ( nonempty
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyI1_type,type,
% 0.16/0.38 nonemptyI1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyI1,definition,
% 0.16/0.38 ( nonemptyI1
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.38 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIL_type,type,
% 0.16/0.38 setadjoinIL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIL,definition,
% 0.16/0.38 ( setadjoinIL
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyinunitempty_type,type,
% 0.16/0.38 emptyinunitempty: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyinunitempty,definition,
% 0.16/0.38 ( emptyinunitempty
% 0.16/0.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIR_type,type,
% 0.16/0.38 setadjoinIR: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinIR,definition,
% 0.16/0.38 ( setadjoinIR
% 0.16/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ A )
% 0.16/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinE_type,type,
% 0.16/0.38 setadjoinE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinE,definition,
% 0.16/0.38 ( setadjoinE
% 0.16/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.38 => ! [Xphi: $o] :
% 0.16/0.38 ( ( ( Xy = Xx )
% 0.16/0.38 => Xphi )
% 0.16/0.38 => ( ( ( in @ Xy @ A )
% 0.16/0.38 => Xphi )
% 0.16/0.38 => Xphi ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinOr_type,type,
% 0.16/0.38 setadjoinOr: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinOr,definition,
% 0.16/0.38 ( setadjoinOr
% 0.16/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.38 => ( ( Xy = Xx )
% 0.16/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setoftrueEq_type,type,
% 0.16/0.38 setoftrueEq: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setoftrueEq,definition,
% 0.16/0.38 ( setoftrueEq
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xx: $i] : $true )
% 0.16/0.38 = A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powersetI_type,type,
% 0.16/0.38 powersetI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetI,definition,
% 0.16/0.38 ( powersetI
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) )
% 0.16/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyinPowerset_type,type,
% 0.16/0.38 emptyinPowerset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyinPowerset,definition,
% 0.16/0.38 ( emptyinPowerset
% 0.16/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyInPowerset_type,type,
% 0.16/0.38 emptyInPowerset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyInPowerset,definition,
% 0.16/0.38 ( emptyInPowerset
% 0.16/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powersetE_type,type,
% 0.16/0.38 powersetE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetE,definition,
% 0.16/0.38 ( powersetE
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.38 => ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setunionI_type,type,
% 0.16/0.38 setunionI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setunionI,definition,
% 0.16/0.38 ( setunionI
% 0.16/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( ( in @ B @ A )
% 0.16/0.38 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setunionE_type,type,
% 0.16/0.38 setunionE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setunionE,definition,
% 0.16/0.38 ( setunionE
% 0.16/0.38 = ( ! [A: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.38 => ! [Xphi: $o] :
% 0.16/0.38 ( ! [B: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( ( in @ B @ A )
% 0.16/0.38 => Xphi ) )
% 0.16/0.38 => Xphi ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subPowSU_type,type,
% 0.16/0.38 subPowSU: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subPowSU,definition,
% 0.16/0.38 ( subPowSU
% 0.16/0.38 = ( ! [A: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuE2_type,type,
% 0.16/0.38 exuE2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuE2,definition,
% 0.16/0.38 ( exuE2
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyImpWitness_type,type,
% 0.16/0.38 nonemptyImpWitness: $o ).
% 0.16/0.38
% 0.16/0.38 thf(nonemptyImpWitness,definition,
% 0.16/0.38 ( nonemptyImpWitness
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( nonempty @ A )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & $true ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(uniqinunit_type,type,
% 0.16/0.38 uniqinunit: $o ).
% 0.16/0.38
% 0.16/0.38 thf(uniqinunit,definition,
% 0.16/0.38 ( uniqinunit
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notinsingleton_type,type,
% 0.16/0.38 notinsingleton: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notinsingleton,definition,
% 0.16/0.38 ( notinsingleton
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx != Xy )
% 0.16/0.38 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(eqinunit_type,type,
% 0.16/0.38 eqinunit: $o ).
% 0.16/0.38
% 0.16/0.38 thf(eqinunit,definition,
% 0.16/0.38 ( eqinunit
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(singletonsswitch_type,type,
% 0.16/0.38 singletonsswitch: $o ).
% 0.16/0.38
% 0.16/0.38 thf(singletonsswitch,definition,
% 0.16/0.38 ( singletonsswitch
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetE_type,type,
% 0.16/0.38 upairsetE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetE,definition,
% 0.16/0.38 ( upairsetE
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.38 => ( ( Xz = Xx )
% 0.16/0.38 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetIL_type,type,
% 0.16/0.38 upairsetIL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetIL,definition,
% 0.16/0.38 ( upairsetIL
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetIR_type,type,
% 0.16/0.38 upairsetIR: $o ).
% 0.16/0.38
% 0.16/0.38 thf(upairsetIR,definition,
% 0.16/0.38 ( upairsetIR
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyE1_type,type,
% 0.16/0.38 emptyE1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyE1,definition,
% 0.16/0.38 ( emptyE1
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( Xphi @ Xx ) )
% 0.16/0.38 => ( ( ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 = emptyset )
% 0.16/0.38 => $false ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(vacuousDall_type,type,
% 0.16/0.38 vacuousDall: $o ).
% 0.16/0.38
% 0.16/0.38 thf(vacuousDall,definition,
% 0.16/0.38 ( vacuousDall
% 0.16/0.38 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ emptyset )
% 0.16/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan1_type,type,
% 0.16/0.38 quantDeMorgan1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan1,definition,
% 0.16/0.38 ( quantDeMorgan1
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ~ ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan2_type,type,
% 0.16/0.38 quantDeMorgan2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan2,definition,
% 0.16/0.38 ( quantDeMorgan2
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ~ ( Xphi @ Xx ) )
% 0.16/0.38 => ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan3_type,type,
% 0.16/0.38 quantDeMorgan3: $o ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan3,definition,
% 0.16/0.38 ( quantDeMorgan3
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( Xphi @ Xx ) )
% 0.16/0.38 => ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan4_type,type,
% 0.16/0.38 quantDeMorgan4: $o ).
% 0.16/0.38
% 0.16/0.38 thf(quantDeMorgan4,definition,
% 0.16/0.38 ( quantDeMorgan4
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ~ ( Xphi @ Xx ) )
% 0.16/0.38 => ~ ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(prop2setI_type,type,
% 0.16/0.38 prop2setI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(prop2setI,definition,
% 0.16/0.38 ( prop2setI
% 0.16/0.38 = ( ! [Xphi: $o] :
% 0.16/0.38 ( Xphi
% 0.16/0.38 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(set2prop_type,type,
% 0.16/0.38 set2prop: $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(prop2set2propI_type,type,
% 0.16/0.38 prop2set2propI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(prop2set2propI,definition,
% 0.16/0.38 ( prop2set2propI
% 0.16/0.38 = ( ! [Xphi: $o] :
% 0.16/0.38 ( Xphi
% 0.16/0.38 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notdexE_type,type,
% 0.16/0.38 notdexE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notdexE,definition,
% 0.16/0.38 ( notdexE
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( Xphi @ Xx ) )
% 0.16/0.38 => ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notdallE_type,type,
% 0.16/0.38 notdallE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notdallE,definition,
% 0.16/0.38 ( notdallE
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( ~ ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( Xphi @ Xx ) )
% 0.16/0.38 => ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuI1_type,type,
% 0.16/0.38 exuI1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuI1,definition,
% 0.16/0.38 ( exuI1
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 & ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) )
% 0.16/0.38 => ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuI3_type,type,
% 0.16/0.38 exuI3: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuI3,definition,
% 0.16/0.38 ( exuI3
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.16/0.38 => ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 => ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) )
% 0.16/0.38 => ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuI2_type,type,
% 0.16/0.38 exuI2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuI2,definition,
% 0.16/0.38 ( exuI2
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ? [Xx: $i] :
% 0.16/0.38 ! [Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xy )
% 0.16/0.38 <=> ( Xy = Xx ) )
% 0.16/0.38 => ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(inCongP_type,type,
% 0.16/0.38 inCongP: $o ).
% 0.16/0.38
% 0.16/0.38 thf(inCongP,definition,
% 0.16/0.38 ( inCongP
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(in__Cong_type,type,
% 0.16/0.38 in__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(in__Cong,definition,
% 0.16/0.38 ( in__Cong
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( ( in @ Xx @ A )
% 0.16/0.38 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuE3u_type,type,
% 0.16/0.38 exuE3u: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuE3u,definition,
% 0.16/0.38 ( exuE3u
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 => ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exu__Cong_type,type,
% 0.16/0.38 exu__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exu__Cong,definition,
% 0.16/0.38 ( exu__Cong
% 0.16/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.38 => ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 <=> ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptyset__Cong_type,type,
% 0.16/0.38 emptyset__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptyset__Cong,definition,
% 0.16/0.38 ( emptyset__Cong
% 0.16/0.38 = ( emptyset = emptyset ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoin__Cong_type,type,
% 0.16/0.38 setadjoin__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoin__Cong,definition,
% 0.16/0.38 ( setadjoin__Cong
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ! [Xz: $i,Xu: $i] :
% 0.16/0.38 ( ( Xz = Xu )
% 0.16/0.38 => ( ( setadjoin @ Xx @ Xz )
% 0.16/0.38 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powerset__Cong_type,type,
% 0.16/0.38 powerset__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powerset__Cong,definition,
% 0.16/0.38 ( powerset__Cong
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ( ( powerset @ A )
% 0.16/0.38 = ( powerset @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setunion__Cong_type,type,
% 0.16/0.38 setunion__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setunion__Cong,definition,
% 0.16/0.38 ( setunion__Cong
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ( ( setunion @ A )
% 0.16/0.38 = ( setunion @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(omega__Cong_type,type,
% 0.16/0.38 omega__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(omega__Cong,definition,
% 0.16/0.38 ( omega__Cong
% 0.16/0.38 = ( omega = omega ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(exuEu_type,type,
% 0.16/0.38 exuEu: $o ).
% 0.16/0.38
% 0.16/0.38 thf(exuEu,definition,
% 0.16/0.38 ( exuEu
% 0.16/0.38 = ( ! [Xphi: $i > $o] :
% 0.16/0.38 ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xphi @ Xx )
% 0.16/0.38 => ( ( Xphi @ Xy )
% 0.16/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(descr__Cong_type,type,
% 0.16/0.38 descr__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(descr__Cong,definition,
% 0.16/0.38 ( descr__Cong
% 0.16/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.16/0.38 ( ( Xx = Xy )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.16/0.38 => ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 => ( ( exu
% 0.16/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.16/0.38 => ( ( descr
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 = ( descr
% 0.16/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstr__Cong_type,type,
% 0.16/0.38 dsetconstr__Cong: $o ).
% 0.16/0.38
% 0.16/0.38 thf(dsetconstr__Cong,definition,
% 0.16/0.38 ( dsetconstr__Cong
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ! [Xy: $i] :
% 0.16/0.38 ( ( in @ Xy @ B )
% 0.16/0.38 => ( ( Xx = Xy )
% 0.16/0.38 => ( ( Xphi @ Xx )
% 0.16/0.38 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.16/0.38 => ( ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 = ( dsetconstr @ B
% 0.16/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subset_type,type,
% 0.16/0.38 subset: $i > $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(disjoint_type,type,
% 0.16/0.38 disjoint: $i > $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(setsmeet_type,type,
% 0.16/0.38 setsmeet: $i > $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(subsetI1_type,type,
% 0.16/0.38 subsetI1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subsetI1,definition,
% 0.16/0.38 ( subsetI1
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ B ) )
% 0.16/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(eqimpsubset2_type,type,
% 0.16/0.38 eqimpsubset2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(eqimpsubset2,definition,
% 0.16/0.38 ( eqimpsubset2
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(eqimpsubset1_type,type,
% 0.16/0.38 eqimpsubset1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(eqimpsubset1,definition,
% 0.16/0.38 ( eqimpsubset1
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( A = B )
% 0.16/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subsetI2_type,type,
% 0.16/0.38 subsetI2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subsetI2,definition,
% 0.16/0.38 ( subsetI2
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ! [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ B ) )
% 0.16/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetsubset_type,type,
% 0.16/0.38 emptysetsubset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(emptysetsubset,definition,
% 0.16/0.38 ( emptysetsubset
% 0.16/0.38 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subsetE_type,type,
% 0.16/0.38 subsetE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subsetE,definition,
% 0.16/0.38 ( subsetE
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subsetE2_type,type,
% 0.16/0.38 subsetE2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subsetE2,definition,
% 0.16/0.38 ( subsetE2
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( ~ ( in @ Xx @ B )
% 0.16/0.38 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notsubsetI_type,type,
% 0.16/0.38 notsubsetI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notsubsetI,definition,
% 0.16/0.38 ( notsubsetI
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ~ ( in @ Xx @ B )
% 0.16/0.38 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notequalI1_type,type,
% 0.16/0.38 notequalI1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notequalI1,definition,
% 0.16/0.38 ( notequalI1
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ~ ( subset @ A @ B )
% 0.16/0.38 => ( A != B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(notequalI2_type,type,
% 0.16/0.38 notequalI2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(notequalI2,definition,
% 0.16/0.38 ( notequalI2
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ~ ( in @ Xx @ B )
% 0.16/0.38 => ( A != B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subsetRefl_type,type,
% 0.16/0.38 subsetRefl: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subsetRefl,definition,
% 0.16/0.38 ( subsetRefl
% 0.16/0.38 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subsetTrans_type,type,
% 0.16/0.38 subsetTrans: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subsetTrans,definition,
% 0.16/0.38 ( subsetTrans
% 0.16/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( ( subset @ B @ C )
% 0.16/0.38 => ( subset @ A @ C ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinSub_type,type,
% 0.16/0.38 setadjoinSub: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinSub,definition,
% 0.16/0.38 ( setadjoinSub
% 0.16/0.38 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinSub2_type,type,
% 0.16/0.38 setadjoinSub2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setadjoinSub2,definition,
% 0.16/0.38 ( setadjoinSub2
% 0.16/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subset2powerset_type,type,
% 0.16/0.38 subset2powerset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subset2powerset,definition,
% 0.16/0.38 ( subset2powerset
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setextsub_type,type,
% 0.16/0.38 setextsub: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setextsub,definition,
% 0.16/0.38 ( setextsub
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( ( subset @ B @ A )
% 0.16/0.38 => ( A = B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(subsetemptysetimpeq_type,type,
% 0.16/0.38 subsetemptysetimpeq: $o ).
% 0.16/0.38
% 0.16/0.38 thf(subsetemptysetimpeq,definition,
% 0.16/0.38 ( subsetemptysetimpeq
% 0.16/0.38 = ( ! [A: $i] :
% 0.16/0.38 ( ( subset @ A @ emptyset )
% 0.16/0.38 => ( A = emptyset ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powersetI1_type,type,
% 0.16/0.38 powersetI1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetI1,definition,
% 0.16/0.38 ( powersetI1
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( subset @ B @ A )
% 0.16/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powersetE1_type,type,
% 0.16/0.38 powersetE1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetE1,definition,
% 0.16/0.38 ( powersetE1
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(inPowerset_type,type,
% 0.16/0.38 inPowerset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(inPowerset,definition,
% 0.16/0.38 ( inPowerset
% 0.16/0.38 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(powersetsubset_type,type,
% 0.16/0.38 powersetsubset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(powersetsubset,definition,
% 0.16/0.38 ( powersetsubset
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sepInPowerset_type,type,
% 0.16/0.38 sepInPowerset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(sepInPowerset,definition,
% 0.16/0.38 ( sepInPowerset
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( in
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 @ ( powerset @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sepSubset_type,type,
% 0.16/0.38 sepSubset: $o ).
% 0.16/0.38
% 0.16/0.38 thf(sepSubset,definition,
% 0.16/0.38 ( sepSubset
% 0.16/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.38 ( subset
% 0.16/0.38 @ ( dsetconstr @ A
% 0.16/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.38 @ A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binunion_type,type,
% 0.16/0.38 binunion: $i > $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(binunionIL_type,type,
% 0.16/0.38 binunionIL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binunionIL,definition,
% 0.16/0.38 ( binunionIL
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(upairset2IR_type,type,
% 0.16/0.38 upairset2IR: $o ).
% 0.16/0.38
% 0.16/0.38 thf(upairset2IR,definition,
% 0.16/0.38 ( upairset2IR
% 0.16/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binunionIR_type,type,
% 0.16/0.38 binunionIR: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binunionIR,definition,
% 0.16/0.38 ( binunionIR
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binunionEcases_type,type,
% 0.16/0.38 binunionEcases: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binunionEcases,definition,
% 0.16/0.38 ( binunionEcases
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.16/0.38 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.38 => ( ( ( in @ Xx @ A )
% 0.16/0.38 => Xphi )
% 0.16/0.38 => ( ( ( in @ Xx @ B )
% 0.16/0.38 => Xphi )
% 0.16/0.38 => Xphi ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binunionE_type,type,
% 0.16/0.38 binunionE: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binunionE,definition,
% 0.16/0.38 ( binunionE
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.16/0.38 => ( ( in @ Xx @ A )
% 0.16/0.38 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binunionLsub_type,type,
% 0.16/0.38 binunionLsub: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binunionLsub,definition,
% 0.16/0.38 ( binunionLsub
% 0.16/0.38 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binunionRsub_type,type,
% 0.16/0.38 binunionRsub: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binunionRsub,definition,
% 0.16/0.38 ( binunionRsub
% 0.16/0.38 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersect_type,type,
% 0.16/0.38 binintersect: $i > $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectI_type,type,
% 0.16/0.38 binintersectI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectI,definition,
% 0.16/0.38 ( binintersectI
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset5_type,type,
% 0.16/0.38 binintersectSubset5: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset5,definition,
% 0.16/0.38 ( binintersectSubset5
% 0.16/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.38 ( ( subset @ C @ A )
% 0.16/0.38 => ( ( subset @ C @ B )
% 0.16/0.38 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectEL_type,type,
% 0.16/0.38 binintersectEL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectEL,definition,
% 0.16/0.38 ( binintersectEL
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectLsub_type,type,
% 0.16/0.38 binintersectLsub: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectLsub,definition,
% 0.16/0.38 ( binintersectLsub
% 0.16/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset2_type,type,
% 0.16/0.38 binintersectSubset2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset2,definition,
% 0.16/0.38 ( binintersectSubset2
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( ( binintersect @ A @ B )
% 0.16/0.38 = A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset3_type,type,
% 0.16/0.38 binintersectSubset3: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset3,definition,
% 0.16/0.38 ( binintersectSubset3
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( ( binintersect @ A @ B )
% 0.16/0.38 = B )
% 0.16/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectER_type,type,
% 0.16/0.38 binintersectER: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectER,definition,
% 0.16/0.38 ( binintersectER
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.16/0.38 => ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(disjointsetsI1_type,type,
% 0.16/0.38 disjointsetsI1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(disjointsetsI1,definition,
% 0.16/0.38 ( disjointsetsI1
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ~ ? [Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 & ( in @ Xx @ B ) )
% 0.16/0.38 => ( ( binintersect @ A @ B )
% 0.16/0.38 = emptyset ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectRsub_type,type,
% 0.16/0.38 binintersectRsub: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectRsub,definition,
% 0.16/0.38 ( binintersectRsub
% 0.16/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset4_type,type,
% 0.16/0.38 binintersectSubset4: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset4,definition,
% 0.16/0.38 ( binintersectSubset4
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( subset @ B @ A )
% 0.16/0.38 => ( ( binintersect @ A @ B )
% 0.16/0.38 = B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset1_type,type,
% 0.16/0.38 binintersectSubset1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(binintersectSubset1,definition,
% 0.16/0.38 ( binintersectSubset1
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( ( binintersect @ A @ B )
% 0.16/0.38 = A )
% 0.16/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(bs114d_type,type,
% 0.16/0.38 bs114d: $o ).
% 0.16/0.38
% 0.16/0.38 thf(bs114d,definition,
% 0.16/0.38 ( bs114d
% 0.16/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.16/0.38 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.16/0.38 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(regular_type,type,
% 0.16/0.38 regular: $i > $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminus_type,type,
% 0.16/0.38 setminus: $i > $i > $i ).
% 0.16/0.38
% 0.16/0.38 thf(setminusI_type,type,
% 0.16/0.38 setminusI: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusI,definition,
% 0.16/0.38 ( setminusI
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ A )
% 0.16/0.38 => ( ~ ( in @ Xx @ B )
% 0.16/0.38 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusEL_type,type,
% 0.16/0.38 setminusEL: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusEL,definition,
% 0.16/0.38 ( setminusEL
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusER_type,type,
% 0.16/0.38 setminusER: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusER,definition,
% 0.16/0.38 ( setminusER
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.38 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusSubset2_type,type,
% 0.16/0.38 setminusSubset2: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusSubset2,definition,
% 0.16/0.38 ( setminusSubset2
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( subset @ A @ B )
% 0.16/0.38 => ( ( setminus @ A @ B )
% 0.16/0.38 = emptyset ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusERneg_type,type,
% 0.16/0.38 setminusERneg: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusERneg,definition,
% 0.16/0.38 ( setminusERneg
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.38 => ( ( in @ Xx @ A )
% 0.16/0.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusELneg_type,type,
% 0.16/0.38 setminusELneg: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusELneg,definition,
% 0.16/0.38 ( setminusELneg
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.16/0.38 => ( ~ ( in @ Xx @ B )
% 0.16/0.38 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusILneg_type,type,
% 0.16/0.38 setminusILneg: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusILneg,definition,
% 0.16/0.38 ( setminusILneg
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ~ ( in @ Xx @ A )
% 0.16/0.38 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusIRneg_type,type,
% 0.16/0.38 setminusIRneg: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusIRneg,definition,
% 0.16/0.38 ( setminusIRneg
% 0.16/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.38 ( ( in @ Xx @ B )
% 0.16/0.38 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusLsub_type,type,
% 0.16/0.38 setminusLsub: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusLsub,definition,
% 0.16/0.38 ( setminusLsub
% 0.16/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(setminusSubset1_type,type,
% 0.16/0.38 setminusSubset1: $o ).
% 0.16/0.38
% 0.16/0.38 thf(setminusSubset1,definition,
% 0.16/0.38 ( setminusSubset1
% 0.16/0.38 = ( ! [A: $i,B: $i] :
% 0.16/0.38 ( ( ( setminus @ A @ B )
% 0.16/0.38 = emptyset )
% 0.16/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiff_type,type,
% 0.16/0.39 symdiff: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffE_type,type,
% 0.16/0.39 symdiffE: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffE,definition,
% 0.16/0.39 ( symdiffE
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.16/0.39 => ! [Xphi: $o] :
% 0.16/0.39 ( ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => ( ( ~ ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => Xphi ) )
% 0.16/0.39 => Xphi ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffI1_type,type,
% 0.16/0.39 symdiffI1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffI1,definition,
% 0.16/0.39 ( symdiffI1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffI2_type,type,
% 0.16/0.39 symdiffI2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffI2,definition,
% 0.16/0.39 ( symdiffI2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffIneg1_type,type,
% 0.16/0.39 symdiffIneg1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffIneg1,definition,
% 0.16/0.39 ( symdiffIneg1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffIneg2_type,type,
% 0.16/0.39 symdiffIneg2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(symdiffIneg2,definition,
% 0.16/0.39 ( symdiffIneg2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ~ ( in @ Xx @ A )
% 0.16/0.39 => ( ~ ( in @ Xx @ B )
% 0.16/0.39 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(iskpair_type,type,
% 0.16/0.39 iskpair: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(secondinupair_type,type,
% 0.16/0.39 secondinupair: $o ).
% 0.16/0.39
% 0.16/0.39 thf(secondinupair,definition,
% 0.16/0.39 ( secondinupair
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairIL_type,type,
% 0.16/0.39 setukpairIL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairIL,definition,
% 0.16/0.39 ( setukpairIL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairIR_type,type,
% 0.16/0.39 setukpairIR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairIR,definition,
% 0.16/0.39 ( setukpairIR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kpairiskpair_type,type,
% 0.16/0.39 kpairiskpair: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kpairiskpair,definition,
% 0.16/0.39 ( kpairiskpair
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kpair_type,type,
% 0.16/0.39 kpair: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(kpairp_type,type,
% 0.16/0.39 kpairp: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kpairp,definition,
% 0.16/0.39 ( kpairp
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprod_type,type,
% 0.16/0.39 cartprod: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsubset_type,type,
% 0.16/0.39 singletonsubset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsubset,definition,
% 0.16/0.39 ( singletonsubset
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletoninpowerset_type,type,
% 0.16/0.39 singletoninpowerset: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletoninpowerset,definition,
% 0.16/0.39 ( singletoninpowerset
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletoninpowunion_type,type,
% 0.16/0.39 singletoninpowunion: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletoninpowunion,definition,
% 0.16/0.39 ( singletoninpowunion
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2E_type,type,
% 0.16/0.39 upairset2E: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairset2E,definition,
% 0.16/0.39 ( upairset2E
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xx )
% 0.16/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairsubunion_type,type,
% 0.16/0.39 upairsubunion: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsubunion,definition,
% 0.16/0.39 ( upairsubunion
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairinpowunion_type,type,
% 0.16/0.39 upairinpowunion: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairinpowunion,definition,
% 0.16/0.39 ( upairinpowunion
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem1_type,type,
% 0.16/0.39 ubforcartprodlem1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem1,definition,
% 0.16/0.39 ( ubforcartprodlem1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem2_type,type,
% 0.16/0.39 ubforcartprodlem2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem2,definition,
% 0.16/0.39 ( ubforcartprodlem2
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem3_type,type,
% 0.16/0.39 ubforcartprodlem3: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ubforcartprodlem3,definition,
% 0.16/0.39 ( ubforcartprodlem3
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairin_type,type,
% 0.16/0.39 cartprodpairin: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairin,definition,
% 0.16/0.39 ( cartprodpairin
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempair1_type,type,
% 0.16/0.39 cartprodmempair1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempair1,definition,
% 0.16/0.39 ( cartprodmempair1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 & ( Xu
% 0.16/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempair_type,type,
% 0.16/0.39 cartprodmempair: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempair,definition,
% 0.16/0.39 ( cartprodmempair
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( iskpair @ Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE2_type,type,
% 0.16/0.39 setunionE2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionE2,definition,
% 0.16/0.39 ( setunionE2
% 0.16/0.39 = ( ! [A: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.39 => ? [X: $i] :
% 0.16/0.39 ( ( in @ X @ A )
% 0.16/0.39 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton1_type,type,
% 0.16/0.39 setunionsingleton1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton1,definition,
% 0.16/0.39 ( setunionsingleton1
% 0.16/0.39 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton2_type,type,
% 0.16/0.39 setunionsingleton2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton2,definition,
% 0.16/0.39 ( setunionsingleton2
% 0.16/0.39 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton_type,type,
% 0.16/0.39 setunionsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setunionsingleton,definition,
% 0.16/0.39 ( setunionsingleton
% 0.16/0.39 = ( ! [Xx: $i] :
% 0.16/0.39 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.16/0.39 = Xx ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singleton_type,type,
% 0.16/0.39 singleton: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(singleton,definition,
% 0.16/0.39 ( singleton
% 0.16/0.39 = ( ^ [A: $i] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( A
% 0.16/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonprop_type,type,
% 0.16/0.39 singletonprop: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonprop,definition,
% 0.16/0.39 ( singletonprop
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) )
% 0.16/0.39 => ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( singleton
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1_type,type,
% 0.16/0.39 ex1: $i > ( $i > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1,definition,
% 0.16/0.39 ( ex1
% 0.16/0.39 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( singleton
% 0.16/0.39 @ ( dsetconstr @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1E1_type,type,
% 0.16/0.39 ex1E1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1E1,definition,
% 0.16/0.39 ( ex1E1
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ( ex1 @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.39 => ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1I_type,type,
% 0.16/0.39 ex1I: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1I,definition,
% 0.16/0.39 ( ex1I
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xy = Xx ) ) )
% 0.16/0.39 => ( ex1 @ A
% 0.16/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ex1I2_type,type,
% 0.16/0.39 ex1I2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ex1I2,definition,
% 0.16/0.39 ( ex1I2
% 0.16/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.39 ( ! [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ A )
% 0.16/0.39 => ( ( Xphi @ Xx )
% 0.16/0.39 => ( ( Xphi @ Xy )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) )
% 0.16/0.39 => ( ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ( Xphi @ Xx ) )
% 0.16/0.39 => ( ex1 @ A
% 0.16/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsuniq_type,type,
% 0.16/0.39 singletonsuniq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(singletonsuniq,definition,
% 0.16/0.39 ( singletonsuniq
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ( setadjoin @ Xx @ emptyset )
% 0.16/0.39 = ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(atmost1p_type,type,
% 0.16/0.39 atmost1p: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(atleast2p_type,type,
% 0.16/0.39 atleast2p: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(atmost2p_type,type,
% 0.16/0.39 atmost2p: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairsetp_type,type,
% 0.16/0.39 upairsetp: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL1_type,type,
% 0.16/0.39 setukpairinjL1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL1,definition,
% 0.16/0.39 ( setukpairinjL1
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kfstsingleton_type,type,
% 0.16/0.39 kfstsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kfstsingleton,definition,
% 0.16/0.39 ( kfstsingleton
% 0.16/0.39 = ( ! [Xu: $i] :
% 0.16/0.39 ( ( iskpair @ Xu )
% 0.16/0.39 => ( singleton
% 0.16/0.39 @ ( dsetconstr @ ( setunion @ Xu )
% 0.16/0.39 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(theprop_type,type,
% 0.16/0.39 theprop: $o ).
