%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU669^1 : 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 : n010.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 8.89s 2.69s
% Output : Refutation 8.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 3189 ( 852 equ; 0 cnn)
% Maximal formula atoms : 187 ( 69 avg)
% Number of connectives : 1896 ( 46 ~; 33 |; 594 &; 458 @)
% ( 4 <=>; 753 =>; 0 <=; 0 <~>)
% Maximal formula depth : 199 ( 33 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 422 ( 418 usr; 198 con; 0-5 aty)
% ( 0 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 199 ( 66 ^; 93 !; 40 ?; 199 :)
% 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_236,type,
sP3: $i > $i > $i > $o > $o ).
thf(func_def_237,type,
sP4: $i > $i > $i > $o ).
thf(func_def_239,type,
sP6: $i > $i > $o ).
thf(func_def_243,type,
sP10: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_244,type,
sP11: $i > $i > $i > $o ).
thf(func_def_245,type,
sP12: $i > $i > $o ).
thf(func_def_246,type,
sP13: $i > $o ).
thf(func_def_247,type,
sP14: $i > $i > $o ).
thf(func_def_248,type,
sP15: $i > $i > $o ).
thf(func_def_249,type,
sP16: $i > $i > $o ).
thf(func_def_252,type,
sP19: $i > $i > $o > $o ).
thf(func_def_256,type,
sP23: ( $i > $i > $o ) > $i > $o ).
thf(func_def_261,type,
sP28: $i > $o ).
thf(func_def_265,type,
sP32: $i > ( $i > $o ) > $o ).
thf(func_def_266,type,
sP33: ( $i > $o ) > $i > $o ).
thf(func_def_277,type,
sP44: ( $i > $o ) > $i > $o ).
thf(func_def_278,type,
sP45: ( $i > $o ) > $i > $o ).
thf(func_def_279,type,
sP46: $i > $i > $o > $o ).
thf(func_def_280,type,
sP47: $i > $i > $i > $o ).
thf(func_def_286,type,
sK53: $i > $o ).
thf(func_def_289,type,
sK56: $i > ( $i > $o ) > $i ).
thf(func_def_305,type,
sK72: $i > $o ).
thf(func_def_306,type,
sK73: ( $i > $o ) > $i ).
thf(func_def_337,type,
sK104: $i > $o ).
thf(func_def_338,type,
sK105: $i > $i ).
thf(func_def_339,type,
sK106: ( $i > $o ) > $i ).
thf(func_def_353,type,
sK120: $i > $o ).
thf(func_def_354,type,
sK121: $i > $o ).
thf(func_def_355,type,
sK122: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_356,type,
sK123: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_357,type,
sK124: $i > $i > $o ).
thf(func_def_387,type,
sK154: $i > $i ).
thf(func_def_389,type,
sK156: $i > $i > $i > $o ).
thf(func_def_401,type,
sK168: $i > $o ).
thf(func_def_409,type,
sK176: $i > $o ).
thf(func_def_412,type,
sK179: $i > ( $i > $o ) > $i ).
thf(func_def_414,type,
sK181: $i > $o ).
thf(func_def_415,type,
sK182: $i > $o ).
thf(func_def_436,type,
sK203: $i > $i > $i ).
thf(func_def_437,type,
sK204: $i > $i > $i ).
thf(func_def_446,type,
sK213: $i > $o ).
thf(func_def_447,type,
sK214: $i > $o ).
thf(func_def_448,type,
sK215: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_449,type,
sK216: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_453,type,
sK220: $i > $o ).
thf(func_def_456,type,
sK223: $i > ( $i > $o ) > $i ).
thf(func_def_470,type,
sK237: $i > $o ).
thf(func_def_477,type,
sK244: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_478,type,
sK245: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_481,type,
sK248: $i > $o ).
thf(func_def_482,type,
sK249: $i > $o ).
thf(func_def_483,type,
sK250: $i > $o ).
thf(func_def_489,type,
sK256: $i > $i > $i ).
thf(func_def_490,type,
sK257: $i > $i > $i ).
thf(func_def_491,type,
sK258: $i > $i > $i ).
thf(func_def_492,type,
sK259: $i > $i > $i ).
thf(func_def_493,type,
sK260: $i > $i > $i ).
thf(func_def_494,type,
sK261: $i > $i > $i ).
thf(func_def_495,type,
sK262: $i > $i > $i ).
thf(func_def_496,type,
sK263: $i > $i > $i > $i ).
thf(func_def_497,type,
sK264: $i > $i ).
thf(func_def_498,type,
sK265: $i > $i ).
thf(func_def_499,type,
sK266: $i > $i ).
thf(func_def_500,type,
sK267: $i > $i ).
thf(func_def_501,type,
sK268: $i > $i > $i ).
thf(func_def_502,type,
sK269: $i > $i > $i ).
thf(func_def_503,type,
sK270: $i > $i > $i ).
thf(func_def_504,type,
sK271: $i > $i > $i > $i ).
thf(func_def_505,type,
sK272: $i > $i > $i > $i ).
thf(func_def_506,type,
sK273: $i > $i ).
thf(func_def_510,type,
sK277: $i > $i > $i ).
thf(func_def_520,type,
sK287: $i > $o ).
thf(func_def_534,type,
sK301: $i > $i > $i > $i ).
thf(func_def_535,type,
sK302: $i > $i > $i > $i ).
thf(func_def_551,type,
sK318: $i > $o ).
thf(func_def_553,type,
sK320: $i > ( $i > $o ) > $i ).
thf(func_def_556,type,
sK323: $i > $o ).
thf(func_def_559,type,
sK326: $i > $i > $i ).
thf(func_def_565,type,
sK332: $i > $o ).
thf(func_def_579,type,
sK346: $i > $o ).
thf(func_def_582,type,
sK349: $i > ( $i > $o ) > $i ).
thf(func_def_591,type,
sK358: $i > $i > $o ).
thf(func_def_592,type,
sK359: ( $i > $i > $o ) > $i > $i ).
thf(func_def_593,type,
sK360: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_594,type,
sK361: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_595,type,
sK362: ( $i > $i > $o ) > $i > $i ).
thf(func_def_596,type,
sK363: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_602,type,
sK369: $i > $i > $i ).
thf(func_def_613,type,
sK380: $i > $o ).
thf(func_def_614,type,
sK381: ( $i > $o ) > $i > $i > $i ).
thf(func_def_622,type,
sK389: $o > $i > $i > $i ).
thf(func_def_629,type,
sK396: $i > $i ).
thf(func_def_634,type,
sK401: $i > $i ).
thf(func_def_635,type,
sK402: $i > $i ).
thf(func_def_644,type,
sK411: $i > $i > $i ).
thf(func_def_659,type,
sK426: $i > $i > $o ).
thf(func_def_666,type,
sK433: $i > $o ).
thf(func_def_668,type,
sK435: $i > ( $i > $o ) > $i ).
thf(func_def_669,type,
sK436: ( $i > $o ) > $i > $i ).
thf(func_def_670,type,
sK437: ( $i > $o ) > $i > $i ).
thf(func_def_671,type,
sK438: $i > ( $i > $o ) > $i ).
thf(func_def_672,type,
sK439: $i > $o ).
thf(func_def_676,type,
sK443: $i > $i > $i ).
thf(func_def_688,type,
sK455: $i > $o ).
thf(func_def_689,type,
sK456: $i > $i ).
thf(func_def_690,type,
sK457: ( $i > $o ) > $i ).
thf(func_def_694,type,
sK461: $i > $i > $i ).
thf(func_def_712,type,
sK479: $i > $o ).
thf(func_def_716,type,
sK483: $i > $o ).
thf(func_def_718,type,
sK485: ( $i > $o ) > $i ).
thf(func_def_719,type,
sK486: ( $i > $o ) > $i ).
thf(func_def_722,type,
sK489: $i > $i > $i ).
thf(func_def_723,type,
sK490: $i > $o ).
thf(func_def_730,type,
sK497: $i > $i > $i ).
thf(func_def_734,type,
sK501: $i > $i ).
thf(func_def_735,type,
sK502: $i > $i > $o ).
thf(func_def_739,type,
sK506: $i > $i ).
thf(func_def_741,type,
sK508: $i > $i ).
thf(func_def_746,type,
sK513: $i > $o ).
thf(func_def_756,type,
sK523: $i > $o ).
thf(func_def_761,type,
sK528: $i > $o ).
thf(func_def_764,type,
sK531: $i > ( $i > $o ) > $i ).
thf(func_def_765,type,
sK532: $i > $o ).
thf(func_def_768,type,
sK535: $i > ( $i > $o ) > $i ).
thf(func_def_779,type,
sK546: $i > $i > $o ).
thf(func_def_784,type,
sK551: ( $i > $o ) > $i > $i ).
thf(func_def_785,type,
sK552: ( $i > $o ) > $i > $i ).
thf(func_def_786,type,
sK553: ( $i > $o ) > $i > $i ).
thf(func_def_788,type,
sK555: $i > $o ).
thf(func_def_789,type,
sK556: $i > $i > $i > $o ).
thf(func_def_796,type,
sK563: $i > $i > $o ).
thf(func_def_800,type,
sK567: $i > $o ).
thf(func_def_801,type,
sK568: ( $i > $o ) > $i > $i ).
thf(func_def_802,type,
sK569: $i > $i ).
thf(func_def_805,type,
sK572: $i > $i ).
thf(func_def_806,type,
sK573: ( $i > $o ) > $i > $i ).
thf(func_def_807,type,
sK574: ( $i > $o ) > $i > $i ).
thf(func_def_808,type,
sK575: $i > ( $i > $o ) > $i ).
thf(func_def_809,type,
sK576: $i > ( $i > $o ) > $i ).
thf(func_def_810,type,
sK577: $i > $i ).
thf(func_def_811,type,
sK578: ( $i > $o ) > $i ).
thf(func_def_812,type,
sK579: ( $i > $o ) > $i > $i ).
thf(func_def_813,type,
sK580: ( $i > $o ) > $i > $i ).
thf(func_def_814,type,
sK581: ( $i > $o ) > $i > $i ).
thf(func_def_815,type,
sK582: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_816,type,
sK583: $i > ( $i > $o ) > $i ).
thf(func_def_817,type,
sK584: ( $i > $o ) > $i ).
thf(func_def_818,type,
sK585: ( $i > $o ) > $i > $i ).
thf(func_def_819,type,
sK586: ( $i > $o ) > $i > $i ).
thf(func_def_820,type,
sK587: ( $i > $o ) > $i ).
thf(func_def_821,type,
sK588: ( $i > $o ) > $i > $i ).
thf(func_def_822,type,
sK589: ( $i > $o ) > $i > $i ).
thf(func_def_823,type,
sK590: ( $i > $o ) > $i ).
thf(func_def_824,type,
sK591: ( $i > $o ) > $i > $i ).
thf(func_def_825,type,
sK592: ( $i > $o ) > $i > $i ).
thf(func_def_826,type,
sK593: ( $i > $o ) > $i > $i ).
thf(func_def_827,type,
sK594: ( $i > $o ) > $i ).
thf(func_def_828,type,
sK595: ( $i > $o ) > $i ).
thf(func_def_830,type,
sK597: $i > ( $i > $o ) > $i ).
thf(func_def_831,type,
sK598: ( $i > $o ) > $i ).
thf(func_def_833,type,
sK600: ( $i > $o ) > $i ).
thf(func_def_834,type,
sK601: $i > $i ).
thf(func_def_835,type,
sK602: $i > $i ).
thf(func_def_836,type,
sK603: $i > $i ).
thf(func_def_840,type,
sK607: ( $i > $o ) > $i > $i ).
thf(func_def_841,type,
sK608: $i > $i ).
thf(func_def_843,type,
sK610: $i > $i ).
thf(func_def_845,type,
sK612: $i > ( $i > $o ) > $i ).
thf(func_def_847,type,
sK614: $i > ( $i > $o ) > $i ).
thf(func_def_848,type,
sK615: ( $i > $o ) > $i ).
thf(func_def_849,type,
sK616: ( $i > $o ) > $i ).
thf(func_def_850,type,
sK617: $i > $i ).
thf(func_def_851,type,
sK618: ( $i > $o ) > $i ).
thf(func_def_852,type,
sK619: ( $i > $o ) > $i > $i ).
thf(func_def_853,type,
sK620: $i > ( $i > $o ) > $i ).
thf(func_def_854,type,
sK621: $i > ( $i > $o ) > $i ).
thf(func_def_855,type,
sK622: ( $i > $o ) > $i ).
thf(func_def_856,type,
sK623: $i > $i ).
thf(func_def_857,type,
sK624: ( $i > $o ) > $i > $i ).
thf(func_def_858,type,
sK625: ( $i > $o ) > $i ).
thf(func_def_859,type,
sK626: ( $i > $o ) > $i ).
thf(func_def_860,type,
sK627: ( $i > $o ) > $i > $i ).
thf(func_def_861,type,
sK628: ( $i > $o ) > $i > $i ).
thf(func_def_862,type,
sK629: $i > ( $i > $o ) > $i ).
thf(func_def_863,type,
sK630: ( $i > $o ) > $i > $i ).
thf(func_def_864,type,
sK631: $i > ( $i > $o ) > $i ).
thf(func_def_865,type,
sK632: $i > ( $i > $o ) > $i ).
thf(func_def_866,type,
sK633: $i > ( $i > $o ) > $i ).
thf(func_def_867,type,
sK634: $i > ( $i > $o ) > $i ).
thf(func_def_869,type,
ph635:
!>[X0: $tType] : X0 ).
thf(func_def_872,type,
sK638: $i > $i > $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_873,type,
sK639: $i > $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(f8021,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f8007,f2483]) ).
thf(f2483,plain,
( ( in @ sK427 @ sK428 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1535]) ).
thf(f1535,plain,
( ( ubforcartprodlem2 = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( binunionEcases = $true )
& ( sepInPowerset = $true )
& ( upairset2IR = $true )
& ( in__Cong = $true )
& ( upairsetIL = $true )
& ( dpsetconstrI = $true )
& ( dsetconstr__Cong = $true )
& ( setminusELneg = $true )
& ( setunionsingleton = $true )
& ( uniqinunit = $true )
& ( binintersectRsub = $true )
& ( replAx = $true )
& ( upairsetIR = $true )
& ( setbeta = $true )
& ( setminusSubset1 = $true )
& ( prop2setE = $true )
& ( setunionAx = $true )
& ( cartprodfstin = $true )
& ( foundationAx = $true )
& ( exuE2 = $true )
& ( subsetemptysetimpeq = $true )
& ( exuE3u = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinAx = $true )
& ( binintersectSubset3 = $true )
& ( ex1I2 = $true )
& ( binintersectSubset2 = $true )
& ( setukpairinjL2 = $true )
& ( exuEu = $true )
& ( descrp = $true )
& ( inPowerset = $true )
& ( setukpairIR = $true )
& ( singletonsubset = $true )
& ( setunionE = $true )
& ( nonemptyImpWitness = $true )
& ( omegaSAx = $true )
& ( symdiffIneg2 = $true )
& ( emptyI = $true )
& ( setunionsingleton2 = $true )
& ( upairsetE = $true )
& ( emptyset__Cong = $true )
& ( powersetI1 = $true )
& ( powersetsubset = $true )
& ( kpairiskpair = $true )
& ( upairsubunion = $true )
& ( cartprodsndin = $true )
& ( ksndpairEq = $true )
& ( notsubsetI = $true )
& ( $true
= ( in @ ( kpair @ sK427 @ sK425 )
@ ( dpsetconstr @ sK428 @ sK424
@ ^ [Y0: $i,Y1: $i] : ( sK426 @ Y0 @ Y1 ) ) ) )
& ( ( in @ sK427 @ sK428 )
!= $true )
& ( dpsetconstrSub = $true )
& ( binintersectEL = $true )
& ( symdiffI2 = $true )
& ( emptyinunitempty = $true )
& ( setoftrueEq = $true )
& ( setukpairinjL = $true )
& ( exuE3e = $true )
& ( setukpairinjL1 = $true )
& ( kpairp = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( emptysetAx = $true )
& ( ubforcartprodlem3 = $true )
& ( setminusSubset2 = $true )
& ( powersetE1 = $true )
& ( exu__Cong = $true )
& ( secondinupair = $true )
& ( powersetE = $true )
& ( subsetE2 = $true )
& ( setunion__Cong = $true )
& ( wellorderingAx = $true )
& ( subsetRefl = $true )
& ( ex1I = $true )
& ( exuE1 = $true )
& ( setextsub = $true )
& ( setadjoinSub = $true )
& ( exuI1 = $true )
& ( setminusERneg = $true )
& ( emptyInPowerset = $true )
& ( setukpairIL = $true )
& ( setadjoinE = $true )
& ( cartprodpairin = $true )
& ( powersetAx = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan1 = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( setadjoinOr = $true )
& ( dpsetconstrERa = $true )
& ( subsetI2 = $true )
& ( emptysetsubset = $true )
& ( subsetTrans = $true )
& ( quantDeMorgan4 = $true )
& ( exuI2 = $true )
& ( kfstsingleton = $true )
& ( setextAx = $true )
& ( setminusLsub = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( subPowSU = $true )
& ( notequalI2 = $true )
& ( notdexE = $true )
& ( singletonsswitch = $true )
& ( binintersectER = $true )
& ( notequalI1 = $true )
& ( sepSubset = $true )
& ( setminusIRneg = $true )
& ( kfstpairEq = $true )
& ( noeltsimpempty = $true )
& ( setunionI = $true )
& ( nonemptyI = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( prop2setI = $true )
& ( setunionE2 = $true )
& ( binintersectSubset1 = $true )
& ( singletoninpowerset = $true )
& ( cartprodfstpairEq = $true )
& ( omegaIndAx = $true )
& ( omega0Ax = $true )
& ( notdallE = $true )
& ( prop2set2propI = $true )
& ( subsetE = $true )
& ( emptysetimpfalse = $true )
& ( setminusEL = $true )
& ( setukpairinjR2 = $true )
& ( eqimpsubset1 = $true )
& ( cartprodsndpairEq = $true )
& ( theprop = $true )
& ( disjointsetsI1 = $true )
& ( singletoninpowunion = $true )
& ( binintersectI = $true )
& ( binunionLsub = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR1 = $true )
& ( binintersectLsub = $true )
& ( binunionRsub = $true )
& ( cartprodmempair = $true )
& ( cartprodmempaircEq = $true )
& ( eqinunit = $true )
& ( emptyE1 = $true )
& ( setOfPairsIsBReln = $true )
& ( dsetconstrER = $true )
& ( ex1E1 = $true )
& ( setukpairinjR12 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI3 = $true )
& ( setadjoinIR = $true )
& ( setminusER = $true )
& ( subsetI1 = $true )
& ( eqimpsubset2 = $true )
& ( binunionIL = $true )
& ( symdiffIneg1 = $true )
& ( setext = $true )
& ( setukpairinjR = $true )
& ( cartprodmempair1 = $true )
& ( setadjoin__Cong = $true )
& ( nonemptyE1 = $true )
& ( singletonsuniq = $true )
& ( powersetI = $true )
& ( upairequniteq = $true )
& ( dsetconstrI = $true )
& ( upairset2E = $true )
& ( symdiffE = $true )
& ( setadjoinIL = $true )
& ( notinemptyset = $true )
& ( vacuousDall = $true )
& ( symdiffI1 = $true )
& ( kpairsurjEq = $true )
& ( binunionIR = $true )
& ( omega__Cong = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR11 = $true )
& ( inCongP = $true )
& ( dsetconstrEL = $true )
& ( cartprodpairsurjEq = $true )
& ( notinsingleton = $true )
& ( setminusILneg = $true )
& ( emptyinPowerset = $true )
& ( setadjoinSub2 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectSubset5 = $true )
& ( singletonprop = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK424,sK425,sK426,sK427,sK428])],[f728,f1534]) ).
thf(f1534,plain,
( ? [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 @ X3 @ X4 ) ) )
=> ( ( $true
= ( in @ ( kpair @ sK427 @ sK425 )
@ ( dpsetconstr @ sK428 @ sK424
@ ^ [Y0: $i,Y1: $i] : ( sK426 @ Y0 @ Y1 ) ) ) )
& ( ( in @ sK427 @ sK428 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f728,plain,
( ( ubforcartprodlem2 = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( binunionEcases = $true )
& ( sepInPowerset = $true )
& ( upairset2IR = $true )
& ( in__Cong = $true )
& ( upairsetIL = $true )
& ( dpsetconstrI = $true )
& ( dsetconstr__Cong = $true )
& ( setminusELneg = $true )
& ( setunionsingleton = $true )
& ( uniqinunit = $true )
& ( binintersectRsub = $true )
& ( replAx = $true )
& ( upairsetIR = $true )
& ( setbeta = $true )
& ( setminusSubset1 = $true )
& ( prop2setE = $true )
& ( setunionAx = $true )
& ( cartprodfstin = $true )
& ( foundationAx = $true )
& ( exuE2 = $true )
& ( subsetemptysetimpeq = $true )
& ( exuE3u = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinAx = $true )
& ( binintersectSubset3 = $true )
& ( ex1I2 = $true )
& ( binintersectSubset2 = $true )
& ( setukpairinjL2 = $true )
& ( exuEu = $true )
& ( descrp = $true )
& ( inPowerset = $true )
& ( setukpairIR = $true )
& ( singletonsubset = $true )
& ( setunionE = $true )
& ( nonemptyImpWitness = $true )
& ( omegaSAx = $true )
& ( symdiffIneg2 = $true )
& ( emptyI = $true )
& ( setunionsingleton2 = $true )
& ( upairsetE = $true )
& ( emptyset__Cong = $true )
& ( powersetI1 = $true )
& ( powersetsubset = $true )
& ( kpairiskpair = $true )
& ( upairsubunion = $true )
& ( cartprodsndin = $true )
& ( ksndpairEq = $true )
& ( notsubsetI = $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 @ X3 @ X4 ) ) )
& ( dpsetconstrSub = $true )
& ( binintersectEL = $true )
& ( symdiffI2 = $true )
& ( emptyinunitempty = $true )
& ( setoftrueEq = $true )
& ( setukpairinjL = $true )
& ( exuE3e = $true )
& ( setukpairinjL1 = $true )
& ( kpairp = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( emptysetAx = $true )
& ( ubforcartprodlem3 = $true )
& ( setminusSubset2 = $true )
& ( powersetE1 = $true )
& ( exu__Cong = $true )
& ( secondinupair = $true )
& ( powersetE = $true )
& ( subsetE2 = $true )
& ( setunion__Cong = $true )
& ( wellorderingAx = $true )
& ( subsetRefl = $true )
& ( ex1I = $true )
& ( exuE1 = $true )
& ( setextsub = $true )
& ( setadjoinSub = $true )
& ( exuI1 = $true )
& ( setminusERneg = $true )
& ( emptyInPowerset = $true )
& ( setukpairIL = $true )
& ( setadjoinE = $true )
& ( cartprodpairin = $true )
& ( powersetAx = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan1 = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( setadjoinOr = $true )
& ( dpsetconstrERa = $true )
& ( subsetI2 = $true )
& ( emptysetsubset = $true )
& ( subsetTrans = $true )
& ( quantDeMorgan4 = $true )
& ( exuI2 = $true )
& ( kfstsingleton = $true )
& ( setextAx = $true )
& ( setminusLsub = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( subPowSU = $true )
& ( notequalI2 = $true )
& ( notdexE = $true )
& ( singletonsswitch = $true )
& ( binintersectER = $true )
& ( notequalI1 = $true )
& ( sepSubset = $true )
& ( setminusIRneg = $true )
& ( kfstpairEq = $true )
& ( noeltsimpempty = $true )
& ( setunionI = $true )
& ( nonemptyI = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( prop2setI = $true )
& ( setunionE2 = $true )
& ( binintersectSubset1 = $true )
& ( singletoninpowerset = $true )
& ( cartprodfstpairEq = $true )
& ( omegaIndAx = $true )
& ( omega0Ax = $true )
& ( notdallE = $true )
& ( prop2set2propI = $true )
& ( subsetE = $true )
& ( emptysetimpfalse = $true )
& ( setminusEL = $true )
& ( setukpairinjR2 = $true )
& ( eqimpsubset1 = $true )
& ( cartprodsndpairEq = $true )
& ( theprop = $true )
& ( disjointsetsI1 = $true )
& ( singletoninpowunion = $true )
& ( binintersectI = $true )
& ( binunionLsub = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR1 = $true )
& ( binintersectLsub = $true )
& ( binunionRsub = $true )
& ( cartprodmempair = $true )
& ( cartprodmempaircEq = $true )
& ( eqinunit = $true )
& ( emptyE1 = $true )
& ( setOfPairsIsBReln = $true )
& ( dsetconstrER = $true )
& ( ex1E1 = $true )
& ( setukpairinjR12 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI3 = $true )
& ( setadjoinIR = $true )
& ( setminusER = $true )
& ( subsetI1 = $true )
& ( eqimpsubset2 = $true )
& ( binunionIL = $true )
& ( symdiffIneg1 = $true )
& ( setext = $true )
& ( setukpairinjR = $true )
& ( cartprodmempair1 = $true )
& ( setadjoin__Cong = $true )
& ( nonemptyE1 = $true )
& ( singletonsuniq = $true )
& ( powersetI = $true )
& ( upairequniteq = $true )
& ( dsetconstrI = $true )
& ( upairset2E = $true )
& ( symdiffE = $true )
& ( setadjoinIL = $true )
& ( notinemptyset = $true )
& ( vacuousDall = $true )
& ( symdiffI1 = $true )
& ( kpairsurjEq = $true )
& ( binunionIR = $true )
& ( omega__Cong = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR11 = $true )
& ( inCongP = $true )
& ( dsetconstrEL = $true )
& ( cartprodpairsurjEq = $true )
& ( notinsingleton = $true )
& ( setminusILneg = $true )
& ( emptyinPowerset = $true )
& ( setadjoinSub2 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectSubset5 = $true )
& ( singletonprop = $true ) ),
inference(flattening,[status(thm)],[f727]) ).
thf(f727,plain,
( ? [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 @ X3 @ X4 ) ) )
& ( 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)],[f474]) ).
thf(f474,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 )
=> ! [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 @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f473]) ).
thf(f473,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
=> ! [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 @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f193]) ).
thf(f193,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
=> ! [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 @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f192]) ).
thf(f192,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
=> ! [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 @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2THF_8088.p',dpsetconstrEL1) ).
thf(f8007,plain,
( ( in @ sK427 @ sK428 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f7991]) ).
thf(f7991,plain,
( ( ( in @ sK427 @ sK428 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3461,f6840]) ).
thf(f6840,plain,
( $true
= ( in @ ( kpair @ sK427 @ sK425 ) @ ( cartprod @ sK428 @ sK424 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6820]) ).
thf(f6820,plain,
( ( $true != $true )
| ( $true
= ( in @ ( kpair @ sK427 @ sK425 ) @ ( cartprod @ sK428 @ sK424 ) ) ) ),
inference(superposition,[status(thm)],[f3413,f3452]) ).
thf(f3452,plain,
( $true
= ( in @ ( kpair @ sK427 @ sK425 )
@ ( dsetconstr @ ( cartprod @ sK428 @ sK424 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK428 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( kpair @ Y1 @ Y2 )
= Y0 )
& ( sK426 @ Y1 @ Y2 )
& ( in @ Y2 @ sK424 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3179]) ).
thf(f3179,plain,
( $true
= ( in @ ( kpair @ sK427 @ sK425 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 ) ) ) ) ) )
@ sK428
@ sK424
@ ^ [Y0: $i,Y1: $i] : ( sK426 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f2484,f2276]) ).
thf(f2276,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] :
( ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f288]) ).
thf(f288,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] :
( ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f287]) ).
thf(f287,plain,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( in @ X5 @ X1 )
& ( X2 @ X4 @ X5 )
& ( ( kpair @ X4 @ X5 )
= X3 ) )
& ( 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] :
( ( in @ X2 @ X4 )
& ( X0 @ X1 @ X2 )
& ( ( kpair @ X1 @ X2 )
= X10 ) )
& ( in @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2THF_8088.p',dpsetconstr) ).
thf(f2484,plain,
( $true
= ( in @ ( kpair @ sK427 @ sK425 )
@ ( dpsetconstr @ sK428 @ sK424
@ ^ [Y0: $i,Y1: $i] : ( sK426 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1535]) ).
thf(f3413,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( in @ X4 @ ( dsetconstr @ X3 @ X5 ) ) )
| ( ( in @ X4 @ X3 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f3412]) ).
thf(f3412,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( ( in @ X4 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3069]) ).
thf(f3069,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( $true != $true )
| ( ( in @ X4 @ X3 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f2194,f2358]) ).
thf(f2358,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f1535]) ).
thf(f2194,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4 @ X3 )
= $true )
| ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f1354]) ).
thf(f1354,plain,
( ( ( dsetconstrEL = $true )
| ( ( $true
!= ( in @ sK322 @ sK321 ) )
& ( $true
= ( in @ sK322
@ ( dsetconstr @ sK321
@ ^ [Y0: $i] : ( sK323 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4 @ X3 )
= $true )
| ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK321,sK322,sK323])],[f1352,f1353]) ).
thf(f1353,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
=> ( ( $true
!= ( in @ sK322 @ sK321 ) )
& ( $true
= ( in @ sK322
@ ( dsetconstr @ sK321
@ ^ [Y0: $i] : ( sK323 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1352,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4 @ X3 )
= $true )
| ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) ) ),
inference(rectify,[status(thm)],[f1351]) ).
thf(f1351,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1 @ X0 ) )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
| ( dsetconstrEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f741]) ).
thf(f741,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1 @ X0 ) )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f246]) ).
thf(f246,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( $true
= ( in @ X1 @ X0 ) ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[status(thm)],[f245]) ).
thf(f245,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( in @ X1 @ X0 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
! [X3: $i,X1: $i,X0: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( in @ X1 @ X3 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2THF_8088.p',dsetconstrEL) ).
thf(f3461,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) )
| ( $true
= ( in @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3016]) ).
thf(f3016,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) )
| ( $true != $true )
| ( $true
= ( in @ X2 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f2129,f2534]) ).
thf(f2534,plain,
cartprodpairmemEL = $true,
inference(cnf_transformation,[status(thm)],[f1535]) ).
thf(f2129,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) )
| ( cartprodpairmemEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f1275]) ).
thf(f1275,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) ) )
| ( cartprodpairmemEL != $true ) )
& ( ( cartprodpairmemEL = $true )
| ( ( $true
!= ( in @ sK280 @ sK278 ) )
& ( $true
= ( in @ ( kpair @ sK280 @ sK279 ) @ ( cartprod @ sK278 @ sK281 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK278,sK279,sK280,sK281])],[f1273,f1274]) ).
thf(f1274,plain,
( ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
& ( $true
= ( in @ ( kpair @ X6 @ X5 ) @ ( cartprod @ X4 @ X7 ) ) ) )
=> ( ( $true
!= ( in @ sK280 @ sK278 ) )
& ( $true
= ( in @ ( kpair @ sK280 @ sK279 ) @ ( cartprod @ sK278 @ sK281 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1273,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) ) )
| ( cartprodpairmemEL != $true ) )
& ( ( cartprodpairmemEL = $true )
| ? [X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( in @ X6 @ X4 )
!= $true )
& ( $true
= ( in @ ( kpair @ X6 @ X5 ) @ ( cartprod @ X4 @ X7 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1272]) ).
thf(f1272,plain,
( ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) ) )
| ( cartprodpairmemEL != $true ) )
& ( ( cartprodpairmemEL = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f660]) ).
thf(f660,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) ) )
<=> ( cartprodpairmemEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f486]) ).
thf(f486,plain,
( ( cartprodpairmemEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( $true
= ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) ) )
=> ( $true
= ( in @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f485]) ).
thf(f485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( in @ ( kpair @ X2 @ X1 ) @ ( cartprod @ X0 @ X3 ) )
=> ( in @ X2 @ X0 ) )
= cartprodpairmemEL ),
inference(rectify,[status(thm)],[f180]) ).
thf(f180,axiom,
! [X3: $i,X2: $i,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ X1 @ X2 ) @ ( cartprod @ X3 @ X4 ) )
=> ( in @ X1 @ X3 ) )
= cartprodpairmemEL ),
file('/export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2THF_8088.p',cartprodpairmemEL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU669^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:30:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU669^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Ordered Pairs - Sets of Pairs
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : (! A:i.! B:i.! phi:i>(i>o).! x:i.! y:i.in (kpair x y)
% 0.30/0.46 % (dpsetconstr A B (^ z,u:i.phi z u)) -> in x A)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC171g [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.38 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 v4.1.0, 1.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 410 ( 191 unt; 218 typ; 191 def)
% 0.30/0.46 % Number of atoms : 1011 ( 285 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 187 ( 5 avg)
% 0.30/0.46 % Number of connectives : 1807 ( 47 ~; 7 |; 38 &;1256 @)
% 0.30/0.46 % ( 14 <=>; 445 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 198 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 221 ( 218 usr; 189 con; 0-3 aty)
% 0.30/0.46 % Number of variables : 581 ( 57 ^; 486 !; 38 ?; 581 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=339
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu_type,type,
% 0.30/0.46 exu: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu,definition,
% 0.30/0.46 ( exu
% 0.30/0.46 = ( ^ [Xphi: $i > $o] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx_type,type,
% 0.30/0.46 setextAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx,definition,
% 0.30/0.46 ( setextAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xx @ B ) )
% 0.30/0.46 => ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx_type,type,
% 0.30/0.46 emptysetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx,definition,
% 0.30/0.46 ( emptysetAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx_type,type,
% 0.30/0.46 setadjoinAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx,definition,
% 0.30/0.46 ( setadjoinAx
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 <=> ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx_type,type,
% 0.30/0.46 powersetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx,definition,
% 0.30/0.46 ( powersetAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 <=> ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx_type,type,
% 0.30/0.46 setunionAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx,definition,
% 0.30/0.46 ( setunionAx
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 <=> ? [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega_type,type,
% 0.30/0.46 omega: $i ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax_type,type,
% 0.30/0.46 omega0Ax: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax,definition,
% 0.30/0.46 ( omega0Ax
% 0.30/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx_type,type,
% 0.30/0.46 omegaSAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx,definition,
% 0.30/0.46 ( omegaSAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx_type,type,
% 0.30/0.46 omegaIndAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx,definition,
% 0.30/0.46 ( omegaIndAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( ( in @ emptyset @ A )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ omega )
% 0.30/0.46 & ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(replAx_type,type,
% 0.30/0.46 replAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(replAx,definition,
% 0.30/0.46 ( replAx
% 0.30/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 <=> ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx_type,type,
% 0.30/0.46 foundationAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx,definition,
% 0.30/0.46 ( foundationAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ( ( in @ B @ A )
% 0.30/0.46 & ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx_type,type,
% 0.30/0.46 wellorderingAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx,definition,
% 0.30/0.46 ( wellorderingAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ? [B: $i] :
% 0.30/0.46 ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) ) )
% 0.30/0.46 & ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xy @ A ) )
% 0.30/0.46 => ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ( ( in @ Xx @ C )
% 0.30/0.46 <=> ( in @ Xy @ C ) ) )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 & ! [C: $i,D: $i] :
% 0.30/0.46 ( ( ( in @ C @ B )
% 0.30/0.46 & ( in @ D @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ D ) )
% 0.30/0.46 | ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ D )
% 0.30/0.46 => ( in @ Xx @ C ) ) ) )
% 0.30/0.46 & ! [C: $i] :
% 0.30/0.46 ( ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.46 => ? [D: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ D @ B )
% 0.30/0.46 & ( in @ Xx @ C )
% 0.30/0.46 & ~ ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ D )
% 0.30/0.46 & ( in @ Xy @ C ) )
% 0.30/0.46 & ! [E: $i] :
% 0.30/0.46 ( ( in @ E @ B )
% 0.30/0.46 => ( ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ E )
% 0.30/0.46 => ( in @ Xy @ D ) )
% 0.30/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr_type,type,
% 0.30/0.46 descr: ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(descrp_type,type,
% 0.30/0.46 descrp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descrp,definition,
% 0.30/0.46 ( descrp
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( Xphi
% 0.30/0.46 @ ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI_type,type,
% 0.30/0.46 dsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI,definition,
% 0.30/0.46 ( dsetconstrI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL_type,type,
% 0.30/0.46 dsetconstrEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL,definition,
% 0.30/0.46 ( dsetconstrEL
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER_type,type,
% 0.30/0.46 dsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER,definition,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1_type,type,
% 0.30/0.46 exuE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1,definition,
% 0.30/0.46 ( exuE1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set_type,type,
% 0.30/0.46 prop2set: $o > $i ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE_type,type,
% 0.30/0.46 prop2setE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE,definition,
% 0.30/0.46 ( prop2setE
% 0.30/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE_type,type,
% 0.30/0.46 emptysetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE,definition,
% 0.30/0.46 ( emptysetE
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse_type,type,
% 0.30/0.46 emptysetimpfalse: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse,definition,
% 0.30/0.46 ( emptysetimpfalse
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => $false ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset_type,type,
% 0.30/0.46 notinemptyset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset,definition,
% 0.30/0.46 ( notinemptyset
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e_type,type,
% 0.30/0.46 exuE3e: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e,definition,
% 0.30/0.46 ( exuE3e
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setext_type,type,
% 0.30/0.46 setext: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setext,definition,
% 0.30/0.46 ( setext
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI_type,type,
% 0.30/0.46 emptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI,definition,
% 0.30/0.46 ( emptyI
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty_type,type,
% 0.30/0.46 noeltsimpempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty,definition,
% 0.30/0.46 ( noeltsimpempty
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta_type,type,
% 0.30/0.46 setbeta: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta,definition,
% 0.30/0.46 ( setbeta
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty_type,type,
% 0.30/0.46 nonempty: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty,definition,
% 0.30/0.46 ( nonempty
% 0.30/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1_type,type,
% 0.30/0.46 nonemptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1,definition,
% 0.30/0.46 ( nonemptyE1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI_type,type,
% 0.30/0.46 nonemptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI,definition,
% 0.30/0.46 ( nonemptyI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( nonempty
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1_type,type,
% 0.30/0.46 nonemptyI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1,definition,
% 0.30/0.46 ( nonemptyI1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL_type,type,
% 0.30/0.46 setadjoinIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL,definition,
% 0.30/0.46 ( setadjoinIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty_type,type,
% 0.30/0.46 emptyinunitempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty,definition,
% 0.30/0.46 ( emptyinunitempty
% 0.30/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIR_type,type,
% 0.30/0.46 setadjoinIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIR,definition,
% 0.30/0.46 ( setadjoinIR
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinE_type,type,
% 0.30/0.46 setadjoinE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinE,definition,
% 0.30/0.46 ( setadjoinE
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ( ( Xy = Xx )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => ( ( ( in @ Xy @ A )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinOr_type,type,
% 0.30/0.46 setadjoinOr: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinOr,definition,
% 0.30/0.46 ( setadjoinOr
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 => ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setoftrueEq_type,type,
% 0.30/0.46 setoftrueEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setoftrueEq,definition,
% 0.30/0.46 ( setoftrueEq
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : $true )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI_type,type,
% 0.30/0.46 powersetI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI,definition,
% 0.30/0.46 ( powersetI
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinPowerset_type,type,
% 0.30/0.46 emptyinPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinPowerset,definition,
% 0.30/0.46 ( emptyinPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyInPowerset_type,type,
% 0.30/0.46 emptyInPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyInPowerset,definition,
% 0.30/0.46 ( emptyInPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE_type,type,
% 0.30/0.46 powersetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE,definition,
% 0.30/0.46 ( powersetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionI_type,type,
% 0.30/0.46 setunionI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionI,definition,
% 0.30/0.46 ( setunionI
% 0.30/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( ( in @ B @ A )
% 0.30/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE_type,type,
% 0.30/0.46 setunionE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE,definition,
% 0.30/0.46 ( setunionE
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ! [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( ( in @ B @ A )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subPowSU_type,type,
% 0.30/0.46 subPowSU: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subPowSU,definition,
% 0.30/0.46 ( subPowSU
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE2_type,type,
% 0.30/0.46 exuE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE2,definition,
% 0.30/0.46 ( exuE2
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyImpWitness_type,type,
% 0.30/0.46 nonemptyImpWitness: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyImpWitness,definition,
% 0.30/0.46 ( nonemptyImpWitness
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & $true ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit_type,type,
% 0.30/0.46 uniqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit,definition,
% 0.30/0.46 ( uniqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinsingleton_type,type,
% 0.30/0.46 notinsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinsingleton,definition,
% 0.30/0.46 ( notinsingleton
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx != Xy )
% 0.30/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit_type,type,
% 0.30/0.46 eqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit,definition,
% 0.30/0.46 ( eqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsswitch_type,type,
% 0.30/0.46 singletonsswitch: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsswitch,definition,
% 0.30/0.46 ( singletonsswitch
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetE_type,type,
% 0.30/0.46 upairsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetE,definition,
% 0.30/0.46 ( upairsetE
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.46 => ( ( Xz = Xx )
% 0.30/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIL_type,type,
% 0.30/0.46 upairsetIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIL,definition,
% 0.30/0.46 ( upairsetIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIR_type,type,
% 0.30/0.46 upairsetIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIR,definition,
% 0.30/0.46 ( upairsetIR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyE1_type,type,
% 0.30/0.46 emptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyE1,definition,
% 0.30/0.46 ( emptyE1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ( ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = emptyset )
% 0.30/0.46 => $false ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall_type,type,
% 0.30/0.46 vacuousDall: $o ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall,definition,
% 0.30/0.46 ( vacuousDall
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan1_type,type,
% 0.30/0.46 quantDeMorgan1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan1,definition,
% 0.30/0.46 ( quantDeMorgan1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan2_type,type,
% 0.30/0.46 quantDeMorgan2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan2,definition,
% 0.30/0.46 ( quantDeMorgan2
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) )
% 0.30/0.46 => ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan3_type,type,
% 0.30/0.46 quantDeMorgan3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan3,definition,
% 0.30/0.46 ( quantDeMorgan3
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan4_type,type,
% 0.30/0.46 quantDeMorgan4: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan4,definition,
% 0.30/0.46 ( quantDeMorgan4
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) )
% 0.30/0.46 => ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setI_type,type,
% 0.30/0.46 prop2setI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setI,definition,
% 0.30/0.46 ( prop2setI
% 0.30/0.46 = ( ! [Xphi: $o] :
% 0.30/0.46 ( Xphi
% 0.30/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(set2prop_type,type,
% 0.30/0.46 set2prop: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set2propI_type,type,
% 0.30/0.46 prop2set2propI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set2propI,definition,
% 0.30/0.46 ( prop2set2propI
% 0.30/0.46 = ( ! [Xphi: $o] :
% 0.30/0.46 ( Xphi
% 0.30/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notdexE_type,type,
% 0.30/0.46 notdexE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notdexE,definition,
% 0.30/0.46 ( notdexE
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notdallE_type,type,
% 0.30/0.46 notdallE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notdallE,definition,
% 0.30/0.46 ( notdallE
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI1_type,type,
% 0.30/0.46 exuI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI1,definition,
% 0.30/0.46 ( exuI1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI3_type,type,
% 0.30/0.46 exuI3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI3,definition,
% 0.30/0.46 ( exuI3
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.30/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI2_type,type,
% 0.30/0.46 exuI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI2,definition,
% 0.30/0.46 ( exuI2
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 <=> ( Xy = Xx ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(inCongP_type,type,
% 0.30/0.46 inCongP: $o ).
% 0.30/0.46
% 0.30/0.46 thf(inCongP,definition,
% 0.30/0.46 ( inCongP
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong_type,type,
% 0.30/0.46 in__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong,definition,
% 0.30/0.46 ( in__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3u_type,type,
% 0.30/0.46 exuE3u: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3u,definition,
% 0.30/0.46 ( exuE3u
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exu__Cong_type,type,
% 0.30/0.46 exu__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu__Cong,definition,
% 0.30/0.46 ( exu__Cong
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 <=> ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset__Cong_type,type,
% 0.30/0.46 emptyset__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset__Cong,definition,
% 0.30/0.46 ( emptyset__Cong
% 0.30/0.46 = ( emptyset = emptyset ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin__Cong_type,type,
% 0.30/0.46 setadjoin__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin__Cong,definition,
% 0.30/0.46 ( setadjoin__Cong
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ! [Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( Xz = Xu )
% 0.30/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.30/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset__Cong_type,type,
% 0.30/0.46 powerset__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powerset__Cong,definition,
% 0.30/0.46 ( powerset__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( powerset @ A )
% 0.30/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion__Cong_type,type,
% 0.30/0.46 setunion__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunion__Cong,definition,
% 0.30/0.46 ( setunion__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( setunion @ A )
% 0.30/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega__Cong_type,type,
% 0.30/0.46 omega__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega__Cong,definition,
% 0.30/0.46 ( omega__Cong
% 0.30/0.46 = ( omega = omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuEu_type,type,
% 0.30/0.46 exuEu: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuEu,definition,
% 0.30/0.46 ( exuEu
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr__Cong_type,type,
% 0.30/0.46 descr__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descr__Cong,definition,
% 0.30/0.46 ( descr__Cong
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.30/0.46 => ( ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr__Cong_type,type,
% 0.30/0.46 dsetconstr__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr__Cong,definition,
% 0.30/0.46 ( dsetconstr__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.30/0.46 => ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = ( dsetconstr @ B
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subset_type,type,
% 0.30/0.46 subset: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(disjoint_type,type,
% 0.30/0.46 disjoint: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setsmeet_type,type,
% 0.30/0.46 setsmeet: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1_type,type,
% 0.30/0.46 subsetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1,definition,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset2_type,type,
% 0.30/0.46 eqimpsubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset2,definition,
% 0.30/0.46 ( eqimpsubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset1_type,type,
% 0.30/0.46 eqimpsubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset1,definition,
% 0.30/0.46 ( eqimpsubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI2_type,type,
% 0.30/0.46 subsetI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI2,definition,
% 0.30/0.46 ( subsetI2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetsubset_type,type,
% 0.30/0.46 emptysetsubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetsubset,definition,
% 0.30/0.46 ( emptysetsubset
% 0.30/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE_type,type,
% 0.30/0.46 subsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE,definition,
% 0.30/0.46 ( subsetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE2_type,type,
% 0.30/0.46 subsetE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE2,definition,
% 0.30/0.46 ( subsetE2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notsubsetI_type,type,
% 0.30/0.46 notsubsetI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notsubsetI,definition,
% 0.30/0.46 ( notsubsetI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI1_type,type,
% 0.30/0.46 notequalI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI1,definition,
% 0.30/0.46 ( notequalI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ~ ( subset @ A @ B )
% 0.30/0.46 => ( A != B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI2_type,type,
% 0.30/0.46 notequalI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI2,definition,
% 0.30/0.46 ( notequalI2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( A != B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetRefl_type,type,
% 0.30/0.46 subsetRefl: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetRefl,definition,
% 0.30/0.46 ( subsetRefl
% 0.30/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetTrans_type,type,
% 0.30/0.46 subsetTrans: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetTrans,definition,
% 0.30/0.46 ( subsetTrans
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( subset @ B @ C )
% 0.30/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub_type,type,
% 0.30/0.46 setadjoinSub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub,definition,
% 0.30/0.46 ( setadjoinSub
% 0.30/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub2_type,type,
% 0.30/0.46 setadjoinSub2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub2,definition,
% 0.30/0.46 ( setadjoinSub2
% 0.30/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subset2powerset_type,type,
% 0.30/0.46 subset2powerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subset2powerset,definition,
% 0.30/0.46 ( subset2powerset
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextsub_type,type,
% 0.30/0.46 setextsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextsub,definition,
% 0.30/0.46 ( setextsub
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( subset @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetemptysetimpeq_type,type,
% 0.30/0.46 subsetemptysetimpeq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetemptysetimpeq,definition,
% 0.30/0.46 ( subsetemptysetimpeq
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( subset @ A @ emptyset )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI1_type,type,
% 0.30/0.46 powersetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI1,definition,
% 0.30/0.46 ( powersetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ B @ A )
% 0.30/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE1_type,type,
% 0.30/0.46 powersetE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE1,definition,
% 0.30/0.46 ( powersetE1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(inPowerset_type,type,
% 0.30/0.46 inPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(inPowerset,definition,
% 0.30/0.46 ( inPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetsubset_type,type,
% 0.30/0.46 powersetsubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetsubset,definition,
% 0.30/0.46 ( powersetsubset
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sepInPowerset_type,type,
% 0.30/0.46 sepInPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(sepInPowerset,definition,
% 0.30/0.46 ( sepInPowerset
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( in
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sepSubset_type,type,
% 0.30/0.46 sepSubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(sepSubset,definition,
% 0.30/0.46 ( sepSubset
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( subset
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunion_type,type,
% 0.30/0.46 binunion: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIL_type,type,
% 0.30/0.46 binunionIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIL,definition,
% 0.30/0.46 ( binunionIL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2IR_type,type,
% 0.30/0.46 upairset2IR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2IR,definition,
% 0.30/0.46 ( upairset2IR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIR_type,type,
% 0.30/0.46 binunionIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIR,definition,
% 0.30/0.46 ( binunionIR
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionEcases_type,type,
% 0.30/0.46 binunionEcases: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionEcases,definition,
% 0.30/0.46 ( binunionEcases
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.30/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.46 => ( ( ( in @ Xx @ A )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => ( ( ( in @ Xx @ B )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionE_type,type,
% 0.30/0.46 binunionE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionE,definition,
% 0.30/0.46 ( binunionE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionLsub_type,type,
% 0.30/0.46 binunionLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionLsub,definition,
% 0.30/0.46 ( binunionLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionRsub_type,type,
% 0.30/0.46 binunionRsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionRsub,definition,
% 0.30/0.46 ( binunionRsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect_type,type,
% 0.30/0.46 binintersect: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI_type,type,
% 0.30/0.46 binintersectI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI,definition,
% 0.30/0.46 ( binintersectI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset5_type,type,
% 0.30/0.46 binintersectSubset5: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset5,definition,
% 0.30/0.46 ( binintersectSubset5
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( subset @ C @ A )
% 0.30/0.46 => ( ( subset @ C @ B )
% 0.30/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL_type,type,
% 0.30/0.46 binintersectEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL,definition,
% 0.30/0.46 ( binintersectEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub_type,type,
% 0.30/0.46 binintersectLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub,definition,
% 0.30/0.46 ( binintersectLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset2_type,type,
% 0.30/0.46 binintersectSubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset2,definition,
% 0.30/0.46 ( binintersectSubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset3_type,type,
% 0.30/0.46 binintersectSubset3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset3,definition,
% 0.30/0.46 ( binintersectSubset3
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( binintersect @ A @ B )
% 0.30/0.46 = B )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER_type,type,
% 0.30/0.46 binintersectER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER,definition,
% 0.30/0.46 ( binintersectER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(disjointsetsI1_type,type,
% 0.30/0.46 disjointsetsI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(disjointsetsI1,definition,
% 0.30/0.46 ( disjointsetsI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xx @ B ) )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectRsub_type,type,
% 0.30/0.46 binintersectRsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectRsub,definition,
% 0.30/0.46 ( binintersectRsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset4_type,type,
% 0.30/0.46 binintersectSubset4: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset4,definition,
% 0.30/0.46 ( binintersectSubset4
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ B @ A )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset1_type,type,
% 0.30/0.46 binintersectSubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset1,definition,
% 0.30/0.46 ( binintersectSubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( binintersect @ A @ B )
% 0.30/0.46 = A )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(bs114d_type,type,
% 0.30/0.46 bs114d: $o ).
% 0.30/0.46
% 0.30/0.46 thf(bs114d,definition,
% 0.30/0.46 ( bs114d
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.30/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(regular_type,type,
% 0.30/0.46 regular: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminus_type,type,
% 0.30/0.46 setminus: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setminusI_type,type,
% 0.30/0.46 setminusI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusI,definition,
% 0.30/0.46 ( setminusI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusEL_type,type,
% 0.30/0.46 setminusEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusEL,definition,
% 0.30/0.46 ( setminusEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER_type,type,
% 0.30/0.46 setminusER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER,definition,
% 0.30/0.46 ( setminusER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset2_type,type,
% 0.30/0.46 setminusSubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset2,definition,
% 0.30/0.46 ( setminusSubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( setminus @ A @ B )
% 0.30/0.46 = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusERneg_type,type,
% 0.30/0.46 setminusERneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusERneg,definition,
% 0.30/0.46 ( setminusERneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusELneg_type,type,
% 0.30/0.46 setminusELneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusELneg,definition,
% 0.30/0.46 ( setminusELneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusILneg_type,type,
% 0.30/0.46 setminusILneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusILneg,definition,
% 0.30/0.46 ( setminusILneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusIRneg_type,type,
% 0.30/0.46 setminusIRneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusIRneg,definition,
% 0.30/0.46 ( setminusIRneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusLsub_type,type,
% 0.30/0.46 setminusLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusLsub,definition,
% 0.30/0.46 ( setminusLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset1_type,type,
% 0.30/0.46 setminusSubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset1,definition,
% 0.30/0.46 ( setminusSubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( setminus @ A @ B )
% 0.30/0.46 = emptyset )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiff_type,type,
% 0.30/0.46 symdiff: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffE_type,type,
% 0.30/0.46 symdiffE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffE,definition,
% 0.30/0.46 ( symdiffE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI1_type,type,
% 0.30/0.46 symdiffI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI1,definition,
% 0.30/0.46 ( symdiffI1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI2_type,type,
% 0.30/0.46 symdiffI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI2,definition,
% 0.30/0.46 ( symdiffI2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg1_type,type,
% 0.30/0.46 symdiffIneg1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg1,definition,
% 0.30/0.46 ( symdiffIneg1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg2_type,type,
% 0.30/0.46 symdiffIneg2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg2,definition,
% 0.30/0.46 ( symdiffIneg2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(iskpair_type,type,
% 0.30/0.46 iskpair: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(secondinupair_type,type,
% 0.30/0.46 secondinupair: $o ).
% 0.30/0.46
% 0.30/0.46 thf(secondinupair,definition,
% 0.30/0.46 ( secondinupair
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairIL_type,type,
% 0.30/0.46 setukpairIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairIL,definition,
% 0.30/0.46 ( setukpairIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairIR_type,type,
% 0.30/0.46 setukpairIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairIR,definition,
% 0.30/0.46 ( setukpairIR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpairiskpair_type,type,
% 0.30/0.46 kpairiskpair: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kpairiskpair,definition,
% 0.30/0.46 ( kpairiskpair
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpair_type,type,
% 0.30/0.46 kpair: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(kpairp_type,type,
% 0.30/0.46 kpairp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kpairp,definition,
% 0.30/0.46 ( kpairp
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprod_type,type,
% 0.30/0.46 cartprod: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsubset_type,type,
% 0.30/0.46 singletonsubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsubset,definition,
% 0.30/0.46 ( singletonsubset
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletoninpowerset_type,type,
% 0.30/0.46 singletoninpowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletoninpowerset,definition,
% 0.30/0.46 ( singletoninpowerset
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletoninpowunion_type,type,
% 0.30/0.46 singletoninpowunion: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletoninpowunion,definition,
% 0.30/0.46 ( singletoninpowunion
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2E_type,type,
% 0.30/0.46 upairset2E: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2E,definition,
% 0.30/0.46 ( upairset2E
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.46 => ( ( Xz = Xx )
% 0.30/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsubunion_type,type,
% 0.30/0.46 upairsubunion: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsubunion,definition,
% 0.30/0.46 ( upairsubunion
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairinpowunion_type,type,
% 0.30/0.46 upairinpowunion: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairinpowunion,definition,
% 0.30/0.46 ( upairinpowunion
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem1_type,type,
% 0.30/0.46 ubforcartprodlem1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem1,definition,
% 0.30/0.46 ( ubforcartprodlem1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem2_type,type,
% 0.30/0.46 ubforcartprodlem2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem2,definition,
% 0.30/0.46 ( ubforcartprodlem2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem3_type,type,
% 0.30/0.46 ubforcartprodlem3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem3,definition,
% 0.30/0.46 ( ubforcartprodlem3
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairin_type,type,
% 0.30/0.46 cartprodpairin: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairin,definition,
% 0.30/0.46 ( cartprodpairin
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempair1_type,type,
% 0.30/0.46 cartprodmempair1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempair1,definition,
% 0.30/0.46 ( cartprodmempair1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 & ( Xu
% 0.30/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempair_type,type,
% 0.30/0.46 cartprodmempair: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempair,definition,
% 0.30/0.46 ( cartprodmempair
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE2_type,type,
% 0.30/0.46 setunionE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE2,definition,
% 0.30/0.46 ( setunionE2
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 => ? [X: $i] :
% 0.30/0.46 ( ( in @ X @ A )
% 0.30/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton1_type,type,
% 0.30/0.46 setunionsingleton1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton1,definition,
% 0.30/0.46 ( setunionsingleton1
% 0.30/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton2_type,type,
% 0.30/0.46 setunionsingleton2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton2,definition,
% 0.30/0.46 ( setunionsingleton2
% 0.30/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton_type,type,
% 0.30/0.46 setunionsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton,definition,
% 0.30/0.46 ( setunionsingleton
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.30/0.46 = Xx ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singleton_type,type,
% 0.30/0.46 singleton: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(singleton,definition,
% 0.30/0.46 ( singleton
% 0.30/0.46 = ( ^ [A: $i] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( A
% 0.30/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletonprop_type,type,
% 0.30/0.46 singletonprop: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonprop,definition,
% 0.30/0.46 ( singletonprop
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) )
% 0.30/0.46 => ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ( singleton
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ex1_type,type,
% 0.30/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1,definition,
% 0.30/0.46 ( ex1
% 0.30/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( singleton
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ex1E1_type,type,
% 0.30/0.46 ex1E1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1E1,definition,
% 0.30/0.46 ( ex1E1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ( ex1 @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ex1I_type,type,
% 0.30/0.46 ex1I: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1I,definition,
% 0.30/0.46 ( ex1I
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xy = Xx ) ) )
% 0.30/0.46 => ( ex1 @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ex1I2_type,type,
% 0.30/0.46 ex1I2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1I2,definition,
% 0.30/0.46 ( ex1I2
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) )
% 0.30/0.46 => ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ( ex1 @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsuniq_type,type,
% 0.30/0.46 singletonsuniq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsuniq,definition,
% 0.30/0.46 ( singletonsuniq
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.30/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(atmost1p_type,type,
% 0.30/0.46 atmost1p: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(atleast2p_type,type,
% 0.30/0.46 atleast2p: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(atmost2p_type,type,
% 0.30/0.46 atmost2p: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetp_type,type,
% 0.30/0.46 upairsetp: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL1_type,type,
% 0.30/0.46 setukpairinjL1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL1,definition,
% 0.30/0.46 ( setukpairinjL1
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kfstsingleton_type,type,
% 0.30/0.46 kfstsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kfstsingleton,definition,
% 0.30/0.46 ( kfstsingleton
% 0.30/0.46 = ( ! [Xu: $i] :
% 0.30/0.46 ( ( iskpair @ Xu )
% 0.30/0.46 => ( singleton
% 0.30/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(theprop_type,type,
% 0.30/0.46 theprop: $o ).