% 0.16/0.39
% 0.16/0.39 thf(theprop,definition,
% 0.16/0.39 ( theprop
% 0.16/0.39 = ( ! [X: $i] :
% 0.16/0.39 ( ( singleton @ X )
% 0.16/0.39 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kfst_type,type,
% 0.16/0.39 kfst: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(kfstpairEq_type,type,
% 0.16/0.39 kfstpairEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kfstpairEq,definition,
% 0.16/0.39 ( kfstpairEq
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.16/0.39 = Xx ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodfstin_type,type,
% 0.16/0.39 cartprodfstin: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodfstin,definition,
% 0.16/0.39 ( cartprodfstin
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL2_type,type,
% 0.16/0.39 setukpairinjL2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL2,definition,
% 0.16/0.39 ( setukpairinjL2
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL_type,type,
% 0.16/0.39 setukpairinjL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjL,definition,
% 0.16/0.39 ( setukpairinjL
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( kpair @ Xx @ Xy )
% 0.16/0.39 = ( kpair @ Xz @ Xu ) )
% 0.16/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR11_type,type,
% 0.16/0.39 setukpairinjR11: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR11,definition,
% 0.16/0.39 ( setukpairinjR11
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR12_type,type,
% 0.16/0.39 setukpairinjR12: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR12,definition,
% 0.16/0.39 ( setukpairinjR12
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( Xx = Xy )
% 0.16/0.39 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR1_type,type,
% 0.16/0.39 setukpairinjR1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR1,definition,
% 0.16/0.39 ( setukpairinjR1
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.39 => ( ( Xz = Xu )
% 0.16/0.39 => ( Xy = Xu ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(upairequniteq_type,type,
% 0.16/0.39 upairequniteq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(upairequniteq,definition,
% 0.16/0.39 ( upairequniteq
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.39 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ Xz @ emptyset ) )
% 0.16/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR2_type,type,
% 0.16/0.39 setukpairinjR2: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR2,definition,
% 0.16/0.39 ( setukpairinjR2
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.16/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.16/0.39 => ( Xy = Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR_type,type,
% 0.16/0.39 setukpairinjR: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setukpairinjR,definition,
% 0.16/0.39 ( setukpairinjR
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.16/0.39 ( ( ( kpair @ Xx @ Xy )
% 0.16/0.39 = ( kpair @ Xz @ Xu ) )
% 0.16/0.39 => ( Xy = Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ksndsingleton_type,type,
% 0.16/0.39 ksndsingleton: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ksndsingleton,definition,
% 0.16/0.39 ( ksndsingleton
% 0.16/0.39 = ( ! [Xu: $i] :
% 0.16/0.39 ( ( iskpair @ Xu )
% 0.16/0.39 => ( singleton
% 0.16/0.39 @ ( dsetconstr @ ( setunion @ Xu )
% 0.16/0.39 @ ^ [Xx: $i] :
% 0.16/0.39 ( Xu
% 0.16/0.39 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(ksnd_type,type,
% 0.16/0.39 ksnd: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(ksndpairEq_type,type,
% 0.16/0.39 ksndpairEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(ksndpairEq,definition,
% 0.16/0.39 ( ksndpairEq
% 0.16/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.16/0.39 = Xy ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(kpairsurjEq_type,type,
% 0.16/0.39 kpairsurjEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(kpairsurjEq,definition,
% 0.16/0.39 ( kpairsurjEq
% 0.16/0.39 = ( ! [Xu: $i] :
% 0.16/0.39 ( ( iskpair @ Xu )
% 0.16/0.39 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.16/0.39 = Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodsndin_type,type,
% 0.16/0.39 cartprodsndin: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodsndin,definition,
% 0.16/0.39 ( cartprodsndin
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairmemEL_type,type,
% 0.16/0.39 cartprodpairmemEL: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairmemEL,definition,
% 0.16/0.39 ( cartprodpairmemEL
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairmemER_type,type,
% 0.16/0.39 cartprodpairmemER: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairmemER,definition,
% 0.16/0.39 ( cartprodpairmemER
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempaircEq_type,type,
% 0.16/0.39 cartprodmempaircEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodmempaircEq,definition,
% 0.16/0.39 ( cartprodmempaircEq
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( kpair @ Xx @ Xy )
% 0.16/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodfstpairEq_type,type,
% 0.16/0.39 cartprodfstpairEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodfstpairEq,definition,
% 0.16/0.39 ( cartprodfstpairEq
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.16/0.39 = Xx ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodsndpairEq_type,type,
% 0.16/0.39 cartprodsndpairEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodsndpairEq,definition,
% 0.16/0.39 ( cartprodsndpairEq
% 0.16/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.16/0.39 = Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairsurjEq_type,type,
% 0.16/0.39 cartprodpairsurjEq: $o ).
% 0.16/0.39
% 0.16/0.39 thf(cartprodpairsurjEq,definition,
% 0.16/0.39 ( cartprodpairsurjEq
% 0.16/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.16/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.16/0.39 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.16/0.39 = Xu ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(breln_type,type,
% 0.16/0.39 breln: $i > $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(breln,definition,
% 0.16/0.39 ( breln
% 0.16/0.39 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstr_type,type,
% 0.16/0.39 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstr,definition,
% 0.16/0.39 ( dpsetconstr
% 0.16/0.39 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.16/0.39 ( dsetconstr @ ( cartprod @ A @ B )
% 0.16/0.39 @ ^ [Xu: $i] :
% 0.16/0.39 ? [Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 & ? [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 & ( Xphi @ Xx @ Xy )
% 0.16/0.39 & ( Xu
% 0.16/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrI_type,type,
% 0.16/0.39 dpsetconstrI: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrI,definition,
% 0.16/0.39 ( dpsetconstrI
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( Xphi @ Xx @ Xy )
% 0.16/0.39 => ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrSub_type,type,
% 0.16/0.39 dpsetconstrSub: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrSub,definition,
% 0.16/0.39 ( dpsetconstrSub
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.16/0.39 ( subset
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.16/0.39 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(setOfPairsIsBReln_type,type,
% 0.16/0.39 setOfPairsIsBReln: $o ).
% 0.16/0.39
% 0.16/0.39 thf(setOfPairsIsBReln,definition,
% 0.16/0.39 ( setOfPairsIsBReln
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.16/0.39 ( breln @ A @ B
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrERa_type,type,
% 0.16/0.39 dpsetconstrERa: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrERa,definition,
% 0.16/0.39 ( dpsetconstrERa
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.16/0.39 ( ( in @ Xx @ A )
% 0.16/0.39 => ! [Xy: $i] :
% 0.16/0.39 ( ( in @ Xy @ B )
% 0.16/0.39 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.16/0.39 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrEL1_type,type,
% 0.16/0.39 dpsetconstrEL1: $o ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrEL1,definition,
% 0.16/0.39 ( dpsetconstrEL1
% 0.16/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.16/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(dpsetconstrEL2,conjecture,
% 0.16/0.39 ( setextAx
% 0.16/0.39 => ( emptysetAx
% 0.16/0.39 => ( setadjoinAx
% 0.16/0.39 => ( powersetAx
% 0.16/0.39 => ( setunionAx
% 0.16/0.39 => ( omega0Ax
% 0.16/0.39 => ( omegaSAx
% 0.16/0.39 => ( omegaIndAx
% 0.16/0.39 => ( replAx
% 0.16/0.39 => ( foundationAx
% 0.16/0.39 => ( wellorderingAx
% 0.16/0.39 => ( descrp
% 0.16/0.39 => ( dsetconstrI
% 0.16/0.39 => ( dsetconstrEL
% 0.16/0.39 => ( dsetconstrER
% 0.16/0.39 => ( exuE1
% 0.16/0.39 => ( prop2setE
% 0.16/0.39 => ( emptysetE
% 0.16/0.39 => ( emptysetimpfalse
% 0.16/0.39 => ( notinemptyset
% 0.16/0.39 => ( exuE3e
% 0.16/0.39 => ( setext
% 0.16/0.39 => ( emptyI
% 0.16/0.39 => ( noeltsimpempty
% 0.16/0.39 => ( setbeta
% 0.16/0.39 => ( nonemptyE1
% 0.16/0.39 => ( nonemptyI
% 0.16/0.39 => ( nonemptyI1
% 0.16/0.39 => ( setadjoinIL
% 0.16/0.39 => ( emptyinunitempty
% 0.16/0.39 => ( setadjoinIR
% 0.16/0.39 => ( setadjoinE
% 0.16/0.39 => ( setadjoinOr
% 0.16/0.39 => ( setoftrueEq
% 0.16/0.39 => ( powersetI
% 0.16/0.39 => ( emptyinPowerset
% 0.16/0.39 => ( emptyInPowerset
% 0.16/0.39 => ( powersetE
% 0.16/0.39 => ( setunionI
% 0.16/0.39 => ( setunionE
% 0.16/0.39 => ( subPowSU
% 0.16/0.39 => ( exuE2
% 0.16/0.39 => ( nonemptyImpWitness
% 0.16/0.39 => ( uniqinunit
% 0.16/0.39 => ( notinsingleton
% 0.16/0.39 => ( eqinunit
% 0.16/0.39 => ( singletonsswitch
% 0.16/0.39 => ( upairsetE
% 0.16/0.39 => ( upairsetIL
% 0.16/0.39 => ( upairsetIR
% 0.16/0.39 => ( emptyE1
% 0.16/0.39 => ( vacuousDall
% 0.16/0.39 => ( quantDeMorgan1
% 0.16/0.39 => ( quantDeMorgan2
% 0.16/0.39 => ( quantDeMorgan3
% 0.16/0.39 => ( quantDeMorgan4
% 0.16/0.39 => ( prop2setI
% 0.16/0.39 => ( prop2set2propI
% 0.16/0.39 => ( notdexE
% 0.16/0.39 => ( notdallE
% 0.16/0.39 => ( exuI1
% 0.16/0.39 => ( exuI3
% 0.16/0.39 => ( exuI2
% 0.16/0.39 => ( inCongP
% 0.16/0.39 => ( in__Cong
% 0.16/0.39 => ( exuE3u
% 0.16/0.39 => ( exu__Cong
% 0.16/0.39 => ( emptyset__Cong
% 0.16/0.39 => ( setadjoin__Cong
% 0.16/0.39 => ( powerset__Cong
% 0.16/0.39 => ( setunion__Cong
% 0.16/0.39 => ( omega__Cong
% 0.16/0.39 => ( exuEu
% 0.16/0.39 => ( descr__Cong
% 0.16/0.39 => ( dsetconstr__Cong
% 0.16/0.39 => ( subsetI1
% 0.16/0.39 => ( eqimpsubset2
% 0.16/0.39 => ( eqimpsubset1
% 0.16/0.39 => ( subsetI2
% 0.16/0.39 => ( emptysetsubset
% 0.16/0.39 => ( subsetE
% 0.16/0.39 => ( subsetE2
% 0.16/0.39 => ( notsubsetI
% 0.16/0.39 => ( notequalI1
% 0.16/0.39 => ( notequalI2
% 0.16/0.39 => ( subsetRefl
% 0.16/0.39 => ( subsetTrans
% 0.16/0.39 => ( setadjoinSub
% 0.16/0.39 => ( setadjoinSub2
% 0.16/0.39 => ( subset2powerset
% 0.16/0.39 => ( setextsub
% 0.16/0.39 => ( subsetemptysetimpeq
% 0.16/0.39 => ( powersetI1
% 0.16/0.39 => ( powersetE1
% 0.16/0.39 => ( inPowerset
% 0.16/0.39 => ( powersetsubset
% 0.16/0.39 => ( sepInPowerset
% 0.16/0.39 => ( sepSubset
% 0.16/0.39 => ( binunionIL
% 0.16/0.39 => ( upairset2IR
% 0.16/0.39 => ( binunionIR
% 0.16/0.39 => ( binunionEcases
% 0.16/0.39 => ( binunionE
% 0.16/0.39 => ( binunionLsub
% 0.16/0.39 => ( binunionRsub
% 0.16/0.39 => ( binintersectI
% 0.16/0.39 => ( binintersectSubset5
% 0.16/0.39 => ( binintersectEL
% 0.16/0.39 => ( binintersectLsub
% 0.16/0.39 => ( binintersectSubset2
% 0.16/0.39 => ( binintersectSubset3
% 0.16/0.39 => ( binintersectER
% 0.16/0.39 => ( disjointsetsI1
% 0.16/0.39 => ( binintersectRsub
% 0.16/0.39 => ( binintersectSubset4
% 0.16/0.39 => ( binintersectSubset1
% 0.16/0.39 => ( bs114d
% 0.16/0.39 => ( setminusI
% 0.16/0.39 => ( setminusEL
% 0.16/0.39 => ( setminusER
% 0.16/0.39 => ( setminusSubset2
% 0.16/0.39 => ( setminusERneg
% 0.16/0.39 => ( setminusELneg
% 0.16/0.39 => ( setminusILneg
% 0.16/0.39 => ( setminusIRneg
% 0.16/0.39 => ( setminusLsub
% 0.16/0.39 => ( setminusSubset1
% 0.16/0.39 => ( symdiffE
% 0.16/0.39 => ( symdiffI1
% 0.16/0.39 => ( symdiffI2
% 0.16/0.39 => ( symdiffIneg1
% 0.16/0.39 => ( symdiffIneg2
% 0.16/0.39 => ( secondinupair
% 0.16/0.39 => ( setukpairIL
% 0.16/0.39 => ( setukpairIR
% 0.16/0.39 => ( kpairiskpair
% 0.16/0.39 => ( kpairp
% 0.16/0.39 => ( singletonsubset
% 0.16/0.39 => ( singletoninpowerset
% 0.16/0.39 => ( singletoninpowunion
% 0.16/0.39 => ( upairset2E
% 0.16/0.39 => ( upairsubunion
% 0.16/0.39 => ( upairinpowunion
% 0.16/0.39 => ( ubforcartprodlem1
% 0.16/0.39 => ( ubforcartprodlem2
% 0.16/0.39 => ( ubforcartprodlem3
% 0.16/0.39 => ( cartprodpairin
% 0.16/0.39 => ( cartprodmempair1
% 0.16/0.39 => ( cartprodmempair
% 0.16/0.39 => ( setunionE2
% 0.16/0.39 => ( setunionsingleton1
% 0.16/0.39 => ( setunionsingleton2
% 0.16/0.39 => ( setunionsingleton
% 0.16/0.39 => ( singletonprop
% 0.16/0.39 => ( ex1E1
% 0.16/0.39 => ( ex1I
% 0.16/0.39 => ( ex1I2
% 0.16/0.39 => ( singletonsuniq
% 0.16/0.39 => ( setukpairinjL1
% 0.16/0.39 => ( kfstsingleton
% 0.16/0.39 => ( theprop
% 0.16/0.39 => ( kfstpairEq
% 0.16/0.39 => ( cartprodfstin
% 0.16/0.39 => ( setukpairinjL2
% 0.16/0.39 => ( setukpairinjL
% 0.16/0.39 => ( setukpairinjR11
% 0.16/0.39 => ( setukpairinjR12
% 0.16/0.39 => ( setukpairinjR1
% 0.16/0.39 => ( upairequniteq
% 0.16/0.39 => ( setukpairinjR2
% 0.16/0.39 => ( setukpairinjR
% 0.16/0.39 => ( ksndsingleton
% 0.16/0.39 => ( ksndpairEq
% 0.16/0.39 => ( kpairsurjEq
% 0.16/0.39 => ( cartprodsndin
% 0.16/0.39 => ( cartprodpairmemEL
% 0.16/0.39 => ( cartprodpairmemER
% 0.16/0.39 => ( cartprodmempaircEq
% 0.16/0.39 => ( cartprodfstpairEq
% 0.16/0.39 => ( cartprodsndpairEq
% 0.16/0.39 => ( cartprodpairsurjEq
% 0.16/0.39 => ( dpsetconstrI
% 0.16/0.39 => ( dpsetconstrSub
% 0.16/0.39 => ( setOfPairsIsBReln
% 0.16/0.39 => ( dpsetconstrERa
% 0.16/0.39 => ( dpsetconstrEL1
% 0.16/0.39 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.16/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.16/0.39 @ ( dpsetconstr @ A @ B
% 0.16/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.16/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.59/1.54 ---- Embedded in THF ---
% 2.59/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.59/1.54 %%% Generated on Tue Feb 24 12:31:05 EST 2026
% 2.59/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.59/1.54 %%% Logic specification used:
% 2.59/1.54 %%% thf(spec, logic, $$dhol).
% 2.59/1.54
% 2.59/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2DTF724.p
% See solution above
% 2.59/1.54 ------------------------
% 2.59/1.58 ---- Cleaned THF ---
% 2.59/1.58 thf(in_type,type,
% 2.59/1.58 in: $i > $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(exu_type,type,
% 2.59/1.58 exu: ( $i > $o ) > $o ).
% 2.59/1.58
% 2.59/1.58 thf(exu,definition,
% 2.59/1.58 ( exu
% 2.59/1.58 = ( ^ [Xphi: $i > $o] :
% 2.59/1.58 ? [Xx: $i] :
% 2.59/1.58 ( ( Xphi @ Xx )
% 2.59/1.58 & ! [Xy: $i] :
% 2.59/1.58 ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setextAx_type,type,
% 2.59/1.58 setextAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setextAx,definition,
% 2.59/1.58 ( setextAx
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 <=> ( in @ Xx @ B ) )
% 2.59/1.58 => ( A = B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptyset_type,type,
% 2.59/1.58 emptyset: $i ).
% 2.59/1.58
% 2.59/1.58 thf(emptysetAx_type,type,
% 2.59/1.58 emptysetAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptysetAx,definition,
% 2.59/1.58 ( emptysetAx
% 2.59/1.58 = ( ! [Xx: $i] :
% 2.59/1.58 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoin_type,type,
% 2.59/1.58 setadjoin: $i > $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinAx_type,type,
% 2.59/1.58 setadjoinAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinAx,definition,
% 2.59/1.58 ( setadjoinAx
% 2.59/1.58 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.59/1.58 <=> ( ( Xy = Xx )
% 2.59/1.58 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(powerset_type,type,
% 2.59/1.58 powerset: $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(powersetAx_type,type,
% 2.59/1.58 powersetAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(powersetAx,definition,
% 2.59/1.58 ( powersetAx
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( in @ B @ ( powerset @ A ) )
% 2.59/1.58 <=> ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setunion_type,type,
% 2.59/1.58 setunion: $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(setunionAx_type,type,
% 2.59/1.58 setunionAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setunionAx,definition,
% 2.59/1.58 ( setunionAx
% 2.59/1.58 = ( ! [A: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( setunion @ A ) )
% 2.59/1.58 <=> ? [B: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 & ( in @ B @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(omega_type,type,
% 2.59/1.58 omega: $i ).
% 2.59/1.58
% 2.59/1.58 thf(omega0Ax_type,type,
% 2.59/1.58 omega0Ax: $o ).
% 2.59/1.58
% 2.59/1.58 thf(omega0Ax,definition,
% 2.59/1.58 ( omega0Ax
% 2.59/1.58 = ( in @ emptyset @ omega ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(omegaSAx_type,type,
% 2.59/1.58 omegaSAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(omegaSAx,definition,
% 2.59/1.58 ( omegaSAx
% 2.59/1.58 = ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ omega )
% 2.59/1.58 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(omegaIndAx_type,type,
% 2.59/1.58 omegaIndAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(omegaIndAx,definition,
% 2.59/1.58 ( omegaIndAx
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ( ( in @ emptyset @ A )
% 2.59/1.58 & ! [Xx: $i] :
% 2.59/1.58 ( ( ( in @ Xx @ omega )
% 2.59/1.58 & ( in @ Xx @ A ) )
% 2.59/1.58 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.59/1.58 => ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ omega )
% 2.59/1.58 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(replAx_type,type,
% 2.59/1.58 replAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(replAx,definition,
% 2.59/1.58 ( replAx
% 2.59/1.58 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( exu
% 2.59/1.58 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.59/1.58 => ? [B: $i] :
% 2.59/1.58 ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 <=> ? [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ A )
% 2.59/1.58 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(foundationAx_type,type,
% 2.59/1.58 foundationAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(foundationAx,definition,
% 2.59/1.58 ( foundationAx
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.59/1.58 => ? [B: $i] :
% 2.59/1.58 ( ( in @ B @ A )
% 2.59/1.58 & ~ ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(wellorderingAx_type,type,
% 2.59/1.58 wellorderingAx: $o ).
% 2.59/1.58
% 2.59/1.58 thf(wellorderingAx,definition,
% 2.59/1.58 ( wellorderingAx
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ? [B: $i] :
% 2.59/1.58 ( ! [C: $i] :
% 2.59/1.58 ( ( in @ C @ B )
% 2.59/1.58 => ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ C )
% 2.59/1.58 => ( in @ Xx @ A ) ) )
% 2.59/1.58 & ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( ( in @ Xx @ A )
% 2.59/1.58 & ( in @ Xy @ A ) )
% 2.59/1.58 => ( ! [C: $i] :
% 2.59/1.58 ( ( in @ C @ B )
% 2.59/1.58 => ( ( in @ Xx @ C )
% 2.59/1.58 <=> ( in @ Xy @ C ) ) )
% 2.59/1.58 => ( Xx = Xy ) ) )
% 2.59/1.58 & ! [C: $i,D: $i] :
% 2.59/1.58 ( ( ( in @ C @ B )
% 2.59/1.58 & ( in @ D @ B ) )
% 2.59/1.58 => ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ C )
% 2.59/1.58 => ( in @ Xx @ D ) )
% 2.59/1.58 | ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ D )
% 2.59/1.58 => ( in @ Xx @ C ) ) ) )
% 2.59/1.58 & ! [C: $i] :
% 2.59/1.58 ( ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ C )
% 2.59/1.58 => ( in @ Xx @ A ) )
% 2.59/1.58 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.59/1.58 => ? [D: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ D @ B )
% 2.59/1.58 & ( in @ Xx @ C )
% 2.59/1.58 & ~ ? [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ D )
% 2.59/1.58 & ( in @ Xy @ C ) )
% 2.59/1.58 & ! [E: $i] :
% 2.59/1.58 ( ( in @ E @ B )
% 2.59/1.58 => ( ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ E )
% 2.59/1.58 => ( in @ Xy @ D ) )
% 2.59/1.58 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(descr_type,type,
% 2.59/1.58 descr: ( $i > $o ) > $i ).
% 2.59/1.58
% 2.59/1.58 thf(descrp_type,type,
% 2.59/1.58 descrp: $o ).
% 2.59/1.58
% 2.59/1.58 thf(descrp,definition,
% 2.59/1.58 ( descrp
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 => ( Xphi
% 2.59/1.58 @ ( descr
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstr_type,type,
% 2.59/1.58 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstrI_type,type,
% 2.59/1.58 dsetconstrI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstrI,definition,
% 2.59/1.58 ( dsetconstrI
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ( Xphi @ Xx )
% 2.59/1.58 => ( in @ Xx
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstrEL_type,type,
% 2.59/1.58 dsetconstrEL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstrEL,definition,
% 2.59/1.58 ( dsetconstrEL
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.59/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstrER_type,type,
% 2.59/1.58 dsetconstrER: $o ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstrER,definition,
% 2.59/1.58 ( dsetconstrER
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.59/1.58 => ( Xphi @ Xx ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exuE1_type,type,
% 2.59/1.58 exuE1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exuE1,definition,
% 2.59/1.58 ( exuE1
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 => ? [Xx: $i] :
% 2.59/1.58 ( ( Xphi @ Xx )
% 2.59/1.58 & ! [Xy: $i] :
% 2.59/1.58 ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(prop2set_type,type,
% 2.59/1.58 prop2set: $o > $i ).