% 0.30/0.46
% 0.30/0.46 thf(theprop,definition,
% 0.30/0.46 ( theprop
% 0.30/0.46 = ( ! [X: $i] :
% 0.30/0.46 ( ( singleton @ X )
% 0.30/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kfst_type,type,
% 0.30/0.46 kfst: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(kfstpairEq_type,type,
% 0.30/0.46 kfstpairEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kfstpairEq,definition,
% 0.30/0.46 ( kfstpairEq
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xx ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodfstin_type,type,
% 0.30/0.46 cartprodfstin: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodfstin,definition,
% 0.30/0.46 ( cartprodfstin
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL2_type,type,
% 0.30/0.46 setukpairinjL2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL2,definition,
% 0.30/0.46 ( setukpairinjL2
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL_type,type,
% 0.30/0.46 setukpairinjL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL,definition,
% 0.30/0.46 ( setukpairinjL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.30/0.46 = ( kpair @ Xz @ Xu ) )
% 0.30/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR11_type,type,
% 0.30/0.46 setukpairinjR11: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR11,definition,
% 0.30/0.46 ( setukpairinjR11
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR12_type,type,
% 0.30/0.46 setukpairinjR12: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR12,definition,
% 0.30/0.46 ( setukpairinjR12
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR1_type,type,
% 0.30/0.46 setukpairinjR1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR1,definition,
% 0.30/0.46 ( setukpairinjR1
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( ( Xz = Xu )
% 0.30/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairequniteq_type,type,
% 0.30/0.46 upairequniteq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairequniteq,definition,
% 0.30/0.46 ( upairequniteq
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR2_type,type,
% 0.30/0.46 setukpairinjR2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR2,definition,
% 0.30/0.46 ( setukpairinjR2
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR_type,type,
% 0.30/0.46 setukpairinjR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR,definition,
% 0.30/0.46 ( setukpairinjR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.30/0.46 = ( kpair @ Xz @ Xu ) )
% 0.30/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ksndsingleton_type,type,
% 0.30/0.46 ksndsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ksndsingleton,definition,
% 0.30/0.46 ( ksndsingleton
% 0.30/0.46 = ( ! [Xu: $i] :
% 0.30/0.46 ( ( iskpair @ Xu )
% 0.30/0.46 => ( singleton
% 0.30/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.46 @ ^ [Xx: $i] :
% 0.30/0.46 ( Xu
% 0.30/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ksnd_type,type,
% 0.30/0.46 ksnd: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(ksndpairEq_type,type,
% 0.30/0.46 ksndpairEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ksndpairEq,definition,
% 0.30/0.46 ( ksndpairEq
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xy ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpairsurjEq_type,type,
% 0.30/0.46 kpairsurjEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kpairsurjEq,definition,
% 0.30/0.46 ( kpairsurjEq
% 0.30/0.46 = ( ! [Xu: $i] :
% 0.30/0.46 ( ( iskpair @ Xu )
% 0.30/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.30/0.46 = Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodsndin_type,type,
% 0.30/0.46 cartprodsndin: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodsndin,definition,
% 0.30/0.46 ( cartprodsndin
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairmemEL_type,type,
% 0.30/0.46 cartprodpairmemEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairmemEL,definition,
% 0.30/0.46 ( cartprodpairmemEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairmemER_type,type,
% 0.30/0.46 cartprodpairmemER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairmemER,definition,
% 0.30/0.46 ( cartprodpairmemER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempaircEq_type,type,
% 0.30/0.46 cartprodmempaircEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempaircEq,definition,
% 0.30/0.46 ( cartprodmempaircEq
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( kpair @ Xx @ Xy )
% 0.30/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodfstpairEq_type,type,
% 0.30/0.46 cartprodfstpairEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodfstpairEq,definition,
% 0.30/0.46 ( cartprodfstpairEq
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodsndpairEq_type,type,
% 0.30/0.46 cartprodsndpairEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodsndpairEq,definition,
% 0.30/0.46 ( cartprodsndpairEq
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairsurjEq_type,type,
% 0.30/0.46 cartprodpairsurjEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairsurjEq,definition,
% 0.30/0.46 ( cartprodpairsurjEq
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.30/0.46 = Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(breln_type,type,
% 0.30/0.46 breln: $i > $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(breln,definition,
% 0.30/0.46 ( breln
% 0.30/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstr_type,type,
% 0.30/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstr,definition,
% 0.30/0.46 ( dpsetconstr
% 0.30/0.46 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.46 ( dsetconstr @ ( cartprod @ A @ B )
% 0.30/0.46 @ ^ [Xu: $i] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 & ( Xphi @ Xx @ Xy )
% 0.30/0.46 & ( Xu
% 0.30/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrI_type,type,
% 0.30/0.46 dpsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrI,definition,
% 0.30/0.46 ( dpsetconstrI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrSub_type,type,
% 0.30/0.46 dpsetconstrSub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrSub,definition,
% 0.30/0.46 ( dpsetconstrSub
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.46 ( subset
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.30/0.46 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setOfPairsIsBReln_type,type,
% 0.30/0.46 setOfPairsIsBReln: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setOfPairsIsBReln,definition,
% 0.30/0.46 ( setOfPairsIsBReln
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.46 ( breln @ A @ B
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrERa_type,type,
% 0.30/0.46 dpsetconstrERa: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrERa,definition,
% 0.30/0.46 ( dpsetconstrERa
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrEL1,conjecture,
% 0.30/0.46 ( setextAx
% 0.30/0.46 => ( emptysetAx
% 0.30/0.46 => ( setadjoinAx
% 0.30/0.46 => ( powersetAx
% 0.30/0.46 => ( setunionAx
% 0.30/0.46 => ( omega0Ax
% 0.30/0.46 => ( omegaSAx
% 0.30/0.46 => ( omegaIndAx
% 0.30/0.46 => ( replAx
% 0.30/0.46 => ( foundationAx
% 0.30/0.46 => ( wellorderingAx
% 0.30/0.46 => ( descrp
% 0.30/0.46 => ( dsetconstrI
% 0.30/0.46 => ( dsetconstrEL
% 0.30/0.46 => ( dsetconstrER
% 0.30/0.46 => ( exuE1
% 0.30/0.46 => ( prop2setE
% 0.30/0.46 => ( emptysetE
% 0.30/0.46 => ( emptysetimpfalse
% 0.30/0.46 => ( notinemptyset
% 0.30/0.46 => ( exuE3e
% 0.30/0.46 => ( setext
% 0.30/0.46 => ( emptyI
% 0.30/0.46 => ( noeltsimpempty
% 0.30/0.46 => ( setbeta
% 0.30/0.46 => ( nonemptyE1
% 0.30/0.46 => ( nonemptyI
% 0.30/0.46 => ( nonemptyI1
% 0.30/0.46 => ( setadjoinIL
% 0.30/0.46 => ( emptyinunitempty
% 0.30/0.46 => ( setadjoinIR
% 0.30/0.46 => ( setadjoinE
% 0.30/0.46 => ( setadjoinOr
% 0.30/0.46 => ( setoftrueEq
% 0.30/0.46 => ( powersetI
% 0.30/0.46 => ( emptyinPowerset
% 0.30/0.46 => ( emptyInPowerset
% 0.30/0.46 => ( powersetE
% 0.30/0.46 => ( setunionI
% 0.30/0.46 => ( setunionE
% 0.30/0.46 => ( subPowSU
% 0.30/0.46 => ( exuE2
% 0.30/0.46 => ( nonemptyImpWitness
% 0.30/0.46 => ( uniqinunit
% 0.30/0.46 => ( notinsingleton
% 0.30/0.46 => ( eqinunit
% 0.30/0.46 => ( singletonsswitch
% 0.30/0.46 => ( upairsetE
% 0.30/0.46 => ( upairsetIL
% 0.30/0.46 => ( upairsetIR
% 0.30/0.46 => ( emptyE1
% 0.30/0.46 => ( vacuousDall
% 0.30/0.46 => ( quantDeMorgan1
% 0.30/0.46 => ( quantDeMorgan2
% 0.30/0.46 => ( quantDeMorgan3
% 0.30/0.46 => ( quantDeMorgan4
% 0.30/0.46 => ( prop2setI
% 0.30/0.46 => ( prop2set2propI
% 0.30/0.46 => ( notdexE
% 0.30/0.46 => ( notdallE
% 0.30/0.46 => ( exuI1
% 0.30/0.46 => ( exuI3
% 0.30/0.46 => ( exuI2
% 0.30/0.46 => ( inCongP
% 0.30/0.46 => ( in__Cong
% 0.30/0.46 => ( exuE3u
% 0.30/0.46 => ( exu__Cong
% 0.30/0.46 => ( emptyset__Cong
% 0.30/0.46 => ( setadjoin__Cong
% 0.30/0.46 => ( powerset__Cong
% 0.30/0.46 => ( setunion__Cong
% 0.30/0.46 => ( omega__Cong
% 0.30/0.46 => ( exuEu
% 0.30/0.46 => ( descr__Cong
% 0.30/0.46 => ( dsetconstr__Cong
% 0.30/0.46 => ( subsetI1
% 0.30/0.46 => ( eqimpsubset2
% 0.30/0.46 => ( eqimpsubset1
% 0.30/0.46 => ( subsetI2
% 0.30/0.46 => ( emptysetsubset
% 0.30/0.46 => ( subsetE
% 0.30/0.46 => ( subsetE2
% 0.30/0.46 => ( notsubsetI
% 0.30/0.46 => ( notequalI1
% 0.30/0.46 => ( notequalI2
% 0.30/0.46 => ( subsetRefl
% 0.30/0.46 => ( subsetTrans
% 0.30/0.46 => ( setadjoinSub
% 0.30/0.46 => ( setadjoinSub2
% 0.30/0.46 => ( subset2powerset
% 0.30/0.46 => ( setextsub
% 0.30/0.46 => ( subsetemptysetimpeq
% 0.30/0.46 => ( powersetI1
% 0.30/0.46 => ( powersetE1
% 0.30/0.46 => ( inPowerset
% 0.30/0.46 => ( powersetsubset
% 0.30/0.46 => ( sepInPowerset
% 0.30/0.46 => ( sepSubset
% 0.30/0.46 => ( binunionIL
% 0.30/0.46 => ( upairset2IR
% 0.30/0.46 => ( binunionIR
% 0.30/0.46 => ( binunionEcases
% 0.30/0.46 => ( binunionE
% 0.30/0.46 => ( binunionLsub
% 0.30/0.46 => ( binunionRsub
% 0.30/0.46 => ( binintersectI
% 0.30/0.46 => ( binintersectSubset5
% 0.30/0.46 => ( binintersectEL
% 0.30/0.46 => ( binintersectLsub
% 0.30/0.46 => ( binintersectSubset2
% 0.30/0.46 => ( binintersectSubset3
% 0.30/0.46 => ( binintersectER
% 0.30/0.46 => ( disjointsetsI1
% 0.30/0.46 => ( binintersectRsub
% 0.30/0.46 => ( binintersectSubset4
% 0.30/0.46 => ( binintersectSubset1
% 0.30/0.46 => ( bs114d
% 0.30/0.46 => ( setminusI
% 0.30/0.46 => ( setminusEL
% 0.30/0.46 => ( setminusER
% 0.30/0.46 => ( setminusSubset2
% 0.30/0.46 => ( setminusERneg
% 0.30/0.46 => ( setminusELneg
% 0.30/0.46 => ( setminusILneg
% 0.30/0.46 => ( setminusIRneg
% 0.30/0.46 => ( setminusLsub
% 0.30/0.46 => ( setminusSubset1
% 0.30/0.46 => ( symdiffE
% 0.30/0.46 => ( symdiffI1
% 0.30/0.46 => ( symdiffI2
% 0.30/0.46 => ( symdiffIneg1
% 0.30/0.46 => ( symdiffIneg2
% 0.30/0.46 => ( secondinupair
% 0.30/0.46 => ( setukpairIL
% 0.30/0.46 => ( setukpairIR
% 0.30/0.46 => ( kpairiskpair
% 0.30/0.46 => ( kpairp
% 0.30/0.46 => ( singletonsubset
% 0.30/0.46 => ( singletoninpowerset
% 0.30/0.46 => ( singletoninpowunion
% 0.30/0.46 => ( upairset2E
% 0.30/0.46 => ( upairsubunion
% 0.30/0.46 => ( upairinpowunion
% 0.30/0.46 => ( ubforcartprodlem1
% 0.30/0.46 => ( ubforcartprodlem2
% 0.30/0.46 => ( ubforcartprodlem3
% 0.30/0.46 => ( cartprodpairin
% 0.30/0.46 => ( cartprodmempair1
% 0.30/0.46 => ( cartprodmempair
% 0.30/0.46 => ( setunionE2
% 0.30/0.46 => ( setunionsingleton1
% 0.30/0.46 => ( setunionsingleton2
% 0.30/0.46 => ( setunionsingleton
% 0.30/0.46 => ( singletonprop
% 0.30/0.46 => ( ex1E1
% 0.30/0.46 => ( ex1I
% 0.30/0.46 => ( ex1I2
% 0.30/0.46 => ( singletonsuniq
% 0.30/0.46 => ( setukpairinjL1
% 0.30/0.46 => ( kfstsingleton
% 0.30/0.46 => ( theprop
% 0.30/0.46 => ( kfstpairEq
% 0.30/0.46 => ( cartprodfstin
% 0.30/0.46 => ( setukpairinjL2
% 0.30/0.46 => ( setukpairinjL
% 0.30/0.46 => ( setukpairinjR11
% 0.30/0.46 => ( setukpairinjR12
% 0.30/0.46 => ( setukpairinjR1
% 0.30/0.46 => ( upairequniteq
% 0.30/0.46 => ( setukpairinjR2
% 0.30/0.46 => ( setukpairinjR
% 0.30/0.46 => ( ksndsingleton
% 0.30/0.46 => ( ksndpairEq
% 0.30/0.46 => ( kpairsurjEq
% 0.30/0.46 => ( cartprodsndin
% 0.30/0.46 => ( cartprodpairmemEL
% 0.30/0.46 => ( cartprodpairmemER
% 0.30/0.46 => ( cartprodmempaircEq
% 0.30/0.46 => ( cartprodfstpairEq
% 0.30/0.46 => ( cartprodsndpairEq
% 0.30/0.46 => ( cartprodpairsurjEq
% 0.30/0.46 => ( dpsetconstrI
% 0.30/0.46 => ( dpsetconstrSub
% 0.30/0.46 => ( setOfPairsIsBReln
% 0.30/0.46 => ( dpsetconstrERa
% 0.30/0.46 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.69/1.51 ---- Embedded in THF ---
% 2.69/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.69/1.52 %%% Generated on Tue Feb 24 12:30:04 EST 2026
% 2.69/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.69/1.52 %%% Logic specification used:
% 2.69/1.52 %%% thf(spec, logic, $$dhol).
% 2.69/1.52
% 2.69/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2DTF8088.p
% See solution above
% 2.69/1.52 ------------------------
% 2.69/1.55 ---- Cleaned THF ---
% 2.69/1.56 thf(in_type,type,
% 2.69/1.56 in: $i > $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(exu_type,type,
% 2.69/1.56 exu: ( $i > $o ) > $o ).
% 2.69/1.56
% 2.69/1.56 thf(exu,definition,
% 2.69/1.56 ( exu
% 2.69/1.56 = ( ^ [Xphi: $i > $o] :
% 2.69/1.56 ? [Xx: $i] :
% 2.69/1.56 ( ( Xphi @ Xx )
% 2.69/1.56 & ! [Xy: $i] :
% 2.69/1.56 ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setextAx_type,type,
% 2.69/1.56 setextAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setextAx,definition,
% 2.69/1.56 ( setextAx
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 <=> ( in @ Xx @ B ) )
% 2.69/1.56 => ( A = B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptyset_type,type,
% 2.69/1.56 emptyset: $i ).
% 2.69/1.56
% 2.69/1.56 thf(emptysetAx_type,type,
% 2.69/1.56 emptysetAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptysetAx,definition,
% 2.69/1.56 ( emptysetAx
% 2.69/1.56 = ( ! [Xx: $i] :
% 2.69/1.56 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoin_type,type,
% 2.69/1.56 setadjoin: $i > $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinAx_type,type,
% 2.69/1.56 setadjoinAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinAx,definition,
% 2.69/1.56 ( setadjoinAx
% 2.69/1.56 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.69/1.56 <=> ( ( Xy = Xx )
% 2.69/1.56 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(powerset_type,type,
% 2.69/1.56 powerset: $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(powersetAx_type,type,
% 2.69/1.56 powersetAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(powersetAx,definition,
% 2.69/1.56 ( powersetAx
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( in @ B @ ( powerset @ A ) )
% 2.69/1.56 <=> ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setunion_type,type,
% 2.69/1.56 setunion: $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(setunionAx_type,type,
% 2.69/1.56 setunionAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setunionAx,definition,
% 2.69/1.56 ( setunionAx
% 2.69/1.56 = ( ! [A: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( setunion @ A ) )
% 2.69/1.56 <=> ? [B: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 & ( in @ B @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(omega_type,type,
% 2.69/1.56 omega: $i ).
% 2.69/1.56
% 2.69/1.56 thf(omega0Ax_type,type,
% 2.69/1.56 omega0Ax: $o ).
% 2.69/1.56
% 2.69/1.56 thf(omega0Ax,definition,
% 2.69/1.56 ( omega0Ax
% 2.69/1.56 = ( in @ emptyset @ omega ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(omegaSAx_type,type,
% 2.69/1.56 omegaSAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(omegaSAx,definition,
% 2.69/1.56 ( omegaSAx
% 2.69/1.56 = ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ omega )
% 2.69/1.56 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(omegaIndAx_type,type,
% 2.69/1.56 omegaIndAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(omegaIndAx,definition,
% 2.69/1.56 ( omegaIndAx
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ( ( in @ emptyset @ A )
% 2.69/1.56 & ! [Xx: $i] :
% 2.69/1.56 ( ( ( in @ Xx @ omega )
% 2.69/1.56 & ( in @ Xx @ A ) )
% 2.69/1.56 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.69/1.56 => ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ omega )
% 2.69/1.56 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(replAx_type,type,
% 2.69/1.56 replAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(replAx,definition,
% 2.69/1.56 ( replAx
% 2.69/1.56 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( exu
% 2.69/1.56 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.69/1.56 => ? [B: $i] :
% 2.69/1.56 ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 <=> ? [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ A )
% 2.69/1.56 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(foundationAx_type,type,
% 2.69/1.56 foundationAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(foundationAx,definition,
% 2.69/1.56 ( foundationAx
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.69/1.56 => ? [B: $i] :
% 2.69/1.56 ( ( in @ B @ A )
% 2.69/1.56 & ~ ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(wellorderingAx_type,type,
% 2.69/1.56 wellorderingAx: $o ).
% 2.69/1.56
% 2.69/1.56 thf(wellorderingAx,definition,
% 2.69/1.56 ( wellorderingAx
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ? [B: $i] :
% 2.69/1.56 ( ! [C: $i] :
% 2.69/1.56 ( ( in @ C @ B )
% 2.69/1.56 => ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ C )
% 2.69/1.56 => ( in @ Xx @ A ) ) )
% 2.69/1.56 & ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( ( in @ Xx @ A )
% 2.69/1.56 & ( in @ Xy @ A ) )
% 2.69/1.56 => ( ! [C: $i] :
% 2.69/1.56 ( ( in @ C @ B )
% 2.69/1.56 => ( ( in @ Xx @ C )
% 2.69/1.56 <=> ( in @ Xy @ C ) ) )
% 2.69/1.56 => ( Xx = Xy ) ) )
% 2.69/1.56 & ! [C: $i,D: $i] :
% 2.69/1.56 ( ( ( in @ C @ B )
% 2.69/1.56 & ( in @ D @ B ) )
% 2.69/1.56 => ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ C )
% 2.69/1.56 => ( in @ Xx @ D ) )
% 2.69/1.56 | ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ D )
% 2.69/1.56 => ( in @ Xx @ C ) ) ) )
% 2.69/1.56 & ! [C: $i] :
% 2.69/1.56 ( ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ C )
% 2.69/1.56 => ( in @ Xx @ A ) )
% 2.69/1.56 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.69/1.56 => ? [D: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ D @ B )
% 2.69/1.56 & ( in @ Xx @ C )
% 2.69/1.56 & ~ ? [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ D )
% 2.69/1.56 & ( in @ Xy @ C ) )
% 2.69/1.56 & ! [E: $i] :
% 2.69/1.56 ( ( in @ E @ B )
% 2.69/1.56 => ( ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ E )
% 2.69/1.56 => ( in @ Xy @ D ) )
% 2.69/1.56 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(descr_type,type,
% 2.69/1.56 descr: ( $i > $o ) > $i ).
% 2.69/1.56
% 2.69/1.56 thf(descrp_type,type,
% 2.69/1.56 descrp: $o ).
% 2.69/1.56
% 2.69/1.56 thf(descrp,definition,
% 2.69/1.56 ( descrp
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 => ( Xphi
% 2.69/1.56 @ ( descr
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstr_type,type,
% 2.69/1.56 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstrI_type,type,
% 2.69/1.56 dsetconstrI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstrI,definition,
% 2.69/1.56 ( dsetconstrI
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ( Xphi @ Xx )
% 2.69/1.56 => ( in @ Xx
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstrEL_type,type,
% 2.69/1.56 dsetconstrEL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstrEL,definition,
% 2.69/1.56 ( dsetconstrEL
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.69/1.56 => ( in @ Xx @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstrER_type,type,
% 2.69/1.56 dsetconstrER: $o ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstrER,definition,
% 2.69/1.56 ( dsetconstrER
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.69/1.56 => ( Xphi @ Xx ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exuE1_type,type,
% 2.69/1.56 exuE1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exuE1,definition,
% 2.69/1.56 ( exuE1
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 => ? [Xx: $i] :
% 2.69/1.56 ( ( Xphi @ Xx )
% 2.69/1.56 & ! [Xy: $i] :
% 2.69/1.56 ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(prop2set_type,type,
% 2.69/1.56 prop2set: $o > $i ).
% 2.69/1.56
% 2.69/1.56 thf(prop2setE_type,type,
% 2.69/1.56 prop2setE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(prop2setE,definition,
% 2.69/1.56 ( prop2setE
% 2.69/1.56 = ( ! [Xphi: $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.69/1.56 => Xphi ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptysetE_type,type,
% 2.69/1.56 emptysetE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptysetE,definition,
% 2.69/1.56 ( emptysetE
% 2.69/1.56 = ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ emptyset )
% 2.69/1.56 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptysetimpfalse_type,type,
% 2.69/1.56 emptysetimpfalse: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptysetimpfalse,definition,
% 2.69/1.56 ( emptysetimpfalse
% 2.69/1.56 = ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ emptyset )
% 2.69/1.56 => $false ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(notinemptyset_type,type,
% 2.69/1.56 notinemptyset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(notinemptyset,definition,
% 2.69/1.56 ( notinemptyset
% 2.69/1.56 = ( ! [Xx: $i] :
% 2.69/1.56 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exuE3e_type,type,
% 2.69/1.56 exuE3e: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exuE3e,definition,
% 2.69/1.56 ( exuE3e
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setext_type,type,
% 2.69/1.56 setext: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setext,definition,
% 2.69/1.56 ( setext
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ Xx @ B ) )
% 2.69/1.56 => ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ A ) )
% 2.69/1.56 => ( A = B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptyI_type,type,
% 2.69/1.56 emptyI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptyI,definition,
% 2.69/1.56 ( emptyI
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ~ ( in @ Xx @ A )
% 2.69/1.56 => ( A = emptyset ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(noeltsimpempty_type,type,
% 2.69/1.56 noeltsimpempty: $o ).
% 2.69/1.56
% 2.69/1.56 thf(noeltsimpempty,definition,
% 2.69/1.56 ( noeltsimpempty
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ~ ( in @ Xx @ A )
% 2.69/1.56 => ( A = emptyset ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setbeta_type,type,
% 2.69/1.56 setbeta: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setbeta,definition,
% 2.69/1.56 ( setbeta
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ( in @ Xx
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.69/1.56 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(nonempty_type,type,
% 2.69/1.56 nonempty: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(nonempty,definition,
% 2.69/1.56 ( nonempty
% 2.69/1.56 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(nonemptyE1_type,type,
% 2.69/1.56 nonemptyE1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(nonemptyE1,definition,
% 2.69/1.56 ( nonemptyE1
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ( nonempty @ A )
% 2.69/1.56 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(nonemptyI_type,type,
% 2.69/1.56 nonemptyI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(nonemptyI,definition,
% 2.69/1.56 ( nonemptyI
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ( Xphi @ Xx )
% 2.69/1.56 => ( nonempty
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(nonemptyI1_type,type,
% 2.69/1.56 nonemptyI1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(nonemptyI1,definition,
% 2.69/1.56 ( nonemptyI1
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.69/1.56 => ( nonempty @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinIL_type,type,
% 2.69/1.56 setadjoinIL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinIL,definition,
% 2.69/1.56 ( setadjoinIL
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptyinunitempty_type,type,
% 2.69/1.56 emptyinunitempty: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptyinunitempty,definition,
% 2.69/1.56 ( emptyinunitempty
% 2.69/1.56 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinIR_type,type,
% 2.69/1.56 setadjoinIR: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinIR,definition,
% 2.69/1.56 ( setadjoinIR
% 2.69/1.56 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ A )
% 2.69/1.56 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinE_type,type,
% 2.69/1.56 setadjoinE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinE,definition,
% 2.69/1.56 ( setadjoinE
% 2.69/1.56 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.69/1.56 => ! [Xphi: $o] :
% 2.69/1.56 ( ( ( Xy = Xx )
% 2.69/1.56 => Xphi )
% 2.69/1.56 => ( ( ( in @ Xy @ A )
% 2.69/1.56 => Xphi )
% 2.69/1.56 => Xphi ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinOr_type,type,
% 2.69/1.56 setadjoinOr: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinOr,definition,
% 2.69/1.56 ( setadjoinOr
% 2.69/1.56 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.69/1.56 => ( ( Xy = Xx )
% 2.69/1.56 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setoftrueEq_type,type,
% 2.69/1.56 setoftrueEq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setoftrueEq,definition,
% 2.69/1.56 ( setoftrueEq
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xx: $i] : $true )
% 2.69/1.56 = A ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(powersetI_type,type,
% 2.69/1.56 powersetI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(powersetI,definition,
% 2.69/1.56 ( powersetI
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ A ) )
% 2.69/1.56 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptyinPowerset_type,type,
% 2.69/1.56 emptyinPowerset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptyinPowerset,definition,
% 2.69/1.56 ( emptyinPowerset
% 2.69/1.56 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptyInPowerset_type,type,
% 2.69/1.56 emptyInPowerset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptyInPowerset,definition,
% 2.69/1.56 ( emptyInPowerset
% 2.69/1.56 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(powersetE_type,type,
% 2.69/1.56 powersetE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(powersetE,definition,
% 2.69/1.56 ( powersetE
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ B @ ( powerset @ A ) )
% 2.69/1.56 => ( ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setunionI_type,type,
% 2.69/1.56 setunionI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setunionI,definition,
% 2.69/1.56 ( setunionI
% 2.69/1.56 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 => ( ( in @ B @ A )
% 2.69/1.56 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setunionE_type,type,
% 2.69/1.56 setunionE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setunionE,definition,
% 2.69/1.56 ( setunionE
% 2.69/1.56 = ( ! [A: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( setunion @ A ) )
% 2.69/1.56 => ! [Xphi: $o] :
% 2.69/1.56 ( ! [B: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 => ( ( in @ B @ A )
% 2.69/1.56 => Xphi ) )
% 2.69/1.56 => Xphi ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subPowSU_type,type,
% 2.69/1.56 subPowSU: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subPowSU,definition,
% 2.69/1.56 ( subPowSU
% 2.69/1.56 = ( ! [A: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exuE2_type,type,
% 2.69/1.56 exuE2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exuE2,definition,
% 2.69/1.56 ( exuE2
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 => ? [Xx: $i] :
% 2.69/1.56 ! [Xy: $i] :
% 2.69/1.56 ( ( Xphi @ Xy )
% 2.69/1.56 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(nonemptyImpWitness_type,type,
% 2.69/1.56 nonemptyImpWitness: $o ).
% 2.69/1.56
% 2.69/1.56 thf(nonemptyImpWitness,definition,
% 2.69/1.56 ( nonemptyImpWitness
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ( nonempty @ A )
% 2.69/1.56 => ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & $true ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(uniqinunit_type,type,
% 2.69/1.56 uniqinunit: $o ).
% 2.69/1.56
% 2.69/1.56 thf(uniqinunit,definition,
% 2.69/1.56 ( uniqinunit
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(notinsingleton_type,type,
% 2.69/1.56 notinsingleton: $o ).
% 2.69/1.56
% 2.69/1.56 thf(notinsingleton,definition,
% 2.69/1.56 ( notinsingleton
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx != Xy )
% 2.69/1.56 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(eqinunit_type,type,
% 2.69/1.56 eqinunit: $o ).
% 2.69/1.56
% 2.69/1.56 thf(eqinunit,definition,
% 2.69/1.56 ( eqinunit
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx = Xy )
% 2.69/1.56 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(singletonsswitch_type,type,
% 2.69/1.56 singletonsswitch: $o ).
% 2.69/1.56
% 2.69/1.56 thf(singletonsswitch,definition,
% 2.69/1.56 ( singletonsswitch
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.69/1.56 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(upairsetE_type,type,
% 2.69/1.56 upairsetE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairsetE,definition,
% 2.69/1.56 ( upairsetE
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.69/1.56 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.69/1.56 => ( ( Xz = Xx )
% 2.69/1.56 | ( Xz = Xy ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(upairsetIL_type,type,
% 2.69/1.56 upairsetIL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairsetIL,definition,
% 2.69/1.56 ( upairsetIL
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(upairsetIR_type,type,
% 2.69/1.56 upairsetIR: $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairsetIR,definition,
% 2.69/1.56 ( upairsetIR
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptyE1_type,type,
% 2.69/1.56 emptyE1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptyE1,definition,
% 2.69/1.56 ( emptyE1
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( Xphi @ Xx ) )
% 2.69/1.56 => ( ( ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 = emptyset )
% 2.69/1.56 => $false ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(vacuousDall_type,type,
% 2.69/1.56 vacuousDall: $o ).
% 2.69/1.56
% 2.69/1.56 thf(vacuousDall,definition,
% 2.69/1.56 ( vacuousDall
% 2.69/1.56 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ emptyset )
% 2.69/1.56 => ( Xphi @ Xx ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(quantDeMorgan1_type,type,
% 2.69/1.56 quantDeMorgan1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(quantDeMorgan1,definition,
% 2.69/1.56 ( quantDeMorgan1
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ~ ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( Xphi @ Xx ) )
% 2.69/1.56 => ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(quantDeMorgan2_type,type,
% 2.69/1.56 quantDeMorgan2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(quantDeMorgan2,definition,
% 2.69/1.56 ( quantDeMorgan2
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ~ ( Xphi @ Xx ) )
% 2.69/1.56 => ~ ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(quantDeMorgan3_type,type,
% 2.69/1.56 quantDeMorgan3: $o ).
% 2.69/1.56
% 2.69/1.56 thf(quantDeMorgan3,definition,
% 2.69/1.56 ( quantDeMorgan3
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ~ ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( Xphi @ Xx ) )
% 2.69/1.56 => ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(quantDeMorgan4_type,type,
% 2.69/1.56 quantDeMorgan4: $o ).
% 2.69/1.56
% 2.69/1.56 thf(quantDeMorgan4,definition,
% 2.69/1.56 ( quantDeMorgan4
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ~ ( Xphi @ Xx ) )
% 2.69/1.56 => ~ ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(prop2setI_type,type,
% 2.69/1.56 prop2setI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(prop2setI,definition,
% 2.69/1.56 ( prop2setI
% 2.69/1.56 = ( ! [Xphi: $o] :
% 2.69/1.56 ( Xphi
% 2.69/1.56 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(set2prop_type,type,
% 2.69/1.56 set2prop: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(prop2set2propI_type,type,
% 2.69/1.56 prop2set2propI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(prop2set2propI,definition,
% 2.69/1.56 ( prop2set2propI
% 2.69/1.56 = ( ! [Xphi: $o] :
% 2.69/1.56 ( Xphi
% 2.69/1.56 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(notdexE_type,type,
% 2.69/1.56 notdexE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(notdexE,definition,
% 2.69/1.56 ( notdexE
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ~ ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( Xphi @ Xx ) )
% 2.69/1.56 => ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(notdallE_type,type,
% 2.69/1.56 notdallE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(notdallE,definition,
% 2.69/1.56 ( notdallE
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ~ ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( Xphi @ Xx ) )
% 2.69/1.56 => ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exuI1_type,type,
% 2.69/1.56 exuI1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exuI1,definition,
% 2.69/1.56 ( exuI1
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ? [Xx: $i] :
% 2.69/1.56 ( ( Xphi @ Xx )
% 2.69/1.56 & ! [Xy: $i] :
% 2.69/1.56 ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xx = Xy ) ) )
% 2.69/1.56 => ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exuI3_type,type,
% 2.69/1.56 exuI3: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exuI3,definition,
% 2.69/1.56 ( exuI3
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.69/1.56 => ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xphi @ Xx )
% 2.69/1.56 => ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xx = Xy ) ) )
% 2.69/1.56 => ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exuI2_type,type,
% 2.69/1.56 exuI2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exuI2,definition,
% 2.69/1.56 ( exuI2
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ? [Xx: $i] :
% 2.69/1.56 ! [Xy: $i] :
% 2.69/1.56 ( ( Xphi @ Xy )
% 2.69/1.56 <=> ( Xy = Xx ) )
% 2.69/1.56 => ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(inCongP_type,type,
% 2.69/1.56 inCongP: $o ).
% 2.69/1.56
% 2.69/1.56 thf(inCongP,definition,
% 2.69/1.56 ( inCongP
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( A = B )
% 2.69/1.56 => ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx = Xy )
% 2.69/1.56 => ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(in__Cong_type,type,
% 2.69/1.56 in__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(in__Cong,definition,
% 2.69/1.56 ( in__Cong
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( A = B )
% 2.69/1.56 => ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx = Xy )
% 2.69/1.56 => ( ( in @ Xx @ A )
% 2.69/1.56 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exuE3u_type,type,
% 2.69/1.56 exuE3u: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exuE3u,definition,
% 2.69/1.56 ( exuE3u
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 => ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xphi @ Xx )
% 2.69/1.56 => ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exu__Cong_type,type,
% 2.69/1.56 exu__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exu__Cong,definition,
% 2.69/1.56 ( exu__Cong
% 2.69/1.56 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.69/1.56 ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx = Xy )
% 2.69/1.56 => ( ( Xphi @ Xx )
% 2.69/1.56 <=> ( Xpsi @ Xy ) ) )
% 2.69/1.56 => ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 <=> ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptyset__Cong_type,type,
% 2.69/1.56 emptyset__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptyset__Cong,definition,
% 2.69/1.56 ( emptyset__Cong
% 2.69/1.56 = ( emptyset = emptyset ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoin__Cong_type,type,
% 2.69/1.56 setadjoin__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoin__Cong,definition,
% 2.69/1.56 ( setadjoin__Cong
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx = Xy )
% 2.69/1.56 => ! [Xz: $i,Xu: $i] :
% 2.69/1.56 ( ( Xz = Xu )
% 2.69/1.56 => ( ( setadjoin @ Xx @ Xz )
% 2.69/1.56 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(powerset__Cong_type,type,
% 2.69/1.56 powerset__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(powerset__Cong,definition,
% 2.69/1.56 ( powerset__Cong
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( A = B )
% 2.69/1.56 => ( ( powerset @ A )
% 2.69/1.56 = ( powerset @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setunion__Cong_type,type,
% 2.69/1.56 setunion__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setunion__Cong,definition,
% 2.69/1.56 ( setunion__Cong
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( A = B )
% 2.69/1.56 => ( ( setunion @ A )
% 2.69/1.56 = ( setunion @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(omega__Cong_type,type,
% 2.69/1.56 omega__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(omega__Cong,definition,
% 2.69/1.56 ( omega__Cong
% 2.69/1.56 = ( omega = omega ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(exuEu_type,type,
% 2.69/1.56 exuEu: $o ).
% 2.69/1.56
% 2.69/1.56 thf(exuEu,definition,
% 2.69/1.56 ( exuEu
% 2.69/1.56 = ( ! [Xphi: $i > $o] :
% 2.69/1.56 ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 => ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xphi @ Xx )
% 2.69/1.56 => ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(descr__Cong_type,type,
% 2.69/1.56 descr__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(descr__Cong,definition,
% 2.69/1.56 ( descr__Cong
% 2.69/1.56 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.69/1.56 ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx = Xy )
% 2.69/1.56 => ( ( Xphi @ Xx )
% 2.69/1.56 <=> ( Xpsi @ Xy ) ) )
% 2.69/1.56 => ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 => ( ( exu
% 2.69/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.69/1.56 => ( ( descr
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 = ( descr
% 2.69/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstr__Cong_type,type,
% 2.69/1.56 dsetconstr__Cong: $o ).
% 2.69/1.56
% 2.69/1.56 thf(dsetconstr__Cong,definition,
% 2.69/1.56 ( dsetconstr__Cong
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( A = B )
% 2.69/1.56 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( ( Xx = Xy )
% 2.69/1.56 => ( ( Xphi @ Xx )
% 2.69/1.56 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.69/1.56 => ( ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 = ( dsetconstr @ B
% 2.69/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subset_type,type,
% 2.69/1.56 subset: $i > $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(disjoint_type,type,
% 2.69/1.56 disjoint: $i > $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(setsmeet_type,type,
% 2.69/1.56 setsmeet: $i > $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(subsetI1_type,type,
% 2.69/1.56 subsetI1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subsetI1,definition,
% 2.69/1.56 ( subsetI1
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ Xx @ B ) )
% 2.69/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(eqimpsubset2_type,type,
% 2.69/1.56 eqimpsubset2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(eqimpsubset2,definition,
% 2.69/1.56 ( eqimpsubset2
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( A = B )
% 2.69/1.56 => ( subset @ B @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(eqimpsubset1_type,type,
% 2.69/1.56 eqimpsubset1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(eqimpsubset1,definition,
% 2.69/1.56 ( eqimpsubset1
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( A = B )
% 2.69/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subsetI2_type,type,
% 2.69/1.56 subsetI2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subsetI2,definition,
% 2.69/1.56 ( subsetI2
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ Xx @ B ) )
% 2.69/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(emptysetsubset_type,type,
% 2.69/1.56 emptysetsubset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(emptysetsubset,definition,
% 2.69/1.56 ( emptysetsubset
% 2.69/1.56 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subsetE_type,type,
% 2.69/1.56 subsetE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subsetE,definition,
% 2.69/1.56 ( subsetE
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subsetE2_type,type,
% 2.69/1.56 subsetE2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subsetE2,definition,
% 2.69/1.56 ( subsetE2
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( ~ ( in @ Xx @ B )
% 2.69/1.56 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(notsubsetI_type,type,
% 2.69/1.56 notsubsetI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(notsubsetI,definition,
% 2.69/1.56 ( notsubsetI
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ~ ( in @ Xx @ B )
% 2.69/1.56 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(notequalI1_type,type,
% 2.69/1.56 notequalI1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(notequalI1,definition,
% 2.69/1.56 ( notequalI1
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ~ ( subset @ A @ B )
% 2.69/1.56 => ( A != B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(notequalI2_type,type,
% 2.69/1.56 notequalI2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(notequalI2,definition,
% 2.69/1.56 ( notequalI2
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ~ ( in @ Xx @ B )
% 2.69/1.56 => ( A != B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subsetRefl_type,type,
% 2.69/1.56 subsetRefl: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subsetRefl,definition,
% 2.69/1.56 ( subsetRefl
% 2.69/1.56 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subsetTrans_type,type,
% 2.69/1.56 subsetTrans: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subsetTrans,definition,
% 2.69/1.56 ( subsetTrans
% 2.69/1.56 = ( ! [A: $i,B: $i,C: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( ( subset @ B @ C )
% 2.69/1.56 => ( subset @ A @ C ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinSub_type,type,
% 2.69/1.56 setadjoinSub: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinSub,definition,
% 2.69/1.56 ( setadjoinSub
% 2.69/1.56 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinSub2_type,type,
% 2.69/1.56 setadjoinSub2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setadjoinSub2,definition,
% 2.69/1.56 ( setadjoinSub2
% 2.69/1.56 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subset2powerset_type,type,
% 2.69/1.56 subset2powerset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subset2powerset,definition,
% 2.69/1.56 ( subset2powerset
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setextsub_type,type,
% 2.69/1.56 setextsub: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setextsub,definition,
% 2.69/1.56 ( setextsub
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( ( subset @ B @ A )
% 2.69/1.56 => ( A = B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(subsetemptysetimpeq_type,type,
% 2.69/1.56 subsetemptysetimpeq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(subsetemptysetimpeq,definition,
% 2.69/1.56 ( subsetemptysetimpeq
% 2.69/1.56 = ( ! [A: $i] :
% 2.69/1.56 ( ( subset @ A @ emptyset )
% 2.69/1.56 => ( A = emptyset ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(powersetI1_type,type,
% 2.69/1.56 powersetI1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(powersetI1,definition,
% 2.69/1.56 ( powersetI1
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( subset @ B @ A )
% 2.69/1.56 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(powersetE1_type,type,
% 2.69/1.56 powersetE1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(powersetE1,definition,
% 2.69/1.56 ( powersetE1
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( in @ B @ ( powerset @ A ) )
% 2.69/1.56 => ( subset @ B @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(inPowerset_type,type,
% 2.69/1.56 inPowerset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(inPowerset,definition,
% 2.69/1.56 ( inPowerset
% 2.69/1.56 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(powersetsubset_type,type,
% 2.69/1.56 powersetsubset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(powersetsubset,definition,
% 2.69/1.56 ( powersetsubset
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(sepInPowerset_type,type,
% 2.69/1.56 sepInPowerset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(sepInPowerset,definition,
% 2.69/1.56 ( sepInPowerset
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( in
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 @ ( powerset @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(sepSubset_type,type,
% 2.69/1.56 sepSubset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(sepSubset,definition,
% 2.69/1.56 ( sepSubset
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( subset
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 @ A ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binunion_type,type,
% 2.69/1.56 binunion: $i > $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(binunionIL_type,type,
% 2.69/1.56 binunionIL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binunionIL,definition,
% 2.69/1.56 ( binunionIL
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(upairset2IR_type,type,
% 2.69/1.56 upairset2IR: $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairset2IR,definition,
% 2.69/1.56 ( upairset2IR
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binunionIR_type,type,
% 2.69/1.56 binunionIR: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binunionIR,definition,
% 2.69/1.56 ( binunionIR
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binunionEcases_type,type,
% 2.69/1.56 binunionEcases: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binunionEcases,definition,
% 2.69/1.56 ( binunionEcases
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.69/1.56 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.69/1.56 => ( ( ( in @ Xx @ A )
% 2.69/1.56 => Xphi )
% 2.69/1.56 => ( ( ( in @ Xx @ B )
% 2.69/1.56 => Xphi )
% 2.69/1.56 => Xphi ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binunionE_type,type,
% 2.69/1.56 binunionE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binunionE,definition,
% 2.69/1.56 ( binunionE
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.69/1.56 => ( ( in @ Xx @ A )
% 2.69/1.56 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binunionLsub_type,type,
% 2.69/1.56 binunionLsub: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binunionLsub,definition,
% 2.69/1.56 ( binunionLsub
% 2.69/1.56 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binunionRsub_type,type,
% 2.69/1.56 binunionRsub: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binunionRsub,definition,
% 2.69/1.56 ( binunionRsub
% 2.69/1.56 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersect_type,type,
% 2.69/1.56 binintersect: $i > $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectI_type,type,
% 2.69/1.56 binintersectI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectI,definition,
% 2.69/1.56 ( binintersectI
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset5_type,type,
% 2.69/1.56 binintersectSubset5: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset5,definition,
% 2.69/1.56 ( binintersectSubset5
% 2.69/1.56 = ( ! [A: $i,B: $i,C: $i] :
% 2.69/1.56 ( ( subset @ C @ A )
% 2.69/1.56 => ( ( subset @ C @ B )
% 2.69/1.56 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectEL_type,type,
% 2.69/1.56 binintersectEL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectEL,definition,
% 2.69/1.56 ( binintersectEL
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.69/1.56 => ( in @ Xx @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectLsub_type,type,
% 2.69/1.56 binintersectLsub: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectLsub,definition,
% 2.69/1.56 ( binintersectLsub
% 2.69/1.56 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset2_type,type,
% 2.69/1.56 binintersectSubset2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset2,definition,
% 2.69/1.56 ( binintersectSubset2
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( ( binintersect @ A @ B )
% 2.69/1.56 = A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset3_type,type,
% 2.69/1.56 binintersectSubset3: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset3,definition,
% 2.69/1.56 ( binintersectSubset3
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( ( binintersect @ A @ B )
% 2.69/1.56 = B )
% 2.69/1.56 => ( subset @ B @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectER_type,type,
% 2.69/1.56 binintersectER: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectER,definition,
% 2.69/1.56 ( binintersectER
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.69/1.56 => ( in @ Xx @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(disjointsetsI1_type,type,
% 2.69/1.56 disjointsetsI1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(disjointsetsI1,definition,
% 2.69/1.56 ( disjointsetsI1
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ~ ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( in @ Xx @ B ) )
% 2.69/1.56 => ( ( binintersect @ A @ B )
% 2.69/1.56 = emptyset ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectRsub_type,type,
% 2.69/1.56 binintersectRsub: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectRsub,definition,
% 2.69/1.56 ( binintersectRsub
% 2.69/1.56 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset4_type,type,
% 2.69/1.56 binintersectSubset4: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset4,definition,
% 2.69/1.56 ( binintersectSubset4
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( subset @ B @ A )
% 2.69/1.56 => ( ( binintersect @ A @ B )
% 2.69/1.56 = B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset1_type,type,
% 2.69/1.56 binintersectSubset1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(binintersectSubset1,definition,
% 2.69/1.56 ( binintersectSubset1
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( ( binintersect @ A @ B )
% 2.69/1.56 = A )
% 2.69/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(bs114d_type,type,
% 2.69/1.56 bs114d: $o ).
% 2.69/1.56
% 2.69/1.56 thf(bs114d,definition,
% 2.69/1.56 ( bs114d
% 2.69/1.56 = ( ! [A: $i,B: $i,C: $i] :
% 2.69/1.56 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.69/1.56 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(regular_type,type,
% 2.69/1.56 regular: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminus_type,type,
% 2.69/1.56 setminus: $i > $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(setminusI_type,type,
% 2.69/1.56 setminusI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusI,definition,
% 2.69/1.56 ( setminusI
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ~ ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusEL_type,type,
% 2.69/1.56 setminusEL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusEL,definition,
% 2.69/1.56 ( setminusEL
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.69/1.56 => ( in @ Xx @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusER_type,type,
% 2.69/1.56 setminusER: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusER,definition,
% 2.69/1.56 ( setminusER
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.69/1.56 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusSubset2_type,type,
% 2.69/1.56 setminusSubset2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusSubset2,definition,
% 2.69/1.56 ( setminusSubset2
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( subset @ A @ B )
% 2.69/1.56 => ( ( setminus @ A @ B )
% 2.69/1.56 = emptyset ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusERneg_type,type,
% 2.69/1.56 setminusERneg: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusERneg,definition,
% 2.69/1.56 ( setminusERneg
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.69/1.56 => ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusELneg_type,type,
% 2.69/1.56 setminusELneg: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusELneg,definition,
% 2.69/1.56 ( setminusELneg
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.69/1.56 => ( ~ ( in @ Xx @ B )
% 2.69/1.56 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusILneg_type,type,
% 2.69/1.56 setminusILneg: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusILneg,definition,
% 2.69/1.56 ( setminusILneg
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ~ ( in @ Xx @ A )
% 2.69/1.56 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusIRneg_type,type,
% 2.69/1.56 setminusIRneg: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusIRneg,definition,
% 2.69/1.56 ( setminusIRneg
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ B )
% 2.69/1.56 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusLsub_type,type,
% 2.69/1.56 setminusLsub: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusLsub,definition,
% 2.69/1.56 ( setminusLsub
% 2.69/1.56 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setminusSubset1_type,type,
% 2.69/1.56 setminusSubset1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setminusSubset1,definition,
% 2.69/1.56 ( setminusSubset1
% 2.69/1.56 = ( ! [A: $i,B: $i] :
% 2.69/1.56 ( ( ( setminus @ A @ B )
% 2.69/1.56 = emptyset )
% 2.69/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(symdiff_type,type,
% 2.69/1.56 symdiff: $i > $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffE_type,type,
% 2.69/1.56 symdiffE: $o ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffE,definition,
% 2.69/1.56 ( symdiffE
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.69/1.56 => ! [Xphi: $o] :
% 2.69/1.56 ( ( ( in @ Xx @ A )
% 2.69/1.56 => ( ~ ( in @ Xx @ B )
% 2.69/1.56 => Xphi ) )
% 2.69/1.56 => ( ( ~ ( in @ Xx @ A )
% 2.69/1.56 => ( ( in @ Xx @ B )
% 2.69/1.56 => Xphi ) )
% 2.69/1.56 => Xphi ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffI1_type,type,
% 2.69/1.56 symdiffI1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffI1,definition,
% 2.69/1.56 ( symdiffI1
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ~ ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffI2_type,type,
% 2.69/1.56 symdiffI2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffI2,definition,
% 2.69/1.56 ( symdiffI2
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ~ ( in @ Xx @ A )
% 2.69/1.56 => ( ( in @ Xx @ B )
% 2.69/1.56 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffIneg1_type,type,
% 2.69/1.56 symdiffIneg1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffIneg1,definition,
% 2.69/1.56 ( symdiffIneg1
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ( in @ Xx @ B )
% 2.69/1.56 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffIneg2_type,type,
% 2.69/1.56 symdiffIneg2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(symdiffIneg2,definition,
% 2.69/1.56 ( symdiffIneg2
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ~ ( in @ Xx @ A )
% 2.69/1.56 => ( ~ ( in @ Xx @ B )
% 2.69/1.56 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(iskpair_type,type,
% 2.69/1.56 iskpair: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(secondinupair_type,type,
% 2.69/1.56 secondinupair: $o ).
% 2.69/1.56
% 2.69/1.56 thf(secondinupair,definition,
% 2.69/1.56 ( secondinupair
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairIL_type,type,
% 2.69/1.56 setukpairIL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairIL,definition,
% 2.69/1.56 ( setukpairIL
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairIR_type,type,
% 2.69/1.56 setukpairIR: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairIR,definition,
% 2.69/1.56 ( setukpairIR
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(kpairiskpair_type,type,
% 2.69/1.56 kpairiskpair: $o ).
% 2.69/1.56
% 2.69/1.56 thf(kpairiskpair,definition,
% 2.69/1.56 ( kpairiskpair
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(kpair_type,type,
% 2.69/1.56 kpair: $i > $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(kpairp_type,type,
% 2.69/1.56 kpairp: $o ).
% 2.69/1.56
% 2.69/1.56 thf(kpairp,definition,
% 2.69/1.56 ( kpairp
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprod_type,type,
% 2.69/1.56 cartprod: $i > $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(singletonsubset_type,type,
% 2.69/1.56 singletonsubset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(singletonsubset,definition,
% 2.69/1.56 ( singletonsubset
% 2.69/1.56 = ( ! [A: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(singletoninpowerset_type,type,
% 2.69/1.56 singletoninpowerset: $o ).
% 2.69/1.56
% 2.69/1.56 thf(singletoninpowerset,definition,
% 2.69/1.56 ( singletoninpowerset
% 2.69/1.56 = ( ! [A: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(singletoninpowunion_type,type,
% 2.69/1.56 singletoninpowunion: $o ).
% 2.69/1.56
% 2.69/1.56 thf(singletoninpowunion,definition,
% 2.69/1.56 ( singletoninpowunion
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(upairset2E_type,type,
% 2.69/1.56 upairset2E: $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairset2E,definition,
% 2.69/1.56 ( upairset2E
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.69/1.56 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.69/1.56 => ( ( Xz = Xx )
% 2.69/1.56 | ( Xz = Xy ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(upairsubunion_type,type,
% 2.69/1.56 upairsubunion: $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairsubunion,definition,
% 2.69/1.56 ( upairsubunion
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(upairinpowunion_type,type,
% 2.69/1.56 upairinpowunion: $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairinpowunion,definition,
% 2.69/1.56 ( upairinpowunion
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ubforcartprodlem1_type,type,
% 2.69/1.56 ubforcartprodlem1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(ubforcartprodlem1,definition,
% 2.69/1.56 ( ubforcartprodlem1
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ubforcartprodlem2_type,type,
% 2.69/1.56 ubforcartprodlem2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(ubforcartprodlem2,definition,
% 2.69/1.56 ( ubforcartprodlem2
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ubforcartprodlem3_type,type,
% 2.69/1.56 ubforcartprodlem3: $o ).
% 2.69/1.56
% 2.69/1.56 thf(ubforcartprodlem3,definition,
% 2.69/1.56 ( ubforcartprodlem3
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodpairin_type,type,
% 2.69/1.56 cartprodpairin: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodpairin,definition,
% 2.69/1.56 ( cartprodpairin
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodmempair1_type,type,
% 2.69/1.56 cartprodmempair1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodmempair1,definition,
% 2.69/1.56 ( cartprodmempair1
% 2.69/1.56 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.69/1.56 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.69/1.56 => ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ? [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 & ( Xu
% 2.69/1.56 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodmempair_type,type,
% 2.69/1.56 cartprodmempair: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodmempair,definition,
% 2.69/1.56 ( cartprodmempair
% 2.69/1.56 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.69/1.56 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.69/1.56 => ( iskpair @ Xu ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setunionE2_type,type,
% 2.69/1.56 setunionE2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setunionE2,definition,
% 2.69/1.56 ( setunionE2
% 2.69/1.56 = ( ! [A: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ ( setunion @ A ) )
% 2.69/1.56 => ? [X: $i] :
% 2.69/1.56 ( ( in @ X @ A )
% 2.69/1.56 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setunionsingleton1_type,type,
% 2.69/1.56 setunionsingleton1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setunionsingleton1,definition,
% 2.69/1.56 ( setunionsingleton1
% 2.69/1.56 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setunionsingleton2_type,type,
% 2.69/1.56 setunionsingleton2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setunionsingleton2,definition,
% 2.69/1.56 ( setunionsingleton2
% 2.69/1.56 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setunionsingleton_type,type,
% 2.69/1.56 setunionsingleton: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setunionsingleton,definition,
% 2.69/1.56 ( setunionsingleton
% 2.69/1.56 = ( ! [Xx: $i] :
% 2.69/1.56 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.69/1.56 = Xx ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(singleton_type,type,
% 2.69/1.56 singleton: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(singleton,definition,
% 2.69/1.56 ( singleton
% 2.69/1.56 = ( ^ [A: $i] :
% 2.69/1.56 ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( A
% 2.69/1.56 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(singletonprop_type,type,
% 2.69/1.56 singletonprop: $o ).
% 2.69/1.56
% 2.69/1.56 thf(singletonprop,definition,
% 2.69/1.56 ( singletonprop
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ A )
% 2.69/1.56 => ( ( Xphi @ Xx )
% 2.69/1.56 => ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) )
% 2.69/1.56 => ( ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( Xphi @ Xx ) )
% 2.69/1.56 => ( singleton
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ex1_type,type,
% 2.69/1.56 ex1: $i > ( $i > $o ) > $o ).
% 2.69/1.56
% 2.69/1.56 thf(ex1,definition,
% 2.69/1.56 ( ex1
% 2.69/1.56 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( singleton
% 2.69/1.56 @ ( dsetconstr @ A
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ex1E1_type,type,
% 2.69/1.56 ex1E1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(ex1E1,definition,
% 2.69/1.56 ( ex1E1
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ( ex1 @ A
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.69/1.56 => ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ex1I_type,type,
% 2.69/1.56 ex1I: $o ).
% 2.69/1.56
% 2.69/1.56 thf(ex1I,definition,
% 2.69/1.56 ( ex1I
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ( ( Xphi @ Xx )
% 2.69/1.56 => ( ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ A )
% 2.69/1.56 => ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xy = Xx ) ) )
% 2.69/1.56 => ( ex1 @ A
% 2.69/1.56 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ex1I2_type,type,
% 2.69/1.56 ex1I2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(ex1I2,definition,
% 2.69/1.56 ( ex1I2
% 2.69/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.69/1.56 ( ! [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ A )
% 2.69/1.56 => ( ( Xphi @ Xx )
% 2.69/1.56 => ( ( Xphi @ Xy )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) )
% 2.69/1.56 => ( ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ( Xphi @ Xx ) )
% 2.69/1.56 => ( ex1 @ A
% 2.69/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(singletonsuniq_type,type,
% 2.69/1.56 singletonsuniq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(singletonsuniq,definition,
% 2.69/1.56 ( singletonsuniq
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( ( setadjoin @ Xx @ emptyset )
% 2.69/1.56 = ( setadjoin @ Xy @ emptyset ) )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(atmost1p_type,type,
% 2.69/1.56 atmost1p: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(atleast2p_type,type,
% 2.69/1.56 atleast2p: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(atmost2p_type,type,
% 2.69/1.56 atmost2p: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairsetp_type,type,
% 2.69/1.56 upairsetp: $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjL1_type,type,
% 2.69/1.56 setukpairinjL1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjL1,definition,
% 2.69/1.56 ( setukpairinjL1
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.69/1.56 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.69/1.56 => ( Xx = Xz ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(kfstsingleton_type,type,
% 2.69/1.56 kfstsingleton: $o ).
% 2.69/1.56
% 2.69/1.56 thf(kfstsingleton,definition,
% 2.69/1.56 ( kfstsingleton
% 2.69/1.56 = ( ! [Xu: $i] :
% 2.69/1.56 ( ( iskpair @ Xu )
% 2.69/1.56 => ( singleton
% 2.69/1.56 @ ( dsetconstr @ ( setunion @ Xu )
% 2.69/1.56 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(theprop_type,type,
% 2.69/1.56 theprop: $o ).
% 2.69/1.56
% 2.69/1.56 thf(theprop,definition,
% 2.69/1.56 ( theprop
% 2.69/1.56 = ( ! [X: $i] :
% 2.69/1.56 ( ( singleton @ X )
% 2.69/1.56 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(kfst_type,type,
% 2.69/1.56 kfst: $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(kfstpairEq_type,type,
% 2.69/1.56 kfstpairEq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(kfstpairEq,definition,
% 2.69/1.56 ( kfstpairEq
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.69/1.56 = Xx ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodfstin_type,type,
% 2.69/1.56 cartprodfstin: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodfstin,definition,
% 2.69/1.56 ( cartprodfstin
% 2.69/1.56 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.69/1.56 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.69/1.56 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjL2_type,type,
% 2.69/1.56 setukpairinjL2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjL2,definition,
% 2.69/1.56 ( setukpairinjL2
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.69/1.56 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.69/1.56 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.69/1.56 => ( Xx = Xz ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjL_type,type,
% 2.69/1.56 setukpairinjL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjL,definition,
% 2.69/1.56 ( setukpairinjL
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.69/1.56 ( ( ( kpair @ Xx @ Xy )
% 2.69/1.56 = ( kpair @ Xz @ Xu ) )
% 2.69/1.56 => ( Xx = Xz ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR11_type,type,
% 2.69/1.56 setukpairinjR11: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR11,definition,
% 2.69/1.56 ( setukpairinjR11
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx = Xy )
% 2.69/1.56 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.69/1.56 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR12_type,type,
% 2.69/1.56 setukpairinjR12: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR12,definition,
% 2.69/1.56 ( setukpairinjR12
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( Xx = Xy )
% 2.69/1.56 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.69/1.56 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR1_type,type,
% 2.69/1.56 setukpairinjR1: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR1,definition,
% 2.69/1.56 ( setukpairinjR1
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.69/1.56 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.69/1.56 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.69/1.56 => ( ( Xz = Xu )
% 2.69/1.56 => ( Xy = Xu ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(upairequniteq_type,type,
% 2.69/1.56 upairequniteq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(upairequniteq,definition,
% 2.69/1.56 ( upairequniteq
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.69/1.56 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.69/1.56 = ( setadjoin @ Xz @ emptyset ) )
% 2.69/1.56 => ( Xx = Xy ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR2_type,type,
% 2.69/1.56 setukpairinjR2: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR2,definition,
% 2.69/1.56 ( setukpairinjR2
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.69/1.56 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.69/1.56 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.69/1.56 => ( Xy = Xu ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR_type,type,
% 2.69/1.56 setukpairinjR: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setukpairinjR,definition,
% 2.69/1.56 ( setukpairinjR
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.69/1.56 ( ( ( kpair @ Xx @ Xy )
% 2.69/1.56 = ( kpair @ Xz @ Xu ) )
% 2.69/1.56 => ( Xy = Xu ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ksndsingleton_type,type,
% 2.69/1.56 ksndsingleton: $o ).