% 2.59/1.58
% 2.59/1.58 thf(prop2setE_type,type,
% 2.59/1.58 prop2setE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(prop2setE,definition,
% 2.59/1.58 ( prop2setE
% 2.59/1.58 = ( ! [Xphi: $o,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.59/1.58 => Xphi ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptysetE_type,type,
% 2.59/1.58 emptysetE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptysetE,definition,
% 2.59/1.58 ( emptysetE
% 2.59/1.58 = ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ emptyset )
% 2.59/1.58 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptysetimpfalse_type,type,
% 2.59/1.58 emptysetimpfalse: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptysetimpfalse,definition,
% 2.59/1.58 ( emptysetimpfalse
% 2.59/1.58 = ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ emptyset )
% 2.59/1.58 => $false ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(notinemptyset_type,type,
% 2.59/1.58 notinemptyset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(notinemptyset,definition,
% 2.59/1.58 ( notinemptyset
% 2.59/1.58 = ( ! [Xx: $i] :
% 2.59/1.58 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exuE3e_type,type,
% 2.59/1.58 exuE3e: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exuE3e,definition,
% 2.59/1.58 ( exuE3e
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setext_type,type,
% 2.59/1.58 setext: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setext,definition,
% 2.59/1.58 ( setext
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ Xx @ B ) )
% 2.59/1.58 => ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ A ) )
% 2.59/1.58 => ( A = B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptyI_type,type,
% 2.59/1.58 emptyI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptyI,definition,
% 2.59/1.58 ( emptyI
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ~ ( in @ Xx @ A )
% 2.59/1.58 => ( A = emptyset ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(noeltsimpempty_type,type,
% 2.59/1.58 noeltsimpempty: $o ).
% 2.59/1.58
% 2.59/1.58 thf(noeltsimpempty,definition,
% 2.59/1.58 ( noeltsimpempty
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ~ ( in @ Xx @ A )
% 2.59/1.58 => ( A = emptyset ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setbeta_type,type,
% 2.59/1.58 setbeta: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setbeta,definition,
% 2.59/1.58 ( setbeta
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ( in @ Xx
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.59/1.58 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(nonempty_type,type,
% 2.59/1.58 nonempty: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(nonempty,definition,
% 2.59/1.58 ( nonempty
% 2.59/1.58 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(nonemptyE1_type,type,
% 2.59/1.58 nonemptyE1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(nonemptyE1,definition,
% 2.59/1.58 ( nonemptyE1
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ( nonempty @ A )
% 2.59/1.58 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(nonemptyI_type,type,
% 2.59/1.58 nonemptyI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(nonemptyI,definition,
% 2.59/1.58 ( nonemptyI
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ( Xphi @ Xx )
% 2.59/1.58 => ( nonempty
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(nonemptyI1_type,type,
% 2.59/1.58 nonemptyI1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(nonemptyI1,definition,
% 2.59/1.58 ( nonemptyI1
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.59/1.58 => ( nonempty @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinIL_type,type,
% 2.59/1.58 setadjoinIL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinIL,definition,
% 2.59/1.58 ( setadjoinIL
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptyinunitempty_type,type,
% 2.59/1.58 emptyinunitempty: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptyinunitempty,definition,
% 2.59/1.58 ( emptyinunitempty
% 2.59/1.58 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinIR_type,type,
% 2.59/1.58 setadjoinIR: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinIR,definition,
% 2.59/1.58 ( setadjoinIR
% 2.59/1.58 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ A )
% 2.59/1.58 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinE_type,type,
% 2.59/1.58 setadjoinE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinE,definition,
% 2.59/1.58 ( setadjoinE
% 2.59/1.58 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.59/1.58 => ! [Xphi: $o] :
% 2.59/1.58 ( ( ( Xy = Xx )
% 2.59/1.58 => Xphi )
% 2.59/1.58 => ( ( ( in @ Xy @ A )
% 2.59/1.58 => Xphi )
% 2.59/1.58 => Xphi ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinOr_type,type,
% 2.59/1.58 setadjoinOr: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinOr,definition,
% 2.59/1.58 ( setadjoinOr
% 2.59/1.58 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.59/1.58 => ( ( Xy = Xx )
% 2.59/1.58 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setoftrueEq_type,type,
% 2.59/1.58 setoftrueEq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setoftrueEq,definition,
% 2.59/1.58 ( setoftrueEq
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xx: $i] : $true )
% 2.59/1.58 = A ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(powersetI_type,type,
% 2.59/1.58 powersetI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(powersetI,definition,
% 2.59/1.58 ( powersetI
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ A ) )
% 2.59/1.58 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptyinPowerset_type,type,
% 2.59/1.58 emptyinPowerset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptyinPowerset,definition,
% 2.59/1.58 ( emptyinPowerset
% 2.59/1.58 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptyInPowerset_type,type,
% 2.59/1.58 emptyInPowerset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptyInPowerset,definition,
% 2.59/1.58 ( emptyInPowerset
% 2.59/1.58 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(powersetE_type,type,
% 2.59/1.58 powersetE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(powersetE,definition,
% 2.59/1.58 ( powersetE
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ B @ ( powerset @ A ) )
% 2.59/1.58 => ( ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setunionI_type,type,
% 2.59/1.58 setunionI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setunionI,definition,
% 2.59/1.58 ( setunionI
% 2.59/1.58 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 => ( ( in @ B @ A )
% 2.59/1.58 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setunionE_type,type,
% 2.59/1.58 setunionE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setunionE,definition,
% 2.59/1.58 ( setunionE
% 2.59/1.58 = ( ! [A: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( setunion @ A ) )
% 2.59/1.58 => ! [Xphi: $o] :
% 2.59/1.58 ( ! [B: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 => ( ( in @ B @ A )
% 2.59/1.58 => Xphi ) )
% 2.59/1.58 => Xphi ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subPowSU_type,type,
% 2.59/1.58 subPowSU: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subPowSU,definition,
% 2.59/1.58 ( subPowSU
% 2.59/1.58 = ( ! [A: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exuE2_type,type,
% 2.59/1.58 exuE2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exuE2,definition,
% 2.59/1.58 ( exuE2
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 => ? [Xx: $i] :
% 2.59/1.58 ! [Xy: $i] :
% 2.59/1.58 ( ( Xphi @ Xy )
% 2.59/1.58 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(nonemptyImpWitness_type,type,
% 2.59/1.58 nonemptyImpWitness: $o ).
% 2.59/1.58
% 2.59/1.58 thf(nonemptyImpWitness,definition,
% 2.59/1.58 ( nonemptyImpWitness
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ( nonempty @ A )
% 2.59/1.58 => ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & $true ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(uniqinunit_type,type,
% 2.59/1.58 uniqinunit: $o ).
% 2.59/1.58
% 2.59/1.58 thf(uniqinunit,definition,
% 2.59/1.58 ( uniqinunit
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(notinsingleton_type,type,
% 2.59/1.58 notinsingleton: $o ).
% 2.59/1.58
% 2.59/1.58 thf(notinsingleton,definition,
% 2.59/1.58 ( notinsingleton
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx != Xy )
% 2.59/1.58 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(eqinunit_type,type,
% 2.59/1.58 eqinunit: $o ).
% 2.59/1.58
% 2.59/1.58 thf(eqinunit,definition,
% 2.59/1.58 ( eqinunit
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx = Xy )
% 2.59/1.58 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(singletonsswitch_type,type,
% 2.59/1.58 singletonsswitch: $o ).
% 2.59/1.58
% 2.59/1.58 thf(singletonsswitch,definition,
% 2.59/1.58 ( singletonsswitch
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.59/1.58 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(upairsetE_type,type,
% 2.59/1.58 upairsetE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairsetE,definition,
% 2.59/1.58 ( upairsetE
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.59/1.58 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.59/1.58 => ( ( Xz = Xx )
% 2.59/1.58 | ( Xz = Xy ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(upairsetIL_type,type,
% 2.59/1.58 upairsetIL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairsetIL,definition,
% 2.59/1.58 ( upairsetIL
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(upairsetIR_type,type,
% 2.59/1.58 upairsetIR: $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairsetIR,definition,
% 2.59/1.58 ( upairsetIR
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptyE1_type,type,
% 2.59/1.58 emptyE1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptyE1,definition,
% 2.59/1.58 ( emptyE1
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( Xphi @ Xx ) )
% 2.59/1.58 => ( ( ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 = emptyset )
% 2.59/1.58 => $false ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(vacuousDall_type,type,
% 2.59/1.58 vacuousDall: $o ).
% 2.59/1.58
% 2.59/1.58 thf(vacuousDall,definition,
% 2.59/1.58 ( vacuousDall
% 2.59/1.58 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ emptyset )
% 2.59/1.58 => ( Xphi @ Xx ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(quantDeMorgan1_type,type,
% 2.59/1.58 quantDeMorgan1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(quantDeMorgan1,definition,
% 2.59/1.58 ( quantDeMorgan1
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ~ ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( Xphi @ Xx ) )
% 2.59/1.58 => ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(quantDeMorgan2_type,type,
% 2.59/1.58 quantDeMorgan2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(quantDeMorgan2,definition,
% 2.59/1.58 ( quantDeMorgan2
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ~ ( Xphi @ Xx ) )
% 2.59/1.58 => ~ ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(quantDeMorgan3_type,type,
% 2.59/1.58 quantDeMorgan3: $o ).
% 2.59/1.58
% 2.59/1.58 thf(quantDeMorgan3,definition,
% 2.59/1.58 ( quantDeMorgan3
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ~ ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( Xphi @ Xx ) )
% 2.59/1.58 => ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(quantDeMorgan4_type,type,
% 2.59/1.58 quantDeMorgan4: $o ).
% 2.59/1.58
% 2.59/1.58 thf(quantDeMorgan4,definition,
% 2.59/1.58 ( quantDeMorgan4
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ~ ( Xphi @ Xx ) )
% 2.59/1.58 => ~ ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(prop2setI_type,type,
% 2.59/1.58 prop2setI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(prop2setI,definition,
% 2.59/1.58 ( prop2setI
% 2.59/1.58 = ( ! [Xphi: $o] :
% 2.59/1.58 ( Xphi
% 2.59/1.58 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(set2prop_type,type,
% 2.59/1.58 set2prop: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(prop2set2propI_type,type,
% 2.59/1.58 prop2set2propI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(prop2set2propI,definition,
% 2.59/1.58 ( prop2set2propI
% 2.59/1.58 = ( ! [Xphi: $o] :
% 2.59/1.58 ( Xphi
% 2.59/1.58 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(notdexE_type,type,
% 2.59/1.58 notdexE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(notdexE,definition,
% 2.59/1.58 ( notdexE
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ~ ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( Xphi @ Xx ) )
% 2.59/1.58 => ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(notdallE_type,type,
% 2.59/1.58 notdallE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(notdallE,definition,
% 2.59/1.58 ( notdallE
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ~ ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( Xphi @ Xx ) )
% 2.59/1.58 => ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exuI1_type,type,
% 2.59/1.58 exuI1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exuI1,definition,
% 2.59/1.58 ( exuI1
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ? [Xx: $i] :
% 2.59/1.58 ( ( Xphi @ Xx )
% 2.59/1.58 & ! [Xy: $i] :
% 2.59/1.58 ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xx = Xy ) ) )
% 2.59/1.58 => ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exuI3_type,type,
% 2.59/1.58 exuI3: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exuI3,definition,
% 2.59/1.58 ( exuI3
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.59/1.58 => ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xphi @ Xx )
% 2.59/1.58 => ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xx = Xy ) ) )
% 2.59/1.58 => ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exuI2_type,type,
% 2.59/1.58 exuI2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exuI2,definition,
% 2.59/1.58 ( exuI2
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ? [Xx: $i] :
% 2.59/1.58 ! [Xy: $i] :
% 2.59/1.58 ( ( Xphi @ Xy )
% 2.59/1.58 <=> ( Xy = Xx ) )
% 2.59/1.58 => ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(inCongP_type,type,
% 2.59/1.58 inCongP: $o ).
% 2.59/1.58
% 2.59/1.58 thf(inCongP,definition,
% 2.59/1.58 ( inCongP
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( A = B )
% 2.59/1.58 => ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx = Xy )
% 2.59/1.58 => ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(in__Cong_type,type,
% 2.59/1.58 in__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(in__Cong,definition,
% 2.59/1.58 ( in__Cong
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( A = B )
% 2.59/1.58 => ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx = Xy )
% 2.59/1.58 => ( ( in @ Xx @ A )
% 2.59/1.58 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exuE3u_type,type,
% 2.59/1.58 exuE3u: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exuE3u,definition,
% 2.59/1.58 ( exuE3u
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 => ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xphi @ Xx )
% 2.59/1.58 => ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exu__Cong_type,type,
% 2.59/1.58 exu__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exu__Cong,definition,
% 2.59/1.58 ( exu__Cong
% 2.59/1.58 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.59/1.58 ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx = Xy )
% 2.59/1.58 => ( ( Xphi @ Xx )
% 2.59/1.58 <=> ( Xpsi @ Xy ) ) )
% 2.59/1.58 => ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 <=> ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptyset__Cong_type,type,
% 2.59/1.58 emptyset__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptyset__Cong,definition,
% 2.59/1.58 ( emptyset__Cong
% 2.59/1.58 = ( emptyset = emptyset ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoin__Cong_type,type,
% 2.59/1.58 setadjoin__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoin__Cong,definition,
% 2.59/1.58 ( setadjoin__Cong
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx = Xy )
% 2.59/1.58 => ! [Xz: $i,Xu: $i] :
% 2.59/1.58 ( ( Xz = Xu )
% 2.59/1.58 => ( ( setadjoin @ Xx @ Xz )
% 2.59/1.58 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(powerset__Cong_type,type,
% 2.59/1.58 powerset__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(powerset__Cong,definition,
% 2.59/1.58 ( powerset__Cong
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( A = B )
% 2.59/1.58 => ( ( powerset @ A )
% 2.59/1.58 = ( powerset @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setunion__Cong_type,type,
% 2.59/1.58 setunion__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setunion__Cong,definition,
% 2.59/1.58 ( setunion__Cong
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( A = B )
% 2.59/1.58 => ( ( setunion @ A )
% 2.59/1.58 = ( setunion @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(omega__Cong_type,type,
% 2.59/1.58 omega__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(omega__Cong,definition,
% 2.59/1.58 ( omega__Cong
% 2.59/1.58 = ( omega = omega ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(exuEu_type,type,
% 2.59/1.58 exuEu: $o ).
% 2.59/1.58
% 2.59/1.58 thf(exuEu,definition,
% 2.59/1.58 ( exuEu
% 2.59/1.58 = ( ! [Xphi: $i > $o] :
% 2.59/1.58 ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 => ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xphi @ Xx )
% 2.59/1.58 => ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(descr__Cong_type,type,
% 2.59/1.58 descr__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(descr__Cong,definition,
% 2.59/1.58 ( descr__Cong
% 2.59/1.58 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.59/1.58 ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx = Xy )
% 2.59/1.58 => ( ( Xphi @ Xx )
% 2.59/1.58 <=> ( Xpsi @ Xy ) ) )
% 2.59/1.58 => ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 => ( ( exu
% 2.59/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.59/1.58 => ( ( descr
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 = ( descr
% 2.59/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstr__Cong_type,type,
% 2.59/1.58 dsetconstr__Cong: $o ).
% 2.59/1.58
% 2.59/1.58 thf(dsetconstr__Cong,definition,
% 2.59/1.58 ( dsetconstr__Cong
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( A = B )
% 2.59/1.58 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( ( Xx = Xy )
% 2.59/1.58 => ( ( Xphi @ Xx )
% 2.59/1.58 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.59/1.58 => ( ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 = ( dsetconstr @ B
% 2.59/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subset_type,type,
% 2.59/1.58 subset: $i > $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(disjoint_type,type,
% 2.59/1.58 disjoint: $i > $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(setsmeet_type,type,
% 2.59/1.58 setsmeet: $i > $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(subsetI1_type,type,
% 2.59/1.58 subsetI1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subsetI1,definition,
% 2.59/1.58 ( subsetI1
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ Xx @ B ) )
% 2.59/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(eqimpsubset2_type,type,
% 2.59/1.58 eqimpsubset2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(eqimpsubset2,definition,
% 2.59/1.58 ( eqimpsubset2
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( A = B )
% 2.59/1.58 => ( subset @ B @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(eqimpsubset1_type,type,
% 2.59/1.58 eqimpsubset1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(eqimpsubset1,definition,
% 2.59/1.58 ( eqimpsubset1
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( A = B )
% 2.59/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subsetI2_type,type,
% 2.59/1.58 subsetI2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subsetI2,definition,
% 2.59/1.58 ( subsetI2
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ Xx @ B ) )
% 2.59/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(emptysetsubset_type,type,
% 2.59/1.58 emptysetsubset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(emptysetsubset,definition,
% 2.59/1.58 ( emptysetsubset
% 2.59/1.58 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subsetE_type,type,
% 2.59/1.58 subsetE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subsetE,definition,
% 2.59/1.58 ( subsetE
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subsetE2_type,type,
% 2.59/1.58 subsetE2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subsetE2,definition,
% 2.59/1.58 ( subsetE2
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( ~ ( in @ Xx @ B )
% 2.59/1.58 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(notsubsetI_type,type,
% 2.59/1.58 notsubsetI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(notsubsetI,definition,
% 2.59/1.58 ( notsubsetI
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ~ ( in @ Xx @ B )
% 2.59/1.58 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(notequalI1_type,type,
% 2.59/1.58 notequalI1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(notequalI1,definition,
% 2.59/1.58 ( notequalI1
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ~ ( subset @ A @ B )
% 2.59/1.58 => ( A != B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(notequalI2_type,type,
% 2.59/1.58 notequalI2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(notequalI2,definition,
% 2.59/1.58 ( notequalI2
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ~ ( in @ Xx @ B )
% 2.59/1.58 => ( A != B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subsetRefl_type,type,
% 2.59/1.58 subsetRefl: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subsetRefl,definition,
% 2.59/1.58 ( subsetRefl
% 2.59/1.58 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subsetTrans_type,type,
% 2.59/1.58 subsetTrans: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subsetTrans,definition,
% 2.59/1.58 ( subsetTrans
% 2.59/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( ( subset @ B @ C )
% 2.59/1.58 => ( subset @ A @ C ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinSub_type,type,
% 2.59/1.58 setadjoinSub: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinSub,definition,
% 2.59/1.58 ( setadjoinSub
% 2.59/1.58 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinSub2_type,type,
% 2.59/1.58 setadjoinSub2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setadjoinSub2,definition,
% 2.59/1.58 ( setadjoinSub2
% 2.59/1.58 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subset2powerset_type,type,
% 2.59/1.58 subset2powerset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subset2powerset,definition,
% 2.59/1.58 ( subset2powerset
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setextsub_type,type,
% 2.59/1.58 setextsub: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setextsub,definition,
% 2.59/1.58 ( setextsub
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( ( subset @ B @ A )
% 2.59/1.58 => ( A = B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(subsetemptysetimpeq_type,type,
% 2.59/1.58 subsetemptysetimpeq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(subsetemptysetimpeq,definition,
% 2.59/1.58 ( subsetemptysetimpeq
% 2.59/1.58 = ( ! [A: $i] :
% 2.59/1.58 ( ( subset @ A @ emptyset )
% 2.59/1.58 => ( A = emptyset ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(powersetI1_type,type,
% 2.59/1.58 powersetI1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(powersetI1,definition,
% 2.59/1.58 ( powersetI1
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( subset @ B @ A )
% 2.59/1.58 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(powersetE1_type,type,
% 2.59/1.58 powersetE1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(powersetE1,definition,
% 2.59/1.58 ( powersetE1
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( in @ B @ ( powerset @ A ) )
% 2.59/1.58 => ( subset @ B @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(inPowerset_type,type,
% 2.59/1.58 inPowerset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(inPowerset,definition,
% 2.59/1.58 ( inPowerset
% 2.59/1.58 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(powersetsubset_type,type,
% 2.59/1.58 powersetsubset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(powersetsubset,definition,
% 2.59/1.58 ( powersetsubset
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(sepInPowerset_type,type,
% 2.59/1.58 sepInPowerset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(sepInPowerset,definition,
% 2.59/1.58 ( sepInPowerset
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( in
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 @ ( powerset @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(sepSubset_type,type,
% 2.59/1.58 sepSubset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(sepSubset,definition,
% 2.59/1.58 ( sepSubset
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( subset
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 @ A ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binunion_type,type,
% 2.59/1.58 binunion: $i > $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(binunionIL_type,type,
% 2.59/1.58 binunionIL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binunionIL,definition,
% 2.59/1.58 ( binunionIL
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(upairset2IR_type,type,
% 2.59/1.58 upairset2IR: $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairset2IR,definition,
% 2.59/1.58 ( upairset2IR
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binunionIR_type,type,
% 2.59/1.58 binunionIR: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binunionIR,definition,
% 2.59/1.58 ( binunionIR
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binunionEcases_type,type,
% 2.59/1.58 binunionEcases: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binunionEcases,definition,
% 2.59/1.58 ( binunionEcases
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.59/1.58 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.59/1.58 => ( ( ( in @ Xx @ A )
% 2.59/1.58 => Xphi )
% 2.59/1.58 => ( ( ( in @ Xx @ B )
% 2.59/1.58 => Xphi )
% 2.59/1.58 => Xphi ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binunionE_type,type,
% 2.59/1.58 binunionE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binunionE,definition,
% 2.59/1.58 ( binunionE
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.59/1.58 => ( ( in @ Xx @ A )
% 2.59/1.58 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binunionLsub_type,type,
% 2.59/1.58 binunionLsub: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binunionLsub,definition,
% 2.59/1.58 ( binunionLsub
% 2.59/1.58 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binunionRsub_type,type,
% 2.59/1.58 binunionRsub: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binunionRsub,definition,
% 2.59/1.58 ( binunionRsub
% 2.59/1.58 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersect_type,type,
% 2.59/1.58 binintersect: $i > $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectI_type,type,
% 2.59/1.58 binintersectI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectI,definition,
% 2.59/1.58 ( binintersectI
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset5_type,type,
% 2.59/1.58 binintersectSubset5: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset5,definition,
% 2.59/1.58 ( binintersectSubset5
% 2.59/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 2.59/1.58 ( ( subset @ C @ A )
% 2.59/1.58 => ( ( subset @ C @ B )
% 2.59/1.58 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectEL_type,type,
% 2.59/1.58 binintersectEL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectEL,definition,
% 2.59/1.58 ( binintersectEL
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.59/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectLsub_type,type,
% 2.59/1.58 binintersectLsub: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectLsub,definition,
% 2.59/1.58 ( binintersectLsub
% 2.59/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset2_type,type,
% 2.59/1.58 binintersectSubset2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset2,definition,
% 2.59/1.58 ( binintersectSubset2
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( ( binintersect @ A @ B )
% 2.59/1.58 = A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset3_type,type,
% 2.59/1.58 binintersectSubset3: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset3,definition,
% 2.59/1.58 ( binintersectSubset3
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( ( binintersect @ A @ B )
% 2.59/1.58 = B )
% 2.59/1.58 => ( subset @ B @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectER_type,type,
% 2.59/1.58 binintersectER: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectER,definition,
% 2.59/1.58 ( binintersectER
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.59/1.58 => ( in @ Xx @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(disjointsetsI1_type,type,
% 2.59/1.58 disjointsetsI1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(disjointsetsI1,definition,
% 2.59/1.58 ( disjointsetsI1
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ~ ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( in @ Xx @ B ) )
% 2.59/1.58 => ( ( binintersect @ A @ B )
% 2.59/1.58 = emptyset ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectRsub_type,type,
% 2.59/1.58 binintersectRsub: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectRsub,definition,
% 2.59/1.58 ( binintersectRsub
% 2.59/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset4_type,type,
% 2.59/1.58 binintersectSubset4: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset4,definition,
% 2.59/1.58 ( binintersectSubset4
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( subset @ B @ A )
% 2.59/1.58 => ( ( binintersect @ A @ B )
% 2.59/1.58 = B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset1_type,type,
% 2.59/1.58 binintersectSubset1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(binintersectSubset1,definition,
% 2.59/1.58 ( binintersectSubset1
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( ( binintersect @ A @ B )
% 2.59/1.58 = A )
% 2.59/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(bs114d_type,type,
% 2.59/1.58 bs114d: $o ).
% 2.59/1.58
% 2.59/1.58 thf(bs114d,definition,
% 2.59/1.58 ( bs114d
% 2.59/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 2.59/1.58 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.59/1.58 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(regular_type,type,
% 2.59/1.58 regular: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminus_type,type,
% 2.59/1.58 setminus: $i > $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(setminusI_type,type,
% 2.59/1.58 setminusI: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusI,definition,
% 2.59/1.58 ( setminusI
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ~ ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusEL_type,type,
% 2.59/1.58 setminusEL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusEL,definition,
% 2.59/1.58 ( setminusEL
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.59/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusER_type,type,
% 2.59/1.58 setminusER: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusER,definition,
% 2.59/1.58 ( setminusER
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.59/1.58 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusSubset2_type,type,
% 2.59/1.58 setminusSubset2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusSubset2,definition,
% 2.59/1.58 ( setminusSubset2
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( subset @ A @ B )
% 2.59/1.58 => ( ( setminus @ A @ B )
% 2.59/1.58 = emptyset ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusERneg_type,type,
% 2.59/1.58 setminusERneg: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusERneg,definition,
% 2.59/1.58 ( setminusERneg
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.59/1.58 => ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusELneg_type,type,
% 2.59/1.58 setminusELneg: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusELneg,definition,
% 2.59/1.58 ( setminusELneg
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.59/1.58 => ( ~ ( in @ Xx @ B )
% 2.59/1.58 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusILneg_type,type,
% 2.59/1.58 setminusILneg: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusILneg,definition,
% 2.59/1.58 ( setminusILneg
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ~ ( in @ Xx @ A )
% 2.59/1.58 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusIRneg_type,type,
% 2.59/1.58 setminusIRneg: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusIRneg,definition,
% 2.59/1.58 ( setminusIRneg
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ B )
% 2.59/1.58 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusLsub_type,type,
% 2.59/1.58 setminusLsub: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusLsub,definition,
% 2.59/1.58 ( setminusLsub
% 2.59/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setminusSubset1_type,type,
% 2.59/1.58 setminusSubset1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setminusSubset1,definition,
% 2.59/1.58 ( setminusSubset1
% 2.59/1.58 = ( ! [A: $i,B: $i] :
% 2.59/1.58 ( ( ( setminus @ A @ B )
% 2.59/1.58 = emptyset )
% 2.59/1.58 => ( subset @ A @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(symdiff_type,type,
% 2.59/1.58 symdiff: $i > $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffE_type,type,
% 2.59/1.58 symdiffE: $o ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffE,definition,
% 2.59/1.58 ( symdiffE
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.59/1.58 => ! [Xphi: $o] :
% 2.59/1.58 ( ( ( in @ Xx @ A )
% 2.59/1.58 => ( ~ ( in @ Xx @ B )
% 2.59/1.58 => Xphi ) )
% 2.59/1.58 => ( ( ~ ( in @ Xx @ A )
% 2.59/1.58 => ( ( in @ Xx @ B )
% 2.59/1.58 => Xphi ) )
% 2.59/1.58 => Xphi ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffI1_type,type,
% 2.59/1.58 symdiffI1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffI1,definition,
% 2.59/1.58 ( symdiffI1
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ~ ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffI2_type,type,
% 2.59/1.58 symdiffI2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffI2,definition,
% 2.59/1.58 ( symdiffI2
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ~ ( in @ Xx @ A )
% 2.59/1.58 => ( ( in @ Xx @ B )
% 2.59/1.58 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffIneg1_type,type,
% 2.59/1.58 symdiffIneg1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffIneg1,definition,
% 2.59/1.58 ( symdiffIneg1
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ( in @ Xx @ B )
% 2.59/1.58 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffIneg2_type,type,
% 2.59/1.58 symdiffIneg2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(symdiffIneg2,definition,
% 2.59/1.58 ( symdiffIneg2
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ~ ( in @ Xx @ A )
% 2.59/1.58 => ( ~ ( in @ Xx @ B )
% 2.59/1.58 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(iskpair_type,type,
% 2.59/1.58 iskpair: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(secondinupair_type,type,
% 2.59/1.58 secondinupair: $o ).