% 2.69/1.56
% 2.69/1.56 thf(ksndsingleton,definition,
% 2.69/1.56 ( ksndsingleton
% 2.69/1.56 = ( ! [Xu: $i] :
% 2.69/1.56 ( ( iskpair @ Xu )
% 2.69/1.56 => ( singleton
% 2.69/1.56 @ ( dsetconstr @ ( setunion @ Xu )
% 2.69/1.56 @ ^ [Xx: $i] :
% 2.69/1.56 ( Xu
% 2.69/1.56 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(ksnd_type,type,
% 2.69/1.56 ksnd: $i > $i ).
% 2.69/1.56
% 2.69/1.56 thf(ksndpairEq_type,type,
% 2.69/1.56 ksndpairEq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(ksndpairEq,definition,
% 2.69/1.56 ( ksndpairEq
% 2.69/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.69/1.56 = Xy ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(kpairsurjEq_type,type,
% 2.69/1.56 kpairsurjEq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(kpairsurjEq,definition,
% 2.69/1.56 ( kpairsurjEq
% 2.69/1.56 = ( ! [Xu: $i] :
% 2.69/1.56 ( ( iskpair @ Xu )
% 2.69/1.56 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.69/1.56 = Xu ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodsndin_type,type,
% 2.69/1.56 cartprodsndin: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodsndin,definition,
% 2.69/1.56 ( cartprodsndin
% 2.69/1.56 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.69/1.56 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.69/1.56 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodpairmemEL_type,type,
% 2.69/1.56 cartprodpairmemEL: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodpairmemEL,definition,
% 2.69/1.56 ( cartprodpairmemEL
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.69/1.56 => ( in @ Xx @ A ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodpairmemER_type,type,
% 2.69/1.56 cartprodpairmemER: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodpairmemER,definition,
% 2.69/1.56 ( cartprodpairmemER
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.69/1.56 => ( in @ Xy @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodmempaircEq_type,type,
% 2.69/1.56 cartprodmempaircEq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodmempaircEq,definition,
% 2.69/1.56 ( cartprodmempaircEq
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( ( kpair @ Xx @ Xy )
% 2.69/1.56 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodfstpairEq_type,type,
% 2.69/1.56 cartprodfstpairEq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodfstpairEq,definition,
% 2.69/1.56 ( cartprodfstpairEq
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.69/1.56 = Xx ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodsndpairEq_type,type,
% 2.69/1.56 cartprodsndpairEq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodsndpairEq,definition,
% 2.69/1.56 ( cartprodsndpairEq
% 2.69/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.69/1.56 = Xy ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodpairsurjEq_type,type,
% 2.69/1.56 cartprodpairsurjEq: $o ).
% 2.69/1.56
% 2.69/1.56 thf(cartprodpairsurjEq,definition,
% 2.69/1.56 ( cartprodpairsurjEq
% 2.69/1.56 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.69/1.56 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.69/1.56 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.69/1.56 = Xu ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(breln_type,type,
% 2.69/1.56 breln: $i > $i > $i > $o ).
% 2.69/1.56
% 2.69/1.56 thf(breln,definition,
% 2.69/1.56 ( breln
% 2.69/1.56 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstr_type,type,
% 2.69/1.56 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstr,definition,
% 2.69/1.56 ( dpsetconstr
% 2.69/1.56 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.69/1.56 ( dsetconstr @ ( cartprod @ A @ B )
% 2.69/1.56 @ ^ [Xu: $i] :
% 2.69/1.56 ? [Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 & ? [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 & ( Xphi @ Xx @ Xy )
% 2.69/1.56 & ( Xu
% 2.69/1.56 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstrI_type,type,
% 2.69/1.56 dpsetconstrI: $o ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstrI,definition,
% 2.69/1.56 ( dpsetconstrI
% 2.69/1.56 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( ( Xphi @ Xx @ Xy )
% 2.69/1.56 => ( in @ ( kpair @ Xx @ Xy )
% 2.69/1.56 @ ( dpsetconstr @ A @ B
% 2.69/1.56 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstrSub_type,type,
% 2.69/1.56 dpsetconstrSub: $o ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstrSub,definition,
% 2.69/1.56 ( dpsetconstrSub
% 2.69/1.56 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.69/1.56 ( subset
% 2.69/1.56 @ ( dpsetconstr @ A @ B
% 2.69/1.56 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.69/1.56 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(setOfPairsIsBReln_type,type,
% 2.69/1.56 setOfPairsIsBReln: $o ).
% 2.69/1.56
% 2.69/1.56 thf(setOfPairsIsBReln,definition,
% 2.69/1.56 ( setOfPairsIsBReln
% 2.69/1.56 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.69/1.56 ( breln @ A @ B
% 2.69/1.56 @ ( dpsetconstr @ A @ B
% 2.69/1.56 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstrERa_type,type,
% 2.69/1.56 dpsetconstrERa: $o ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstrERa,definition,
% 2.69/1.56 ( dpsetconstrERa
% 2.69/1.56 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.69/1.56 ( ( in @ Xx @ A )
% 2.69/1.56 => ! [Xy: $i] :
% 2.69/1.56 ( ( in @ Xy @ B )
% 2.69/1.56 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.69/1.56 @ ( dpsetconstr @ A @ B
% 2.69/1.56 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.69/1.56 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.69/1.56
% 2.69/1.56 thf(dpsetconstrEL1,conjecture,
% 2.69/1.56 ( setextAx
% 2.69/1.56 => ( emptysetAx
% 2.69/1.56 => ( setadjoinAx
% 2.69/1.56 => ( powersetAx
% 2.69/1.56 => ( setunionAx
% 2.69/1.56 => ( omega0Ax
% 2.69/1.56 => ( omegaSAx
% 2.69/1.56 => ( omegaIndAx
% 2.69/1.56 => ( replAx
% 2.69/1.56 => ( foundationAx
% 2.69/1.56 => ( wellorderingAx
% 2.69/1.56 => ( descrp
% 2.69/1.56 => ( dsetconstrI
% 2.69/1.56 => ( dsetconstrEL
% 2.69/1.56 => ( dsetconstrER
% 2.69/1.56 => ( exuE1
% 2.69/1.56 => ( prop2setE
% 2.69/1.56 => ( emptysetE
% 2.69/1.56 => ( emptysetimpfalse
% 2.69/1.56 => ( notinemptyset
% 2.69/1.56 => ( exuE3e
% 2.69/1.56 => ( setext
% 2.69/1.56 => ( emptyI
% 2.69/1.56 => ( noeltsimpempty
% 2.69/1.56 => ( setbeta
% 2.69/1.56 => ( nonemptyE1
% 2.69/1.56 => ( nonemptyI
% 2.69/1.56 => ( nonemptyI1
% 2.69/1.56 => ( setadjoinIL
% 2.69/1.56 => ( emptyinunitempty
% 2.69/1.56 => ( setadjoinIR
% 2.69/1.56 => ( setadjoinE
% 2.69/1.56 => ( setadjoinOr
% 2.69/1.56 => ( setoftrueEq
% 2.69/1.56 => ( powersetI
% 2.69/1.56 => ( emptyinPowerset
% 2.69/1.56 => ( emptyInPowerset
% 2.69/1.56 => ( powersetE
% 2.69/1.56 => ( setunionI
% 2.69/1.56 => ( setunionE
% 2.69/1.56 => ( subPowSU
% 2.69/1.56 => ( exuE2
% 2.69/1.56 => ( nonemptyImpWitness
% 2.69/1.56 => ( uniqinunit
% 2.69/1.56 => ( notinsingleton
% 2.69/1.56 => ( eqinunit
% 2.69/1.56 => ( singletonsswitch
% 2.69/1.56 => ( upairsetE
% 2.69/1.56 => ( upairsetIL
% 2.69/1.56 => ( upairsetIR
% 2.69/1.56 => ( emptyE1
% 2.69/1.56 => ( vacuousDall
% 2.69/1.56 => ( quantDeMorgan1
% 2.69/1.56 => ( quantDeMorgan2
% 2.69/1.56 => ( quantDeMorgan3
% 2.69/1.56 => ( quantDeMorgan4
% 2.69/1.56 => ( prop2setI
% 2.69/1.56 => ( prop2set2propI
% 2.69/1.56 => ( notdexE
% 2.69/1.56 => ( notdallE
% 2.69/1.56 => ( exuI1
% 2.69/1.56 => ( exuI3
% 2.69/1.56 => ( exuI2
% 2.69/1.56 => ( inCongP
% 2.69/1.56 => ( in__Cong
% 2.69/1.56 => ( exuE3u
% 2.69/1.56 => ( exu__Cong
% 2.69/1.56 => ( emptyset__Cong
% 2.69/1.56 => ( setadjoin__Cong
% 2.69/1.56 => ( powerset__Cong
% 2.69/1.56 => ( setunion__Cong
% 2.69/1.56 => ( omega__Cong
% 2.69/1.56 => ( exuEu
% 2.69/1.56 => ( descr__Cong
% 2.69/1.56 => ( dsetconstr__Cong
% 2.69/1.56 => ( subsetI1
% 2.69/1.56 => ( eqimpsubset2
% 2.69/1.56 => ( eqimpsubset1
% 2.69/1.56 => ( subsetI2
% 2.69/1.56 => ( emptysetsubset
% 2.69/1.56 => ( subsetE
% 2.69/1.56 => ( subsetE2
% 2.69/1.56 => ( notsubsetI
% 2.69/1.56 => ( notequalI1
% 2.69/1.56 => ( notequalI2
% 2.69/1.56 => ( subsetRefl
% 2.69/1.56 => ( subsetTrans
% 2.69/1.56 => ( setadjoinSub
% 2.69/1.56 => ( setadjoinSub2
% 2.69/1.56 => ( subset2powerset
% 2.69/1.56 => ( setextsub
% 2.69/1.56 => ( subsetemptysetimpeq
% 2.69/1.56 => ( powersetI1
% 2.69/1.56 => ( powersetE1
% 2.69/1.56 => ( inPowerset
% 2.69/1.56 => ( powersetsubset
% 2.69/1.56 => ( sepInPowerset
% 2.69/1.56 => ( sepSubset
% 2.69/1.56 => ( binunionIL
% 2.69/1.56 => ( upairset2IR
% 2.69/1.56 => ( binunionIR
% 2.69/1.56 => ( binunionEcases
% 2.69/1.56 => ( binunionE
% 2.69/1.56 => ( binunionLsub
% 2.69/1.56 => ( binunionRsub
% 2.69/1.56 => ( binintersectI
% 2.69/1.56 => ( binintersectSubset5
% 2.69/1.56 => ( binintersectEL
% 2.69/1.56 => ( binintersectLsub
% 2.69/1.56 => ( binintersectSubset2
% 2.69/1.56 => ( binintersectSubset3
% 2.69/1.56 => ( binintersectER
% 2.69/1.56 => ( disjointsetsI1
% 2.69/1.56 => ( binintersectRsub
% 2.69/1.56 => ( binintersectSubset4
% 2.69/1.56 => ( binintersectSubset1
% 2.69/1.56 => ( bs114d
% 2.69/1.56 => ( setminusI
% 2.69/1.56 => ( setminusEL
% 2.69/1.56 => ( setminusER
% 2.69/1.56 => ( setminusSubset2
% 2.69/1.56 => ( setminusERneg
% 2.69/1.56 => ( setminusELneg
% 2.69/1.56 => ( setminusILneg
% 2.69/1.56 => ( setminusIRneg
% 2.69/1.56 => ( setminusLsub
% 2.69/1.56 => ( setminusSubset1
% 2.69/1.56 => ( symdiffE
% 2.69/1.56 => ( symdiffI1
% 2.69/1.56 => ( symdiffI2
% 2.69/1.56 => ( symdiffIneg1
% 2.69/1.56 => ( symdiffIneg2
% 2.69/1.56 => ( secondinupair
% 2.69/1.56 => ( setukpairIL
% 2.69/1.56 => ( setukpairIR
% 2.69/1.56 => ( kpairiskpair
% 2.69/1.56 => ( kpairp
% 2.69/1.56 => ( singletonsubset
% 2.69/1.56 => ( singletoninpowerset
% 2.69/1.56 => ( singletoninpowunion
% 2.69/1.56 => ( upairset2E
% 2.69/1.56 => ( upairsubunion
% 2.69/1.56 => ( upairinpowunion
% 2.69/1.56 => ( ubforcartprodlem1
% 2.69/1.56 => ( ubforcartprodlem2
% 2.69/1.56 => ( ubforcartprodlem3
% 2.69/1.56 => ( cartprodpairin
% 2.69/1.56 => ( cartprodmempair1
% 2.69/1.56 => ( cartprodmempair
% 2.69/1.56 => ( setunionE2
% 2.69/1.56 => ( setunionsingleton1
% 2.69/1.56 => ( setunionsingleton2
% 2.69/1.56 => ( setunionsingleton
% 2.69/1.56 => ( singletonprop
% 2.69/1.56 => ( ex1E1
% 2.69/1.56 => ( ex1I
% 2.69/1.56 => ( ex1I2
% 2.69/1.56 => ( singletonsuniq
% 2.69/1.56 => ( setukpairinjL1
% 2.69/1.56 => ( kfstsingleton
% 2.69/1.56 => ( theprop
% 2.69/1.56 => ( kfstpairEq
% 2.69/1.56 => ( cartprodfstin
% 2.69/1.56 => ( setukpairinjL2
% 2.69/1.56 => ( setukpairinjL
% 2.69/1.56 => ( setukpairinjR11
% 2.69/1.56 => ( setukpairinjR12
% 2.69/1.56 => ( setukpairinjR1
% 2.69/1.56 => ( upairequniteq
% 2.69/1.56 => ( setukpairinjR2
% 2.69/1.56 => ( setukpairinjR
% 2.69/1.56 => ( ksndsingleton
% 2.69/1.56 => ( ksndpairEq
% 2.69/1.56 => ( kpairsurjEq
% 2.69/1.56 => ( cartprodsndin
% 2.69/1.56 => ( cartprodpairmemEL
% 2.69/1.56 => ( cartprodpairmemER
% 2.69/1.56 => ( cartprodmempaircEq
% 2.69/1.56 => ( cartprodfstpairEq
% 2.69/1.56 => ( cartprodsndpairEq
% 2.69/1.56 => ( cartprodpairsurjEq
% 2.69/1.56 => ( dpsetconstrI
% 2.69/1.56 => ( dpsetconstrSub
% 2.69/1.56 => ( setOfPairsIsBReln
% 2.69/1.56 => ( dpsetconstrERa
% 2.69/1.56 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.69/1.56 ( ( in @ ( kpair @ Xx @ Xy )
% 2.69/1.56 @ ( dpsetconstr @ A @ B
% 2.69/1.56 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.69/1.56 => ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.69/1.56 ------------------------
% 2.69/1.59 % (8320)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_8088 for (2999ds/27Mi)
% 2.69/1.59 % (8318)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/183Mi)
% 2.69/1.59 % (8323)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_8088 for (2999ds/275Mi)
% 2.69/1.59 % (8319)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_8088 for (2999ds/4Mi)
% 2.69/1.59 % (8321)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/2Mi)
% 2.69/1.59 % (8322)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_8088 for (2999ds/2Mi)
% 2.69/1.59 % (8324)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/18Mi)
% 2.69/1.59 % (8320)Instruction limit reached!
% 2.69/1.59 % (8320)------------------------------
% 2.69/1.59 % (8320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (8320)Termination reason: Unknown
% 2.69/1.59 % (8320)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (8320)Memory used [KB]: 1918
% 2.69/1.59 % (8320)Time elapsed: 0.009 s
% 2.69/1.59 % (8320)Instructions burned: 29 (million)
% 2.69/1.59 % (8320)------------------------------
% 2.69/1.59 % (8320)------------------------------
% 2.69/1.59 % (8321)Instruction limit reached!
% 2.69/1.59 % (8321)------------------------------
% 2.69/1.59 % (8321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (8321)Termination reason: Unknown
% 2.69/1.59 % (8321)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (8321)Memory used [KB]: 1279
% 2.69/1.59 % (8321)Time elapsed: 0.004 s
% 2.69/1.59 % (8321)Instructions burned: 3 (million)
% 2.69/1.59 % (8321)------------------------------
% 2.69/1.59 % (8321)------------------------------
% 2.69/1.59 % (8322)Instruction limit reached!
% 2.69/1.59 % (8322)------------------------------
% 2.69/1.59 % (8322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.59 % (8322)Termination reason: Unknown
% 2.69/1.59 % (8322)Termination phase: shuffling
% 2.69/1.59
% 2.69/1.59 % (8322)Memory used [KB]: 1279
% 2.69/1.59 % (8322)Time elapsed: 0.004 s
% 2.69/1.59 % (8322)Instructions burned: 3 (million)
% 2.69/1.59 % (8322)------------------------------
% 2.69/1.59 % (8322)------------------------------
% 2.69/1.60 % (8319)Instruction limit reached!
% 2.69/1.60 % (8319)------------------------------
% 2.69/1.60 % (8319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.60 % (8319)Termination reason: Unknown
% 2.69/1.60 % (8319)Termination phase: shuffling
% 2.69/1.60
% 2.69/1.60 % (8319)Memory used [KB]: 1407
% 2.69/1.60 % (8319)Time elapsed: 0.005 s
% 2.69/1.60 % (8319)Instructions burned: 5 (million)
% 2.69/1.60 % (8319)------------------------------
% 2.69/1.60 % (8319)------------------------------
% 2.77/1.60 % (8334)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/3Mi)
% 2.77/1.60 % (8334)Instruction limit reached!
% 2.77/1.60 % (8334)------------------------------
% 2.77/1.60 % (8334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.60 % (8334)Termination reason: Unknown
% 2.77/1.60 % (8334)Termination phase: shuffling
% 2.77/1.60
% 2.77/1.60 % (8334)Memory used [KB]: 1279
% 2.77/1.60 % (8334)Time elapsed: 0.002 s
% 2.77/1.60 % (8334)Instructions burned: 3 (million)
% 2.77/1.60 % (8334)------------------------------
% 2.77/1.60 % (8334)------------------------------
% 2.77/1.61 % (8324)Instruction limit reached!
% 2.77/1.61 % (8324)------------------------------
% 2.77/1.61 % (8324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.61 % (8324)Termination reason: Unknown
% 2.77/1.61 % (8324)Termination phase: Property scanning
% 2.77/1.61
% 2.77/1.61 % (8324)Memory used [KB]: 1663
% 2.77/1.61 % (8324)Time elapsed: 0.014 s
% 2.77/1.61 % (8324)Instructions burned: 18 (million)
% 2.77/1.61 % (8324)------------------------------
% 2.77/1.61 % (8324)------------------------------
% 2.77/1.61 % (8337)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_8088 for (2999ds/15Mi)
% 2.77/1.61 % (8336)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_8088 for (2999ds/37Mi)
% 2.77/1.61 % (8338)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_8088 for (2999ds/3Mi)
% 2.77/1.61 % (8343)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_8088 for (2999ds/1041Mi)
% 2.77/1.62 % (8338)Instruction limit reached!
% 2.77/1.62 % (8338)------------------------------
% 2.77/1.62 % (8338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.62 % (8338)Termination reason: Unknown
% 2.77/1.62 % (8338)Termination phase: shuffling
% 2.77/1.62
% 2.77/1.62 % (8338)Memory used [KB]: 1407
% 2.77/1.62 % (8338)Time elapsed: 0.004 s
% 2.77/1.62 % (8338)Instructions burned: 4 (million)
% 2.77/1.62 % (8338)------------------------------
% 2.77/1.62 % (8338)------------------------------
% 2.77/1.62 % (8337)Instruction limit reached!
% 2.77/1.62 % (8337)------------------------------
% 2.77/1.62 % (8337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.62 % (8337)Termination reason: Unknown
% 2.77/1.62 % (8337)Termination phase: shuffling
% 2.77/1.62
% 2.77/1.62 % (8337)Memory used [KB]: 1663
% 2.77/1.62 % (8337)Time elapsed: 0.009 s
% 2.77/1.62 % (8337)Instructions burned: 16 (million)
% 2.77/1.62 % (8337)------------------------------
% 2.77/1.62 % (8337)------------------------------
% 2.77/1.63 % (8345)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/7Mi)
% 2.77/1.63 % (8347)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/16Mi)
% 2.77/1.63 % (8345)Instruction limit reached!
% 2.77/1.63 % (8345)------------------------------
% 2.77/1.63 % (8345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.63 % (8345)Termination reason: Unknown
% 2.77/1.63 % (8345)Termination phase: shuffling
% 2.77/1.63
% 2.77/1.63 % (8345)Memory used [KB]: 1407
% 2.77/1.63 % (8345)Time elapsed: 0.007 s
% 2.77/1.63 % (8345)Instructions burned: 8 (million)
% 2.77/1.63 % (8345)------------------------------
% 2.77/1.63 % (8345)------------------------------
% 2.77/1.63 % (8349)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_8088 for (2999ds/3Mi)
% 2.77/1.63 % (8349)Instruction limit reached!
% 2.77/1.63 % (8349)------------------------------
% 2.77/1.63 % (8349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.63 % (8349)Termination reason: Unknown
% 2.77/1.63 % (8349)Termination phase: shuffling
% 2.77/1.63
% 2.77/1.63 % (8349)Memory used [KB]: 1407
% 2.77/1.63 % (8349)Time elapsed: 0.002 s
% 2.77/1.63 % (8349)Instructions burned: 4 (million)
% 2.77/1.63 % (8349)------------------------------
% 2.77/1.63 % (8349)------------------------------
% 2.77/1.63 % (8336)Instruction limit reached!
% 2.77/1.63 % (8336)------------------------------
% 2.77/1.63 % (8336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.63 % (8336)Termination reason: Unknown
% 2.77/1.63 % (8336)Termination phase: Property scanning
% 2.77/1.63
% 2.77/1.63 % (8336)Memory used [KB]: 1918
% 2.77/1.63 % (8336)Time elapsed: 0.021 s
% 2.77/1.63 % (8336)Instructions burned: 38 (million)
% 2.77/1.63 % (8336)------------------------------
% 2.77/1.63 % (8336)------------------------------
% 2.77/1.63 % (8347)Instruction limit reached!
% 2.77/1.63 % (8347)------------------------------
% 2.77/1.63 % (8347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.63 % (8347)Termination reason: Unknown
% 2.77/1.63 % (8347)Termination phase: shuffling
% 2.77/1.63
% 2.77/1.63 % (8347)Memory used [KB]: 1791
% 2.77/1.63 % (8347)Time elapsed: 0.007 s
% 2.77/1.63 % (8347)Instructions burned: 17 (million)
% 2.77/1.63 % (8347)------------------------------
% 2.77/1.63 % (8347)------------------------------
% 2.77/1.64 % (8318)Instruction limit reached!
% 2.77/1.64 % (8318)------------------------------
% 2.77/1.64 % (8318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.64 % (8318)Termination reason: Unknown
% 2.77/1.64 % (8318)Termination phase: Saturation
% 2.77/1.64
% 2.77/1.64 % (8318)Memory used [KB]: 7419
% 2.77/1.64 % (8318)Time elapsed: 0.055 s
% 2.77/1.64 % (8318)Instructions burned: 185 (million)
% 2.77/1.64 % (8318)------------------------------
% 2.77/1.64 % (8318)------------------------------
% 2.77/1.64 % (8355)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/7Mi)
% 2.77/1.64 % (8355)Instruction limit reached!
% 2.77/1.64 % (8355)------------------------------
% 2.77/1.64 % (8355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.64 % (8355)Termination reason: Unknown
% 2.77/1.64 % (8355)Termination phase: shuffling
% 2.77/1.64
% 2.77/1.64 % (8355)Memory used [KB]: 1407
% 2.77/1.64 % (8355)Time elapsed: 0.003 s
% 2.77/1.64 % (8355)Instructions burned: 7 (million)
% 2.77/1.64 % (8355)------------------------------
% 2.77/1.64 % (8355)------------------------------
% 2.77/1.64 % (8358)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/4Mi)
% 2.77/1.65 % (8358)Instruction limit reached!
% 2.77/1.65 % (8358)------------------------------
% 2.77/1.65 % (8358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.65 % (8358)Termination reason: Unknown
% 2.77/1.65 % (8358)Termination phase: shuffling
% 2.77/1.65
% 2.77/1.65 % (8358)Memory used [KB]: 1407
% 2.77/1.65 % (8358)Time elapsed: 0.003 s
% 2.77/1.65 % (8358)Instructions burned: 4 (million)
% 2.77/1.65 % (8358)------------------------------
% 2.77/1.65 % (8358)------------------------------
% 2.77/1.65 % (8354)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_8088 for (2999ds/3Mi)
% 2.77/1.65 % (8354)Instruction limit reached!
% 2.77/1.65 % (8354)------------------------------
% 2.77/1.65 % (8354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.65 % (8354)Termination reason: Unknown
% 2.77/1.65 % (8354)Termination phase: shuffling
% 2.77/1.65
% 2.77/1.65 % (8354)Memory used [KB]: 1279
% 2.77/1.65 % (8354)Time elapsed: 0.003 s
% 2.77/1.65 % (8354)Instructions burned: 3 (million)
% 2.77/1.65 % (8354)------------------------------
% 2.77/1.65 % (8354)------------------------------
% 2.77/1.65 % (8357)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/3Mi)
% 2.77/1.65 % (8362)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/18Mi)
% 2.77/1.65 % (8357)Instruction limit reached!
% 2.77/1.65 % (8357)------------------------------
% 2.77/1.65 % (8357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.65 % (8357)Termination reason: Unknown
% 2.77/1.65 % (8357)Termination phase: shuffling
% 2.77/1.65
% 2.77/1.65 % (8357)Memory used [KB]: 1407
% 2.77/1.65 % (8357)Time elapsed: 0.004 s
% 2.77/1.65 % (8357)Instructions burned: 4 (million)
% 2.77/1.65 % (8357)------------------------------
% 2.77/1.65 % (8357)------------------------------
% 2.77/1.65 % (8364)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/710Mi)
% 2.77/1.66 % (8362)Instruction limit reached!
% 2.77/1.66 % (8362)------------------------------
% 2.77/1.66 % (8362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.66 % (8362)Termination reason: Unknown
% 2.77/1.66 % (8362)Termination phase: shuffling
% 2.77/1.66
% 2.77/1.66 % (8362)Memory used [KB]: 1663
% 2.77/1.66 % (8362)Time elapsed: 0.007 s
% 2.77/1.66 % (8362)Instructions burned: 18 (million)
% 2.77/1.66 % (8362)------------------------------
% 2.77/1.66 % (8362)------------------------------
% 2.77/1.66 % (8366)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/6Mi)
% 2.77/1.66 % (8366)Instruction limit reached!
% 2.77/1.66 % (8366)------------------------------
% 2.77/1.66 % (8366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.66 % (8366)Termination reason: Unknown
% 2.77/1.66 % (8366)Termination phase: shuffling
% 2.77/1.66
% 2.77/1.66 % (8366)Memory used [KB]: 1407
% 2.77/1.66 % (8366)Time elapsed: 0.004 s
% 2.77/1.66 % (8366)Instructions burned: 7 (million)
% 2.77/1.66 % (8366)------------------------------
% 2.77/1.66 % (8366)------------------------------
% 2.77/1.66 % (8368)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_8088 for (2999ds/902Mi)
% 2.77/1.66 % (8370)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_8088 for (2999ds/21Mi)
% 2.77/1.67 % (8373)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/5Mi)
% 2.77/1.67 % (8373)Instruction limit reached!
% 2.77/1.67 % (8373)------------------------------
% 2.77/1.67 % (8373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.67 % (8373)Termination reason: Unknown
% 2.77/1.67 % (8373)Termination phase: shuffling
% 2.77/1.67
% 2.77/1.67 % (8373)Memory used [KB]: 1407
% 2.77/1.67 % (8373)Time elapsed: 0.003 s
% 2.77/1.67 % (8373)Instructions burned: 7 (million)
% 2.77/1.67 % (8373)------------------------------
% 2.77/1.67 % (8373)------------------------------
% 2.77/1.67 % (8374)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_8088 for (2999ds/6Mi)
% 2.77/1.67 % (8374)Instruction limit reached!
% 2.77/1.67 % (8374)------------------------------
% 2.77/1.67 % (8374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.67 % (8374)Termination reason: Unknown
% 2.77/1.67 % (8374)Termination phase: shuffling
% 2.77/1.67
% 2.77/1.67 % (8374)Memory used [KB]: 1407
% 2.77/1.67 % (8374)Time elapsed: 0.004 s
% 2.77/1.67 % (8374)Instructions burned: 8 (million)
% 2.77/1.67 % (8374)------------------------------
% 2.77/1.67 % (8374)------------------------------
% 2.77/1.67 % (8370)Instruction limit reached!
% 2.77/1.67 % (8370)------------------------------
% 2.77/1.67 % (8370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.67 % (8370)Termination reason: Unknown
% 2.77/1.67 % (8370)Termination phase: shuffling
% 2.77/1.67
% 2.77/1.67 % (8370)Memory used [KB]: 1791
% 2.77/1.67 % (8370)Time elapsed: 0.008 s
% 2.77/1.67 % (8370)Instructions burned: 22 (million)
% 2.77/1.67 % (8370)------------------------------
% 2.77/1.67 % (8370)------------------------------
% 2.77/1.68 % (8323)Instruction limit reached!
% 2.77/1.68 % (8323)------------------------------
% 2.77/1.68 % (8323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.68 % (8323)Termination reason: Unknown
% 2.77/1.68 % (8323)Termination phase: Saturation
% 2.77/1.68
% 2.77/1.68 % (8323)Memory used [KB]: 8315
% 2.77/1.68 % (8323)Time elapsed: 0.092 s
% 2.77/1.68 % (8323)Instructions burned: 275 (million)
% 2.77/1.68 % (8323)------------------------------
% 2.77/1.68 % (8323)------------------------------
% 2.77/1.68 % (8377)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8088 for (2999ds/377Mi)
% 2.77/1.68 % (8380)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_8088 for (2999ds/19Mi)
% 2.77/1.68 % (8378)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_8088 for (2999ds/779Mi)
% 2.77/1.68 % (8380)Instruction limit reached!
% 2.77/1.68 % (8380)------------------------------
% 2.77/1.68 % (8380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.68 % (8380)Termination reason: Unknown
% 2.77/1.68 % (8380)Termination phase: shuffling
% 2.77/1.68
% 2.77/1.68 % (8380)Memory used [KB]: 1663
% 2.77/1.68 % (8380)Time elapsed: 0.006 s
% 2.77/1.68 % (8380)Instructions burned: 19 (million)
% 2.77/1.68 % (8380)------------------------------
% 2.77/1.68 % (8380)------------------------------
% 2.77/1.69 % (8384)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8088 for (2998ds/879Mi)
% 2.77/1.69 % (8390)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8088 for (2998ds/17Mi)
% 2.77/1.70 % (8390)Instruction limit reached!
% 2.77/1.70 % (8390)------------------------------
% 2.77/1.70 % (8390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.70 % (8390)Termination reason: Unknown
% 2.77/1.70 % (8390)Termination phase: shuffling
% 2.77/1.70
% 2.77/1.70 % (8390)Memory used [KB]: 1663
% 2.77/1.70 % (8390)Time elapsed: 0.006 s
% 2.77/1.70 % (8390)Instructions burned: 17 (million)
% 2.77/1.70 % (8390)------------------------------
% 2.77/1.70 % (8390)------------------------------
% 2.77/1.71 % (8391)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_8088 for (2998ds/3Mi)
% 2.77/1.71 % (8391)Instruction limit reached!
% 2.77/1.71 % (8391)------------------------------
% 2.77/1.71 % (8391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.71 % (8391)Termination reason: Unknown
% 2.77/1.71 % (8391)Termination phase: shuffling
% 2.77/1.71
% 2.77/1.71 % (8391)Memory used [KB]: 1279
% 2.77/1.71 % (8391)Time elapsed: 0.002 s
% 2.77/1.71 % (8391)Instructions burned: 4 (million)
% 2.77/1.71 % (8391)------------------------------
% 2.77/1.71 % (8391)------------------------------
% 2.77/1.72 % (8400)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_8088 for (2998ds/30Mi)
% 2.77/1.73 % (8400)Instruction limit reached!
% 2.77/1.73 % (8400)------------------------------
% 2.77/1.73 % (8400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.73 % (8400)Termination reason: Unknown
% 2.77/1.73 % (8400)Termination phase: shuffling
% 2.77/1.73
% 2.77/1.73 % (8400)Memory used [KB]: 1918
% 2.77/1.73 % (8400)Time elapsed: 0.009 s
% 2.77/1.73 % (8400)Instructions burned: 30 (million)
% 2.77/1.73 % (8400)------------------------------
% 2.77/1.73 % (8400)------------------------------
% 2.77/1.74 % (8411)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_8088 for (2998ds/127Mi)
% 2.77/1.77 % (8411)Instruction limit reached!
% 2.77/1.77 % (8411)------------------------------
% 2.77/1.77 % (8411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.77 % (8411)Termination reason: Unknown
% 2.77/1.77 % (8411)Termination phase: Saturation
% 2.77/1.77
% 2.77/1.77 % (8411)Memory used [KB]: 6908
% 2.77/1.77 % (8411)Time elapsed: 0.035 s
% 2.77/1.77 % (8411)Instructions burned: 127 (million)
% 2.77/1.77 % (8411)------------------------------
% 2.77/1.77 % (8411)------------------------------
% 2.77/1.78 % (8432)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_8088 for (2998ds/100Mi)
% 2.77/1.79 % (8377)Instruction limit reached!
% 2.77/1.79 % (8377)------------------------------
% 2.77/1.79 % (8377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.79 % (8377)Termination reason: Unknown
% 2.77/1.79 % (8377)Termination phase: Saturation
% 2.77/1.79
% 2.77/1.79 % (8377)Memory used [KB]: 8315
% 2.77/1.79 % (8377)Time elapsed: 0.115 s
% 2.77/1.79 % (8377)Instructions burned: 378 (million)
% 2.77/1.79 % (8377)------------------------------
% 2.77/1.79 % (8377)------------------------------
% 2.77/1.80 % (8439)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_8088 for (2997ds/3Mi)
% 2.77/1.80 % (8439)Instruction limit reached!
% 2.77/1.80 % (8439)------------------------------
% 2.77/1.80 % (8439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.80 % (8439)Termination reason: Unknown
% 2.77/1.80 % (8439)Termination phase: shuffling
% 2.77/1.80
% 2.77/1.80 % (8439)Memory used [KB]: 1407
% 2.77/1.80 % (8439)Time elapsed: 0.002 s
% 2.77/1.80 % (8439)Instructions burned: 3 (million)
% 2.77/1.80 % (8439)------------------------------
% 2.77/1.80 % (8439)------------------------------
% 2.77/1.81 % (8432)Instruction limit reached!
% 2.77/1.81 % (8432)------------------------------
% 2.77/1.81 % (8432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.81 % (8432)Termination reason: Unknown
% 2.77/1.81 % (8432)Termination phase: Saturation
% 2.77/1.81
% 2.77/1.81 % (8432)Memory used [KB]: 6780
% 2.77/1.81 % (8432)Time elapsed: 0.027 s
% 2.77/1.81 % (8432)Instructions burned: 102 (million)
% 2.77/1.81 % (8432)------------------------------
% 2.77/1.81 % (8432)------------------------------
% 2.77/1.81 % (8448)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_8088 for (2997ds/20Mi)
% 2.77/1.82 % (8451)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_8088 for (2997ds/86Mi)
% 2.77/1.82 % (8448)Instruction limit reached!
% 2.77/1.82 % (8448)------------------------------
% 2.77/1.82 % (8448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.82 % (8448)Termination reason: Unknown
% 2.77/1.82 % (8448)Termination phase: Property scanning
% 2.77/1.82
% 2.77/1.82 % (8448)Memory used [KB]: 1663
% 2.77/1.82 % (8448)Time elapsed: 0.008 s
% 2.77/1.82 % (8448)Instructions burned: 22 (million)
% 2.77/1.82 % (8448)------------------------------
% 2.77/1.82 % (8448)------------------------------
% 2.77/1.83 % (8457)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_8088 for (2997ds/107Mi)
% 2.77/1.84 % (8451)Instruction limit reached!
% 2.77/1.84 % (8451)------------------------------
% 2.77/1.84 % (8451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.84 % (8451)Termination reason: Unknown
% 2.77/1.84 % (8451)Termination phase: Property scanning
% 2.77/1.84
% 2.77/1.84 % (8451)Memory used [KB]: 2046
% 2.77/1.84 % (8451)Time elapsed: 0.024 s
% 2.77/1.84 % (8451)Instructions burned: 88 (million)
% 2.77/1.84 % (8451)------------------------------
% 2.77/1.84 % (8451)------------------------------
% 2.77/1.85 % (8466)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_8088 for (2997ds/39Mi)
% 2.77/1.86 % (8457)Instruction limit reached!
% 2.77/1.86 % (8457)------------------------------
% 2.77/1.86 % (8457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.86 % (8457)Termination reason: Unknown
% 2.77/1.86 % (8457)Termination phase: Saturation
% 2.77/1.86
% 2.77/1.86 % (8457)Memory used [KB]: 6652
% 2.77/1.86 % (8457)Time elapsed: 0.029 s
% 2.77/1.86 % (8457)Instructions burned: 110 (million)
% 2.77/1.86 % (8457)------------------------------
% 2.77/1.86 % (8457)------------------------------
% 2.77/1.86 % (8466)Instruction limit reached!
% 2.77/1.86 % (8466)------------------------------
% 2.77/1.86 % (8466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.86 % (8466)Termination reason: Unknown
% 2.77/1.86 % (8466)Termination phase: Property scanning
% 2.77/1.86
% 2.77/1.86 % (8466)Memory used [KB]: 1918
% 2.77/1.86 % (8466)Time elapsed: 0.011 s
% 2.77/1.86 % (8466)Instructions burned: 39 (million)
% 2.77/1.86 % (8466)------------------------------
% 2.77/1.86 % (8466)------------------------------
% 2.77/1.86 % (8474)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_8088 for (2997ds/448Mi)
% 2.77/1.87 % (8476)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_8088 for (2997ds/46Mi)
% 2.77/1.88 % (8364)Instruction limit reached!
% 2.77/1.88 % (8364)------------------------------
% 2.77/1.88 % (8364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.88 % (8343)Instruction limit reached!
% 2.77/1.88 % (8343)------------------------------
% 2.77/1.88 % (8343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.88 % (8343)Termination reason: Unknown
% 2.77/1.88 % (8364)Termination reason: Unknown
% 2.77/1.88 % (8364)Termination phase: Saturation
% 2.77/1.88 % (8343)Termination phase: Saturation
% 2.77/1.88
% 2.77/1.88
% 2.77/1.88 % (8364)Memory used [KB]: 9338
% 2.77/1.88 % (8343)Memory used [KB]: 11001
% 2.77/1.88 % (8364)Time elapsed: 0.227 s
% 2.77/1.88 % (8343)Time elapsed: 0.265 s
% 2.77/1.88 % (8364)Instructions burned: 711 (million)
% 2.77/1.88 % (8343)Instructions burned: 1043 (million)
% 2.77/1.88 % (8364)------------------------------
% 2.77/1.88 % (8364)------------------------------
% 2.77/1.88 % (8343)------------------------------
% 2.77/1.88 % (8343)------------------------------
% 2.77/1.88 % (8476)Instruction limit reached!
% 2.77/1.88 % (8476)------------------------------
% 2.77/1.88 % (8476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.88 % (8476)Termination reason: Unknown
% 2.77/1.88 % (8476)Termination phase: Property scanning
% 2.77/1.88
% 2.77/1.88 % (8476)Memory used [KB]: 1918
% 2.77/1.88 % (8476)Time elapsed: 0.013 s
% 2.77/1.88 % (8476)Instructions burned: 46 (million)
% 2.77/1.88 % (8476)------------------------------
% 2.77/1.88 % (8476)------------------------------
% 2.77/1.88 % (8378)Instruction limit reached!
% 2.77/1.88 % (8378)------------------------------
% 2.77/1.88 % (8378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.88 % (8378)Termination reason: Unknown
% 2.77/1.88 % (8378)Termination phase: Saturation
% 2.77/1.88
% 2.77/1.88 % (8378)Memory used [KB]: 6908
% 2.77/1.88 % (8378)Time elapsed: 0.204 s
% 2.77/1.88 % (8378)Instructions burned: 779 (million)
% 2.77/1.88 % (8378)------------------------------
% 2.77/1.88 % (8378)------------------------------
% 2.77/1.89 % (8484)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_8088 for (2996ds/507Mi)
% 2.77/1.89 % (8486)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_8088 for (2996ds/149Mi)
% 2.77/1.89 % (8483)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_8088 for (2996ds/98Mi)
% 2.77/1.89 % (8487)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_8088 for (2996ds/39Mi)
% 2.77/1.90 % (8487)Instruction limit reached!
% 2.77/1.90 % (8487)------------------------------
% 2.77/1.90 % (8487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.90 % (8487)Termination reason: Unknown
% 2.77/1.90 % (8487)Termination phase: Property scanning
% 2.77/1.90
% 2.77/1.90 % (8487)Memory used [KB]: 1918
% 2.77/1.90 % (8487)Time elapsed: 0.012 s
% 2.77/1.90 % (8487)Instructions burned: 39 (million)
% 2.77/1.90 % (8487)------------------------------
% 2.77/1.90 % (8487)------------------------------
% 2.77/1.91 % (8483)Instruction limit reached!
% 2.77/1.91 % (8483)------------------------------
% 2.77/1.91 % (8483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.91 % (8483)Termination reason: Unknown
% 2.77/1.91 % (8483)Termination phase: Saturation
% 2.77/1.91
% 2.77/1.91 % (8483)Memory used [KB]: 2174
% 2.77/1.91 % (8483)Time elapsed: 0.026 s
% 2.77/1.91 % (8483)Instructions burned: 98 (million)
% 2.77/1.91 % (8483)------------------------------
% 2.77/1.91 % (8483)------------------------------
% 2.77/1.91 % (8495)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_8088 for (2996ds/6Mi)
% 2.77/1.92 % (8495)Instruction limit reached!
% 2.77/1.92 % (8495)------------------------------
% 2.77/1.92 % (8495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.92 % (8495)Termination reason: Unknown
% 2.77/1.92 % (8495)Termination phase: shuffling
% 2.77/1.92
% 2.77/1.92 % (8495)Memory used [KB]: 1407
% 2.77/1.92 % (8495)Time elapsed: 0.004 s
% 2.77/1.92 % (8495)Instructions burned: 8 (million)
% 2.77/1.92 % (8495)------------------------------
% 2.77/1.92 % (8495)------------------------------
% 2.77/1.92 % (8501)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_8088 for (2996ds/1087Mi)
% 2.77/1.93 % (8502)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_8088 for (2996ds/47Mi)
% 2.77/1.93 % (8486)Instruction limit reached!
% 2.77/1.93 % (8486)------------------------------
% 2.77/1.93 % (8486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.93 % (8486)Termination reason: Unknown
% 2.77/1.93 % (8486)Termination phase: Saturation
% 2.77/1.93
% 2.77/1.93 % (8486)Memory used [KB]: 7291
% 2.77/1.93 % (8486)Time elapsed: 0.042 s
% 2.77/1.93 % (8486)Instructions burned: 150 (million)
% 2.77/1.93 % (8486)------------------------------
% 2.77/1.93 % (8486)------------------------------
% 2.77/1.94 % (8509)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_8088 for (2996ds/44Mi)
% 2.77/1.94 % (8502)Instruction limit reached!
% 2.77/1.94 % (8502)------------------------------
% 2.77/1.94 % (8502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.94 % (8502)Termination reason: Unknown
% 2.77/1.94 % (8502)Termination phase: Preprocessing 3
% 2.77/1.94
% 2.77/1.94 % (8502)Memory used [KB]: 2046
% 2.77/1.94 % (8502)Time elapsed: 0.015 s
% 2.77/1.94 % (8502)Instructions burned: 48 (million)
% 2.77/1.94 % (8502)------------------------------
% 2.77/1.94 % (8502)------------------------------
% 2.77/1.95 % (8512)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_8088 for (2996ds/432Mi)
% 2.77/1.95 % (8509)Instruction limit reached!
% 2.77/1.95 % (8509)------------------------------
% 2.77/1.95 % (8509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.95 % (8509)Termination reason: Unknown
% 2.77/1.95 % (8509)Termination phase: Property scanning
% 2.77/1.95
% 2.77/1.95 % (8509)Memory used [KB]: 1918
% 2.77/1.95 % (8509)Time elapsed: 0.013 s
% 2.77/1.95 % (8509)Instructions burned: 48 (million)
% 2.77/1.95 % (8509)------------------------------
% 2.77/1.95 % (8509)------------------------------
% 2.77/1.95 % (8368)Instruction limit reached!
% 2.77/1.95 % (8368)------------------------------
% 2.77/1.95 % (8368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.95 % (8368)Termination reason: Unknown
% 2.77/1.95 % (8368)Termination phase: Saturation
% 2.77/1.95
% 2.77/1.95 % (8368)Memory used [KB]: 10490
% 2.77/1.95 % (8368)Time elapsed: 0.296 s
% 2.77/1.95 % (8368)Instructions burned: 903 (million)
% 2.77/1.95 % (8368)------------------------------
% 2.77/1.95 % (8368)------------------------------
% 2.77/1.96 % (8384)Refutation not found, non-redundant clauses discarded% (8384)------------------------------
% 2.77/1.96 % (8384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.96 % (8384)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.77/1.96
% 2.77/1.96 % (8384)Memory used [KB]: 8571
% 2.77/1.96 % (8384)Time elapsed: 0.269 s
% 2.77/1.96 % (8384)Instructions burned: 861 (million)
% 2.77/1.96 % (8384)------------------------------
% 2.77/1.96 % (8384)------------------------------
% 2.77/1.96 % (8516)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_8088 for (2996ds/62Mi)
% 2.77/1.96 % (8518)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_8088 for (2996ds/31Mi)
% 2.77/1.97 % (8520)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_8088 for (2996ds/96Mi)
% 2.77/1.97 % (8518)Instruction limit reached!
% 2.77/1.97 % (8518)------------------------------
% 2.77/1.97 % (8518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.97 % (8518)Termination reason: Unknown
% 2.77/1.97 % (8518)Termination phase: Property scanning
% 2.77/1.97
% 2.77/1.97 % (8518)Memory used [KB]: 1918
% 2.77/1.97 % (8518)Time elapsed: 0.010 s
% 2.77/1.97 % (8518)Instructions burned: 31 (million)
% 2.77/1.97 % (8518)------------------------------
% 2.77/1.97 % (8518)------------------------------
% 2.77/1.97 % (8474)Instruction limit reached!
% 2.77/1.97 % (8474)------------------------------
% 2.77/1.97 % (8474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.97 % (8474)Termination reason: Unknown
% 2.77/1.97 % (8474)Termination phase: Saturation
% 2.77/1.97
% 2.77/1.97 % (8474)Memory used [KB]: 6780
% 2.77/1.97 % (8474)Time elapsed: 0.111 s
% 2.77/1.97 % (8474)Instructions burned: 452 (million)
% 2.77/1.97 % (8474)------------------------------
% 2.77/1.97 % (8474)------------------------------
% 2.77/1.98 % (8516)Instruction limit reached!
% 2.77/1.98 % (8516)------------------------------
% 2.77/1.98 % (8516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.98 % (8516)Termination reason: Unknown
% 2.77/1.98 % (8516)Termination phase: Property scanning
% 2.77/1.98
% 2.77/1.98 % (8516)Memory used [KB]: 1918
% 2.77/1.98 % (8516)Time elapsed: 0.018 s
% 2.77/1.98 % (8516)Instructions burned: 65 (million)
% 2.77/1.98 % (8516)------------------------------
% 2.77/1.98 % (8516)------------------------------
% 2.77/1.98 % (8523)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_8088 for (2995ds/453Mi)
% 2.77/1.98 % (8525)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_8088 for (2995ds/71Mi)
% 2.77/1.99 % (8527)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_8088 for (2995ds/83Mi)
% 2.77/1.99 % (8520)Instruction limit reached!
% 2.77/1.99 % (8520)------------------------------
% 2.77/1.99 % (8520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.99 % (8520)Termination reason: Unknown
% 2.77/1.99 % (8520)Termination phase: Saturation
% 2.77/1.99
% 2.77/1.99 % (8520)Memory used [KB]: 6652
% 2.77/1.99 % (8520)Time elapsed: 0.026 s
% 2.77/1.99 % (8520)Instructions burned: 96 (million)
% 2.77/1.99 % (8520)------------------------------
% 2.77/1.99 % (8520)------------------------------
% 2.77/2.00 % (8533)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_8088 for (2995ds/11Mi)
% 2.77/2.00 % (8525)Instruction limit reached!
% 2.77/2.00 % (8525)------------------------------
% 2.77/2.00 % (8525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/2.00 % (8525)Termination reason: Unknown
% 2.77/2.00 % (8525)Termination phase: Property scanning
% 2.77/2.00
% 2.77/2.00 % (8525)Memory used [KB]: 2174
% 2.77/2.00 % (8525)Time elapsed: 0.020 s
% 2.77/2.00 % (8525)Instructions burned: 74 (million)
% 2.77/2.00 % (8525)------------------------------
% 2.77/2.00 % (8525)------------------------------
% 2.77/2.00 % (8533)Instruction limit reached!
% 2.77/2.00 % (8533)------------------------------
% 2.77/2.00 % (8533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/2.00 % (8533)Termination reason: Unknown
% 2.77/2.00 % (8533)Termination phase: shuffling
% 2.77/2.00
% 2.77/2.00 % (8533)Memory used [KB]: 1535
% 2.77/2.00 % (8533)Time elapsed: 0.004 s
% 2.77/2.00 % (8533)Instructions burned: 12 (million)
% 2.77/2.00 % (8533)------------------------------
% 2.77/2.00 % (8533)------------------------------
% 2.77/2.01 % (8527)Instruction limit reached!
% 2.77/2.01 % (8527)------------------------------
% 2.77/2.01 % (8527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/2.01 % (8527)Termination reason: Unknown
% 2.77/2.01 % (8527)Termination phase: Function definition elimination
% 2.77/2.01
% 2.77/2.01 % (8527)Memory used [KB]: 2046
% 2.77/2.01 % (8527)Time elapsed: 0.022 s
% 2.77/2.01 % (8527)Instructions burned: 85 (million)
% 2.77/2.01 % (8527)------------------------------
% 2.77/2.01 % (8527)------------------------------
% 5.75/2.01 % (8539)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_8088 for (2995ds/41Mi)
% 5.75/2.01 % (8540)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8088 for (2995ds/6Mi)
% 5.75/2.02 % (8540)Instruction limit reached!
% 5.75/2.02 % (8540)------------------------------
% 5.75/2.02 % (8540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.02 % (8540)Termination reason: Unknown
% 5.75/2.02 % (8540)Termination phase: shuffling
% 5.75/2.02
% 5.75/2.02 % (8540)Memory used [KB]: 1407
% 5.75/2.02 % (8540)Time elapsed: 0.003 s
% 5.75/2.02 % (8540)Instructions burned: 7 (million)
% 5.75/2.02 % (8540)------------------------------
% 5.75/2.02 % (8540)------------------------------
% 5.75/2.02 % (8542)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_8088 for (2995ds/150Mi)
% 5.75/2.02 % (8539)Instruction limit reached!
% 5.75/2.02 % (8539)------------------------------
% 5.75/2.02 % (8539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.02 % (8539)Termination reason: Unknown
% 5.75/2.02 % (8539)Termination phase: Property scanning
% 5.75/2.02
% 5.75/2.02 % (8539)Memory used [KB]: 1918
% 5.75/2.02 % (8539)Time elapsed: 0.012 s
% 5.75/2.02 % (8539)Instructions burned: 43 (million)
% 5.75/2.02 % (8539)------------------------------
% 5.75/2.02 % (8539)------------------------------
% 5.75/2.02 % (8544)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_8088 for (2995ds/343Mi)
% 5.75/2.03 % (8547)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_8088 for (2995ds/109Mi)
% 5.75/2.04 % (8484)Instruction limit reached!
% 5.75/2.04 % (8484)------------------------------
% 5.75/2.04 % (8484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.04 % (8484)Termination reason: Unknown
% 5.75/2.04 % (8484)Termination phase: Saturation
% 5.75/2.04
% 5.75/2.04 % (8484)Memory used [KB]: 7547
% 5.75/2.04 % (8484)Time elapsed: 0.149 s
% 5.75/2.04 % (8484)Instructions burned: 507 (million)
% 5.75/2.04 % (8484)------------------------------
% 5.75/2.04 % (8484)------------------------------
% 5.75/2.05 % (8551)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_8088 for (2995ds/253Mi)
% 5.75/2.06 % (8512)Instruction limit reached!
% 5.75/2.06 % (8512)------------------------------
% 5.75/2.06 % (8512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.06 % (8512)Termination reason: Unknown
% 5.75/2.06 % (8512)Termination phase: Saturation
% 5.75/2.06
% 5.75/2.06 % (8512)Memory used [KB]: 3454
% 5.75/2.06 % (8512)Time elapsed: 0.109 s
% 5.75/2.06 % (8512)Instructions burned: 435 (million)
% 5.75/2.06 % (8512)------------------------------
% 5.75/2.06 % (8512)------------------------------
% 5.75/2.06 % (8542)Instruction limit reached!
% 5.75/2.06 % (8542)------------------------------
% 5.75/2.06 % (8542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.06 % (8542)Termination reason: Unknown
% 5.75/2.06 % (8542)Termination phase: Saturation
% 5.75/2.06
% 5.75/2.06 % (8542)Memory used [KB]: 8187
% 5.75/2.06 % (8542)Time elapsed: 0.044 s
% 5.75/2.06 % (8542)Instructions burned: 150 (million)
% 5.75/2.06 % (8542)------------------------------
% 5.75/2.06 % (8542)------------------------------
% 5.75/2.06 % (8547)Instruction limit reached!
% 5.75/2.06 % (8547)------------------------------
% 5.75/2.06 % (8547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.06 % (8547)Termination reason: Unknown
% 5.75/2.06 % (8547)Termination phase: Saturation
% 5.75/2.06
% 5.75/2.06 % (8547)Memory used [KB]: 6780
% 5.75/2.06 % (8547)Time elapsed: 0.029 s
% 5.75/2.06 % (8547)Instructions burned: 110 (million)
% 5.75/2.06 % (8547)------------------------------
% 5.75/2.06 % (8547)------------------------------
% 5.75/2.07 % (8564)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_8088 for (2995ds/140Mi)
% 5.75/2.07 % (8567)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_8088 for (2995ds/614Mi)
% 5.75/2.07 % (8568)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_8088 for (2995ds/202Mi)
% 5.75/2.10 % (8564)Instruction limit reached!
% 5.75/2.10 % (8564)------------------------------
% 5.75/2.10 % (8564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.10 % (8564)Termination reason: Unknown
% 5.75/2.10 % (8564)Termination phase: Saturation
% 5.75/2.10
% 5.75/2.10 % (8564)Memory used [KB]: 6908
% 5.75/2.10 % (8564)Time elapsed: 0.039 s
% 5.75/2.10 % (8564)Instructions burned: 140 (million)
% 5.75/2.10 % (8564)------------------------------
% 5.75/2.10 % (8564)------------------------------
% 6.23/2.11 % (8588)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_8088 for (2994ds/339Mi)
% 6.23/2.12 % (8551)Instruction limit reached!
% 6.23/2.12 % (8551)------------------------------
% 6.23/2.12 % (8551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.12 % (8551)Termination reason: Unknown
% 6.23/2.12 % (8551)Termination phase: Saturation
% 6.23/2.12
% 6.23/2.12 % (8551)Memory used [KB]: 8443
% 6.23/2.12 % (8551)Time elapsed: 0.078 s
% 6.23/2.12 % (8551)Instructions burned: 254 (million)
% 6.23/2.12 % (8551)------------------------------
% 6.23/2.12 % (8551)------------------------------
% 6.23/2.12 % (8544)Instruction limit reached!
% 6.23/2.12 % (8544)------------------------------
% 6.23/2.12 % (8544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.12 % (8544)Termination reason: Unknown
% 6.23/2.12 % (8544)Termination phase: Saturation
% 6.23/2.12
% 6.23/2.12 % (8544)Memory used [KB]: 8059
% 6.23/2.12 % (8544)Time elapsed: 0.099 s
% 6.23/2.12 % (8544)Instructions burned: 344 (million)
% 6.23/2.12 % (8544)------------------------------
% 6.23/2.12 % (8544)------------------------------
% 6.23/2.13 % (8568)Instruction limit reached!
% 6.23/2.13 % (8568)------------------------------
% 6.23/2.13 % (8568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.13 % (8568)Termination reason: Unknown
% 6.23/2.13 % (8568)Termination phase: Saturation
% 6.23/2.13
% 6.23/2.13 % (8568)Memory used [KB]: 8955
% 6.23/2.13 % (8568)Time elapsed: 0.062 s
% 6.23/2.13 % (8568)Instructions burned: 204 (million)
% 6.23/2.13 % (8568)------------------------------
% 6.23/2.13 % (8568)------------------------------
% 6.23/2.13 % (8593)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_8088 for (2994ds/283Mi)
% 6.23/2.13 % (8594)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_8088 for (2994ds/134Mi)
% 6.23/2.14 % (8595)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_8088 for (2994ds/298Mi)
% 6.23/2.15 % (8523)Instruction limit reached!
% 6.23/2.15 % (8523)------------------------------
% 6.23/2.15 % (8523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.15 % (8523)Termination reason: Unknown
% 6.23/2.15 % (8523)Termination phase: Saturation
% 6.23/2.15
% 6.23/2.15 % (8523)Memory used [KB]: 6780
% 6.23/2.15 % (8523)Time elapsed: 0.167 s
% 6.23/2.15 % (8523)Instructions burned: 455 (million)
% 6.23/2.15 % (8523)------------------------------
% 6.23/2.15 % (8523)------------------------------
% 6.23/2.17 % (8596)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_8088 for (2994ds/192Mi)
% 6.23/2.17 % (8594)Instruction limit reached!