% 2.59/1.58
% 2.59/1.58 thf(secondinupair,definition,
% 2.59/1.58 ( secondinupair
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairIL_type,type,
% 2.59/1.58 setukpairIL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairIL,definition,
% 2.59/1.58 ( setukpairIL
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairIR_type,type,
% 2.59/1.58 setukpairIR: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairIR,definition,
% 2.59/1.58 ( setukpairIR
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(kpairiskpair_type,type,
% 2.59/1.58 kpairiskpair: $o ).
% 2.59/1.58
% 2.59/1.58 thf(kpairiskpair,definition,
% 2.59/1.58 ( kpairiskpair
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(kpair_type,type,
% 2.59/1.58 kpair: $i > $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(kpairp_type,type,
% 2.59/1.58 kpairp: $o ).
% 2.59/1.58
% 2.59/1.58 thf(kpairp,definition,
% 2.59/1.58 ( kpairp
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprod_type,type,
% 2.59/1.58 cartprod: $i > $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(singletonsubset_type,type,
% 2.59/1.58 singletonsubset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(singletonsubset,definition,
% 2.59/1.58 ( singletonsubset
% 2.59/1.58 = ( ! [A: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(singletoninpowerset_type,type,
% 2.59/1.58 singletoninpowerset: $o ).
% 2.59/1.58
% 2.59/1.58 thf(singletoninpowerset,definition,
% 2.59/1.58 ( singletoninpowerset
% 2.59/1.58 = ( ! [A: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(singletoninpowunion_type,type,
% 2.59/1.58 singletoninpowunion: $o ).
% 2.59/1.58
% 2.59/1.58 thf(singletoninpowunion,definition,
% 2.59/1.58 ( singletoninpowunion
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(upairset2E_type,type,
% 2.59/1.58 upairset2E: $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairset2E,definition,
% 2.59/1.58 ( upairset2E
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.59/1.58 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.59/1.58 => ( ( Xz = Xx )
% 2.59/1.58 | ( Xz = Xy ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(upairsubunion_type,type,
% 2.59/1.58 upairsubunion: $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairsubunion,definition,
% 2.59/1.58 ( upairsubunion
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(upairinpowunion_type,type,
% 2.59/1.58 upairinpowunion: $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairinpowunion,definition,
% 2.59/1.58 ( upairinpowunion
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ubforcartprodlem1_type,type,
% 2.59/1.58 ubforcartprodlem1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(ubforcartprodlem1,definition,
% 2.59/1.58 ( ubforcartprodlem1
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ubforcartprodlem2_type,type,
% 2.59/1.58 ubforcartprodlem2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(ubforcartprodlem2,definition,
% 2.59/1.58 ( ubforcartprodlem2
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ubforcartprodlem3_type,type,
% 2.59/1.58 ubforcartprodlem3: $o ).
% 2.59/1.58
% 2.59/1.58 thf(ubforcartprodlem3,definition,
% 2.59/1.58 ( ubforcartprodlem3
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodpairin_type,type,
% 2.59/1.58 cartprodpairin: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodpairin,definition,
% 2.59/1.58 ( cartprodpairin
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodmempair1_type,type,
% 2.59/1.58 cartprodmempair1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodmempair1,definition,
% 2.59/1.58 ( cartprodmempair1
% 2.59/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.59/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.59/1.58 => ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ? [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 & ( Xu
% 2.59/1.58 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodmempair_type,type,
% 2.59/1.58 cartprodmempair: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodmempair,definition,
% 2.59/1.58 ( cartprodmempair
% 2.59/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.59/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.59/1.58 => ( iskpair @ Xu ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setunionE2_type,type,
% 2.59/1.58 setunionE2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setunionE2,definition,
% 2.59/1.58 ( setunionE2
% 2.59/1.58 = ( ! [A: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ ( setunion @ A ) )
% 2.59/1.58 => ? [X: $i] :
% 2.59/1.58 ( ( in @ X @ A )
% 2.59/1.58 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setunionsingleton1_type,type,
% 2.59/1.58 setunionsingleton1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setunionsingleton1,definition,
% 2.59/1.58 ( setunionsingleton1
% 2.59/1.58 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setunionsingleton2_type,type,
% 2.59/1.58 setunionsingleton2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setunionsingleton2,definition,
% 2.59/1.58 ( setunionsingleton2
% 2.59/1.58 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setunionsingleton_type,type,
% 2.59/1.58 setunionsingleton: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setunionsingleton,definition,
% 2.59/1.58 ( setunionsingleton
% 2.59/1.58 = ( ! [Xx: $i] :
% 2.59/1.58 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.59/1.58 = Xx ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(singleton_type,type,
% 2.59/1.58 singleton: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(singleton,definition,
% 2.59/1.58 ( singleton
% 2.59/1.58 = ( ^ [A: $i] :
% 2.59/1.58 ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( A
% 2.59/1.58 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(singletonprop_type,type,
% 2.59/1.58 singletonprop: $o ).
% 2.59/1.58
% 2.59/1.58 thf(singletonprop,definition,
% 2.59/1.58 ( singletonprop
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ A )
% 2.59/1.58 => ( ( Xphi @ Xx )
% 2.59/1.58 => ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) )
% 2.59/1.58 => ( ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( Xphi @ Xx ) )
% 2.59/1.58 => ( singleton
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ex1_type,type,
% 2.59/1.58 ex1: $i > ( $i > $o ) > $o ).
% 2.59/1.58
% 2.59/1.58 thf(ex1,definition,
% 2.59/1.58 ( ex1
% 2.59/1.58 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( singleton
% 2.59/1.58 @ ( dsetconstr @ A
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ex1E1_type,type,
% 2.59/1.58 ex1E1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(ex1E1,definition,
% 2.59/1.58 ( ex1E1
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ( ex1 @ A
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.59/1.58 => ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ex1I_type,type,
% 2.59/1.58 ex1I: $o ).
% 2.59/1.58
% 2.59/1.58 thf(ex1I,definition,
% 2.59/1.58 ( ex1I
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ( ( Xphi @ Xx )
% 2.59/1.58 => ( ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ A )
% 2.59/1.58 => ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xy = Xx ) ) )
% 2.59/1.58 => ( ex1 @ A
% 2.59/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ex1I2_type,type,
% 2.59/1.58 ex1I2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(ex1I2,definition,
% 2.59/1.58 ( ex1I2
% 2.59/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.59/1.58 ( ! [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ A )
% 2.59/1.58 => ( ( Xphi @ Xx )
% 2.59/1.58 => ( ( Xphi @ Xy )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) )
% 2.59/1.58 => ( ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ( Xphi @ Xx ) )
% 2.59/1.58 => ( ex1 @ A
% 2.59/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(singletonsuniq_type,type,
% 2.59/1.58 singletonsuniq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(singletonsuniq,definition,
% 2.59/1.58 ( singletonsuniq
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( ( setadjoin @ Xx @ emptyset )
% 2.59/1.58 = ( setadjoin @ Xy @ emptyset ) )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(atmost1p_type,type,
% 2.59/1.58 atmost1p: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(atleast2p_type,type,
% 2.59/1.58 atleast2p: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(atmost2p_type,type,
% 2.59/1.58 atmost2p: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairsetp_type,type,
% 2.59/1.58 upairsetp: $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjL1_type,type,
% 2.59/1.58 setukpairinjL1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjL1,definition,
% 2.59/1.58 ( setukpairinjL1
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.59/1.58 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.59/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(kfstsingleton_type,type,
% 2.59/1.58 kfstsingleton: $o ).
% 2.59/1.58
% 2.59/1.58 thf(kfstsingleton,definition,
% 2.59/1.58 ( kfstsingleton
% 2.59/1.58 = ( ! [Xu: $i] :
% 2.59/1.58 ( ( iskpair @ Xu )
% 2.59/1.58 => ( singleton
% 2.59/1.58 @ ( dsetconstr @ ( setunion @ Xu )
% 2.59/1.58 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(theprop_type,type,
% 2.59/1.58 theprop: $o ).
% 2.59/1.58
% 2.59/1.58 thf(theprop,definition,
% 2.59/1.58 ( theprop
% 2.59/1.58 = ( ! [X: $i] :
% 2.59/1.58 ( ( singleton @ X )
% 2.59/1.58 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(kfst_type,type,
% 2.59/1.58 kfst: $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(kfstpairEq_type,type,
% 2.59/1.58 kfstpairEq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(kfstpairEq,definition,
% 2.59/1.58 ( kfstpairEq
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.59/1.58 = Xx ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodfstin_type,type,
% 2.59/1.58 cartprodfstin: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodfstin,definition,
% 2.59/1.58 ( cartprodfstin
% 2.59/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.59/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.59/1.58 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjL2_type,type,
% 2.59/1.58 setukpairinjL2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjL2,definition,
% 2.59/1.58 ( setukpairinjL2
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.59/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.59/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.59/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjL_type,type,
% 2.59/1.58 setukpairinjL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjL,definition,
% 2.59/1.58 ( setukpairinjL
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.59/1.58 ( ( ( kpair @ Xx @ Xy )
% 2.59/1.58 = ( kpair @ Xz @ Xu ) )
% 2.59/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR11_type,type,
% 2.59/1.58 setukpairinjR11: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR11,definition,
% 2.59/1.58 ( setukpairinjR11
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx = Xy )
% 2.59/1.58 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.59/1.58 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR12_type,type,
% 2.59/1.58 setukpairinjR12: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR12,definition,
% 2.59/1.58 ( setukpairinjR12
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( Xx = Xy )
% 2.59/1.58 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.59/1.58 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR1_type,type,
% 2.59/1.58 setukpairinjR1: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR1,definition,
% 2.59/1.58 ( setukpairinjR1
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.59/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.59/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.59/1.58 => ( ( Xz = Xu )
% 2.59/1.58 => ( Xy = Xu ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(upairequniteq_type,type,
% 2.59/1.58 upairequniteq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(upairequniteq,definition,
% 2.59/1.58 ( upairequniteq
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.59/1.58 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.59/1.58 = ( setadjoin @ Xz @ emptyset ) )
% 2.59/1.58 => ( Xx = Xy ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR2_type,type,
% 2.59/1.58 setukpairinjR2: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR2,definition,
% 2.59/1.58 ( setukpairinjR2
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.59/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.59/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.59/1.58 => ( Xy = Xu ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR_type,type,
% 2.59/1.58 setukpairinjR: $o ).
% 2.59/1.58
% 2.59/1.58 thf(setukpairinjR,definition,
% 2.59/1.58 ( setukpairinjR
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.59/1.58 ( ( ( kpair @ Xx @ Xy )
% 2.59/1.58 = ( kpair @ Xz @ Xu ) )
% 2.59/1.58 => ( Xy = Xu ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ksndsingleton_type,type,
% 2.59/1.58 ksndsingleton: $o ).
% 2.59/1.58
% 2.59/1.58 thf(ksndsingleton,definition,
% 2.59/1.58 ( ksndsingleton
% 2.59/1.58 = ( ! [Xu: $i] :
% 2.59/1.58 ( ( iskpair @ Xu )
% 2.59/1.58 => ( singleton
% 2.59/1.58 @ ( dsetconstr @ ( setunion @ Xu )
% 2.59/1.58 @ ^ [Xx: $i] :
% 2.59/1.58 ( Xu
% 2.59/1.58 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(ksnd_type,type,
% 2.59/1.58 ksnd: $i > $i ).
% 2.59/1.58
% 2.59/1.58 thf(ksndpairEq_type,type,
% 2.59/1.58 ksndpairEq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(ksndpairEq,definition,
% 2.59/1.58 ( ksndpairEq
% 2.59/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.59/1.58 = Xy ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(kpairsurjEq_type,type,
% 2.59/1.58 kpairsurjEq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(kpairsurjEq,definition,
% 2.59/1.58 ( kpairsurjEq
% 2.59/1.58 = ( ! [Xu: $i] :
% 2.59/1.58 ( ( iskpair @ Xu )
% 2.59/1.58 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.59/1.58 = Xu ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodsndin_type,type,
% 2.59/1.58 cartprodsndin: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodsndin,definition,
% 2.59/1.58 ( cartprodsndin
% 2.59/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.59/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.59/1.58 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodpairmemEL_type,type,
% 2.59/1.58 cartprodpairmemEL: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodpairmemEL,definition,
% 2.59/1.58 ( cartprodpairmemEL
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.59/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodpairmemER_type,type,
% 2.59/1.58 cartprodpairmemER: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodpairmemER,definition,
% 2.59/1.58 ( cartprodpairmemER
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.59/1.58 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.59/1.58 => ( in @ Xy @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodmempaircEq_type,type,
% 2.59/1.58 cartprodmempaircEq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodmempaircEq,definition,
% 2.59/1.58 ( cartprodmempaircEq
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( ( kpair @ Xx @ Xy )
% 2.59/1.58 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodfstpairEq_type,type,
% 2.59/1.58 cartprodfstpairEq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodfstpairEq,definition,
% 2.59/1.58 ( cartprodfstpairEq
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.59/1.58 = Xx ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodsndpairEq_type,type,
% 2.59/1.58 cartprodsndpairEq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodsndpairEq,definition,
% 2.59/1.58 ( cartprodsndpairEq
% 2.59/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 => ! [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.58 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.59/1.58 = Xy ) ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodpairsurjEq_type,type,
% 2.59/1.58 cartprodpairsurjEq: $o ).
% 2.59/1.58
% 2.59/1.58 thf(cartprodpairsurjEq,definition,
% 2.59/1.58 ( cartprodpairsurjEq
% 2.59/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.59/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.59/1.58 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.59/1.58 = Xu ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(breln_type,type,
% 2.59/1.58 breln: $i > $i > $i > $o ).
% 2.59/1.58
% 2.59/1.58 thf(breln,definition,
% 2.59/1.58 ( breln
% 2.59/1.58 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.59/1.58
% 2.59/1.58 thf(dpsetconstr_type,type,
% 2.59/1.58 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.59/1.58
% 2.59/1.58 thf(dpsetconstr,definition,
% 2.59/1.58 ( dpsetconstr
% 2.59/1.58 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.59/1.58 ( dsetconstr @ ( cartprod @ A @ B )
% 2.59/1.58 @ ^ [Xu: $i] :
% 2.59/1.58 ? [Xx: $i] :
% 2.59/1.58 ( ( in @ Xx @ A )
% 2.59/1.58 & ? [Xy: $i] :
% 2.59/1.58 ( ( in @ Xy @ B )
% 2.59/1.59 & ( Xphi @ Xx @ Xy )
% 2.59/1.59 & ( Xu
% 2.59/1.59 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrI_type,type,
% 2.59/1.59 dpsetconstrI: $o ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrI,definition,
% 2.59/1.59 ( dpsetconstrI
% 2.59/1.59 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.59/1.59 ( ( in @ Xx @ A )
% 2.59/1.59 => ! [Xy: $i] :
% 2.59/1.59 ( ( in @ Xy @ B )
% 2.59/1.59 => ( ( Xphi @ Xx @ Xy )
% 2.59/1.59 => ( in @ ( kpair @ Xx @ Xy )
% 2.59/1.59 @ ( dpsetconstr @ A @ B
% 2.59/1.59 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrSub_type,type,
% 2.59/1.59 dpsetconstrSub: $o ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrSub,definition,
% 2.59/1.59 ( dpsetconstrSub
% 2.59/1.59 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.59/1.59 ( subset
% 2.59/1.59 @ ( dpsetconstr @ A @ B
% 2.59/1.59 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.59/1.59 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.59/1.59
% 2.59/1.59 thf(setOfPairsIsBReln_type,type,
% 2.59/1.59 setOfPairsIsBReln: $o ).
% 2.59/1.59
% 2.59/1.59 thf(setOfPairsIsBReln,definition,
% 2.59/1.59 ( setOfPairsIsBReln
% 2.59/1.59 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.59/1.59 ( breln @ A @ B
% 2.59/1.59 @ ( dpsetconstr @ A @ B
% 2.59/1.59 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrERa_type,type,
% 2.59/1.59 dpsetconstrERa: $o ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrERa,definition,
% 2.59/1.59 ( dpsetconstrERa
% 2.59/1.59 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.59/1.59 ( ( in @ Xx @ A )
% 2.59/1.59 => ! [Xy: $i] :
% 2.59/1.59 ( ( in @ Xy @ B )
% 2.59/1.59 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.59/1.59 @ ( dpsetconstr @ A @ B
% 2.59/1.59 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.59/1.59 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrEL1_type,type,
% 2.59/1.59 dpsetconstrEL1: $o ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrEL1,definition,
% 2.59/1.59 ( dpsetconstrEL1
% 2.59/1.59 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.59/1.59 ( ( in @ ( kpair @ Xx @ Xy )
% 2.59/1.59 @ ( dpsetconstr @ A @ B
% 2.59/1.59 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.59/1.59 => ( in @ Xx @ A ) ) ) ) ).
% 2.59/1.59
% 2.59/1.59 thf(dpsetconstrEL2,conjecture,
% 2.59/1.59 ( setextAx
% 2.59/1.59 => ( emptysetAx
% 2.59/1.59 => ( setadjoinAx
% 2.59/1.59 => ( powersetAx
% 2.59/1.59 => ( setunionAx
% 2.59/1.59 => ( omega0Ax
% 2.59/1.59 => ( omegaSAx
% 2.59/1.59 => ( omegaIndAx
% 2.59/1.59 => ( replAx
% 2.59/1.59 => ( foundationAx
% 2.59/1.59 => ( wellorderingAx
% 2.59/1.59 => ( descrp
% 2.59/1.59 => ( dsetconstrI
% 2.59/1.59 => ( dsetconstrEL
% 2.59/1.59 => ( dsetconstrER
% 2.59/1.59 => ( exuE1
% 2.59/1.59 => ( prop2setE
% 2.59/1.59 => ( emptysetE
% 2.59/1.59 => ( emptysetimpfalse
% 2.59/1.59 => ( notinemptyset
% 2.59/1.59 => ( exuE3e
% 2.59/1.59 => ( setext
% 2.59/1.59 => ( emptyI
% 2.59/1.59 => ( noeltsimpempty
% 2.59/1.59 => ( setbeta
% 2.59/1.59 => ( nonemptyE1
% 2.59/1.59 => ( nonemptyI
% 2.59/1.59 => ( nonemptyI1
% 2.59/1.59 => ( setadjoinIL
% 2.59/1.59 => ( emptyinunitempty
% 2.59/1.59 => ( setadjoinIR
% 2.59/1.59 => ( setadjoinE
% 2.59/1.59 => ( setadjoinOr
% 2.59/1.59 => ( setoftrueEq
% 2.59/1.59 => ( powersetI
% 2.59/1.59 => ( emptyinPowerset
% 2.59/1.59 => ( emptyInPowerset
% 2.59/1.59 => ( powersetE
% 2.59/1.59 => ( setunionI
% 2.59/1.59 => ( setunionE
% 2.59/1.59 => ( subPowSU
% 2.59/1.59 => ( exuE2
% 2.59/1.59 => ( nonemptyImpWitness
% 2.59/1.59 => ( uniqinunit
% 2.59/1.59 => ( notinsingleton
% 2.59/1.59 => ( eqinunit
% 2.59/1.59 => ( singletonsswitch
% 2.59/1.59 => ( upairsetE
% 2.59/1.59 => ( upairsetIL
% 2.59/1.59 => ( upairsetIR
% 2.59/1.59 => ( emptyE1
% 2.59/1.59 => ( vacuousDall
% 2.59/1.59 => ( quantDeMorgan1
% 2.59/1.59 => ( quantDeMorgan2
% 2.59/1.59 => ( quantDeMorgan3
% 2.59/1.59 => ( quantDeMorgan4
% 2.59/1.59 => ( prop2setI
% 2.59/1.59 => ( prop2set2propI
% 2.59/1.59 => ( notdexE
% 2.59/1.59 => ( notdallE
% 2.59/1.59 => ( exuI1
% 2.59/1.59 => ( exuI3
% 2.59/1.59 => ( exuI2
% 2.59/1.59 => ( inCongP
% 2.59/1.59 => ( in__Cong
% 2.59/1.59 => ( exuE3u
% 2.59/1.59 => ( exu__Cong
% 2.59/1.59 => ( emptyset__Cong
% 2.59/1.59 => ( setadjoin__Cong
% 2.59/1.59 => ( powerset__Cong
% 2.59/1.59 => ( setunion__Cong
% 2.59/1.59 => ( omega__Cong
% 2.59/1.59 => ( exuEu
% 2.59/1.59 => ( descr__Cong
% 2.59/1.59 => ( dsetconstr__Cong
% 2.59/1.59 => ( subsetI1
% 2.59/1.59 => ( eqimpsubset2
% 2.59/1.59 => ( eqimpsubset1
% 2.59/1.59 => ( subsetI2
% 2.59/1.59 => ( emptysetsubset
% 2.59/1.59 => ( subsetE
% 2.59/1.59 => ( subsetE2
% 2.59/1.59 => ( notsubsetI
% 2.59/1.59 => ( notequalI1
% 2.59/1.59 => ( notequalI2
% 2.59/1.59 => ( subsetRefl
% 2.59/1.59 => ( subsetTrans
% 2.59/1.59 => ( setadjoinSub
% 2.59/1.59 => ( setadjoinSub2
% 2.59/1.59 => ( subset2powerset
% 2.59/1.59 => ( setextsub
% 2.59/1.59 => ( subsetemptysetimpeq
% 2.59/1.59 => ( powersetI1
% 2.59/1.59 => ( powersetE1
% 2.59/1.59 => ( inPowerset
% 2.59/1.59 => ( powersetsubset
% 2.59/1.59 => ( sepInPowerset
% 2.59/1.59 => ( sepSubset
% 2.59/1.59 => ( binunionIL
% 2.59/1.59 => ( upairset2IR
% 2.59/1.59 => ( binunionIR
% 2.59/1.59 => ( binunionEcases
% 2.59/1.59 => ( binunionE
% 2.59/1.59 => ( binunionLsub
% 2.59/1.59 => ( binunionRsub
% 2.59/1.59 => ( binintersectI
% 2.59/1.59 => ( binintersectSubset5
% 2.59/1.59 => ( binintersectEL
% 2.59/1.59 => ( binintersectLsub
% 2.59/1.59 => ( binintersectSubset2
% 2.59/1.59 => ( binintersectSubset3
% 2.59/1.59 => ( binintersectER
% 2.59/1.59 => ( disjointsetsI1
% 2.59/1.59 => ( binintersectRsub
% 2.59/1.59 => ( binintersectSubset4
% 2.59/1.59 => ( binintersectSubset1
% 2.59/1.59 => ( bs114d
% 2.59/1.59 => ( setminusI
% 2.59/1.59 => ( setminusEL
% 2.59/1.59 => ( setminusER
% 2.59/1.59 => ( setminusSubset2
% 2.59/1.59 => ( setminusERneg
% 2.59/1.59 => ( setminusELneg
% 2.59/1.59 => ( setminusILneg
% 2.59/1.59 => ( setminusIRneg
% 2.59/1.59 => ( setminusLsub
% 2.59/1.59 => ( setminusSubset1
% 2.59/1.59 => ( symdiffE
% 2.59/1.59 => ( symdiffI1
% 2.59/1.59 => ( symdiffI2
% 2.59/1.59 => ( symdiffIneg1
% 2.59/1.59 => ( symdiffIneg2
% 2.59/1.59 => ( secondinupair
% 2.59/1.59 => ( setukpairIL
% 2.59/1.59 => ( setukpairIR
% 2.59/1.59 => ( kpairiskpair
% 2.59/1.59 => ( kpairp
% 2.59/1.59 => ( singletonsubset
% 2.59/1.59 => ( singletoninpowerset
% 2.59/1.59 => ( singletoninpowunion
% 2.59/1.59 => ( upairset2E
% 2.59/1.59 => ( upairsubunion
% 2.59/1.59 => ( upairinpowunion
% 2.59/1.59 => ( ubforcartprodlem1
% 2.59/1.59 => ( ubforcartprodlem2
% 2.59/1.59 => ( ubforcartprodlem3
% 2.59/1.59 => ( cartprodpairin
% 2.59/1.59 => ( cartprodmempair1
% 2.59/1.59 => ( cartprodmempair
% 2.59/1.59 => ( setunionE2
% 2.59/1.59 => ( setunionsingleton1
% 2.59/1.59 => ( setunionsingleton2
% 2.59/1.59 => ( setunionsingleton
% 2.59/1.59 => ( singletonprop
% 2.59/1.59 => ( ex1E1
% 2.59/1.59 => ( ex1I
% 2.59/1.59 => ( ex1I2
% 2.59/1.59 => ( singletonsuniq
% 2.59/1.59 => ( setukpairinjL1
% 2.59/1.59 => ( kfstsingleton
% 2.59/1.59 => ( theprop
% 2.59/1.59 => ( kfstpairEq
% 2.59/1.59 => ( cartprodfstin
% 2.59/1.59 => ( setukpairinjL2
% 2.59/1.59 => ( setukpairinjL
% 2.59/1.59 => ( setukpairinjR11
% 2.59/1.59 => ( setukpairinjR12
% 2.59/1.59 => ( setukpairinjR1
% 2.59/1.59 => ( upairequniteq
% 2.59/1.59 => ( setukpairinjR2
% 2.59/1.59 => ( setukpairinjR
% 2.59/1.59 => ( ksndsingleton
% 2.59/1.59 => ( ksndpairEq
% 2.59/1.59 => ( kpairsurjEq
% 2.59/1.59 => ( cartprodsndin
% 2.59/1.59 => ( cartprodpairmemEL
% 2.59/1.59 => ( cartprodpairmemER
% 2.59/1.59 => ( cartprodmempaircEq
% 2.59/1.59 => ( cartprodfstpairEq
% 2.59/1.59 => ( cartprodsndpairEq
% 2.59/1.59 => ( cartprodpairsurjEq
% 2.59/1.59 => ( dpsetconstrI
% 2.59/1.59 => ( dpsetconstrSub
% 2.59/1.59 => ( setOfPairsIsBReln
% 2.59/1.59 => ( dpsetconstrERa
% 2.59/1.59 => ( dpsetconstrEL1
% 2.59/1.59 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.59/1.59 ( ( in @ ( kpair @ Xx @ Xy )
% 2.59/1.59 @ ( dpsetconstr @ A @ B
% 2.59/1.59 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.59/1.59 => ( in @ Xy @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.59/1.59 ------------------------
% 2.72/1.62 % (839)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/18Mi)
% 2.72/1.62 % (835)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_724 for (2999ds/27Mi)
% 2.72/1.62 % (837)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_724 for (2999ds/2Mi)
% 2.72/1.62 % (838)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_724 for (2999ds/275Mi)
% 2.72/1.62 % (836)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/2Mi)
% 2.72/1.62 % (833)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/183Mi)
% 2.72/1.62 % (834)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_724 for (2999ds/4Mi)
% 2.72/1.62 % (836)Instruction limit reached!