% 6.23/2.17 % (8594)------------------------------
% 6.23/2.17 % (8594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.17 % (8594)Termination reason: Unknown
% 6.23/2.17 % (8594)Termination phase: Saturation
% 6.23/2.17
% 6.23/2.17 % (8594)Memory used [KB]: 7036
% 6.23/2.17 % (8594)Time elapsed: 0.037 s
% 6.23/2.17 % (8594)Instructions burned: 136 (million)
% 6.23/2.17 % (8594)------------------------------
% 6.23/2.17 % (8594)------------------------------
% 6.23/2.18 % (8597)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_8088 for (2994ds/258Mi)
% 6.66/2.20 % (8593)Instruction limit reached!
% 6.66/2.20 % (8593)------------------------------
% 6.66/2.20 % (8593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.20 % (8593)Termination reason: Unknown
% 6.66/2.20 % (8593)Termination phase: Saturation
% 6.66/2.20
% 6.66/2.20 % (8593)Memory used [KB]: 7419
% 6.66/2.20 % (8593)Time elapsed: 0.073 s
% 6.66/2.20 % (8593)Instructions burned: 284 (million)
% 6.66/2.20 % (8593)------------------------------
% 6.66/2.20 % (8593)------------------------------
% 6.66/2.21 % (8588)Instruction limit reached!
% 6.66/2.21 % (8588)------------------------------
% 6.66/2.21 % (8588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.21 % (8588)Termination reason: Unknown
% 6.66/2.21 % (8588)Termination phase: Saturation
% 6.66/2.21
% 6.66/2.21 % (8588)Memory used [KB]: 7931
% 6.66/2.21 % (8588)Time elapsed: 0.098 s
% 6.66/2.21 % (8588)Instructions burned: 340 (million)
% 6.66/2.21 % (8588)------------------------------
% 6.66/2.21 % (8588)------------------------------
% 6.66/2.21 % (8598)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_8088 for (2993ds/90Mi)
% 6.66/2.22 % (8595)Instruction limit reached!
% 6.66/2.22 % (8595)------------------------------
% 6.66/2.22 % (8595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.22 % (8595)Termination reason: Unknown
% 6.66/2.22 % (8595)Termination phase: Saturation
% 6.66/2.22
% 6.66/2.22 % (8595)Memory used [KB]: 6780
% 6.66/2.22 % (8595)Time elapsed: 0.076 s
% 6.66/2.22 % (8595)Instructions burned: 299 (million)
% 6.66/2.22 % (8595)------------------------------
% 6.66/2.22 % (8595)------------------------------
% 6.66/2.22 % (8599)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_8088 for (2993ds/231Mi)
% 6.66/2.22 % (8596)Instruction limit reached!
% 6.66/2.22 % (8596)------------------------------
% 6.66/2.22 % (8596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.22 % (8596)Termination reason: Unknown
% 6.66/2.22 % (8596)Termination phase: Saturation
% 6.66/2.22
% 6.66/2.22 % (8596)Memory used [KB]: 7419
% 6.66/2.22 % (8596)Time elapsed: 0.057 s
% 6.66/2.22 % (8596)Instructions burned: 195 (million)
% 6.66/2.22 % (8596)------------------------------
% 6.66/2.22 % (8596)------------------------------
% 6.66/2.23 % (8600)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_8088 for (2993ds/458Mi)
% 6.66/2.23 % (8601)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_8088 for (2993ds/31Mi)
% 6.66/2.24 % (8598)Instruction limit reached!
% 6.66/2.24 % (8598)------------------------------
% 6.66/2.24 % (8598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.24 % (8598)Termination reason: Unknown
% 6.66/2.24 % (8598)Termination phase: Twee Goal Transformation
% 6.66/2.24
% 6.66/2.24 % (8598)Memory used [KB]: 2558
% 6.66/2.24 % (8598)Time elapsed: 0.025 s
% 6.66/2.24 % (8598)Instructions burned: 91 (million)
% 6.66/2.24 % (8598)------------------------------
% 6.66/2.24 % (8598)------------------------------
% 6.66/2.24 % (8601)Instruction limit reached!
% 6.66/2.24 % (8601)------------------------------
% 6.66/2.24 % (8601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.24 % (8601)Termination reason: Unknown
% 6.66/2.24 % (8601)Termination phase: Property scanning
% 6.66/2.24
% 6.66/2.24 % (8601)Memory used [KB]: 1918
% 6.66/2.24 % (8601)Time elapsed: 0.011 s
% 6.66/2.24 % (8601)Instructions burned: 32 (million)
% 6.66/2.24 % (8601)------------------------------
% 6.66/2.24 % (8601)------------------------------
% 6.66/2.25 % (8602)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_8088 for (2993ds/297Mi)
% 6.66/2.25 % (8597)Instruction limit reached!
% 6.66/2.25 % (8597)------------------------------
% 6.66/2.25 % (8597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.25 % (8597)Termination reason: Unknown
% 6.66/2.25 % (8597)Termination phase: Saturation
% 6.66/2.25
% 6.66/2.25 % (8597)Memory used [KB]: 7803
% 6.66/2.25 % (8597)Time elapsed: 0.072 s
% 6.66/2.25 % (8597)Instructions burned: 260 (million)
% 6.66/2.25 % (8597)------------------------------
% 6.66/2.25 % (8597)------------------------------
% 6.66/2.25 % (8603)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_8088 for (2993ds/987Mi)
% 6.66/2.25 % (8567)Instruction limit reached!
% 6.66/2.25 % (8567)------------------------------
% 6.66/2.25 % (8567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.25 % (8567)Termination reason: Unknown
% 6.66/2.25 % (8567)Termination phase: Saturation
% 6.66/2.25
% 6.66/2.25 % (8567)Memory used [KB]: 8571
% 6.66/2.25 % (8567)Time elapsed: 0.185 s
% 6.66/2.25 % (8567)Instructions burned: 615 (million)
% 6.66/2.25 % (8567)------------------------------
% 6.66/2.25 % (8567)------------------------------
% 6.66/2.26 % (8604)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_8088 for (2993ds/182Mi)
% 6.66/2.26 % (8605)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_8088 for (2993ds/182Mi)
% 6.66/2.27 % (8501)Instruction limit reached!
% 6.66/2.27 % (8501)------------------------------
% 6.66/2.27 % (8501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.27 % (8501)Termination reason: Unknown
% 6.66/2.27 % (8501)Termination phase: Saturation
% 6.66/2.27
% 6.66/2.27 % (8501)Memory used [KB]: 10618
% 6.66/2.27 % (8501)Time elapsed: 0.349 s
% 6.66/2.27 % (8501)Instructions burned: 1088 (million)
% 6.66/2.27 % (8501)------------------------------
% 6.66/2.27 % (8501)------------------------------
% 6.66/2.28 % (8606)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_8088 for (2993ds/154Mi)
% 6.66/2.29 % (8599)Instruction limit reached!
% 6.66/2.29 % (8599)------------------------------
% 6.66/2.29 % (8599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.29 % (8599)Termination reason: Unknown
% 6.66/2.29 % (8599)Termination phase: Saturation
% 6.66/2.29
% 6.66/2.29 % (8599)Memory used [KB]: 12153
% 6.66/2.29 % (8599)Time elapsed: 0.067 s
% 6.66/2.29 % (8599)Instructions burned: 233 (million)
% 6.66/2.29 % (8599)------------------------------
% 6.66/2.29 % (8599)------------------------------
% 7.49/2.30 % (8607)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_8088 for (2992ds/79Mi)
% 7.49/2.31 % (8604)Instruction limit reached!
% 7.49/2.31 % (8604)------------------------------
% 7.49/2.31 % (8604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.31 % (8604)Termination reason: Unknown
% 7.49/2.31 % (8604)Termination phase: Saturation
% 7.49/2.31
% 7.49/2.31 % (8604)Memory used [KB]: 7419
% 7.49/2.31 % (8604)Time elapsed: 0.051 s
% 7.49/2.31 % (8604)Instructions burned: 183 (million)
% 7.49/2.31 % (8604)------------------------------
% 7.49/2.31 % (8604)------------------------------
% 7.49/2.32 % (8607)Instruction limit reached!
% 7.49/2.32 % (8607)------------------------------
% 7.49/2.32 % (8607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.32 % (8607)Termination reason: Unknown
% 7.49/2.32 % (8607)Termination phase: Property scanning
% 7.49/2.32
% 7.49/2.32 % (8607)Memory used [KB]: 2046
% 7.49/2.32 % (8607)Time elapsed: 0.022 s
% 7.49/2.32 % (8607)Instructions burned: 80 (million)
% 7.49/2.32 % (8607)------------------------------
% 7.49/2.32 % (8607)------------------------------
% 7.49/2.32 % (8608)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_8088 for (2992ds/216Mi)
% 7.49/2.32 % (8605)Instruction limit reached!
% 7.49/2.32 % (8605)------------------------------
% 7.49/2.32 % (8605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.32 % (8605)Termination reason: Unknown
% 7.49/2.32 % (8605)Termination phase: Saturation
% 7.49/2.32
% 7.49/2.32 % (8605)Memory used [KB]: 9978
% 7.49/2.32 % (8605)Time elapsed: 0.077 s
% 7.49/2.32 % (8605)Instructions burned: 186 (million)
% 7.49/2.32 % (8605)------------------------------
% 7.49/2.32 % (8605)------------------------------
% 7.49/2.32 % (8606)Instruction limit reached!
% 7.49/2.32 % (8606)------------------------------
% 7.49/2.32 % (8606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.32 % (8606)Termination reason: Unknown
% 7.49/2.32 % (8606)Termination phase: Saturation
% 7.49/2.32
% 7.49/2.32 % (8606)Memory used [KB]: 6780
% 7.49/2.32 % (8606)Time elapsed: 0.041 s
% 7.49/2.32 % (8606)Instructions burned: 157 (million)
% 7.49/2.32 % (8606)------------------------------
% 7.49/2.32 % (8606)------------------------------
% 7.49/2.32 % (8602)Instruction limit reached!
% 7.49/2.32 % (8602)------------------------------
% 7.49/2.32 % (8602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.32 % (8602)Termination reason: Unknown
% 7.49/2.32 % (8602)Termination phase: Saturation
% 7.49/2.32
% 7.49/2.32 % (8602)Memory used [KB]: 8315
% 7.49/2.32 % (8602)Time elapsed: 0.077 s
% 7.49/2.32 % (8602)Instructions burned: 298 (million)
% 7.49/2.32 % (8602)------------------------------
% 7.49/2.32 % (8602)------------------------------
% 7.49/2.33 % (8609)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_8088 for (2992ds/114Mi)
% 7.49/2.33 % (8610)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_8088 for (2992ds/922Mi)
% 7.49/2.33 % (8611)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_8088 for (2992ds/182Mi)
% 7.49/2.33 % (8612)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_8088 for (2992ds/164Mi)
% 7.49/2.36 % (8609)Instruction limit reached!
% 7.49/2.36 % (8609)------------------------------
% 7.49/2.36 % (8609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.36 % (8609)Termination reason: Unknown
% 7.49/2.36 % (8609)Termination phase: Saturation
% 7.49/2.36
% 7.49/2.36 % (8609)Memory used [KB]: 6908
% 7.49/2.36 % (8609)Time elapsed: 0.032 s
% 7.49/2.36 % (8609)Instructions burned: 116 (million)
% 7.49/2.36 % (8609)------------------------------
% 7.49/2.36 % (8609)------------------------------
% 7.49/2.36 % (8600)Instruction limit reached!
% 7.49/2.36 % (8600)------------------------------
% 7.49/2.36 % (8600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.36 % (8600)Termination reason: Unknown
% 7.49/2.36 % (8600)Termination phase: Saturation
% 7.49/2.36
% 7.49/2.36 % (8600)Memory used [KB]: 8187
% 7.49/2.36 % (8600)Time elapsed: 0.136 s
% 7.49/2.36 % (8600)Instructions burned: 458 (million)
% 7.49/2.36 % (8600)------------------------------
% 7.49/2.36 % (8600)------------------------------
% 7.49/2.37 % (8613)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_8088 for (2992ds/50Mi)
% 7.49/2.37 % (8614)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_8088 for (2992ds/368Mi)
% 7.49/2.37 % (8608)Instruction limit reached!
% 7.49/2.37 % (8608)------------------------------
% 7.49/2.37 % (8608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.37 % (8608)Termination reason: Unknown
% 7.49/2.37 % (8608)Termination phase: Saturation
% 7.49/2.37
% 7.49/2.37 % (8608)Memory used [KB]: 6780
% 7.49/2.37 % (8608)Time elapsed: 0.056 s
% 7.49/2.37 % (8608)Instructions burned: 218 (million)
% 7.49/2.37 % (8608)------------------------------
% 7.49/2.37 % (8608)------------------------------
% 7.49/2.38 % (8612)Instruction limit reached!
% 7.49/2.38 % (8612)------------------------------
% 7.49/2.38 % (8612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.38 % (8612)Termination reason: Unknown
% 7.49/2.38 % (8612)Termination phase: Saturation
% 7.49/2.38
% 7.49/2.38 % (8612)Memory used [KB]: 2430
% 7.49/2.38 % (8612)Time elapsed: 0.045 s
% 7.49/2.38 % (8612)Instructions burned: 164 (million)
% 7.49/2.38 % (8612)------------------------------
% 7.49/2.38 % (8612)------------------------------
% 7.49/2.38 % (8611)Instruction limit reached!
% 7.49/2.38 % (8611)------------------------------
% 7.49/2.38 % (8611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.38 % (8611)Termination reason: Unknown
% 7.49/2.38 % (8611)Termination phase: Saturation
% 7.49/2.38
% 7.49/2.38 % (8611)Memory used [KB]: 6780
% 7.49/2.38 % (8611)Time elapsed: 0.048 s
% 7.49/2.38 % (8611)Instructions burned: 184 (million)
% 7.49/2.38 % (8611)------------------------------
% 7.49/2.38 % (8611)------------------------------
% 7.49/2.38 % (8613)Instruction limit reached!
% 7.49/2.38 % (8613)------------------------------
% 7.49/2.38 % (8613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.38 % (8613)Termination reason: Unknown
% 7.49/2.38 % (8613)Termination phase: Property scanning
% 7.49/2.38
% 7.49/2.38 % (8613)Memory used [KB]: 1918
% 7.49/2.38 % (8613)Time elapsed: 0.014 s
% 7.49/2.38 % (8613)Instructions burned: 50 (million)
% 7.49/2.38 % (8613)------------------------------
% 7.49/2.38 % (8613)------------------------------
% 7.49/2.38 % (8615)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_8088 for (2991ds/1021Mi)
% 7.49/2.39 % (8616)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_8088 for (2991ds/267Mi)
% 7.49/2.39 % (8617)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_8088 for (2991ds/204Mi)
% 7.49/2.39 % (8618)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_8088 for (2991ds/26Mi)
% 8.18/2.40 % (8618)Instruction limit reached!
% 8.18/2.40 % (8618)------------------------------
% 8.18/2.40 % (8618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.40 % (8618)Termination reason: Unknown
% 8.18/2.40 % (8618)Termination phase: shuffling
% 8.18/2.40
% 8.18/2.40 % (8618)Memory used [KB]: 1791
% 8.18/2.40 % (8618)Time elapsed: 0.008 s
% 8.18/2.40 % (8618)Instructions burned: 26 (million)
% 8.18/2.40 % (8618)------------------------------
% 8.18/2.40 % (8618)------------------------------
% 8.18/2.41 % (8619)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_8088 for (2991ds/53Mi)
% 8.18/2.42 % (8619)Instruction limit reached!
% 8.18/2.42 % (8619)------------------------------
% 8.18/2.42 % (8619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.42 % (8619)Termination reason: Unknown
% 8.18/2.42 % (8619)Termination phase: Property scanning
% 8.18/2.42
% 8.18/2.42 % (8619)Memory used [KB]: 1918
% 8.18/2.42 % (8619)Time elapsed: 0.015 s
% 8.18/2.42 % (8619)Instructions burned: 56 (million)
% 8.18/2.42 % (8619)------------------------------
% 8.18/2.42 % (8619)------------------------------
% 8.18/2.43 % (8620)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_8088 for (2991ds/4436Mi)
% 8.18/2.44 % (8617)Instruction limit reached!
% 8.18/2.44 % (8617)------------------------------
% 8.18/2.44 % (8617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.44 % (8617)Termination reason: Unknown
% 8.18/2.44 % (8617)Termination phase: Saturation
% 8.18/2.44
% 8.18/2.44 % (8617)Memory used [KB]: 7547
% 8.18/2.44 % (8617)Time elapsed: 0.055 s
% 8.18/2.44 % (8617)Instructions burned: 204 (million)
% 8.18/2.44 % (8617)------------------------------
% 8.18/2.44 % (8617)------------------------------
% 8.18/2.45 % (8621)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_8088 for (2991ds/1539Mi)
% 8.18/2.45 % (8616)Instruction limit reached!
% 8.18/2.45 % (8616)------------------------------
% 8.18/2.45 % (8616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.45 % (8616)Termination reason: Unknown
% 8.18/2.45 % (8616)Termination phase: Saturation
% 8.18/2.45
% 8.18/2.45 % (8616)Memory used [KB]: 6908
% 8.18/2.45 % (8616)Time elapsed: 0.068 s
% 8.18/2.45 % (8616)Instructions burned: 268 (million)
% 8.18/2.45 % (8616)------------------------------
% 8.18/2.45 % (8616)------------------------------
% 8.18/2.46 % (8622)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_8088 for (2991ds/408Mi)
% 8.18/2.48 % (8614)Instruction limit reached!
% 8.18/2.48 % (8614)------------------------------
% 8.18/2.48 % (8614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.48 % (8614)Termination reason: Unknown
% 8.18/2.48 % (8614)Termination phase: Saturation
% 8.18/2.48
% 8.18/2.48 % (8614)Memory used [KB]: 8187
% 8.18/2.48 % (8614)Time elapsed: 0.109 s
% 8.18/2.48 % (8614)Instructions burned: 369 (million)
% 8.18/2.48 % (8614)------------------------------
% 8.18/2.48 % (8614)------------------------------
% 8.18/2.49 % (8623)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_8088 for (2990ds/5205Mi)
% 8.48/2.51 % (8603)Instruction limit reached!
% 8.48/2.51 % (8603)------------------------------
% 8.48/2.51 % (8603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.51 % (8603)Termination reason: Unknown
% 8.48/2.51 % (8603)Termination phase: Saturation
% 8.48/2.51
% 8.48/2.51 % (8603)Memory used [KB]: 10874
% 8.48/2.51 % (8603)Time elapsed: 0.265 s
% 8.48/2.51 % (8603)Instructions burned: 987 (million)
% 8.48/2.51 % (8603)------------------------------
% 8.48/2.51 % (8603)------------------------------
% 8.48/2.52 % (8624)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_8088 for (2990ds/1913Mi)
% 8.48/2.59 % (8622)Instruction limit reached!
% 8.48/2.59 % (8622)------------------------------
% 8.48/2.59 % (8622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.59 % (8622)Termination reason: Unknown
% 8.48/2.59 % (8622)Termination phase: Saturation
% 8.48/2.59
% 8.48/2.59 % (8622)Memory used [KB]: 9722
% 8.48/2.59 % (8622)Time elapsed: 0.129 s
% 8.48/2.59 % (8622)Instructions burned: 410 (million)
% 8.48/2.59 % (8622)------------------------------
% 8.48/2.59 % (8622)------------------------------
% 8.89/2.60 % (8625)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_8088 for (2989ds/4350Mi)
% 8.89/2.62 % (8610)Instruction limit reached!
% 8.89/2.62 % (8610)------------------------------
% 8.89/2.62 % (8610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.62 % (8610)Termination reason: Unknown
% 8.89/2.62 % (8610)Termination phase: Saturation
% 8.89/2.62
% 8.89/2.62 % (8610)Memory used [KB]: 9978
% 8.89/2.62 % (8610)Time elapsed: 0.290 s
% 8.89/2.62 % (8610)Instructions burned: 924 (million)
% 8.89/2.62 % (8610)------------------------------
% 8.89/2.62 % (8610)------------------------------
% 8.89/2.63 % (8626)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_8088 for (2989ds/68Mi)
% 8.89/2.64 % (8626)Instruction limit reached!
% 8.89/2.64 % (8626)------------------------------
% 8.89/2.64 % (8626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.64 % (8626)Termination reason: Unknown
% 8.89/2.64 % (8626)Termination phase: Property scanning
% 8.89/2.64
% 8.89/2.64 % (8626)Memory used [KB]: 2046
% 8.89/2.64 % (8626)Time elapsed: 0.019 s
% 8.89/2.64 % (8626)Instructions burned: 71 (million)
% 8.89/2.64 % (8626)------------------------------
% 8.89/2.64 % (8626)------------------------------
% 8.89/2.65 % (8627)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_8088 for (2989ds/358Mi)
% 8.89/2.69 % (8615)First to succeed.
% 8.89/2.69 % (8615)Refutation found. Thanks to Tanya!
% 8.89/2.69 % SZS status Theorem for DTF2THF_8088
% 8.89/2.69 % SZS output start Proof for DTF2THF_8088
% 8.89/2.69 thf(func_def_0, type, in: $i > $i > $o).
% 8.89/2.69 thf(func_def_1, type, exu: ($i > $o) > $o).
% 8.89/2.69 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 8.89/2.69 thf(func_def_8, type, powerset: $i > $i).
% 8.89/2.69 thf(func_def_10, type, setunion: $i > $i).
% 8.89/2.69 thf(func_def_19, type, descr: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_26, type, prop2set: $o > $i).
% 8.89/2.69 thf(func_def_36, type, nonempty: $i > $o).
% 8.89/2.69 thf(func_def_69, type, set2prop: $i > $o).
% 8.89/2.69 thf(func_def_88, type, subset: $i > $i > $o).
% 8.89/2.69 thf(func_def_89, type, disjoint: $i > $i > $o).
% 8.89/2.69 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 8.89/2.69 thf(func_def_114, type, binunion: $i > $i > $i).
% 8.89/2.69 thf(func_def_122, type, binintersect: $i > $i > $i).
% 8.89/2.69 thf(func_def_135, type, regular: $i > $o).
% 8.89/2.69 thf(func_def_136, type, setminus: $i > $i > $i).
% 8.89/2.69 thf(func_def_147, type, symdiff: $i > $i > $i).
% 8.89/2.69 thf(func_def_153, type, iskpair: $i > $o).
% 8.89/2.69 thf(func_def_158, type, kpair: $i > $i > $i).
% 8.89/2.69 thf(func_def_160, type, cartprod: $i > $i > $i).
% 8.89/2.69 thf(func_def_177, type, singleton: $i > $o).
% 8.89/2.69 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 8.89/2.69 thf(func_def_184, type, atmost1p: $i > $o).
% 8.89/2.69 thf(func_def_185, type, atleast2p: $i > $o).
% 8.89/2.69 thf(func_def_186, type, atmost2p: $i > $o).
% 8.89/2.69 thf(func_def_187, type, upairsetp: $i > $o).
% 8.89/2.69 thf(func_def_191, type, kfst: $i > $i).
% 8.89/2.69 thf(func_def_203, type, ksnd: $i > $i).
% 8.89/2.69 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 8.89/2.69 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 8.89/2.69 thf(func_def_236, type, sP3: $i > $i > $i > $o > $o).
% 8.89/2.69 thf(func_def_237, type, sP4: $i > $i > $i > $o).
% 8.89/2.69 thf(func_def_239, type, sP6: $i > $i > $o).
% 8.89/2.69 thf(func_def_243, type, sP10: ($i > $o) > ($i > $o) > $i > $i > $o).
% 8.89/2.69 thf(func_def_244, type, sP11: $i > $i > $i > $o).
% 8.89/2.69 thf(func_def_245, type, sP12: $i > $i > $o).
% 8.89/2.69 thf(func_def_246, type, sP13: $i > $o).
% 8.89/2.69 thf(func_def_247, type, sP14: $i > $i > $o).
% 8.89/2.69 thf(func_def_248, type, sP15: $i > $i > $o).
% 8.89/2.69 thf(func_def_249, type, sP16: $i > $i > $o).
% 8.89/2.69 thf(func_def_252, type, sP19: $i > $i > $o > $o).
% 8.89/2.69 thf(func_def_256, type, sP23: ($i > $i > $o) > $i > $o).
% 8.89/2.69 thf(func_def_261, type, sP28: $i > $o).
% 8.89/2.69 thf(func_def_265, type, sP32: $i > ($i > $o) > $o).
% 8.89/2.69 thf(func_def_266, type, sP33: ($i > $o) > $i > $o).
% 8.89/2.69 thf(func_def_277, type, sP44: ($i > $o) > $i > $o).
% 8.89/2.69 thf(func_def_278, type, sP45: ($i > $o) > $i > $o).
% 8.89/2.69 thf(func_def_279, type, sP46: $i > $i > $o > $o).
% 8.89/2.69 thf(func_def_280, type, sP47: $i > $i > $i > $o).
% 8.89/2.69 thf(func_def_286, type, sK53: $i > $o).
% 8.89/2.69 thf(func_def_289, type, sK56: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_305, type, sK72: $i > $o).
% 8.89/2.69 thf(func_def_306, type, sK73: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_337, type, sK104: $i > $o).
% 8.89/2.69 thf(func_def_338, type, sK105: $i > $i).
% 8.89/2.69 thf(func_def_339, type, sK106: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_353, type, sK120: $i > $o).
% 8.89/2.69 thf(func_def_354, type, sK121: $i > $o).
% 8.89/2.69 thf(func_def_355, type, sK122: ($i > $o) > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_356, type, sK123: ($i > $o) > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_357, type, sK124: $i > $i > $o).
% 8.89/2.69 thf(func_def_387, type, sK154: $i > $i).
% 8.89/2.69 thf(func_def_389, type, sK156: $i > $i > $i > $o).
% 8.89/2.69 thf(func_def_401, type, sK168: $i > $o).
% 8.89/2.69 thf(func_def_409, type, sK176: $i > $o).
% 8.89/2.69 thf(func_def_412, type, sK179: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_414, type, sK181: $i > $o).
% 8.89/2.69 thf(func_def_415, type, sK182: $i > $o).
% 8.89/2.69 thf(func_def_436, type, sK203: $i > $i > $i).
% 8.89/2.69 thf(func_def_437, type, sK204: $i > $i > $i).
% 8.89/2.69 thf(func_def_446, type, sK213: $i > $o).
% 8.89/2.69 thf(func_def_447, type, sK214: $i > $o).
% 8.89/2.69 thf(func_def_448, type, sK215: ($i > $o) > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_449, type, sK216: ($i > $o) > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_453, type, sK220: $i > $o).
% 8.89/2.69 thf(func_def_456, type, sK223: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_470, type, sK237: $i > $o).
% 8.89/2.69 thf(func_def_477, type, sK244: ($i > $o) > ($i > $o) > $i > $i > $i).
% 8.89/2.69 thf(func_def_478, type, sK245: ($i > $o) > ($i > $o) > $i > $i > $i).
% 8.89/2.69 thf(func_def_481, type, sK248: $i > $o).
% 8.89/2.69 thf(func_def_482, type, sK249: $i > $o).
% 8.89/2.69 thf(func_def_483, type, sK250: $i > $o).
% 8.89/2.69 thf(func_def_489, type, sK256: $i > $i > $i).
% 8.89/2.69 thf(func_def_490, type, sK257: $i > $i > $i).
% 8.89/2.69 thf(func_def_491, type, sK258: $i > $i > $i).
% 8.89/2.69 thf(func_def_492, type, sK259: $i > $i > $i).
% 8.89/2.69 thf(func_def_493, type, sK260: $i > $i > $i).
% 8.89/2.69 thf(func_def_494, type, sK261: $i > $i > $i).
% 8.89/2.69 thf(func_def_495, type, sK262: $i > $i > $i).
% 8.89/2.69 thf(func_def_496, type, sK263: $i > $i > $i > $i).
% 8.89/2.69 thf(func_def_497, type, sK264: $i > $i).
% 8.89/2.69 thf(func_def_498, type, sK265: $i > $i).
% 8.89/2.69 thf(func_def_499, type, sK266: $i > $i).
% 8.89/2.69 thf(func_def_500, type, sK267: $i > $i).
% 8.89/2.69 thf(func_def_501, type, sK268: $i > $i > $i).
% 8.89/2.69 thf(func_def_502, type, sK269: $i > $i > $i).
% 8.89/2.69 thf(func_def_503, type, sK270: $i > $i > $i).
% 8.89/2.69 thf(func_def_504, type, sK271: $i > $i > $i > $i).
% 8.89/2.69 thf(func_def_505, type, sK272: $i > $i > $i > $i).
% 8.89/2.69 thf(func_def_506, type, sK273: $i > $i).
% 8.89/2.69 thf(func_def_510, type, sK277: $i > $i > $i).
% 8.89/2.69 thf(func_def_520, type, sK287: $i > $o).
% 8.89/2.69 thf(func_def_534, type, sK301: $i > $i > $i > $i).
% 8.89/2.69 thf(func_def_535, type, sK302: $i > $i > $i > $i).
% 8.89/2.69 thf(func_def_551, type, sK318: $i > $o).
% 8.89/2.69 thf(func_def_553, type, sK320: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_556, type, sK323: $i > $o).
% 8.89/2.69 thf(func_def_559, type, sK326: $i > $i > $i).
% 8.89/2.69 thf(func_def_565, type, sK332: $i > $o).
% 8.89/2.69 thf(func_def_579, type, sK346: $i > $o).
% 8.89/2.69 thf(func_def_582, type, sK349: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_591, type, sK358: $i > $i > $o).
% 8.89/2.69 thf(func_def_592, type, sK359: ($i > $i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_593, type, sK360: $i > ($i > $i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_594, type, sK361: $i > ($i > $i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_595, type, sK362: ($i > $i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_596, type, sK363: $i > ($i > $i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_602, type, sK369: $i > $i > $i).
% 8.89/2.69 thf(func_def_613, type, sK380: $i > $o).