% 2.72/1.62 % (836)------------------------------
% 2.72/1.62 % (836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.62 % (836)Termination reason: Unknown
% 2.72/1.62 % (836)Termination phase: shuffling
% 2.72/1.62
% 2.72/1.62 % (837)Instruction limit reached!
% 2.72/1.62 % (837)------------------------------
% 2.72/1.62 % (837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.62 % (836)Memory used [KB]: 1279
% 2.72/1.62 % (836)Time elapsed: 0.003 s
% 2.72/1.62 % (836)Instructions burned: 2 (million)
% 2.72/1.62 % (836)------------------------------
% 2.72/1.62 % (836)------------------------------
% 2.72/1.62 % (837)Termination reason: Unknown
% 2.72/1.62 % (837)Termination phase: shuffling
% 2.72/1.62
% 2.72/1.62 % (837)Memory used [KB]: 1279
% 2.72/1.62 % (837)Time elapsed: 0.003 s
% 2.72/1.62 % (837)Instructions burned: 2 (million)
% 2.72/1.62 % (837)------------------------------
% 2.72/1.62 % (837)------------------------------
% 2.72/1.62 % (834)Instruction limit reached!
% 2.72/1.62 % (834)------------------------------
% 2.72/1.62 % (834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.62 % (834)Termination reason: Unknown
% 2.72/1.62 % (834)Termination phase: shuffling
% 2.72/1.62
% 2.72/1.62 % (834)Memory used [KB]: 1407
% 2.72/1.62 % (834)Time elapsed: 0.003 s
% 2.72/1.62 % (834)Instructions burned: 4 (million)
% 2.72/1.62 % (834)------------------------------
% 2.72/1.62 % (834)------------------------------
% 2.72/1.63 % (839)Instruction limit reached!
% 2.72/1.63 % (839)------------------------------
% 2.72/1.63 % (839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.63 % (839)Termination reason: Unknown
% 2.72/1.63 % (839)Termination phase: Property scanning
% 2.72/1.63
% 2.72/1.63 % (839)Memory used [KB]: 1663
% 2.72/1.63 % (839)Time elapsed: 0.011 s
% 2.72/1.63 % (839)Instructions burned: 18 (million)
% 2.72/1.63 % (839)------------------------------
% 2.72/1.63 % (839)------------------------------
% 2.72/1.63 % (835)Instruction limit reached!
% 2.72/1.63 % (835)------------------------------
% 2.72/1.63 % (835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.63 % (835)Termination reason: Unknown
% 2.72/1.63 % (835)Termination phase: shuffling
% 2.72/1.63
% 2.72/1.63 % (835)Memory used [KB]: 1918
% 2.72/1.63 % (835)Time elapsed: 0.014 s
% 2.72/1.63 % (835)Instructions burned: 28 (million)
% 2.72/1.63 % (835)------------------------------
% 2.72/1.63 % (835)------------------------------
% 2.72/1.63 % (840)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/3Mi)
% 2.72/1.63 % (841)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_724 for (2999ds/37Mi)
% 2.72/1.63 % (842)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_724 for (2999ds/15Mi)
% 2.72/1.63 % (840)Instruction limit reached!
% 2.72/1.63 % (840)------------------------------
% 2.72/1.63 % (840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.63 % (840)Termination reason: Unknown
% 2.72/1.63 % (840)Termination phase: shuffling
% 2.72/1.63
% 2.72/1.63 % (840)Memory used [KB]: 1279
% 2.72/1.63 % (840)Time elapsed: 0.003 s
% 2.72/1.63 % (840)Instructions burned: 3 (million)
% 2.72/1.63 % (840)------------------------------
% 2.72/1.63 % (840)------------------------------
% 2.72/1.64 % (843)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_724 for (2999ds/3Mi)
% 2.72/1.64 % (842)Instruction limit reached!
% 2.72/1.64 % (842)------------------------------
% 2.72/1.64 % (842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.64 % (842)Termination reason: Unknown
% 2.72/1.64 % (842)Termination phase: shuffling
% 2.72/1.64
% 2.72/1.64 % (842)Memory used [KB]: 1663
% 2.72/1.64 % (842)Time elapsed: 0.009 s
% 2.72/1.64 % (842)Instructions burned: 15 (million)
% 2.72/1.64 % (842)------------------------------
% 2.72/1.64 % (842)------------------------------
% 2.72/1.64 % (843)Instruction limit reached!
% 2.72/1.64 % (843)------------------------------
% 2.72/1.64 % (843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.64 % (843)Termination reason: Unknown
% 2.72/1.64 % (843)Termination phase: shuffling
% 2.72/1.64
% 2.72/1.64 % (843)Memory used [KB]: 1279
% 2.72/1.64 % (843)Time elapsed: 0.003 s
% 2.72/1.64 % (843)Instructions burned: 4 (million)
% 2.72/1.64 % (843)------------------------------
% 2.72/1.64 % (843)------------------------------
% 2.72/1.65 % (844)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_724 for (2999ds/1041Mi)
% 2.72/1.65 % (841)Instruction limit reached!
% 2.72/1.65 % (841)------------------------------
% 2.72/1.65 % (841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.65 % (841)Termination reason: Unknown
% 2.72/1.65 % (841)Termination phase: Property scanning
% 2.72/1.65
% 2.72/1.65 % (841)Memory used [KB]: 1918
% 2.72/1.65 % (841)Time elapsed: 0.018 s
% 2.72/1.65 % (841)Instructions burned: 37 (million)
% 2.72/1.65 % (841)------------------------------
% 2.72/1.65 % (841)------------------------------
% 2.72/1.65 % (845)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/7Mi)
% 2.72/1.65 % (845)Instruction limit reached!
% 2.72/1.65 % (845)------------------------------
% 2.72/1.65 % (845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.65 % (845)Termination reason: Unknown
% 2.72/1.65 % (845)Termination phase: shuffling
% 2.72/1.65
% 2.72/1.65 % (845)Memory used [KB]: 1407
% 2.72/1.65 % (845)Time elapsed: 0.005 s
% 2.72/1.65 % (845)Instructions burned: 8 (million)
% 2.72/1.65 % (845)------------------------------
% 2.72/1.65 % (845)------------------------------
% 2.72/1.66 % (846)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/16Mi)
% 2.72/1.66 % (847)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_724 for (2999ds/3Mi)
% 2.72/1.66 % (847)Instruction limit reached!
% 2.72/1.66 % (847)------------------------------
% 2.72/1.66 % (847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.66 % (847)Termination reason: Unknown
% 2.72/1.66 % (847)Termination phase: shuffling
% 2.72/1.66
% 2.72/1.66 % (847)Memory used [KB]: 1279
% 2.72/1.66 % (847)Time elapsed: 0.003 s
% 2.72/1.66 % (847)Instructions burned: 3 (million)
% 2.72/1.66 % (847)------------------------------
% 2.72/1.66 % (847)------------------------------
% 2.72/1.66 % (846)Instruction limit reached!
% 2.72/1.66 % (846)------------------------------
% 2.72/1.66 % (846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.67 % (846)Termination reason: Unknown
% 2.72/1.67 % (846)Termination phase: shuffling
% 2.72/1.67
% 2.72/1.67 % (846)Memory used [KB]: 1663
% 2.72/1.67 % (846)Time elapsed: 0.009 s
% 2.72/1.67 % (846)Instructions burned: 16 (million)
% 2.72/1.67 % (846)------------------------------
% 2.72/1.67 % (846)------------------------------
% 2.72/1.67 % (848)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_724 for (2999ds/3Mi)
% 2.72/1.67 % (848)Instruction limit reached!
% 2.72/1.67 % (848)------------------------------
% 2.72/1.67 % (848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.67 % (848)Termination reason: Unknown
% 2.72/1.67 % (848)Termination phase: shuffling
% 2.72/1.67
% 2.72/1.67 % (848)Memory used [KB]: 1279
% 2.72/1.67 % (848)Time elapsed: 0.003 s
% 2.72/1.67 % (848)Instructions burned: 3 (million)
% 2.72/1.67 % (848)------------------------------
% 2.72/1.67 % (848)------------------------------
% 2.72/1.67 % (849)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/7Mi)
% 2.72/1.67 % (849)Instruction limit reached!
% 2.72/1.67 % (849)------------------------------
% 2.72/1.67 % (849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.67 % (849)Termination reason: Unknown
% 2.72/1.67 % (849)Termination phase: shuffling
% 2.72/1.67
% 2.72/1.67 % (849)Memory used [KB]: 1407
% 2.72/1.67 % (849)Time elapsed: 0.005 s
% 2.72/1.67 % (849)Instructions burned: 8 (million)
% 2.72/1.67 % (849)------------------------------
% 2.72/1.67 % (849)------------------------------
% 2.72/1.68 % (850)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/3Mi)
% 2.72/1.68 % (850)Instruction limit reached!
% 2.72/1.68 % (850)------------------------------
% 2.72/1.68 % (850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.68 % (850)Termination reason: Unknown
% 2.72/1.68 % (850)Termination phase: shuffling
% 2.72/1.68
% 2.72/1.68 % (850)Memory used [KB]: 1407
% 2.72/1.68 % (850)Time elapsed: 0.003 s
% 2.72/1.68 % (850)Instructions burned: 4 (million)
% 2.72/1.68 % (850)------------------------------
% 2.72/1.68 % (850)------------------------------
% 2.72/1.68 % (851)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/4Mi)
% 2.72/1.68 % (852)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/18Mi)
% 2.72/1.68 % (851)Instruction limit reached!
% 2.72/1.68 % (851)------------------------------
% 2.72/1.68 % (851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.68 % (851)Termination reason: Unknown
% 2.72/1.68 % (851)Termination phase: shuffling
% 2.72/1.68
% 2.72/1.68 % (851)Memory used [KB]: 1407
% 2.72/1.68 % (851)Time elapsed: 0.004 s
% 2.72/1.68 % (851)Instructions burned: 6 (million)
% 2.72/1.68 % (851)------------------------------
% 2.72/1.68 % (851)------------------------------
% 2.72/1.69 % (853)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/710Mi)
% 2.72/1.69 % (852)Instruction limit reached!
% 2.72/1.69 % (852)------------------------------
% 2.72/1.69 % (852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.69 % (852)Termination reason: Unknown
% 2.72/1.69 % (852)Termination phase: shuffling
% 2.72/1.69
% 2.72/1.69 % (852)Memory used [KB]: 1663
% 2.72/1.69 % (852)Time elapsed: 0.010 s
% 2.72/1.69 % (852)Instructions burned: 18 (million)
% 2.72/1.69 % (852)------------------------------
% 2.72/1.69 % (852)------------------------------
% 2.72/1.69 % (854)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/6Mi)
% 2.72/1.70 % (854)Instruction limit reached!
% 2.72/1.70 % (854)------------------------------
% 2.72/1.70 % (854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.70 % (854)Termination reason: Unknown
% 2.72/1.70 % (854)Termination phase: shuffling
% 2.72/1.70
% 2.72/1.70 % (854)Memory used [KB]: 1407
% 2.72/1.70 % (854)Time elapsed: 0.004 s
% 2.72/1.70 % (854)Instructions burned: 6 (million)
% 2.72/1.70 % (854)------------------------------
% 2.72/1.70 % (854)------------------------------
% 2.72/1.70 % (833)Instruction limit reached!
% 2.72/1.70 % (833)------------------------------
% 2.72/1.70 % (833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.70 % (833)Termination reason: Unknown
% 2.72/1.70 % (833)Termination phase: Saturation
% 2.72/1.70
% 2.72/1.70 % (833)Memory used [KB]: 7419
% 2.72/1.70 % (833)Time elapsed: 0.083 s
% 2.72/1.70 % (833)Instructions burned: 183 (million)
% 2.72/1.70 % (833)------------------------------
% 2.72/1.70 % (833)------------------------------
% 2.72/1.70 % (855)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_724 for (2999ds/902Mi)
% 2.72/1.71 % (856)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_724 for (2999ds/21Mi)
% 2.72/1.71 % (857)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_724 for (2999ds/5Mi)
% 2.72/1.71 % (858)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_724 for (2998ds/6Mi)
% 2.72/1.71 % (857)Instruction limit reached!
% 2.72/1.71 % (857)------------------------------
% 2.72/1.71 % (857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.71 % (857)Termination reason: Unknown
% 2.72/1.71 % (857)Termination phase: shuffling
% 2.72/1.71
% 2.72/1.71 % (857)Memory used [KB]: 1407
% 2.72/1.71 % (857)Time elapsed: 0.004 s
% 2.72/1.71 % (857)Instructions burned: 6 (million)
% 2.72/1.71 % (857)------------------------------
% 2.72/1.71 % (857)------------------------------
% 2.72/1.72 % (856)Instruction limit reached!
% 2.72/1.72 % (856)------------------------------
% 2.72/1.72 % (856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.72 % (856)Termination reason: Unknown
% 2.72/1.72 % (856)Termination phase: shuffling
% 2.72/1.72
% 2.72/1.72 % (856)Memory used [KB]: 1791
% 2.72/1.72 % (856)Time elapsed: 0.011 s
% 2.72/1.72 % (856)Instructions burned: 21 (million)
% 2.72/1.72 % (856)------------------------------
% 2.72/1.72 % (856)------------------------------
% 2.72/1.72 % (858)Instruction limit reached!
% 2.72/1.72 % (858)------------------------------
% 2.72/1.72 % (858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.72 % (858)Termination reason: Unknown
% 2.72/1.72 % (858)Termination phase: shuffling
% 2.72/1.72
% 2.72/1.72 % (858)Memory used [KB]: 1407
% 2.72/1.72 % (858)Time elapsed: 0.005 s
% 2.72/1.72 % (858)Instructions burned: 8 (million)
% 2.72/1.72 % (858)------------------------------
% 2.72/1.72 % (858)------------------------------
% 2.72/1.73 % (859)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_724 for (2998ds/377Mi)
% 2.72/1.73 % (860)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_724 for (2998ds/779Mi)
% 2.72/1.73 % (861)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_724 for (2998ds/19Mi)
% 2.72/1.74 % (861)Instruction limit reached!
% 2.72/1.74 % (861)------------------------------
% 2.72/1.74 % (861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.74 % (861)Termination reason: Unknown
% 2.72/1.74 % (861)Termination phase: shuffling
% 2.72/1.74
% 2.72/1.74 % (861)Memory used [KB]: 1791
% 2.72/1.74 % (861)Time elapsed: 0.010 s
% 2.72/1.74 % (861)Instructions burned: 19 (million)
% 2.72/1.74 % (861)------------------------------
% 2.72/1.74 % (861)------------------------------
% 2.72/1.75 % (838)Instruction limit reached!
% 2.72/1.75 % (838)------------------------------
% 2.72/1.75 % (838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.75 % (838)Termination reason: Unknown
% 2.72/1.75 % (838)Termination phase: Saturation
% 2.72/1.75
% 2.72/1.75 % (838)Memory used [KB]: 8443
% 2.72/1.75 % (838)Time elapsed: 0.137 s
% 2.72/1.75 % (838)Instructions burned: 276 (million)
% 2.72/1.75 % (838)------------------------------
% 2.72/1.75 % (838)------------------------------
% 2.72/1.76 % (862)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_724 for (2998ds/879Mi)
% 2.72/1.77 % (864)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_724 for (2998ds/17Mi)
% 2.72/1.78 % (864)Instruction limit reached!
% 2.72/1.78 % (864)------------------------------
% 2.72/1.78 % (864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.78 % (864)Termination reason: Unknown
% 2.72/1.78 % (864)Termination phase: shuffling
% 2.72/1.78
% 2.72/1.78 % (864)Memory used [KB]: 1663
% 2.72/1.78 % (864)Time elapsed: 0.010 s
% 2.72/1.78 % (864)Instructions burned: 18 (million)
% 2.72/1.78 % (864)------------------------------
% 2.72/1.78 % (864)------------------------------
% 2.72/1.79 % (865)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_724 for (2998ds/3Mi)
% 2.72/1.79 % (865)Instruction limit reached!
% 2.72/1.79 % (865)------------------------------
% 2.72/1.79 % (865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.79 % (865)Termination reason: Unknown
% 2.72/1.79 % (865)Termination phase: shuffling
% 2.72/1.79
% 2.72/1.79 % (865)Memory used [KB]: 1279
% 2.72/1.79 % (865)Time elapsed: 0.003 s
% 2.72/1.79 % (865)Instructions burned: 3 (million)
% 2.72/1.79 % (865)------------------------------
% 2.72/1.79 % (865)------------------------------
% 2.72/1.81 % (866)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_724 for (2998ds/30Mi)
% 2.72/1.82 % (866)Instruction limit reached!
% 2.72/1.82 % (866)------------------------------
% 2.72/1.82 % (866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.82 % (866)Termination reason: Unknown
% 2.72/1.82 % (866)Termination phase: Property scanning
% 2.72/1.82
% 2.72/1.82 % (866)Memory used [KB]: 1918
% 2.72/1.82 % (866)Time elapsed: 0.016 s
% 2.72/1.82 % (866)Instructions burned: 31 (million)
% 2.72/1.82 % (866)------------------------------
% 2.72/1.82 % (866)------------------------------
% 2.72/1.84 % (867)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_724 for (2997ds/127Mi)
% 2.72/1.90 % (867)Instruction limit reached!
% 2.72/1.90 % (867)------------------------------
% 2.72/1.90 % (867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.90 % (867)Termination reason: Unknown
% 2.72/1.90 % (867)Termination phase: Saturation
% 2.72/1.90
% 2.72/1.90 % (867)Memory used [KB]: 6908
% 2.72/1.90 % (867)Time elapsed: 0.058 s
% 2.72/1.90 % (867)Instructions burned: 128 (million)
% 2.72/1.90 % (867)------------------------------
% 2.72/1.90 % (867)------------------------------
% 2.72/1.91 % (859)Instruction limit reached!
% 2.72/1.91 % (859)------------------------------
% 2.72/1.91 % (859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.91 % (859)Termination reason: Unknown
% 2.72/1.91 % (859)Termination phase: Saturation
% 2.72/1.91
% 2.72/1.91 % (859)Memory used [KB]: 8187
% 2.72/1.91 % (859)Time elapsed: 0.179 s
% 2.72/1.91 % (859)Instructions burned: 377 (million)
% 2.72/1.91 % (859)------------------------------
% 2.72/1.91 % (859)------------------------------
% 2.72/1.91 % (868)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_724 for (2997ds/100Mi)
% 2.72/1.93 % (869)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_724 for (2996ds/3Mi)
% 2.72/1.93 % (869)Instruction limit reached!
% 2.72/1.93 % (869)------------------------------
% 2.72/1.93 % (869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.93 % (869)Termination reason: Unknown
% 2.72/1.93 % (869)Termination phase: shuffling
% 2.72/1.93
% 2.72/1.93 % (869)Memory used [KB]: 1279
% 2.72/1.93 % (869)Time elapsed: 0.003 s
% 2.72/1.93 % (869)Instructions burned: 3 (million)
% 2.72/1.93 % (869)------------------------------
% 2.72/1.93 % (869)------------------------------
% 2.72/1.94 % (870)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_724 for (2996ds/20Mi)
% 2.72/1.95 % (870)Instruction limit reached!
% 2.72/1.95 % (870)------------------------------
% 2.72/1.95 % (870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.95 % (870)Termination reason: Unknown
% 2.72/1.95 % (870)Termination phase: Property scanning
% 2.72/1.95
% 2.72/1.95 % (870)Memory used [KB]: 1663
% 2.72/1.95 % (870)Time elapsed: 0.012 s
% 2.72/1.95 % (870)Instructions burned: 22 (million)
% 2.72/1.95 % (870)------------------------------
% 2.72/1.95 % (870)------------------------------
% 2.72/1.96 % (868)Instruction limit reached!
% 2.72/1.96 % (868)------------------------------
% 2.72/1.96 % (868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.96 % (868)Termination reason: Unknown
% 2.72/1.96 % (868)Termination phase: Saturation
% 2.72/1.96
% 2.72/1.96 % (868)Memory used [KB]: 6780
% 2.72/1.96 % (868)Time elapsed: 0.046 s
% 2.72/1.96 % (868)Instructions burned: 101 (million)
% 2.72/1.96 % (868)------------------------------
% 2.72/1.96 % (868)------------------------------
% 2.72/1.97 % (871)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_724 for (2996ds/86Mi)
% 2.72/1.97 % (872)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_724 for (2996ds/107Mi)
% 2.72/2.01 % (871)Instruction limit reached!
% 2.72/2.01 % (871)------------------------------
% 2.72/2.01 % (871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/2.01 % (871)Termination reason: Unknown
% 2.72/2.01 % (871)Termination phase: Property scanning
% 2.72/2.01
% 2.72/2.01 % (871)Memory used [KB]: 2046
% 2.72/2.01 % (871)Time elapsed: 0.039 s
% 2.72/2.01 % (871)Instructions burned: 86 (million)
% 2.72/2.01 % (871)------------------------------
% 2.72/2.01 % (871)------------------------------
% 2.72/2.02 % (860)Instruction limit reached!
% 2.72/2.02 % (860)------------------------------
% 2.72/2.02 % (860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/2.02 % (860)Termination reason: Unknown
% 2.72/2.02 % (860)Termination phase: Saturation
% 2.72/2.02
% 2.72/2.02 % (860)Memory used [KB]: 7164
% 2.72/2.02 % (860)Time elapsed: 0.288 s
% 2.72/2.02 % (860)Instructions burned: 779 (million)
% 2.72/2.02 % (860)------------------------------
% 2.72/2.02 % (860)------------------------------
% 2.72/2.02 % (872)Instruction limit reached!
% 2.72/2.02 % (872)------------------------------
% 2.72/2.02 % (872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/2.02 % (872)Termination reason: Unknown
% 2.72/2.02 % (872)Termination phase: Saturation
% 2.72/2.02
% 2.72/2.02 % (872)Memory used [KB]: 6652
% 2.72/2.02 % (872)Time elapsed: 0.048 s
% 2.72/2.02 % (872)Instructions burned: 107 (million)
% 2.72/2.02 % (872)------------------------------
% 2.72/2.02 % (872)------------------------------
% 2.72/2.02 % (873)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_724 for (2995ds/39Mi)
% 5.55/2.04 % (874)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_724 for (2995ds/448Mi)
% 5.55/2.04 % (875)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_724 for (2995ds/46Mi)
% 5.55/2.04 % (844)Instruction limit reached!
% 5.55/2.04 % (844)------------------------------
% 5.55/2.04 % (844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.04 % (844)Termination reason: Unknown
% 5.55/2.04 % (844)Termination phase: Saturation
% 5.55/2.04
% 5.55/2.04 % (844)Memory used [KB]: 10746
% 5.55/2.04 % (844)Time elapsed: 0.395 s
% 5.55/2.04 % (844)Instructions burned: 1041 (million)
% 5.55/2.04 % (844)------------------------------
% 5.55/2.04 % (844)------------------------------
% 5.55/2.04 % (873)Instruction limit reached!
% 5.55/2.04 % (873)------------------------------
% 5.55/2.04 % (873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.04 % (873)Termination reason: Unknown
% 5.55/2.04 % (873)Termination phase: Property scanning
% 5.55/2.04
% 5.55/2.04 % (873)Memory used [KB]: 1918
% 5.55/2.04 % (873)Time elapsed: 0.020 s
% 5.55/2.04 % (873)Instructions burned: 40 (million)
% 5.55/2.04 % (873)------------------------------
% 5.55/2.04 % (873)------------------------------
% 5.55/2.05 % (853)Instruction limit reached!
% 5.55/2.05 % (853)------------------------------
% 5.55/2.05 % (853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.05 % (853)Termination reason: Unknown
% 5.55/2.05 % (853)Termination phase: Saturation
% 5.55/2.05
% 5.55/2.05 % (853)Memory used [KB]: 9466
% 5.55/2.05 % (853)Time elapsed: 0.359 s
% 5.55/2.05 % (853)Instructions burned: 710 (million)
% 5.55/2.05 % (853)------------------------------
% 5.55/2.05 % (853)------------------------------
% 5.55/2.06 % (876)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_724 for (2995ds/98Mi)
% 5.55/2.06 % (877)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_724 for (2995ds/507Mi)
% 5.55/2.06 % (875)Instruction limit reached!
% 5.55/2.06 % (875)------------------------------
% 5.55/2.06 % (875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.06 % (875)Termination reason: Unknown
% 5.55/2.06 % (875)Termination phase: SInE selection
% 5.55/2.06
% 5.55/2.06 % (875)Memory used [KB]: 1918
% 5.55/2.06 % (875)Time elapsed: 0.023 s
% 5.55/2.06 % (875)Instructions burned: 48 (million)
% 5.55/2.06 % (875)------------------------------
% 5.55/2.06 % (875)------------------------------
% 5.55/2.06 % (878)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_724 for (2995ds/149Mi)
% 5.55/2.07 % (879)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_724 for (2995ds/39Mi)
% 5.55/2.09 % (879)Instruction limit reached!
% 5.55/2.09 % (879)------------------------------
% 5.55/2.09 % (879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.09 % (879)Termination reason: Unknown
% 5.55/2.09 % (879)Termination phase: Property scanning
% 5.55/2.09
% 5.55/2.09 % (879)Memory used [KB]: 1918
% 5.55/2.09 % (879)Time elapsed: 0.019 s
% 5.55/2.09 % (879)Instructions burned: 39 (million)
% 5.55/2.09 % (879)------------------------------
% 5.55/2.09 % (879)------------------------------
% 5.55/2.10 % (876)Instruction limit reached!
% 5.55/2.10 % (876)------------------------------
% 5.55/2.10 % (876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.10 % (876)Termination reason: Unknown
% 5.55/2.10 % (876)Termination phase: Saturation
% 5.55/2.10
% 5.55/2.10 % (876)Memory used [KB]: 2174
% 5.55/2.10 % (876)Time elapsed: 0.044 s
% 5.55/2.10 % (876)Instructions burned: 98 (million)
% 5.55/2.10 % (876)------------------------------
% 5.55/2.10 % (876)------------------------------
% 5.55/2.11 % (880)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_724 for (2995ds/6Mi)
% 5.55/2.11 % (880)Instruction limit reached!
% 5.55/2.11 % (880)------------------------------
% 5.55/2.11 % (880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.55/2.11 % (880)Termination reason: Unknown
% 5.55/2.11 % (880)Termination phase: shuffling
% 5.55/2.11
% 5.55/2.11 % (880)Memory used [KB]: 1407
% 5.55/2.11 % (880)Time elapsed: 0.004 s
% 5.55/2.11 % (880)Instructions burned: 6 (million)
% 5.55/2.11 % (880)------------------------------
% 5.55/2.11 % (880)------------------------------
% 5.55/2.11 % (881)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_724 for (2995ds/1087Mi)
% 6.06/2.13 % (882)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_724 for (2994ds/47Mi)
% 6.06/2.13 % (878)Instruction limit reached!
% 6.06/2.13 % (878)------------------------------
% 6.06/2.13 % (878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.13 % (878)Termination reason: Unknown
% 6.06/2.13 % (878)Termination phase: Saturation
% 6.06/2.13
% 6.06/2.13 % (878)Memory used [KB]: 7291
% 6.06/2.13 % (878)Time elapsed: 0.069 s
% 6.06/2.13 % (878)Instructions burned: 149 (million)
% 6.06/2.13 % (878)------------------------------
% 6.06/2.13 % (878)------------------------------
% 6.06/2.14 % (855)Instruction limit reached!
% 6.06/2.14 % (855)------------------------------
% 6.06/2.14 % (855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.14 % (855)Termination reason: Unknown
% 6.06/2.14 % (855)Termination phase: Saturation
% 6.06/2.14
% 6.06/2.14 % (855)Memory used [KB]: 10618
% 6.06/2.14 % (855)Time elapsed: 0.440 s
% 6.06/2.14 % (855)Instructions burned: 903 (million)
% 6.06/2.14 % (855)------------------------------
% 6.06/2.14 % (855)------------------------------
% 6.06/2.15 % (882)Instruction limit reached!
% 6.06/2.15 % (882)------------------------------
% 6.06/2.15 % (882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.15 % (882)Termination reason: Unknown
% 6.06/2.15 % (882)Termination phase: Naming
% 6.06/2.15
% 6.06/2.15 % (882)Memory used [KB]: 2046
% 6.06/2.15 % (882)Time elapsed: 0.023 s
% 6.06/2.15 % (882)Instructions burned: 48 (million)
% 6.06/2.15 % (882)------------------------------
% 6.06/2.15 % (882)------------------------------
% 6.06/2.15 % (883)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_724 for (2994ds/44Mi)
% 6.06/2.15 % (884)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_724 for (2994ds/432Mi)
% 6.06/2.16 % (885)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_724 for (2994ds/62Mi)
% 6.06/2.17 % (883)Instruction limit reached!
% 6.06/2.17 % (883)------------------------------
% 6.06/2.17 % (883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.17 % (883)Termination reason: Unknown
% 6.06/2.17 % (883)Termination phase: Property scanning
% 6.06/2.17
% 6.06/2.17 % (883)Memory used [KB]: 1918
% 6.06/2.17 % (883)Time elapsed: 0.022 s
% 6.06/2.17 % (883)Instructions burned: 46 (million)
% 6.06/2.17 % (883)------------------------------
% 6.06/2.17 % (883)------------------------------
% 6.06/2.18 % (886)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_724 for (2994ds/31Mi)
% 6.06/2.19 % (885)Instruction limit reached!
% 6.06/2.19 % (885)------------------------------
% 6.06/2.19 % (885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.19 % (885)Termination reason: Unknown
% 6.06/2.19 % (885)Termination phase: Property scanning
% 6.06/2.19
% 6.06/2.19 % (885)Memory used [KB]: 1918
% 6.06/2.19 % (885)Time elapsed: 0.029 s
% 6.06/2.19 % (885)Instructions burned: 63 (million)
% 6.06/2.19 % (885)------------------------------
% 6.06/2.19 % (885)------------------------------
% 6.06/2.19 % (862)Instruction limit reached!
% 6.06/2.19 % (862)------------------------------
% 6.06/2.19 % (862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.19 % (862)Termination reason: Unknown
% 6.06/2.19 % (862)Termination phase: Saturation
% 6.06/2.19
% 6.06/2.19 % (862)Memory used [KB]: 8571
% 6.06/2.19 % (862)Time elapsed: 0.435 s
% 6.06/2.19 % (862)Instructions burned: 880 (million)
% 6.06/2.19 % (862)------------------------------
% 6.06/2.19 % (862)------------------------------
% 6.37/2.20 % (886)Instruction limit reached!
% 6.37/2.20 % (886)------------------------------
% 6.37/2.20 % (886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.20 % (886)Termination reason: Unknown
% 6.37/2.20 % (886)Termination phase: Property scanning
% 6.37/2.20
% 6.37/2.20 % (886)Memory used [KB]: 1918
% 6.37/2.20 % (886)Time elapsed: 0.017 s
% 6.37/2.20 % (886)Instructions burned: 33 (million)
% 6.37/2.20 % (886)------------------------------
% 6.37/2.20 % (886)------------------------------
% 6.37/2.21 % (874)Instruction limit reached!
% 6.37/2.21 % (874)------------------------------
% 6.37/2.21 % (874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.21 % (874)Termination reason: Unknown
% 6.37/2.21 % (874)Termination phase: Saturation
% 6.37/2.21
% 6.37/2.21 % (874)Memory used [KB]: 6908
% 6.37/2.21 % (874)Time elapsed: 0.172 s
% 6.37/2.21 % (874)Instructions burned: 449 (million)
% 6.37/2.21 % (874)------------------------------
% 6.37/2.21 % (874)------------------------------
% 6.37/2.21 % (887)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_724 for (2993ds/96Mi)
% 6.37/2.21 % (888)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_724 for (2993ds/453Mi)
% 6.37/2.22 % (889)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_724 for (2993ds/71Mi)
% 6.37/2.22 % (890)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_724 for (2993ds/83Mi)
% 6.37/2.25 % (889)Instruction limit reached!
% 6.37/2.25 % (889)------------------------------
% 6.37/2.25 % (889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.25 % (889)Termination reason: Unknown
% 6.37/2.25 % (889)Termination phase: Function definition elimination
% 6.37/2.25
% 6.37/2.25 % (889)Memory used [KB]: 2174
% 6.37/2.25 % (889)Time elapsed: 0.033 s
% 6.37/2.25 % (889)Instructions burned: 71 (million)
% 6.37/2.25 % (889)------------------------------
% 6.37/2.25 % (889)------------------------------
% 6.37/2.25 % (887)Instruction limit reached!
% 6.37/2.25 % (887)------------------------------
% 6.37/2.25 % (887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.25 % (887)Termination reason: Unknown
% 6.37/2.25 % (887)Termination phase: Saturation
% 6.37/2.25
% 6.37/2.25 % (887)Memory used [KB]: 6652
% 6.37/2.25 % (887)Time elapsed: 0.044 s
% 6.37/2.25 % (887)Instructions burned: 97 (million)
% 6.37/2.25 % (887)------------------------------
% 6.37/2.25 % (887)------------------------------
% 6.37/2.26 % (890)Instruction limit reached!
% 6.37/2.26 % (890)------------------------------
% 6.37/2.26 % (890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.26 % (890)Termination reason: Unknown
% 6.37/2.26 % (890)Termination phase: Property scanning
% 6.37/2.26
% 6.37/2.26 % (890)Memory used [KB]: 2046
% 6.37/2.26 % (890)Time elapsed: 0.038 s
% 6.37/2.26 % (890)Instructions burned: 83 (million)
% 6.37/2.26 % (890)------------------------------
% 6.37/2.26 % (890)------------------------------
% 6.37/2.26 % (891)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_724 for (2993ds/11Mi)
% 6.37/2.27 % (892)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_724 for (2993ds/41Mi)
% 6.37/2.27 % (891)Instruction limit reached!
% 6.37/2.27 % (891)------------------------------
% 6.37/2.27 % (891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.27 % (891)Termination reason: Unknown
% 6.37/2.27 % (891)Termination phase: shuffling
% 6.37/2.27
% 6.37/2.27 % (891)Memory used [KB]: 1535
% 6.37/2.27 % (891)Time elapsed: 0.007 s
% 6.37/2.27 % (891)Instructions burned: 12 (million)
% 6.37/2.27 % (891)------------------------------
% 6.37/2.27 % (891)------------------------------
% 6.37/2.28 % (893)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_724 for (2993ds/6Mi)
% 6.37/2.28 % (893)Instruction limit reached!
% 6.37/2.28 % (893)------------------------------
% 6.37/2.28 % (893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.28 % (893)Termination reason: Unknown
% 6.37/2.28 % (893)Termination phase: shuffling
% 6.37/2.28
% 6.37/2.28 % (893)Memory used [KB]: 1407
% 6.37/2.28 % (893)Time elapsed: 0.004 s
% 6.37/2.28 % (893)Instructions burned: 6 (million)
% 6.37/2.28 % (893)------------------------------
% 6.37/2.28 % (893)------------------------------
% 6.37/2.28 % (892)Instruction limit reached!
% 6.37/2.28 % (892)------------------------------
% 6.37/2.28 % (892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.28 % (892)Termination reason: Unknown
% 6.37/2.28 % (892)Termination phase: Property scanning
% 6.37/2.28
% 6.37/2.28 % (892)Memory used [KB]: 1918
% 6.37/2.28 % (892)Time elapsed: 0.020 s
% 6.37/2.28 % (892)Instructions burned: 42 (million)
% 6.37/2.28 % (892)------------------------------
% 6.37/2.28 % (892)------------------------------
% 6.37/2.28 % (894)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_724 for (2993ds/150Mi)
% 6.37/2.29 % (895)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_724 for (2993ds/343Mi)
% 6.82/2.30 % (877)Instruction limit reached!
% 6.82/2.30 % (877)------------------------------
% 6.82/2.30 % (877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.30 % (877)Termination reason: Unknown
% 6.82/2.30 % (877)Termination phase: Saturation
% 6.82/2.30
% 6.82/2.30 % (877)Memory used [KB]: 7547
% 6.82/2.30 % (877)Time elapsed: 0.242 s
% 6.82/2.30 % (877)Instructions burned: 507 (million)
% 6.82/2.30 % (877)------------------------------
% 6.82/2.30 % (877)------------------------------
% 6.82/2.30 % (896)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_724 for (2993ds/109Mi)
% 6.82/2.31 % (897)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_724 for (2992ds/253Mi)
% 6.82/2.33 % (884)Instruction limit reached!
% 6.82/2.33 % (884)------------------------------
% 6.82/2.33 % (884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.33 % (884)Termination reason: Unknown
% 6.82/2.33 % (884)Termination phase: Saturation
% 6.82/2.33
% 6.82/2.33 % (884)Memory used [KB]: 3454
% 6.82/2.33 % (884)Time elapsed: 0.173 s
% 6.82/2.33 % (884)Instructions burned: 433 (million)
% 6.82/2.33 % (884)------------------------------
% 6.82/2.33 % (884)------------------------------
% 6.82/2.34 % (898)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_724 for (2992ds/140Mi)
% 6.82/2.35 % (896)Instruction limit reached!
% 6.82/2.35 % (896)------------------------------
% 6.82/2.35 % (896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.35 % (896)Termination reason: Unknown
% 6.82/2.35 % (896)Termination phase: Saturation
% 6.82/2.35
% 6.82/2.35 % (896)Memory used [KB]: 6652
% 6.82/2.35 % (896)Time elapsed: 0.049 s
% 6.82/2.35 % (896)Instructions burned: 111 (million)
% 6.82/2.35 % (896)------------------------------
% 6.82/2.35 % (896)------------------------------
% 6.82/2.36 % (894)Instruction limit reached!
% 6.82/2.36 % (894)------------------------------
% 6.82/2.36 % (894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.36 % (894)Termination reason: Unknown
% 6.82/2.36 % (894)Termination phase: Saturation
% 6.82/2.36
% 6.82/2.36 % (894)Memory used [KB]: 8059
% 6.82/2.36 % (894)Time elapsed: 0.073 s
% 6.82/2.36 % (894)Instructions burned: 151 (million)
% 6.82/2.36 % (894)------------------------------
% 6.82/2.36 % (894)------------------------------
% 6.82/2.36 % (899)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_724 for (2992ds/614Mi)
% 6.82/2.37 % (900)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_724 for (2992ds/202Mi)
% 6.82/2.38 % (888)Instruction limit reached!
% 6.82/2.38 % (888)------------------------------
% 6.82/2.38 % (888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.38 % (888)Termination reason: Unknown
% 6.82/2.38 % (888)Termination phase: Saturation
% 6.82/2.38
% 6.82/2.38 % (888)Memory used [KB]: 6908
% 6.82/2.38 % (888)Time elapsed: 0.178 s
% 6.82/2.38 % (888)Instructions burned: 455 (million)
% 6.82/2.38 % (888)------------------------------
% 6.82/2.38 % (888)------------------------------
% 7.61/2.40 % (901)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_724 for (2992ds/339Mi)
% 7.61/2.40 % (898)Instruction limit reached!
% 7.61/2.40 % (898)------------------------------
% 7.61/2.40 % (898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.40 % (898)Termination reason: Unknown
% 7.61/2.40 % (898)Termination phase: Saturation
% 7.61/2.40
% 7.61/2.40 % (898)Memory used [KB]: 6908
% 7.61/2.40 % (898)Time elapsed: 0.063 s
% 7.61/2.40 % (898)Instructions burned: 140 (million)
% 7.61/2.40 % (898)------------------------------
% 7.61/2.40 % (898)------------------------------
% 7.61/2.42 % (902)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_724 for (2991ds/283Mi)
% 7.61/2.44 % (897)Instruction limit reached!
% 7.61/2.44 % (897)------------------------------
% 7.61/2.44 % (897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.44 % (897)Termination reason: Unknown
% 7.61/2.44 % (897)Termination phase: Saturation
% 7.61/2.44
% 7.61/2.44 % (897)Memory used [KB]: 8443
% 7.61/2.44 % (897)Time elapsed: 0.124 s
% 7.61/2.44 % (897)Instructions burned: 253 (million)
% 7.61/2.44 % (897)------------------------------
% 7.61/2.44 % (897)------------------------------
% 7.61/2.45 % (895)Instruction limit reached!
% 7.61/2.45 % (895)------------------------------
% 7.61/2.45 % (895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.45 % (895)Termination reason: Unknown
% 7.61/2.45 % (895)Termination phase: Saturation
% 7.61/2.45
% 7.61/2.45 % (895)Memory used [KB]: 8059
% 7.61/2.45 % (895)Time elapsed: 0.159 s
% 7.61/2.45 % (895)Instructions burned: 343 (million)
% 7.61/2.45 % (895)------------------------------
% 7.61/2.45 % (895)------------------------------
% 7.61/2.45 % (903)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_724 for (2991ds/134Mi)
% 7.61/2.47 % (904)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_724 for (2991ds/298Mi)
% 7.61/2.47 % (900)Instruction limit reached!
% 7.61/2.47 % (900)------------------------------
% 7.61/2.47 % (900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.47 % (900)Termination reason: Unknown
% 7.61/2.47 % (900)Termination phase: Saturation
% 7.61/2.47
% 7.61/2.47 % (900)Memory used [KB]: 8955
% 7.61/2.47 % (900)Time elapsed: 0.099 s
% 7.61/2.47 % (900)Instructions burned: 202 (million)
% 7.61/2.47 % (900)------------------------------
% 7.61/2.47 % (900)------------------------------
% 7.61/2.49 % (905)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_724 for (2991ds/192Mi)
% 8.11/2.51 % (903)Instruction limit reached!
% 8.11/2.51 % (903)------------------------------
% 8.11/2.51 % (903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.51 % (903)Termination reason: Unknown
% 8.11/2.51 % (903)Termination phase: Saturation
% 8.11/2.51
% 8.11/2.51 % (903)Memory used [KB]: 7036
% 8.11/2.51 % (903)Time elapsed: 0.062 s
% 8.11/2.51 % (903)Instructions burned: 134 (million)
% 8.11/2.51 % (903)------------------------------
% 8.11/2.51 % (903)------------------------------
% 8.11/2.53 % (908)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_724 for (2990ds/258Mi)
% 8.11/2.53 % (902)Instruction limit reached!
% 8.11/2.53 % (902)------------------------------
% 8.11/2.53 % (902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.53 % (902)Termination reason: Unknown
% 8.11/2.53 % (902)Termination phase: Saturation
% 8.11/2.53
% 8.11/2.53 % (902)Memory used [KB]: 6908
% 8.11/2.53 % (902)Time elapsed: 0.114 s
% 8.11/2.53 % (902)Instructions burned: 285 (million)
% 8.11/2.53 % (902)------------------------------
% 8.11/2.53 % (902)------------------------------
% 8.11/2.55 % (909)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_724 for (2990ds/90Mi)
% 8.11/2.56 % (901)Instruction limit reached!
% 8.11/2.56 % (901)------------------------------
% 8.11/2.56 % (901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.56 % (901)Termination reason: Unknown
% 8.11/2.56 % (901)Termination phase: Saturation
% 8.11/2.56
% 8.11/2.56 % (901)Memory used [KB]: 7803
% 8.11/2.56 % (901)Time elapsed: 0.160 s
% 8.11/2.56 % (901)Instructions burned: 340 (million)
% 8.11/2.56 % (901)------------------------------
% 8.11/2.56 % (901)------------------------------
% 8.11/2.57 % (905)Instruction limit reached!
% 8.11/2.57 % (905)------------------------------
% 8.11/2.57 % (905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.57 % (905)Termination reason: Unknown
% 8.11/2.57 % (905)Termination phase: Saturation
% 8.11/2.57
% 8.11/2.57 % (905)Memory used [KB]: 7419
% 8.11/2.57 % (905)Time elapsed: 0.088 s
% 8.11/2.57 % (905)Instructions burned: 194 (million)
% 8.11/2.57 % (905)------------------------------
% 8.11/2.57 % (905)------------------------------
% 8.11/2.58 % (910)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_724 for (2990ds/231Mi)
% 8.11/2.59 % (909)Instruction limit reached!
% 8.11/2.59 % (909)------------------------------
% 8.11/2.59 % (909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.59 % (909)Termination reason: Unknown
% 8.11/2.59 % (909)Termination phase: Twee Goal Transformation
% 8.11/2.59
% 8.11/2.59 % (909)Memory used [KB]: 2558
% 8.11/2.59 % (909)Time elapsed: 0.041 s
% 8.11/2.59 % (909)Instructions burned: 90 (million)
% 8.11/2.59 % (909)------------------------------
% 8.11/2.59 % (909)------------------------------
% 8.11/2.59 % (912)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_724 for (2990ds/458Mi)
% 8.11/2.59 % (904)Instruction limit reached!
% 8.11/2.59 % (904)------------------------------
% 8.11/2.59 % (904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.59 % (904)Termination reason: Unknown
% 8.11/2.59 % (904)Termination phase: Saturation
% 8.11/2.59
% 8.11/2.59 % (904)Memory used [KB]: 6780
% 8.11/2.59 % (904)Time elapsed: 0.125 s
% 8.11/2.59 % (904)Instructions burned: 299 (million)
% 8.11/2.59 % (904)------------------------------
% 8.11/2.59 % (904)------------------------------
% 8.79/2.60 % (913)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_724 for (2990ds/31Mi)
% 8.79/2.61 % (914)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_724 for (2990ds/297Mi)
% 8.79/2.62 % (913)Instruction limit reached!
% 8.79/2.62 % (913)------------------------------
% 8.79/2.62 % (913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.62 % (913)Termination reason: Unknown
% 8.79/2.62 % (913)Termination phase: Property scanning
% 8.79/2.62
% 8.79/2.62 % (913)Memory used [KB]: 1918
% 8.79/2.62 % (913)Time elapsed: 0.016 s
% 8.79/2.62 % (913)Instructions burned: 32 (million)
% 8.79/2.62 % (913)------------------------------
% 8.79/2.62 % (913)------------------------------
% 8.79/2.63 % (915)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_724 for (2989ds/987Mi)
% 8.79/2.65 % (908)Instruction limit reached!
% 8.79/2.65 % (908)------------------------------
% 8.79/2.65 % (908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.65 % (908)Termination reason: Unknown
% 8.79/2.65 % (908)Termination phase: Saturation
% 8.79/2.65
% 8.79/2.65 % (908)Memory used [KB]: 7675
% 8.79/2.65 % (908)Time elapsed: 0.119 s
% 8.79/2.65 % (908)Instructions burned: 258 (million)
% 8.79/2.65 % (908)------------------------------
% 8.79/2.65 % (908)------------------------------
% 8.79/2.66 % (881)Instruction limit reached!
% 8.79/2.66 % (881)------------------------------
% 8.79/2.66 % (881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.66 % (881)Termination reason: Unknown
% 8.79/2.66 % (881)Termination phase: Saturation
% 8.79/2.66
% 8.79/2.66 % (881)Memory used [KB]: 10618
% 8.79/2.66 % (881)Time elapsed: 0.567 s
% 8.79/2.66 % (881)Instructions burned: 1088 (million)
% 8.79/2.66 % (881)------------------------------
% 8.79/2.66 % (881)------------------------------
% 8.79/2.66 % (899)Instruction limit reached!
% 8.79/2.66 % (899)------------------------------
% 8.79/2.66 % (899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.66 % (899)Termination reason: Unknown
% 8.79/2.66 % (899)Termination phase: Saturation
% 8.79/2.66
% 8.79/2.66 % (899)Memory used [KB]: 8571
% 8.79/2.66 % (899)Time elapsed: 0.298 s
% 8.79/2.66 % (899)Instructions burned: 614 (million)
% 8.79/2.66 % (899)------------------------------
% 8.79/2.66 % (899)------------------------------
% 8.79/2.66 % (916)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_724 for (2989ds/182Mi)
% 8.79/2.68 % (917)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_724 for (2989ds/182Mi)
% 8.79/2.68 % (918)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_724 for (2989ds/154Mi)
% 8.79/2.68 % (910)Instruction limit reached!
% 8.79/2.68 % (910)------------------------------
% 8.79/2.68 % (910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.79/2.68 % (910)Termination reason: Unknown
% 8.79/2.68 % (910)Termination phase: Saturation
% 8.79/2.68
% 8.79/2.68 % (910)Memory used [KB]: 12153
% 8.79/2.68 % (910)Time elapsed: 0.109 s
% 8.79/2.68 % (910)Instructions burned: 232 (million)
% 8.79/2.68 % (910)------------------------------
% 8.79/2.68 % (910)------------------------------
% 9.96/2.70 % (919)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_724 for (2989ds/79Mi)
% 9.96/2.73 % (914)Instruction limit reached!
% 9.96/2.73 % (914)------------------------------
% 9.96/2.73 % (914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.73 % (914)Termination reason: Unknown
% 9.96/2.73 % (914)Termination phase: Saturation
% 9.96/2.73
% 9.96/2.73 % (914)Memory used [KB]: 8443
% 9.96/2.73 % (914)Time elapsed: 0.120 s
% 9.96/2.73 % (914)Instructions burned: 298 (million)
% 9.96/2.73 % (914)------------------------------
% 9.96/2.73 % (914)------------------------------
% 9.96/2.74 % (919)Instruction limit reached!
% 9.96/2.74 % (919)------------------------------
% 9.96/2.74 % (919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.74 % (919)Termination reason: Unknown
% 9.96/2.74 % (919)Termination phase: Property scanning
% 9.96/2.74
% 9.96/2.74 % (919)Memory used [KB]: 2174
% 9.96/2.74 % (919)Time elapsed: 0.037 s
% 9.96/2.74 % (919)Instructions burned: 80 (million)
% 9.96/2.74 % (919)------------------------------
% 9.96/2.74 % (919)------------------------------
% 9.96/2.74 % (918)Instruction limit reached!
% 9.96/2.74 % (918)------------------------------
% 9.96/2.74 % (918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.74 % (918)Termination reason: Unknown
% 9.96/2.74 % (918)Termination phase: Saturation
% 9.96/2.74
% 9.96/2.74 % (918)Memory used [KB]: 6780
% 9.96/2.74 % (918)Time elapsed: 0.066 s
% 9.96/2.74 % (918)Instructions burned: 154 (million)
% 9.96/2.74 % (918)------------------------------
% 9.96/2.74 % (918)------------------------------
% 9.96/2.74 % (920)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_724 for (2988ds/216Mi)
% 9.96/2.75 % (916)Instruction limit reached!
% 9.96/2.75 % (916)------------------------------
% 9.96/2.75 % (916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.75 % (916)Termination reason: Unknown
% 9.96/2.75 % (916)Termination phase: Saturation
% 9.96/2.75
% 9.96/2.75 % (916)Memory used [KB]: 7419
% 9.96/2.75 % (916)Time elapsed: 0.084 s
% 9.96/2.75 % (916)Instructions burned: 183 (million)
% 9.96/2.75 % (916)------------------------------
% 9.96/2.75 % (916)------------------------------
% 9.96/2.75 % (921)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_724 for (2988ds/114Mi)
% 9.96/2.76 % (922)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_724 for (2988ds/922Mi)
% 9.96/2.76 % (923)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_724 for (2988ds/182Mi)
% 9.96/2.76 % (917)Instruction limit reached!