% 8.89/2.69 thf(func_def_614, type, sK381: ($i > $o) > $i > $i > $i).
% 8.89/2.69 thf(func_def_622, type, sK389: $o > $i > $i > $i).
% 8.89/2.69 thf(func_def_629, type, sK396: $i > $i).
% 8.89/2.69 thf(func_def_634, type, sK401: $i > $i).
% 8.89/2.69 thf(func_def_635, type, sK402: $i > $i).
% 8.89/2.69 thf(func_def_644, type, sK411: $i > $i > $i).
% 8.89/2.69 thf(func_def_659, type, sK426: $i > $i > $o).
% 8.89/2.69 thf(func_def_666, type, sK433: $i > $o).
% 8.89/2.69 thf(func_def_668, type, sK435: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_669, type, sK436: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_670, type, sK437: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_671, type, sK438: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_672, type, sK439: $i > $o).
% 8.89/2.69 thf(func_def_676, type, sK443: $i > $i > $i).
% 8.89/2.69 thf(func_def_688, type, sK455: $i > $o).
% 8.89/2.69 thf(func_def_689, type, sK456: $i > $i).
% 8.89/2.69 thf(func_def_690, type, sK457: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_694, type, sK461: $i > $i > $i).
% 8.89/2.69 thf(func_def_712, type, sK479: $i > $o).
% 8.89/2.69 thf(func_def_716, type, sK483: $i > $o).
% 8.89/2.69 thf(func_def_718, type, sK485: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_719, type, sK486: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_722, type, sK489: $i > $i > $i).
% 8.89/2.69 thf(func_def_723, type, sK490: $i > $o).
% 8.89/2.69 thf(func_def_730, type, sK497: $i > $i > $i).
% 8.89/2.69 thf(func_def_734, type, sK501: $i > $i).
% 8.89/2.69 thf(func_def_735, type, sK502: $i > $i > $o).
% 8.89/2.69 thf(func_def_739, type, sK506: $i > $i).
% 8.89/2.69 thf(func_def_741, type, sK508: $i > $i).
% 8.89/2.69 thf(func_def_746, type, sK513: $i > $o).
% 8.89/2.69 thf(func_def_756, type, sK523: $i > $o).
% 8.89/2.69 thf(func_def_761, type, sK528: $i > $o).
% 8.89/2.69 thf(func_def_764, type, sK531: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_765, type, sK532: $i > $o).
% 8.89/2.69 thf(func_def_768, type, sK535: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_779, type, sK546: $i > $i > $o).
% 8.89/2.69 thf(func_def_784, type, sK551: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_785, type, sK552: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_786, type, sK553: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_788, type, sK555: $i > $o).
% 8.89/2.69 thf(func_def_789, type, sK556: $i > $i > $i > $o).
% 8.89/2.69 thf(func_def_796, type, sK563: $i > $i > $o).
% 8.89/2.69 thf(func_def_800, type, sK567: $i > $o).
% 8.89/2.69 thf(func_def_801, type, sK568: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_802, type, sK569: $i > $i).
% 8.89/2.69 thf(func_def_805, type, sK572: $i > $i).
% 8.89/2.69 thf(func_def_806, type, sK573: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_807, type, sK574: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_808, type, sK575: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_809, type, sK576: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_810, type, sK577: $i > $i).
% 8.89/2.69 thf(func_def_811, type, sK578: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_812, type, sK579: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_813, type, sK580: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_814, type, sK581: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_815, type, sK582: $i > $i > ($i > $i > $o) > $i).
% 8.89/2.69 thf(func_def_816, type, sK583: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_817, type, sK584: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_818, type, sK585: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_819, type, sK586: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_820, type, sK587: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_821, type, sK588: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_822, type, sK589: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_823, type, sK590: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_824, type, sK591: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_825, type, sK592: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_826, type, sK593: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_827, type, sK594: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_828, type, sK595: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_830, type, sK597: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_831, type, sK598: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_833, type, sK600: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_834, type, sK601: $i > $i).
% 8.89/2.69 thf(func_def_835, type, sK602: $i > $i).
% 8.89/2.69 thf(func_def_836, type, sK603: $i > $i).
% 8.89/2.69 thf(func_def_840, type, sK607: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_841, type, sK608: $i > $i).
% 8.89/2.69 thf(func_def_843, type, sK610: $i > $i).
% 8.89/2.69 thf(func_def_845, type, sK612: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_847, type, sK614: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_848, type, sK615: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_849, type, sK616: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_850, type, sK617: $i > $i).
% 8.89/2.69 thf(func_def_851, type, sK618: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_852, type, sK619: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_853, type, sK620: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_854, type, sK621: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_855, type, sK622: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_856, type, sK623: $i > $i).
% 8.89/2.69 thf(func_def_857, type, sK624: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_858, type, sK625: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_859, type, sK626: ($i > $o) > $i).
% 8.89/2.69 thf(func_def_860, type, sK627: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_861, type, sK628: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_862, type, sK629: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_863, type, sK630: ($i > $o) > $i > $i).
% 8.89/2.69 thf(func_def_864, type, sK631: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_865, type, sK632: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_866, type, sK633: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_867, type, sK634: $i > ($i > $o) > $i).
% 8.89/2.69 thf(func_def_869, type, ph635: !>[X0: $tType]:(X0)).
% 8.89/2.69 thf(func_def_872, type, sK638: $i > $i > $i > $i > ($i > $i > $o) > $i).
% 8.89/2.69 thf(func_def_873, type, sK639: $i > $i > $i > ($i > $i > $o) > $i > $i).
% 8.89/2.69 thf(f8021,plain,(
% 8.89/2.69 $false),
% 8.89/2.69 inference(subsumption_resolution,[status(thm)],[f8007,f2483])).
% 8.89/2.69 thf(f2483,plain,(
% 8.89/2.69 ((in @ sK427 @ sK428) != $true)),
% 8.89/2.69 inference(cnf_transformation,[status(thm)],[f1535])).
% 8.89/2.69 thf(f1535,plain,(
% 8.89/2.69 (ubforcartprodlem2 = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (binunionEcases = $true) & (sepInPowerset = $true) & (upairset2IR = $true) & (in__Cong = $true) & (upairsetIL = $true) & (dpsetconstrI = $true) & (dsetconstr__Cong = $true) & (setminusELneg = $true) & (setunionsingleton = $true) & (uniqinunit = $true) & (binintersectRsub = $true) & (replAx = $true) & (upairsetIR = $true) & (setbeta = $true) & (setminusSubset1 = $true) & (prop2setE = $true) & (setunionAx = $true) & (cartprodfstin = $true) & (foundationAx = $true) & (exuE2 = $true) & (subsetemptysetimpeq = $true) & (exuE3u = $true) & (nonemptyI1 = $true) & (quantDeMorgan2 = $true) & (setadjoinAx = $true) & (binintersectSubset3 = $true) & (ex1I2 = $true) & (binintersectSubset2 = $true) & (setukpairinjL2 = $true) & (exuEu = $true) & (descrp = $true) & (inPowerset = $true) & (setukpairIR = $true) & (singletonsubset = $true) & (setunionE = $true) & (nonemptyImpWitness = $true) & (omegaSAx = $true) & (symdiffIneg2 = $true) & (emptyI = $true) & (setunionsingleton2 = $true) & (upairsetE = $true) & (emptyset__Cong = $true) & (powersetI1 = $true) & (powersetsubset = $true) & (kpairiskpair = $true) & (upairsubunion = $true) & (cartprodsndin = $true) & (ksndpairEq = $true) & (notsubsetI = $true) & (($true = (in @ (kpair @ sK427 @ sK425) @ (dpsetconstr @ sK428 @ sK424 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK426 @ Y0 @ Y1))))))) & ((in @ sK427 @ sK428) != $true)) & (dpsetconstrSub = $true) & (binintersectEL = $true) & (symdiffI2 = $true) & (emptyinunitempty = $true) & (setoftrueEq = $true) & (setukpairinjL = $true) & (exuE3e = $true) & (setukpairinjL1 = $true) & (kpairp = $true) & (powerset__Cong = $true) & (binunionE = $true) & (emptysetAx = $true) & (ubforcartprodlem3 = $true) & (setminusSubset2 = $true) & (powersetE1 = $true) & (exu__Cong = $true) & (secondinupair = $true) & (powersetE = $true) & (subsetE2 = $true) & (setunion__Cong = $true) & (wellorderingAx = $true) & (subsetRefl = $true) & (ex1I = $true) & (exuE1 = $true) & (setextsub = $true) & (setadjoinSub = $true) & (exuI1 = $true) & (setminusERneg = $true) & (emptyInPowerset = $true) & (setukpairIL = $true) & (setadjoinE = $true) & (cartprodpairin = $true) & (powersetAx = $true) & (subset2powerset = $true) & (quantDeMorgan1 = $true) & (setminusI = $true) & (bs114d = $true) & (setadjoinOr = $true) & (dpsetconstrERa = $true) & (subsetI2 = $true) & (emptysetsubset = $true) & (subsetTrans = $true) & (quantDeMorgan4 = $true) & (exuI2 = $true) & (kfstsingleton = $true) & (setextAx = $true) & (setminusLsub = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (subPowSU = $true) & (notequalI2 = $true) & (notdexE = $true) & (singletonsswitch = $true) & (binintersectER = $true) & (notequalI1 = $true) & (sepSubset = $true) & (setminusIRneg = $true) & (kfstpairEq = $true) & (noeltsimpempty = $true) & (setunionI = $true) & (nonemptyI = $true) & (emptysetE = $true) & (descr__Cong = $true) & (prop2setI = $true) & (setunionE2 = $true) & (binintersectSubset1 = $true) & (singletoninpowerset = $true) & (cartprodfstpairEq = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (notdallE = $true) & (prop2set2propI = $true) & (subsetE = $true) & (emptysetimpfalse = $true) & (setminusEL = $true) & (setukpairinjR2 = $true) & (eqimpsubset1 = $true) & (cartprodsndpairEq = $true) & (theprop = $true) & (disjointsetsI1 = $true) & (singletoninpowunion = $true) & (binintersectI = $true) & (binunionLsub = $true) & (setunionsingleton1 = $true) & (setukpairinjR1 = $true) & (binintersectLsub = $true) & (binunionRsub = $true) & (cartprodmempair = $true) & (cartprodmempaircEq = $true) & (eqinunit = $true) & (emptyE1 = $true) & (setOfPairsIsBReln = $true) & (dsetconstrER = $true) & (ex1E1 = $true) & (setukpairinjR12 = $true) & (quantDeMorgan3 = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (setminusER = $true) & (subsetI1 = $true) & (eqimpsubset2 = $true) & (binunionIL = $true) & (symdiffIneg1 = $true) & (setext = $true) & (setukpairinjR = $true) & (cartprodmempair1 = $true) & (setadjoin__Cong = $true) & (nonemptyE1 = $true) & (singletonsuniq = $true) & (powersetI = $true) & (upairequniteq = $true) & (dsetconstrI = $true) & (upairset2E = $true) & (symdiffE = $true) & (setadjoinIL = $true) & (notinemptyset = $true) & (vacuousDall = $true) & (symdiffI1 = $true) & (kpairsurjEq = $true) & (binunionIR = $true) & (omega__Cong = $true) & (ksndsingleton = $true) & (setukpairinjR11 = $true) & (inCongP = $true) & (dsetconstrEL = $true) & (cartprodpairsurjEq = $true) & (notinsingleton = $true) & (setminusILneg = $true) & (emptyinPowerset = $true) & (setadjoinSub2 = $true) & (binintersectSubset4 = $true) & (binintersectSubset5 = $true) & (singletonprop = $true)),
% 8.89/2.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK424,sK425,sK426,sK427,sK428])],[f728,f1534])).
% 8.89/2.69 thf(f1534,plain,(
% 8.89/2.69 ? [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 @ X3 @ X4))) => (($true = (in @ (kpair @ sK427 @ sK425) @ (dpsetconstr @ sK428 @ sK424 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK426 @ Y0 @ Y1))))))) & ((in @ sK427 @ sK428) != $true))),
% 8.89/2.69 introduced(definition,[],[choice_axiom])).
% 8.89/2.69 thf(f728,plain,(
% 8.89/2.69 (ubforcartprodlem2 = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (binunionEcases = $true) & (sepInPowerset = $true) & (upairset2IR = $true) & (in__Cong = $true) & (upairsetIL = $true) & (dpsetconstrI = $true) & (dsetconstr__Cong = $true) & (setminusELneg = $true) & (setunionsingleton = $true) & (uniqinunit = $true) & (binintersectRsub = $true) & (replAx = $true) & (upairsetIR = $true) & (setbeta = $true) & (setminusSubset1 = $true) & (prop2setE = $true) & (setunionAx = $true) & (cartprodfstin = $true) & (foundationAx = $true) & (exuE2 = $true) & (subsetemptysetimpeq = $true) & (exuE3u = $true) & (nonemptyI1 = $true) & (quantDeMorgan2 = $true) & (setadjoinAx = $true) & (binintersectSubset3 = $true) & (ex1I2 = $true) & (binintersectSubset2 = $true) & (setukpairinjL2 = $true) & (exuEu = $true) & (descrp = $true) & (inPowerset = $true) & (setukpairIR = $true) & (singletonsubset = $true) & (setunionE = $true) & (nonemptyImpWitness = $true) & (omegaSAx = $true) & (symdiffIneg2 = $true) & (emptyI = $true) & (setunionsingleton2 = $true) & (upairsetE = $true) & (emptyset__Cong = $true) & (powersetI1 = $true) & (powersetsubset = $true) & (kpairiskpair = $true) & (upairsubunion = $true) & (cartprodsndin = $true) & (ksndpairEq = $true) & (notsubsetI = $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 @ X3 @ X4))) & (dpsetconstrSub = $true) & (binintersectEL = $true) & (symdiffI2 = $true) & (emptyinunitempty = $true) & (setoftrueEq = $true) & (setukpairinjL = $true) & (exuE3e = $true) & (setukpairinjL1 = $true) & (kpairp = $true) & (powerset__Cong = $true) & (binunionE = $true) & (emptysetAx = $true) & (ubforcartprodlem3 = $true) & (setminusSubset2 = $true) & (powersetE1 = $true) & (exu__Cong = $true) & (secondinupair = $true) & (powersetE = $true) & (subsetE2 = $true) & (setunion__Cong = $true) & (wellorderingAx = $true) & (subsetRefl = $true) & (ex1I = $true) & (exuE1 = $true) & (setextsub = $true) & (setadjoinSub = $true) & (exuI1 = $true) & (setminusERneg = $true) & (emptyInPowerset = $true) & (setukpairIL = $true) & (setadjoinE = $true) & (cartprodpairin = $true) & (powersetAx = $true) & (subset2powerset = $true) & (quantDeMorgan1 = $true) & (setminusI = $true) & (bs114d = $true) & (setadjoinOr = $true) & (dpsetconstrERa = $true) & (subsetI2 = $true) & (emptysetsubset = $true) & (subsetTrans = $true) & (quantDeMorgan4 = $true) & (exuI2 = $true) & (kfstsingleton = $true) & (setextAx = $true) & (setminusLsub = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (subPowSU = $true) & (notequalI2 = $true) & (notdexE = $true) & (singletonsswitch = $true) & (binintersectER = $true) & (notequalI1 = $true) & (sepSubset = $true) & (setminusIRneg = $true) & (kfstpairEq = $true) & (noeltsimpempty = $true) & (setunionI = $true) & (nonemptyI = $true) & (emptysetE = $true) & (descr__Cong = $true) & (prop2setI = $true) & (setunionE2 = $true) & (binintersectSubset1 = $true) & (singletoninpowerset = $true) & (cartprodfstpairEq = $true) & (omegaIndAx = $true) & (omega0Ax = $true) & (notdallE = $true) & (prop2set2propI = $true) & (subsetE = $true) & (emptysetimpfalse = $true) & (setminusEL = $true) & (setukpairinjR2 = $true) & (eqimpsubset1 = $true) & (cartprodsndpairEq = $true) & (theprop = $true) & (disjointsetsI1 = $true) & (singletoninpowunion = $true) & (binintersectI = $true) & (binunionLsub = $true) & (setunionsingleton1 = $true) & (setukpairinjR1 = $true) & (binintersectLsub = $true) & (binunionRsub = $true) & (cartprodmempair = $true) & (cartprodmempaircEq = $true) & (eqinunit = $true) & (emptyE1 = $true) & (setOfPairsIsBReln = $true) & (dsetconstrER = $true) & (ex1E1 = $true) & (setukpairinjR12 = $true) & (quantDeMorgan3 = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (setminusER = $true) & (subsetI1 = $true) & (eqimpsubset2 = $true) & (binunionIL = $true) & (symdiffIneg1 = $true) & (setext = $true) & (setukpairinjR = $true) & (cartprodmempair1 = $true) & (setadjoin__Cong = $true) & (nonemptyE1 = $true) & (singletonsuniq = $true) & (powersetI = $true) & (upairequniteq = $true) & (dsetconstrI = $true) & (upairset2E = $true) & (symdiffE = $true) & (setadjoinIL = $true) & (notinemptyset = $true) & (vacuousDall = $true) & (symdiffI1 = $true) & (kpairsurjEq = $true) & (binunionIR = $true) & (omega__Cong = $true) & (ksndsingleton = $true) & (setukpairinjR11 = $true) & (inCongP = $true) & (dsetconstrEL = $true) & (cartprodpairsurjEq = $true) & (notinsingleton = $true) & (setminusILneg = $true) & (emptyinPowerset = $true) & (setadjoinSub2 = $true) & (binintersectSubset4 = $true) & (binintersectSubset5 = $true) & (singletonprop = $true)),
% 8.89/2.69 inference(flattening,[status(thm)],[f727])).
% 8.89/2.69 thf(f727,plain,(
% 8.89/2.69 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [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 @ X3 @ X4))) & (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)),
% 8.89/2.69 inference(ennf_transformation,[status(thm)],[f474])).
% 8.89/2.69 thf(f474,plain,(
% 8.89/2.69 ~((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) => ! [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 @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.89/2.69 inference(fool_elimination,[status(thm)],[f473])).
% 8.89/2.69 thf(f473,plain,(
% 8.89/2.69 ~(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 => ! [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 @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.89/2.69 inference(rectify,[status(thm)],[f193])).
% 8.89/2.69 thf(f193,negated_conjecture,(
% 8.89/2.69 ~(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 => ! [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 @ X1 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.89/2.69 inference(negated_conjecture,[status(cth)],[f192])).
% 8.89/2.69 thf(f192,conjecture,(
% 8.89/2.69 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 => ! [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 @ X1 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.89/2.69 file('/export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2THF_8088.p',dpsetconstrEL1)).
% 8.89/2.69 thf(f8007,plain,(
% 8.89/2.69 ((in @ sK427 @ sK428) = $true)),
% 8.89/2.69 inference(trivial_inequality_removal,[status(thm)],[f7991])).
% 8.89/2.69 thf(f7991,plain,(
% 8.89/2.69 ((in @ sK427 @ sK428) = $true) | ($true != $true)),
% 8.89/2.69 inference(superposition,[status(thm)],[f3461,f6840])).
% 8.89/2.69 thf(f6840,plain,(
% 8.89/2.69 ($true = (in @ (kpair @ sK427 @ sK425) @ (cartprod @ sK428 @ sK424)))),
% 8.89/2.69 inference(trivial_inequality_removal,[status(thm)],[f6820])).
% 8.89/2.69 thf(f6820,plain,(
% 8.89/2.69 ($true != $true) | ($true = (in @ (kpair @ sK427 @ sK425) @ (cartprod @ sK428 @ sK424)))),
% 8.89/2.69 inference(superposition,[status(thm)],[f3413,f3452])).
% 8.89/2.69 thf(f3452,plain,(
% 8.89/2.69 ($true = (in @ (kpair @ sK427 @ sK425) @ (dsetconstr @ (cartprod @ sK428 @ sK424) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK428) & (?? @ $i @ (^[Y2 : $i]: ((((kpair @ Y1 @ Y2) = Y0) & (sK426 @ Y1 @ Y2)) & (in @ Y2 @ sK424)))))))))))),
% 8.89/2.69 inference(beta_eta_normalization,[status(thm)],[f3179])).
% 8.89/2.69 thf(f3179,plain,(
% 8.89/2.69 ($true = (in @ (kpair @ sK427 @ sK425) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))))))))))))) @ sK428 @ sK424 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK426 @ Y0 @ Y1)))))))),
% 8.89/2.69 inference(definition_unfolding,[status(thm)],[f2484,f2276])).
% 8.89/2.69 thf(f2276,plain,(
% 8.89/2.69 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))))))))))))))),
% 8.89/2.69 inference(cnf_transformation,[status(thm)],[f288])).
% 8.89/2.69 thf(f288,plain,(
% 8.89/2.69 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))))))))))))))),
% 8.89/2.69 inference(fool_elimination,[status(thm)],[f287])).
% 8.89/2.69 thf(f287,plain,(
% 8.89/2.69 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : ((in @ X5 @ X1) & (X2 @ X4 @ X5) & ((kpair @ X4 @ X5) = X3)) & (in @ X4 @ X0)))))))),
% 8.89/2.69 inference(rectify,[status(thm)],[f187])).
% 8.89/2.69 thf(f187,axiom,(
% 8.89/2.69 (dpsetconstr = (^[X3 : $i, X4 : $i, X0 : $i > $i > $o] : (dsetconstr @ (cartprod @ X3 @ X4) @ (^[X10 : $i] : (? [X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X4) & (X0 @ X1 @ X2) & ((kpair @ X1 @ X2) = X10)) & (in @ X1 @ X3)))))))),
% 8.89/2.69 file('/export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2THF_8088.p',dpsetconstr)).
% 8.89/2.69 thf(f2484,plain,(
% 8.89/2.69 ($true = (in @ (kpair @ sK427 @ sK425) @ (dpsetconstr @ sK428 @ sK424 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK426 @ Y0 @ Y1)))))))),
% 8.89/2.69 inference(cnf_transformation,[status(thm)],[f1535])).
% 8.89/2.69 thf(f3413,plain,(
% 8.89/2.69 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (in @ X4 @ (dsetconstr @ X3 @ X5))) | ((in @ X4 @ X3) = $true)) )),
% 8.89/2.69 inference(beta_eta_normalization,[status(thm)],[f3412])).
% 8.89/2.69 thf(f3412,plain,(
% 8.89/2.69 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) | ((in @ X4 @ X3) = $true)) )),
% 8.89/2.69 inference(trivial_inequality_removal,[status(thm)],[f3069])).
% 8.89/2.69 thf(f3069,plain,(
% 8.89/2.69 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) | ($true != $true) | ((in @ X4 @ X3) = $true)) )),
% 8.89/2.69 inference(definition_unfolding,[status(thm)],[f2194,f2358])).
% 8.89/2.69 thf(f2358,plain,(
% 8.89/2.69 (dsetconstrEL = $true)),
% 8.89/2.69 inference(cnf_transformation,[status(thm)],[f1535])).
% 8.89/2.69 thf(f2194,plain,(
% 8.89/2.69 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ X3) = $true) | ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) | (dsetconstrEL != $true)) )),
% 8.89/2.69 inference(cnf_transformation,[status(thm)],[f1354])).
% 8.89/2.69 thf(f1354,plain,(
% 8.89/2.69 ((dsetconstrEL = $true) | (($true != (in @ sK322 @ sK321)) & ($true = (in @ sK322 @ (dsetconstr @ sK321 @ (^[Y0 : $i]: (sK323 @ Y0))))))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ X3) = $true) | ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (dsetconstrEL != $true))),
% 8.89/2.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK321,sK322,sK323])],[f1352,f1353])).
% 8.89/2.69 thf(f1353,plain,(
% 8.89/2.69 ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ X0)) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) => (($true != (in @ sK322 @ sK321)) & ($true = (in @ sK322 @ (dsetconstr @ sK321 @ (^[Y0 : $i]: (sK323 @ Y0))))))),
% 8.89/2.69 introduced(definition,[],[choice_axiom])).
% 8.89/2.69 thf(f1352,plain,(
% 8.89/2.69 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ X0)) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ X3) = $true) | ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (dsetconstrEL != $true))),
% 8.89/2.69 inference(rectify,[status(thm)],[f1351])).
% 8.89/2.69 thf(f1351,plain,(
% 8.89/2.69 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ X0)) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) & (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) | (dsetconstrEL != $true))),
% 8.89/2.69 inference(nnf_transformation,[status(thm)],[f741])).
% 8.89/2.69 thf(f741,plain,(
% 8.89/2.69 (dsetconstrEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ X0)) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))),
% 8.89/2.69 inference(ennf_transformation,[status(thm)],[f246])).
% 8.89/2.69 thf(f246,plain,(
% 8.89/2.69 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ($true = (in @ X1 @ X0))) <=> (dsetconstrEL = $true)),
% 8.89/2.69 inference(fool_elimination,[status(thm)],[f245])).
% 8.89/2.69 thf(f245,plain,(
% 8.89/2.69 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (in @ X1 @ X0)) = dsetconstrEL)),
% 8.89/2.69 inference(rectify,[status(thm)],[f15])).
% 8.89/2.69 thf(f15,axiom,(
% 8.89/2.69 (! [X3 : $i,X1 : $i,X0 : $i > $o] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)) = dsetconstrEL)),
% 8.89/2.69 file('/export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2THF_8088.p',dsetconstrEL)).
% 8.89/2.69 thf(f3461,plain,(
% 8.89/2.69 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3))) | ($true = (in @ X2 @ X0))) )),
% 8.89/2.69 inference(trivial_inequality_removal,[status(thm)],[f3016])).
% 8.89/2.69 thf(f3016,plain,(
% 8.89/2.69 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3))) | ($true != $true) | ($true = (in @ X2 @ X0))) )),
% 8.89/2.69 inference(definition_unfolding,[status(thm)],[f2129,f2534])).
% 8.89/2.69 thf(f2534,plain,(
% 8.89/2.69 (cartprodpairmemEL = $true)),
% 8.89/2.69 inference(cnf_transformation,[status(thm)],[f1535])).
% 8.89/2.69 thf(f2129,plain,(
% 8.89/2.69 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ X2 @ X0)) | ($true != (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3))) | (cartprodpairmemEL != $true)) )),
% 8.89/2.69 inference(cnf_transformation,[status(thm)],[f1275])).
% 8.89/2.69 thf(f1275,plain,(
% 8.89/2.69 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (($true = (in @ X2 @ X0)) | ($true != (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3)))) | (cartprodpairmemEL != $true)) & ((cartprodpairmemEL = $true) | (($true != (in @ sK280 @ sK278)) & ($true = (in @ (kpair @ sK280 @ sK279) @ (cartprod @ sK278 @ sK281)))))),
% 8.89/2.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK278,sK279,sK280,sK281])],[f1273,f1274])).
% 8.89/2.69 thf(f1274,plain,(
% 8.89/2.69 ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((in @ X6 @ X4) != $true) & ($true = (in @ (kpair @ X6 @ X5) @ (cartprod @ X4 @ X7)))) => (($true != (in @ sK280 @ sK278)) & ($true = (in @ (kpair @ sK280 @ sK279) @ (cartprod @ sK278 @ sK281))))),
% 8.89/2.69 introduced(definition,[],[choice_axiom])).
% 8.89/2.69 thf(f1273,plain,(
% 8.89/2.69 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (($true = (in @ X2 @ X0)) | ($true != (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3)))) | (cartprodpairmemEL != $true)) & ((cartprodpairmemEL = $true) | ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((in @ X6 @ X4) != $true) & ($true = (in @ (kpair @ X6 @ X5) @ (cartprod @ X4 @ X7)))))),
% 8.89/2.69 inference(rectify,[status(thm)],[f1272])).
% 8.89/2.69 thf(f1272,plain,(
% 8.89/2.69 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (($true = (in @ X2 @ X0)) | ($true != (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3)))) | (cartprodpairmemEL != $true)) & ((cartprodpairmemEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (($true != (in @ X2 @ X0)) & ($true = (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3)))))),
% 8.89/2.69 inference(nnf_transformation,[status(thm)],[f660])).
% 8.89/2.69 thf(f660,plain,(
% 8.89/2.69 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (($true = (in @ X2 @ X0)) | ($true != (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3)))) <=> (cartprodpairmemEL = $true)),
% 8.89/2.69 inference(ennf_transformation,[status(thm)],[f486])).
% 8.89/2.69 thf(f486,plain,(
% 8.89/2.69 (cartprodpairmemEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (($true = (in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3))) => ($true = (in @ X2 @ X0)))),
% 8.89/2.69 inference(fool_elimination,[status(thm)],[f485])).
% 8.89/2.69 thf(f485,plain,(
% 8.89/2.69 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((in @ (kpair @ X2 @ X1) @ (cartprod @ X0 @ X3)) => (in @ X2 @ X0)) = cartprodpairmemEL)),
% 8.89/2.69 inference(rectify,[status(thm)],[f180])).
% 8.89/2.69 thf(f180,axiom,(
% 8.89/2.69 (! [X3 : $i,X2 : $i,X1 : $i,X4 : $i] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X1 @ X3)) = cartprodpairmemEL)),
% 8.89/2.69 file('/export/starexec/sandbox/tmp/tmp.5XAEdEbcFq/DTF2THF_8088.p',cartprodpairmemEL)).
% 8.89/2.69 % SZS output end Proof for DTF2THF_8088
% 8.89/2.69 % (8615)------------------------------
% 8.89/2.69 % (8615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.69 % (8615)Termination reason: Refutation
% 8.89/2.69
% 8.89/2.69 % (8615)Memory used [KB]: 10746
% 8.89/2.69 % (8615)Time elapsed: 0.307 s
% 8.89/2.69 % (8615)Instructions burned: 971 (million)
% 8.89/2.69 % (8615)------------------------------
% 8.89/2.69 % (8615)------------------------------
% 8.89/2.69 % (8311)Success in time 1.117 s
%------------------------------------------------------------------------------