% 9.96/2.76 % (917)------------------------------
% 9.96/2.76 % (917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.76 % (917)Termination reason: Unknown
% 9.96/2.76 % (917)Termination phase: Saturation
% 9.96/2.76
% 9.96/2.76 % (917)Memory used [KB]: 10106
% 9.96/2.76 % (917)Time elapsed: 0.089 s
% 9.96/2.76 % (917)Instructions burned: 182 (million)
% 9.96/2.76 % (917)------------------------------
% 9.96/2.76 % (917)------------------------------
% 9.96/2.78 % (924)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_724 for (2988ds/164Mi)
% 10.42/2.80 % (921)Instruction limit reached!
% 10.42/2.80 % (921)------------------------------
% 10.42/2.80 % (921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.42/2.80 % (921)Termination reason: Unknown
% 10.42/2.80 % (921)Termination phase: Saturation
% 10.42/2.80
% 10.42/2.80 % (921)Memory used [KB]: 6908
% 10.42/2.80 % (921)Time elapsed: 0.052 s
% 10.42/2.80 % (921)Instructions burned: 114 (million)
% 10.42/2.80 % (921)------------------------------
% 10.42/2.80 % (921)------------------------------
% 10.42/2.81 % (912)Instruction limit reached!
% 10.42/2.81 % (912)------------------------------
% 10.42/2.81 % (912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.42/2.81 % (912)Termination reason: Unknown
% 10.42/2.81 % (912)Termination phase: Saturation
% 10.42/2.81
% 10.42/2.81 % (912)Memory used [KB]: 8187
% 10.42/2.81 % (912)Time elapsed: 0.218 s
% 10.42/2.81 % (912)Instructions burned: 458 (million)
% 10.42/2.81 % (912)------------------------------
% 10.42/2.81 % (912)------------------------------
% 10.42/2.82 % (925)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_724 for (2987ds/50Mi)
% 10.42/2.82 % (926)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_724 for (2987ds/368Mi)
% 10.42/2.83 % (920)Instruction limit reached!
% 10.42/2.83 % (920)------------------------------
% 10.42/2.83 % (920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.42/2.83 % (920)Termination reason: Unknown
% 10.42/2.83 % (920)Termination phase: Saturation
% 10.42/2.83
% 10.42/2.83 % (920)Memory used [KB]: 6780
% 10.42/2.83 % (920)Time elapsed: 0.090 s
% 10.42/2.83 % (920)Instructions burned: 216 (million)
% 10.42/2.83 % (920)------------------------------
% 10.42/2.83 % (920)------------------------------
% 10.42/2.84 % (923)Instruction limit reached!
% 10.42/2.84 % (923)------------------------------
% 10.42/2.84 % (923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.42/2.84 % (923)Termination reason: Unknown
% 10.42/2.84 % (923)Termination phase: Saturation
% 10.42/2.84
% 10.42/2.84 % (923)Memory used [KB]: 6780
% 10.42/2.84 % (923)Time elapsed: 0.078 s
% 10.42/2.84 % (923)Instructions burned: 184 (million)
% 10.42/2.84 % (923)------------------------------
% 10.42/2.84 % (923)------------------------------
% 10.42/2.84 % (925)Instruction limit reached!
% 10.42/2.84 % (925)------------------------------
% 10.42/2.84 % (925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.42/2.84 % (925)Termination reason: Unknown
% 10.42/2.84 % (925)Termination phase: Property scanning
% 10.42/2.84
% 10.42/2.84 % (925)Memory used [KB]: 2046
% 10.42/2.84 % (925)Time elapsed: 0.024 s
% 10.42/2.84 % (925)Instructions burned: 50 (million)
% 10.42/2.84 % (925)------------------------------
% 10.42/2.84 % (925)------------------------------
% 10.42/2.85 % (927)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_724 for (2987ds/1021Mi)
% 10.42/2.85 % (924)Instruction limit reached!
% 10.42/2.85 % (924)------------------------------
% 10.42/2.85 % (924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.42/2.85 % (924)Termination reason: Unknown
% 10.42/2.85 % (924)Termination phase: Saturation
% 10.42/2.85
% 10.42/2.85 % (924)Memory used [KB]: 2430
% 10.42/2.85 % (924)Time elapsed: 0.073 s
% 10.42/2.85 % (924)Instructions burned: 164 (million)
% 10.42/2.85 % (924)------------------------------
% 10.42/2.85 % (924)------------------------------
% 10.42/2.86 % (928)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_724 for (2987ds/267Mi)
% 10.42/2.86 % (929)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_724 for (2987ds/204Mi)
% 10.42/2.87 % (930)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_724 for (2987ds/26Mi)
% 10.42/2.88 % (930)Instruction limit reached!
% 10.42/2.88 % (930)------------------------------
% 10.42/2.88 % (930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.42/2.88 % (930)Termination reason: Unknown
% 10.42/2.88 % (930)Termination phase: shuffling
% 10.42/2.88
% 10.42/2.88 % (930)Memory used [KB]: 1791
% 10.42/2.88 % (930)Time elapsed: 0.013 s
% 10.42/2.88 % (930)Instructions burned: 26 (million)
% 10.42/2.88 % (930)------------------------------
% 10.42/2.88 % (930)------------------------------
% 10.42/2.89 % (931)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_724 for (2987ds/53Mi)
% 11.08/2.92 % (931)Instruction limit reached!
% 11.08/2.92 % (931)------------------------------
% 11.08/2.92 % (931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.08/2.92 % (931)Termination reason: Unknown
% 11.08/2.92 % (931)Termination phase: Property scanning
% 11.08/2.92
% 11.08/2.92 % (931)Memory used [KB]: 1918
% 11.08/2.92 % (931)Time elapsed: 0.025 s
% 11.08/2.92 % (931)Instructions burned: 54 (million)
% 11.08/2.92 % (931)------------------------------
% 11.08/2.92 % (931)------------------------------
% 11.08/2.93 % (932)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_724 for (2986ds/4436Mi)
% 11.08/2.95 % (929)Instruction limit reached!
% 11.08/2.95 % (929)------------------------------
% 11.08/2.95 % (929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.08/2.95 % (929)Termination reason: Unknown
% 11.08/2.95 % (929)Termination phase: Saturation
% 11.08/2.95
% 11.08/2.95 % (929)Memory used [KB]: 7419
% 11.08/2.95 % (929)Time elapsed: 0.090 s
% 11.08/2.95 % (929)Instructions burned: 204 (million)
% 11.08/2.95 % (929)------------------------------
% 11.08/2.95 % (929)------------------------------
% 11.08/2.96 % (933)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_724 for (2986ds/1539Mi)
% 11.08/2.96 % (928)Instruction limit reached!
% 11.08/2.96 % (928)------------------------------
% 11.08/2.96 % (928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.08/2.96 % (928)Termination reason: Unknown
% 11.08/2.96 % (928)Termination phase: Saturation
% 11.08/2.96
% 11.08/2.96 % (928)Memory used [KB]: 6908
% 11.08/2.96 % (928)Time elapsed: 0.109 s
% 11.08/2.96 % (928)Instructions burned: 269 (million)
% 11.08/2.96 % (928)------------------------------
% 11.08/2.96 % (928)------------------------------
% 11.08/2.98 % (934)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_724 for (2986ds/408Mi)
% 11.08/3.00 % (926)Instruction limit reached!
% 11.08/3.00 % (926)------------------------------
% 11.08/3.00 % (926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.08/3.00 % (926)Termination reason: Unknown
% 11.08/3.00 % (926)Termination phase: Saturation
% 11.08/3.00
% 11.08/3.00 % (926)Memory used [KB]: 8187
% 11.08/3.00 % (926)Time elapsed: 0.200 s
% 11.08/3.00 % (926)Instructions burned: 369 (million)
% 11.08/3.00 % (926)------------------------------
% 11.08/3.00 % (926)------------------------------
% 11.08/3.00 % (915)Instruction limit reached!
% 11.08/3.00 % (915)------------------------------
% 11.08/3.00 % (915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.08/3.00 % (915)Termination reason: Unknown
% 11.08/3.00 % (915)Termination phase: Saturation
% 11.08/3.00
% 11.08/3.00 % (915)Memory used [KB]: 11001
% 11.08/3.00 % (915)Time elapsed: 0.370 s
% 11.08/3.00 % (915)Instructions burned: 988 (million)
% 11.08/3.00 % (915)------------------------------
% 11.08/3.00 % (915)------------------------------
% 11.08/3.02 % (935)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_724 for (2985ds/5205Mi)
% 11.08/3.02 % (936)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_724 for (2985ds/1913Mi)
% 13.09/3.19 % (934)Instruction limit reached!
% 13.09/3.19 % (934)------------------------------
% 13.09/3.19 % (934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.09/3.19 % (934)Termination reason: Unknown
% 13.09/3.19 % (934)Termination phase: Saturation
% 13.09/3.19
% 13.09/3.19 % (934)Memory used [KB]: 9722
% 13.09/3.19 % (934)Time elapsed: 0.212 s
% 13.09/3.19 % (934)Instructions burned: 409 (million)
% 13.09/3.19 % (934)------------------------------
% 13.09/3.19 % (934)------------------------------
% 13.45/3.21 % (937)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_724 for (2983ds/4350Mi)
% 13.45/3.22 % (922)Instruction limit reached!
% 13.45/3.22 % (922)------------------------------
% 13.45/3.22 % (922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.45/3.22 % (922)Termination reason: Unknown
% 13.45/3.22 % (922)Termination phase: Saturation
% 13.45/3.22
% 13.45/3.22 % (922)Memory used [KB]: 9978
% 13.45/3.22 % (922)Time elapsed: 0.459 s
% 13.45/3.22 % (922)Instructions burned: 922 (million)
% 13.45/3.22 % (922)------------------------------
% 13.45/3.22 % (922)------------------------------
% 13.45/3.23 % (938)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_724 for (2983ds/68Mi)
% 13.45/3.26 % (938)Instruction limit reached!
% 13.45/3.26 % (938)------------------------------
% 13.45/3.26 % (938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.45/3.26 % (938)Termination reason: Unknown
% 13.45/3.26 % (938)Termination phase: Property scanning
% 13.45/3.26
% 13.45/3.26 % (938)Memory used [KB]: 2046
% 13.45/3.26 % (938)Time elapsed: 0.032 s
% 13.45/3.26 % (938)Instructions burned: 70 (million)
% 13.45/3.26 % (938)------------------------------
% 13.45/3.26 % (938)------------------------------
% 13.45/3.28 % (939)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_724 for (2983ds/358Mi)
% 13.83/3.32 % (927)First to succeed.
% 13.83/3.32 % (927)Refutation found. Thanks to Tanya!
% 13.83/3.32 % SZS status Theorem for DTF2THF_724
% 13.83/3.32 % SZS output start Proof for DTF2THF_724
% 13.83/3.32 thf(func_def_0, type, in: $i > $i > $o).
% 13.83/3.32 thf(func_def_1, type, exu: ($i > $o) > $o).
% 13.83/3.32 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 13.83/3.32 thf(func_def_8, type, powerset: $i > $i).
% 13.83/3.32 thf(func_def_10, type, setunion: $i > $i).
% 13.83/3.32 thf(func_def_19, type, descr: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_26, type, prop2set: $o > $i).
% 13.83/3.32 thf(func_def_36, type, nonempty: $i > $o).
% 13.83/3.32 thf(func_def_69, type, set2prop: $i > $o).
% 13.83/3.32 thf(func_def_88, type, subset: $i > $i > $o).
% 13.83/3.32 thf(func_def_89, type, disjoint: $i > $i > $o).
% 13.83/3.32 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 13.83/3.32 thf(func_def_114, type, binunion: $i > $i > $i).
% 13.83/3.32 thf(func_def_122, type, binintersect: $i > $i > $i).
% 13.83/3.32 thf(func_def_135, type, regular: $i > $o).
% 13.83/3.32 thf(func_def_136, type, setminus: $i > $i > $i).
% 13.83/3.32 thf(func_def_147, type, symdiff: $i > $i > $i).
% 13.83/3.32 thf(func_def_153, type, iskpair: $i > $o).
% 13.83/3.32 thf(func_def_158, type, kpair: $i > $i > $i).
% 13.83/3.32 thf(func_def_160, type, cartprod: $i > $i > $i).
% 13.83/3.32 thf(func_def_177, type, singleton: $i > $o).
% 13.83/3.32 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 13.83/3.32 thf(func_def_184, type, atmost1p: $i > $o).
% 13.83/3.32 thf(func_def_185, type, atleast2p: $i > $o).
% 13.83/3.32 thf(func_def_186, type, atmost2p: $i > $o).
% 13.83/3.32 thf(func_def_187, type, upairsetp: $i > $o).
% 13.83/3.32 thf(func_def_191, type, kfst: $i > $i).
% 13.83/3.32 thf(func_def_203, type, ksnd: $i > $i).
% 13.83/3.32 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 13.83/3.32 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 13.83/3.32 thf(func_def_243, type, sP9: $o > $i > $i > $o).
% 13.83/3.32 thf(func_def_249, type, sP15: ($i > $i > $o) > $i > $o).
% 13.83/3.32 thf(func_def_254, type, sP20: $i > $o).
% 13.83/3.32 thf(func_def_259, type, sP25: ($i > $o) > ($i > $o) > $i > $i > $o).
% 13.83/3.32 thf(func_def_260, type, sP26: ($i > $o) > $i > $o).
% 13.83/3.32 thf(func_def_261, type, sP27: $i > ($i > $o) > $o).
% 13.83/3.32 thf(func_def_262, type, sP28: ($i > $o) > $i > $o).
% 13.83/3.32 thf(func_def_263, type, sP29: ($i > $o) > $i > $o).
% 13.83/3.32 thf(func_def_266, type, sP32: $i > $i > $o).
% 13.83/3.32 thf(func_def_270, type, sP36: $i > $i > $i > $o).
% 13.83/3.32 thf(func_def_271, type, sP37: $i > $i > $o).
% 13.83/3.32 thf(func_def_272, type, sP38: $i > $o).
% 13.83/3.32 thf(func_def_273, type, sP39: $i > $i > $o).
% 13.83/3.32 thf(func_def_274, type, sP40: $i > $i > $o).
% 13.83/3.32 thf(func_def_275, type, sP41: $i > $i > $o).
% 13.83/3.32 thf(func_def_278, type, sP44: $o > $i > $i > $i > $o).
% 13.83/3.32 thf(func_def_279, type, sP45: $i > $i > $i > $o).
% 13.83/3.32 thf(func_def_280, type, sP46: $i > $i > $o > $o).
% 13.83/3.32 thf(func_def_281, type, sP47: $i > $i > $i > $o).
% 13.83/3.32 thf(func_def_300, type, sK66: $i > $i > $i).
% 13.83/3.32 thf(func_def_330, type, sK96: $i > $i > $o).
% 13.83/3.32 thf(func_def_352, type, sK118: $i > $i > $i).
% 13.83/3.32 thf(func_def_354, type, sK120: $i > $o).
% 13.83/3.32 thf(func_def_356, type, sK122: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_360, type, sK126: $i > $i > $o).
% 13.83/3.32 thf(func_def_378, type, sK144: $i > $i > $i > $i).
% 13.83/3.32 thf(func_def_379, type, sK145: $i > $i > $i > $i).
% 13.83/3.32 thf(func_def_380, type, sK146: $i > $i > $o).
% 13.83/3.32 thf(func_def_385, type, sK151: $i > $o).
% 13.83/3.32 thf(func_def_386, type, sK152: $i > $i).
% 13.83/3.32 thf(func_def_387, type, sK153: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_389, type, sK155: $i > $o).
% 13.83/3.32 thf(func_def_402, type, sK168: $i > $o).
% 13.83/3.32 thf(func_def_403, type, sK169: $i > $o).
% 13.83/3.32 thf(func_def_404, type, sK170: ($i > $o) > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_405, type, sK171: ($i > $o) > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_408, type, sK174: $i > $o).
% 13.83/3.32 thf(func_def_410, type, sK176: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_415, type, sK181: $i > $o).
% 13.83/3.32 thf(func_def_417, type, sK183: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_419, type, sK185: $i > $i).
% 13.83/3.32 thf(func_def_424, type, sK190: $i > $o).
% 13.83/3.32 thf(func_def_434, type, sK200: $i > $i > $i).
% 13.83/3.32 thf(func_def_435, type, sK201: $i > $o).
% 13.83/3.32 thf(func_def_437, type, sK203: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_439, type, sK205: $i > $o).
% 13.83/3.32 thf(func_def_446, type, sK212: $i > $o).
% 13.83/3.32 thf(func_def_469, type, sK235: $i > $o).
% 13.83/3.32 thf(func_def_470, type, sK236: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_475, type, sK241: $i > $o).
% 13.83/3.32 thf(func_def_476, type, sK242: $i > $i).
% 13.83/3.32 thf(func_def_477, type, sK243: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_480, type, sK246: $i > $i > $i).
% 13.83/3.32 thf(func_def_485, type, sK251: $i > $i > $o).
% 13.83/3.32 thf(func_def_490, type, sK256: $i > $i > $o).
% 13.83/3.32 thf(func_def_492, type, sK258: $i > ($i > $i > $o) > $i).
% 13.83/3.32 thf(func_def_493, type, sK259: $i > ($i > $i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_494, type, sK260: $i > ($i > $i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_495, type, sK261: ($i > $i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_496, type, sK262: $i > ($i > $i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_498, type, sK264: $i > $i > $o).
% 13.83/3.32 thf(func_def_508, type, sK274: $i > $o).
% 13.83/3.32 thf(func_def_510, type, sK276: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_511, type, sK277: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_518, type, sK284: $i > $o).
% 13.83/3.32 thf(func_def_540, type, sK306: $i > $i > $i).
% 13.83/3.32 thf(func_def_541, type, sK307: $i > $o).
% 13.83/3.32 thf(func_def_544, type, sK310: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_564, type, sK330: $i > $i).
% 13.83/3.32 thf(func_def_567, type, sK333: $i > $i).
% 13.83/3.32 thf(func_def_568, type, sK334: $i > $i).
% 13.83/3.32 thf(func_def_570, type, sK336: $i > $o).
% 13.83/3.32 thf(func_def_573, type, sK339: $i > $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_580, type, sK346: $i > $i).
% 13.83/3.32 thf(func_def_600, type, sK366: $i > $i > $o).
% 13.83/3.32 thf(func_def_603, type, sK369: $i > $o).
% 13.83/3.32 thf(func_def_605, type, sK371: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_615, type, sK381: $i > $o).
% 13.83/3.32 thf(func_def_617, type, sK383: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_618, type, sK384: $i > $o).
% 13.83/3.32 thf(func_def_621, type, sK387: ($i > $o) > ($i > $o) > $i > $i > $i).
% 13.83/3.32 thf(func_def_622, type, sK388: ($i > $o) > ($i > $o) > $i > $i > $i).
% 13.83/3.32 thf(func_def_625, type, sK391: $i > $o).
% 13.83/3.32 thf(func_def_626, type, sK392: $i > $o).
% 13.83/3.32 thf(func_def_633, type, sK399: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_634, type, sK400: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_635, type, sK401: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_636, type, sK402: $i > $o).
% 13.83/3.32 thf(func_def_640, type, sK406: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_641, type, sK407: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_642, type, sK408: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_644, type, sK410: $i > $o).
% 13.83/3.32 thf(func_def_655, type, sK421: $i > $o).
% 13.83/3.32 thf(func_def_667, type, sK433: $i > $o).
% 13.83/3.32 thf(func_def_671, type, sK437: $i > $o).
% 13.83/3.32 thf(func_def_674, type, sK440: $i > $o).
% 13.83/3.32 thf(func_def_676, type, sK442: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_685, type, sK451: $i > $o).
% 13.83/3.32 thf(func_def_687, type, sK453: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_692, type, sK458: $i > $i > $i).
% 13.83/3.32 thf(func_def_693, type, sK459: $i > $i > $i).
% 13.83/3.32 thf(func_def_699, type, sK465: $i > $i > $i).
% 13.83/3.32 thf(func_def_704, type, sK470: $i > $o).
% 13.83/3.32 thf(func_def_705, type, sK471: $i > $o).
% 13.83/3.32 thf(func_def_706, type, sK472: ($i > $o) > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_707, type, sK473: ($i > $o) > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_714, type, sK480: $i > $o).
% 13.83/3.32 thf(func_def_724, type, sK490: $i > $i > $i).
% 13.83/3.32 thf(func_def_725, type, sK491: $i > $i > $i).
% 13.83/3.32 thf(func_def_726, type, sK492: $i > $i > $i).
% 13.83/3.32 thf(func_def_727, type, sK493: $i > $i > $i).
% 13.83/3.32 thf(func_def_728, type, sK494: $i > $i > $i).
% 13.83/3.32 thf(func_def_729, type, sK495: $i > $i > $i).
% 13.83/3.32 thf(func_def_730, type, sK496: $i > $i > $i).
% 13.83/3.32 thf(func_def_731, type, sK497: $i > $i > $i > $i).
% 13.83/3.32 thf(func_def_732, type, sK498: $i > $i).
% 13.83/3.32 thf(func_def_733, type, sK499: $i > $i).
% 13.83/3.32 thf(func_def_734, type, sK500: $i > $i).
% 13.83/3.32 thf(func_def_735, type, sK501: $i > $i).
% 13.83/3.32 thf(func_def_736, type, sK502: $i > $i > $i).
% 13.83/3.32 thf(func_def_737, type, sK503: $i > $i > $i).
% 13.83/3.32 thf(func_def_738, type, sK504: $i > $i > $i).
% 13.83/3.32 thf(func_def_739, type, sK505: $i > $i > $i > $i).
% 13.83/3.32 thf(func_def_740, type, sK506: $i > $i > $i > $i).
% 13.83/3.32 thf(func_def_741, type, sK507: $i > $i).
% 13.83/3.32 thf(func_def_748, type, sK514: $o > $i > $i > $i).
% 13.83/3.32 thf(func_def_753, type, sK519: $i > $i > $i).
% 13.83/3.32 thf(func_def_770, type, sK536: $i > $i > $i > $o).
% 13.83/3.32 thf(func_def_774, type, sK540: $i > $o).
% 13.83/3.32 thf(func_def_776, type, sK542: $i > $i > $i).
% 13.83/3.32 thf(func_def_779, type, sK545: $i > $o).
% 13.83/3.32 thf(func_def_785, type, sK551: $i > $i > $i > $o).
% 13.83/3.32 thf(func_def_801, type, sK567: $i > $i).
% 13.83/3.32 thf(func_def_802, type, sK568: $i > $i).
% 13.83/3.32 thf(func_def_806, type, sK572: $i > $i).
% 13.83/3.32 thf(func_def_812, type, sK578: $i > $i).
% 13.83/3.32 thf(func_def_813, type, sK579: $i > $i).
% 13.83/3.32 thf(func_def_814, type, sK580: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_815, type, sK581: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_816, type, sK582: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_817, type, sK583: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_818, type, sK584: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_819, type, sK585: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_820, type, sK586: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_821, type, sK587: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_822, type, sK588: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_823, type, sK589: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_824, type, sK590: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_825, type, sK591: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_826, type, sK592: ($i > $i > $o) > $i > $i > $i).
% 13.83/3.32 thf(func_def_827, type, sK593: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_828, type, sK594: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_829, type, sK595: $i > $i).
% 13.83/3.32 thf(func_def_830, type, sK596: $i > $i).
% 13.83/3.32 thf(func_def_831, type, sK597: $i > $i).
% 13.83/3.32 thf(func_def_832, type, sK598: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_833, type, sK599: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_834, type, sK600: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_835, type, sK601: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_836, type, sK602: $i > $i).
% 13.83/3.32 thf(func_def_837, type, sK603: $i > $i).
% 13.83/3.32 thf(func_def_838, type, sK604: $i > $i).
% 13.83/3.32 thf(func_def_842, type, sK608: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_843, type, sK609: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_844, type, sK610: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_845, type, sK611: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_846, type, sK612: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_848, type, sK614: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_849, type, sK615: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_850, type, sK616: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_851, type, sK617: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_852, type, sK618: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_853, type, sK619: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_855, type, sK621: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_857, type, sK623: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_858, type, sK624: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_859, type, sK625: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_860, type, sK626: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_861, type, sK627: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_862, type, sK628: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_863, type, sK629: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_864, type, sK630: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_865, type, sK631: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_866, type, sK632: ($i > $o) > $i).
% 13.83/3.32 thf(func_def_867, type, sK633: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_869, type, sK635: $i > ($i > $o) > $i).
% 13.83/3.32 thf(func_def_870, type, sK636: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_871, type, sK637: ($i > $o) > $i > $i).
% 13.83/3.32 thf(func_def_872, type, sK638: $i > $i).
% 13.83/3.32 thf(func_def_874, type, ph639: !>[X0: $tType]:(X0)).
% 13.83/3.32 thf(func_def_877, type, sK642: $i > $i > $i > $i > ($i > $i > $o) > $i).
% 13.83/3.32 thf(func_def_878, type, sK643: $i > $i > $i > ($i > $i > $o) > $i > $i).
% 13.83/3.32 thf(f7952,plain,(
% 13.83/3.32 $false),
% 13.83/3.32 inference(subsumption_resolution,[status(thm)],[f7951,f2121])).
% 13.83/3.32 thf(f2121,plain,(
% 13.83/3.32 ((in @ sK250 @ sK249) != $true)),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f1222])).
% 13.83/3.32 thf(f1222,plain,(
% 13.83/3.32 (singletonsswitch = $true) & (disjointsetsI1 = $true) & (upairinpowunion = $true) & (cartprodfstin = $true) & (setbeta = $true) & (singletoninpowerset = $true) & (kfstsingleton = $true) & (singletonprop = $true) & (setOfPairsIsBReln = $true) & (cartprodpairsurjEq = $true) & (subsetTrans = $true) & (cartprodsndpairEq = $true) & (powersetI = $true) & (binunionE = $true) & (setminusSubset2 = $true) & (ksndpairEq = $true) & (setminusIRneg = $true) & (notinemptyset = $true) & (powersetsubset = $true) & (binintersectI = $true) & (binintersectEL = $true) & (upairequniteq = $true) & (wellorderingAx = $true) & (emptysetimpfalse = $true) & (sepInPowerset = $true) & (exuE3e = $true) & (setoftrueEq = $true) & (ex1I2 = $true) & (setukpairinjR12 = $true) & (replAx = $true) & (secondinupair = $true) & (nonemptyI = $true) & (setunionE2 = $true) & (emptyInPowerset = $true) & (dpsetconstrERa = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (setminusLsub = $true) & (binintersectLsub = $true) & (powersetAx = $true) & (foundationAx = $true) & (setunionsingleton = $true) & (exuE1 = $true) & (binunionIL = $true) & (binintersectER = $true) & (vacuousDall = $true) & (subPowSU = $true) & (setadjoinSub2 = $true) & (subsetE2 = $true) & (notinsingleton = $true) & (setminusI = $true) & (setukpairinjL2 = $true) & (symdiffIneg1 = $true) & (kfstpairEq = $true) & (binunionRsub = $true) & (cartprodpairin = $true) & (ksndsingleton = $true) & (prop2setE = $true) & (exuI2 = $true) & (exuEu = $true) & (setukpairIR = $true) & (setminusERneg = $true) & (upairsetE = $true) & (nonemptyI1 = $true) & (subsetI1 = $true) & (quantDeMorgan2 = $true) & (binintersectSubset1 = $true) & (binunionLsub = $true) & (exuI1 = $true) & (subsetI2 = $true) & (cartprodpairmemER = $true) & (setukpairinjR2 = $true) & (ubforcartprodlem3 = $true) & (kpairiskpair = $true) & (emptysetE = $true) & (symdiffI1 = $true) & (cartprodmempair = $true) & (setminusSubset1 = $true) & (notequalI2 = $true) & (subset2powerset = $true) & (binunionIR = $true) & (notsubsetI = $true) & (setadjoinOr = $true) & (nonemptyImpWitness = $true) & (setunionsingleton1 = $true) & (symdiffI2 = $true) & (eqinunit = $true) & (setunionI = $true) & (emptysetAx = $true) & (setukpairIL = $true) & (binintersectSubset5 = $true) & (cartprodfstpairEq = $true) & (kpairsurjEq = $true) & (kpairp = $true) & (powersetI1 = $true) & (emptyinPowerset = $true) & (prop2set2propI = $true) & (dsetconstrEL = $true) & (quantDeMorgan4 = $true) & (notdexE = $true) & (ex1E1 = $true) & (omegaSAx = $true) & (setminusELneg = $true) & (powersetE = $true) & (setadjoinSub = $true) & (emptyE1 = $true) & (setminusER = $true) & (theprop = $true) & (setunionE = $true) & (subsetRefl = $true) & (notequalI1 = $true) & (setminusEL = $true) & (ubforcartprodlem2 = $true) & (setukpairinjL = $true) & (uniqinunit = $true) & (upairsubunion = $true) & (setadjoin__Cong = $true) & (cartprodpairmemEL = $true) & (eqimpsubset1 = $true) & (in__Cong = $true) & (upairset2E = $true) & (setadjoinIL = $true) & (powerset__Cong = $true) & (dpsetconstrI = $true) & (inPowerset = $true) & (cartprodmempair1 = $true) & (prop2setI = $true) & (symdiffE = $true) & (setukpairinjL1 = $true) & (setunion__Cong = $true) & (symdiffIneg2 = $true) & (upairset2IR = $true) & (binintersectSubset3 = $true) & (dsetconstrER = $true) & (emptyset__Cong = $true) & (setukpairinjR1 = $true) & (emptyI = $true) & (quantDeMorgan1 = $true) & (cartprodsndin = $true) & (exuI3 = $true) & (setadjoinAx = $true) & (setadjoinIR = $true) & (dsetconstrI = $true) & (noeltsimpempty = $true) & (nonemptyE1 = $true) & (setukpairinjR = $true) & (singletonsuniq = $true) & (inCongP = $true) & (cartprodmempaircEq = $true) & (exuE3u = $true) & (setextAx = $true) & (subsetE = $true) & (descr__Cong = $true) & (binintersectSubset2 = $true) & (setextsub = $true) & (binintersectRsub = $true) & (subsetemptysetimpeq = $true) & (((in @ sK250 @ sK249) != $true) & ((in @ (kpair @ sK252 @ sK250) @ (dpsetconstr @ sK253 @ sK249 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK251 @ Y0 @ Y1)))))) = $true)) & (sepSubset = $true) & (quantDeMorgan3 = $true) & (setukpairinjR11 = $true) & (omega__Cong = $true) & (emptysetsubset = $true) & (setadjoinE = $true) & (setunionsingleton2 = $true) & (emptyinunitempty = $true) & (notdallE = $true) & (ubforcartprodlem1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (dpsetconstrSub = $true) & (singletoninpowunion = $true) & (setext = $true) & (setminusILneg = $true) & (exu__Cong = $true) & (dsetconstr__Cong = $true) & (descrp = $true) & (powersetE1 = $true) & (binintersectSubset4 = $true) & (dpsetconstrEL1 = $true) & (setunionAx = $true) & (binunionEcases = $true) & (singletonsubset = $true) & (ex1I = $true) & (bs114d = $true) & (exuE2 = $true) & (eqimpsubset2 = $true)),
% 13.83/3.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK249,sK250,sK251,sK252,sK253])],[f687,f1221])).
% 13.83/3.32 thf(f1221,plain,(
% 13.83/3.32 ? [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (($true != (in @ X1 @ X0)) & ($true = (in @ (kpair @ X3 @ X1) @ (dpsetconstr @ X4 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) => (((in @ sK250 @ sK249) != $true) & ((in @ (kpair @ sK252 @ sK250) @ (dpsetconstr @ sK253 @ sK249 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK251 @ Y0 @ Y1)))))) = $true))),
% 13.83/3.32 introduced(definition,[],[choice_axiom])).
% 13.83/3.32 thf(f687,plain,(
% 13.83/3.32 (singletonsswitch = $true) & (disjointsetsI1 = $true) & (upairinpowunion = $true) & (cartprodfstin = $true) & (setbeta = $true) & (singletoninpowerset = $true) & (kfstsingleton = $true) & (singletonprop = $true) & (setOfPairsIsBReln = $true) & (cartprodpairsurjEq = $true) & (subsetTrans = $true) & (cartprodsndpairEq = $true) & (powersetI = $true) & (binunionE = $true) & (setminusSubset2 = $true) & (ksndpairEq = $true) & (setminusIRneg = $true) & (notinemptyset = $true) & (powersetsubset = $true) & (binintersectI = $true) & (binintersectEL = $true) & (upairequniteq = $true) & (wellorderingAx = $true) & (emptysetimpfalse = $true) & (sepInPowerset = $true) & (exuE3e = $true) & (setoftrueEq = $true) & (ex1I2 = $true) & (setukpairinjR12 = $true) & (replAx = $true) & (secondinupair = $true) & (nonemptyI = $true) & (setunionE2 = $true) & (emptyInPowerset = $true) & (dpsetconstrERa = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (setminusLsub = $true) & (binintersectLsub = $true) & (powersetAx = $true) & (foundationAx = $true) & (setunionsingleton = $true) & (exuE1 = $true) & (binunionIL = $true) & (binintersectER = $true) & (vacuousDall = $true) & (subPowSU = $true) & (setadjoinSub2 = $true) & (subsetE2 = $true) & (notinsingleton = $true) & (setminusI = $true) & (setukpairinjL2 = $true) & (symdiffIneg1 = $true) & (kfstpairEq = $true) & (binunionRsub = $true) & (cartprodpairin = $true) & (ksndsingleton = $true) & (prop2setE = $true) & (exuI2 = $true) & (exuEu = $true) & (setukpairIR = $true) & (setminusERneg = $true) & (upairsetE = $true) & (nonemptyI1 = $true) & (subsetI1 = $true) & (quantDeMorgan2 = $true) & (binintersectSubset1 = $true) & (binunionLsub = $true) & (exuI1 = $true) & (subsetI2 = $true) & (cartprodpairmemER = $true) & (setukpairinjR2 = $true) & (ubforcartprodlem3 = $true) & (kpairiskpair = $true) & (emptysetE = $true) & (symdiffI1 = $true) & (cartprodmempair = $true) & (setminusSubset1 = $true) & (notequalI2 = $true) & (subset2powerset = $true) & (binunionIR = $true) & (notsubsetI = $true) & (setadjoinOr = $true) & (nonemptyImpWitness = $true) & (setunionsingleton1 = $true) & (symdiffI2 = $true) & (eqinunit = $true) & (setunionI = $true) & (emptysetAx = $true) & (setukpairIL = $true) & (binintersectSubset5 = $true) & (cartprodfstpairEq = $true) & (kpairsurjEq = $true) & (kpairp = $true) & (powersetI1 = $true) & (emptyinPowerset = $true) & (prop2set2propI = $true) & (dsetconstrEL = $true) & (quantDeMorgan4 = $true) & (notdexE = $true) & (ex1E1 = $true) & (omegaSAx = $true) & (setminusELneg = $true) & (powersetE = $true) & (setadjoinSub = $true) & (emptyE1 = $true) & (setminusER = $true) & (theprop = $true) & (setunionE = $true) & (subsetRefl = $true) & (notequalI1 = $true) & (setminusEL = $true) & (ubforcartprodlem2 = $true) & (setukpairinjL = $true) & (uniqinunit = $true) & (upairsubunion = $true) & (setadjoin__Cong = $true) & (cartprodpairmemEL = $true) & (eqimpsubset1 = $true) & (in__Cong = $true) & (upairset2E = $true) & (setadjoinIL = $true) & (powerset__Cong = $true) & (dpsetconstrI = $true) & (inPowerset = $true) & (cartprodmempair1 = $true) & (prop2setI = $true) & (symdiffE = $true) & (setukpairinjL1 = $true) & (setunion__Cong = $true) & (symdiffIneg2 = $true) & (upairset2IR = $true) & (binintersectSubset3 = $true) & (dsetconstrER = $true) & (emptyset__Cong = $true) & (setukpairinjR1 = $true) & (emptyI = $true) & (quantDeMorgan1 = $true) & (cartprodsndin = $true) & (exuI3 = $true) & (setadjoinAx = $true) & (setadjoinIR = $true) & (dsetconstrI = $true) & (noeltsimpempty = $true) & (nonemptyE1 = $true) & (setukpairinjR = $true) & (singletonsuniq = $true) & (inCongP = $true) & (cartprodmempaircEq = $true) & (exuE3u = $true) & (setextAx = $true) & (subsetE = $true) & (descr__Cong = $true) & (binintersectSubset2 = $true) & (setextsub = $true) & (binintersectRsub = $true) & (subsetemptysetimpeq = $true) & ? [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (($true != (in @ X1 @ X0)) & ($true = (in @ (kpair @ X3 @ X1) @ (dpsetconstr @ X4 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) & (sepSubset = $true) & (quantDeMorgan3 = $true) & (setukpairinjR11 = $true) & (omega__Cong = $true) & (emptysetsubset = $true) & (setadjoinE = $true) & (setunionsingleton2 = $true) & (emptyinunitempty = $true) & (notdallE = $true) & (ubforcartprodlem1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (dpsetconstrSub = $true) & (singletoninpowunion = $true) & (setext = $true) & (setminusILneg = $true) & (exu__Cong = $true) & (dsetconstr__Cong = $true) & (descrp = $true) & (powersetE1 = $true) & (binintersectSubset4 = $true) & (dpsetconstrEL1 = $true) & (setunionAx = $true) & (binunionEcases = $true) & (singletonsubset = $true) & (ex1I = $true) & (bs114d = $true) & (exuE2 = $true) & (eqimpsubset2 = $true)),
% 13.83/3.32 inference(flattening,[status(thm)],[f686])).
% 13.83/3.32 thf(f686,plain,(
% 13.83/3.32 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (($true != (in @ X1 @ X0)) & ($true = (in @ (kpair @ X3 @ X1) @ (dpsetconstr @ X4 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) & (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)),
% 13.83/3.32 inference(ennf_transformation,[status(thm)],[f282])).
% 13.83/3.32 thf(f282,plain,(
% 13.83/3.32 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (($true = (in @ (kpair @ X3 @ X1) @ (dpsetconstr @ X4 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) => ($true = (in @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.83/3.32 inference(fool_elimination,[status(thm)],[f281])).
% 13.83/3.32 thf(f281,plain,(
% 13.83/3.32 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : ((in @ (kpair @ X3 @ X1) @ (dpsetconstr @ X4 @ X0 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6)))) => (in @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.83/3.32 inference(rectify,[status(thm)],[f194])).
% 13.83/3.32 thf(f194,negated_conjecture,(
% 13.83/3.32 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => ! [X4 : $i,X2 : $i,X0 : $i > $i > $o,X1 : $i,X3 : $i] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X2 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.83/3.32 inference(negated_conjecture,[status(cth)],[f193])).
% 13.83/3.32 thf(f193,conjecture,(
% 13.83/3.32 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => ! [X4 : $i,X2 : $i,X0 : $i > $i > $o,X1 : $i,X3 : $i] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.83/3.32 file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',dpsetconstrEL2)).
% 13.83/3.32 thf(f7951,plain,(
% 13.83/3.32 ((in @ sK250 @ sK249) = $true)),
% 13.83/3.32 inference(forward_demodulation,[status(thm)],[f7934,f4141])).
% 13.83/3.32 thf(f4141,plain,(
% 13.83/3.32 ( ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1)) = X1)) )),
% 13.83/3.32 inference(trivial_inequality_removal,[status(thm)],[f3005])).
% 13.83/3.32 thf(f3005,plain,(
% 13.83/3.32 ( ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1)) = X1) | ($true != $true)) )),
% 13.83/3.32 inference(definition_unfolding,[status(thm)],[f2090,f2263])).
% 13.83/3.32 thf(f2263,plain,(
% 13.83/3.32 (ksndpairEq = $true)),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f1222])).
% 13.83/3.32 thf(f2090,plain,(
% 13.83/3.32 ( ! [X0 : $i,X1 : $i] : (((ksnd @ (kpair @ X0 @ X1)) = X1) | (ksndpairEq != $true)) )),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f1220])).
% 13.83/3.32 thf(f1220,plain,(
% 13.83/3.32 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ((ksnd @ (kpair @ sK247 @ sK248)) != sK248))),
% 13.83/3.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK247,sK248])],[f1218,f1219])).
% 13.83/3.32 thf(f1219,plain,(
% 13.83/3.32 ? [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) != X3) => ((ksnd @ (kpair @ sK247 @ sK248)) != sK248)),
% 13.83/3.32 introduced(definition,[],[choice_axiom])).
% 13.83/3.32 thf(f1218,plain,(
% 13.83/3.32 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ? [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) != X3))),
% 13.83/3.32 inference(rectify,[status(thm)],[f1217])).
% 13.83/3.32 thf(f1217,plain,(
% 13.83/3.32 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1) | (ksndpairEq != $true)) & ((ksndpairEq = $true) | ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1))),
% 13.83/3.32 inference(nnf_transformation,[status(thm)],[f199])).
% 13.83/3.32 thf(f199,plain,(
% 13.83/3.32 ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1) <=> (ksndpairEq = $true)),
% 13.83/3.32 inference(fool_elimination,[status(thm)],[f198])).
% 13.83/3.32 thf(f198,plain,(
% 13.83/3.32 (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1) = ksndpairEq)),
% 13.83/3.32 inference(rectify,[status(thm)],[f177])).
% 13.83/3.32 thf(f177,axiom,(
% 13.83/3.32 (! [X1 : $i,X2 : $i] : ((ksnd @ (kpair @ X1 @ X2)) = X2) = ksndpairEq)),
% 13.83/3.32 file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',ksndpairEq)).
% 13.83/3.32 thf(f7934,plain,(
% 13.83/3.32 ($true = (in @ (ksnd @ (kpair @ sK252 @ sK250)) @ sK249))),
% 13.83/3.32 inference(trivial_inequality_removal,[status(thm)],[f7922])).
% 13.83/3.32 thf(f7922,plain,(
% 13.83/3.32 ($true = (in @ (ksnd @ (kpair @ sK252 @ sK250)) @ sK249)) | ($true != $true)),
% 13.83/3.32 inference(superposition,[status(thm)],[f3751,f6576])).
% 13.83/3.32 thf(f6576,plain,(
% 13.83/3.32 ((in @ (kpair @ sK252 @ sK250) @ (cartprod @ sK253 @ sK249)) = $true)),
% 13.83/3.32 inference(trivial_inequality_removal,[status(thm)],[f6572])).
% 13.83/3.32 thf(f6572,plain,(
% 13.83/3.32 ((in @ (kpair @ sK252 @ sK250) @ (cartprod @ sK253 @ sK249)) = $true) | ($true != $true)),
% 13.83/3.32 inference(superposition,[status(thm)],[f3487,f3642])).
% 13.83/3.32 thf(f3642,plain,(
% 13.83/3.32 ($true = (in @ (kpair @ sK252 @ sK250) @ (dsetconstr @ (cartprod @ sK253 @ sK249) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK253) & (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK249) & (sK251 @ Y1 @ Y2)) & ((kpair @ Y1 @ Y2) = Y0)))))))))))),
% 13.83/3.32 inference(beta_eta_normalization,[status(thm)],[f3007])).
% 13.83/3.32 thf(f3007,plain,(
% 13.83/3.32 ((in @ (kpair @ sK252 @ sK250) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))) @ sK253 @ sK249 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK251 @ Y0 @ Y1)))))) = $true)),
% 13.83/3.32 inference(definition_unfolding,[status(thm)],[f2120,f1879])).
% 13.83/3.32 thf(f1879,plain,(
% 13.83/3.32 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f221])).
% 13.83/3.32 thf(f221,plain,(
% 13.83/3.32 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y1) & (Y2 @ Y4 @ Y5)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 13.83/3.32 inference(fool_elimination,[status(thm)],[f220])).
% 13.83/3.32 thf(f220,plain,(
% 13.83/3.32 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : (((kpair @ X4 @ X5) = X3) & (X2 @ X4 @ X5) & (in @ X5 @ X1)) & (in @ X4 @ X0)))))))),
% 13.83/3.32 inference(rectify,[status(thm)],[f187])).
% 13.83/3.32 thf(f187,axiom,(
% 13.83/3.32 (dpsetconstr = (^[X3 : $i, X4 : $i, X0 : $i > $i > $o] : (dsetconstr @ (cartprod @ X3 @ X4) @ (^[X10 : $i] : (? [X1 : $i] : (? [X2 : $i] : (((kpair @ X1 @ X2) = X10) & (X0 @ X1 @ X2) & (in @ X2 @ X4)) & (in @ X1 @ X3)))))))),
% 13.83/3.32 file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',dpsetconstr)).
% 13.83/3.32 thf(f2120,plain,(
% 13.83/3.32 ((in @ (kpair @ sK252 @ sK250) @ (dpsetconstr @ sK253 @ sK249 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK251 @ Y0 @ Y1)))))) = $true)),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f1222])).
% 13.83/3.32 thf(f3487,plain,(
% 13.83/3.32 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != (in @ X1 @ (dsetconstr @ X2 @ X0))) | ($true = (in @ X1 @ X2))) )),
% 13.83/3.32 inference(beta_eta_normalization,[status(thm)],[f3486])).
% 13.83/3.32 thf(f3486,plain,(
% 13.83/3.32 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (in @ X1 @ X2)) | ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) )),
% 13.83/3.32 inference(trivial_inequality_removal,[status(thm)],[f2934])).
% 13.83/3.32 thf(f2934,plain,(
% 13.83/3.32 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (in @ X1 @ X2)) | ($true != $true)) )),
% 13.83/3.32 inference(definition_unfolding,[status(thm)],[f2006,f2181])).
% 13.83/3.32 thf(f2181,plain,(
% 13.83/3.32 (dsetconstrEL = $true)),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f1222])).
% 13.83/3.32 thf(f2006,plain,(
% 13.83/3.32 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (in @ X1 @ X2)) | (dsetconstrEL != $true)) )),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f1117])).
% 13.83/3.32 thf(f1117,plain,(
% 13.83/3.32 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (in @ X1 @ X2))) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | (((in @ sK191 @ (dsetconstr @ sK192 @ (^[Y0 : $i]: (sK190 @ Y0)))) = $true) & ($true != (in @ sK191 @ sK192))))),
% 13.83/3.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK190,sK191,sK192])],[f1115,f1116])).
% 13.83/3.32 thf(f1116,plain,(
% 13.83/3.32 ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0))))) & ($true != (in @ X4 @ X5))) => (((in @ sK191 @ (dsetconstr @ sK192 @ (^[Y0 : $i]: (sK190 @ Y0)))) = $true) & ($true != (in @ sK191 @ sK192)))),
% 13.83/3.32 introduced(definition,[],[choice_axiom])).
% 13.83/3.32 thf(f1115,plain,(
% 13.83/3.32 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (in @ X1 @ X2))) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0))))) & ($true != (in @ X4 @ X5))))),
% 13.83/3.32 inference(rectify,[status(thm)],[f1114])).
% 13.83/3.32 thf(f1114,plain,(
% 13.83/3.32 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (in @ X1 @ X2))) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) & ($true != (in @ X1 @ X2))))),
% 13.83/3.32 inference(nnf_transformation,[status(thm)],[f619])).
% 13.83/3.32 thf(f619,plain,(
% 13.83/3.32 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (in @ X1 @ X2))) <=> (dsetconstrEL = $true)),
% 13.83/3.32 inference(ennf_transformation,[status(thm)],[f431])).
% 13.83/3.32 thf(f431,plain,(
% 13.83/3.32 (dsetconstrEL = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ($true = (in @ X1 @ X2)))),
% 13.83/3.32 inference(fool_elimination,[status(thm)],[f430])).
% 13.83/3.32 thf(f430,plain,(
% 13.83/3.32 (dsetconstrEL = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (in @ X1 @ X2)))),
% 13.83/3.32 inference(rectify,[status(thm)],[f15])).
% 13.83/3.32 thf(f15,axiom,(
% 13.83/3.32 (dsetconstrEL = ! [X0 : $i > $o,X1 : $i,X3 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)))),
% 13.83/3.32 file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',dsetconstrEL)).
% 13.83/3.32 thf(f3751,plain,(
% 13.83/3.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (cartprod @ X4 @ X5)) != $true) | ((in @ (ksnd @ X3) @ X5) = $true)) )),
% 13.83/3.32 inference(trivial_inequality_removal,[status(thm)],[f3275])).
% 13.83/3.32 thf(f3275,plain,(
% 13.83/3.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ (ksnd @ X3) @ X5) = $true) | ((in @ X3 @ (cartprod @ X4 @ X5)) != $true)) )),
% 13.83/3.32 inference(definition_unfolding,[status(thm)],[f2632,f2140])).
% 13.83/3.32 thf(f2140,plain,(
% 13.83/3.32 (cartprodsndin = $true)),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f1222])).
% 13.83/3.32 thf(f2632,plain,(
% 13.83/3.32 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (cartprod @ X4 @ X5)) != $true) | ((in @ (ksnd @ X3) @ X5) = $true) | (cartprodsndin != $true)) )),
% 13.83/3.32 inference(cnf_transformation,[status(thm)],[f1642])).
% 13.83/3.32 thf(f1642,plain,(
% 13.83/3.32 ((cartprodsndin = $true) | (((in @ sK484 @ (cartprod @ sK485 @ sK486)) = $true) & ($true != (in @ (ksnd @ sK484) @ sK486)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (cartprod @ X4 @ X5)) != $true) | ((in @ (ksnd @ X3) @ X5) = $true)) | (cartprodsndin != $true))),
% 13.83/3.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK484,sK485,sK486])],[f1640,f1641])).
% 13.83/3.32 thf(f1641,plain,(
% 13.83/3.32 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X1 @ X2))) & ((in @ (ksnd @ X0) @ X2) != $true)) => (((in @ sK484 @ (cartprod @ sK485 @ sK486)) = $true) & ($true != (in @ (ksnd @ sK484) @ sK486)))),
% 13.83/3.32 introduced(definition,[],[choice_axiom])).
% 13.83/3.32 thf(f1640,plain,(
% 13.83/3.32 ((cartprodsndin = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X1 @ X2))) & ((in @ (ksnd @ X0) @ X2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (cartprod @ X4 @ X5)) != $true) | ((in @ (ksnd @ X3) @ X5) = $true)) | (cartprodsndin != $true))),
% 13.83/3.32 inference(rectify,[status(thm)],[f1639])).
% 13.83/3.32 thf(f1639,plain,(
% 13.83/3.32 ((cartprodsndin = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X1 @ X2))) & ((in @ (ksnd @ X0) @ X2) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (cartprod @ X1 @ X2))) | ((in @ (ksnd @ X0) @ X2) = $true)) | (cartprodsndin != $true))),
% 13.83/3.32 inference(nnf_transformation,[status(thm)],[f673])).
% 13.83/3.32 thf(f673,plain,(
% 13.83/3.32 (cartprodsndin = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (cartprod @ X1 @ X2))) | ((in @ (ksnd @ X0) @ X2) = $true))),
% 13.83/3.32 inference(ennf_transformation,[status(thm)],[f382])).
% 13.83/3.32 thf(f382,plain,(
% 13.83/3.32 (cartprodsndin = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X1 @ X2))) => ((in @ (ksnd @ X0) @ X2) = $true))),
% 13.83/3.32 inference(fool_elimination,[status(thm)],[f381])).
% 13.83/3.32 thf(f381,plain,(
% 13.83/3.32 (cartprodsndin = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X1 @ X2)) => (in @ (ksnd @ X0) @ X2)))),
% 13.83/3.32 inference(rectify,[status(thm)],[f179])).
% 13.83/3.32 thf(f179,axiom,(
% 13.83/3.32 (cartprodsndin = ! [X10 : $i,X3 : $i,X4 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4)))),
% 13.83/3.32 file('/export/starexec/sandbox/tmp/tmp.t6uuIKRcU7/DTF2THF_724.p',cartprodsndin)).
% 13.83/3.32 % SZS output end Proof for DTF2THF_724
% 13.83/3.32 % (927)------------------------------
% 13.83/3.32 % (927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.83/3.32 % (927)Termination reason: Refutation
% 13.83/3.32
% 13.83/3.32 % (927)Memory used [KB]: 10490
% 13.83/3.32 % (927)Time elapsed: 0.497 s
% 13.83/3.32 % (927)Instructions burned: 935 (million)
% 13.83/3.32 % (927)------------------------------
% 13.83/3.32 % (927)------------------------------
% 13.83/3.32 % (832)Success in time 1.737 s
%------------------------------------------------------------------------------