%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU715^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 09:36:36 AM UTC 2026
% Result : Theorem 51.53s 8.73s
% Output : Refutation 51.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of formulae : 132 ( 22 unt; 0 typ; 5 def)
% Number of atoms : 5816 (1617 equ; 0 cnn)
% Maximal formula atoms : 240 ( 44 avg)
% Number of connectives : 3410 ( 250 ~; 231 |;1016 &; 904 @)
% ( 17 <=>; 992 =>; 0 <=; 0 <~>)
% Maximal formula depth : 245 ( 19 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 436 ( 433 usr; 252 con; 0-4 aty)
% Number of variables : 229 ( 0 ^; 174 !; 55 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_283,type,
sP0: $i > $i > $i > $o > $o ).
thf(func_def_288,type,
sP5: $i > $i > $i > $i > $o ).
thf(func_def_290,type,
sP7: $i > $i > $o ).
thf(func_def_291,type,
sP8: $i > $o ).
thf(func_def_292,type,
sP9: $i > $i > $o ).
thf(func_def_293,type,
sP10: $i > $i > $o ).
thf(func_def_304,type,
sK21: $i > $o ).
thf(func_def_309,type,
sK26: $i > $i > $i ).
thf(func_def_317,type,
sK34: $i > $i > $o ).
thf(func_def_322,type,
sK39: $i > $i ).
thf(func_def_325,type,
sK42: $i > $i > ( $i > $i ) > $i ).
thf(func_def_337,type,
sK54: $i > $i > $o ).
thf(func_def_353,type,
sK70: $i > $o ).
thf(func_def_356,type,
sK73: $i > ( $i > $o ) > $i ).
thf(func_def_360,type,
sK77: $i > $o ).
thf(func_def_361,type,
sK78: $i > $o ).
thf(func_def_362,type,
sK79: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_363,type,
sK80: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_371,type,
sK88: $i > $o ).
thf(func_def_376,type,
sK93: $i > ( $i > $o ) > $i ).
thf(func_def_377,type,
sK94: $i > $o ).
thf(func_def_387,type,
sK104: $i > $i > $i ).
thf(func_def_400,type,
sK117: $i > $o ).
thf(func_def_404,type,
sK121: $i > $o ).
thf(func_def_405,type,
sK122: $i > ( $i > $i ) > $i > $i ).
thf(func_def_407,type,
sK124: $i > $i ).
thf(func_def_418,type,
sK135: $i > $i > $i > $i ).
thf(func_def_419,type,
sK136: $i > $i > $i > $i ).
thf(func_def_436,type,
sK153: $i > $i ).
thf(func_def_450,type,
sK167: $i > $i > $o ).
thf(func_def_462,type,
sK179: $i > $o ).
thf(func_def_477,type,
sK194: $i > $i > $i > $i > $i ).
thf(func_def_478,type,
sK195: $i > $i > $i > $i > $i ).
thf(func_def_501,type,
sK218: $i > $o ).
thf(func_def_508,type,
sK225: $i > $i ).
thf(func_def_512,type,
sK229: $i > $i > $o ).
thf(func_def_530,type,
sK247: $i > $i > $i ).
thf(func_def_535,type,
sK252: ( $i > $o ) > $i ).
thf(func_def_536,type,
sK253: ( $i > $o ) > $i ).
thf(func_def_537,type,
sK254: $i > $o ).
thf(func_def_539,type,
sK256: $i > $i > ( $i > $o ) > $i ).
thf(func_def_540,type,
sK257: $i > $o ).
thf(func_def_546,type,
sK263: $i > $o ).
thf(func_def_569,type,
sK286: $i > $i > $i ).
thf(func_def_570,type,
sK287: $i > $i > $i ).
thf(func_def_581,type,
sK298: $i > $i > $i ).
thf(func_def_582,type,
sK299: $i > $o ).
thf(func_def_587,type,
sK304: $i > $i > $o ).
thf(func_def_588,type,
sK305: $i > $i > $i ).
thf(func_def_597,type,
sK314: $i > $o ).
thf(func_def_600,type,
sK317: $i > ( $i > $o ) > $i ).
thf(func_def_601,type,
sK318: $i > ( $i > $o ) > $i ).
thf(func_def_609,type,
sK326: $i > $i > $o ).
thf(func_def_610,type,
sK327: $i > $i ).
thf(func_def_611,type,
sK328: $i > $i ).
thf(func_def_612,type,
sK329: ( $i > $i > $o ) > $i > $i ).
thf(func_def_613,type,
sK330: ( $i > $i > $o ) > $i > $i ).
thf(func_def_614,type,
sK331: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_629,type,
sK346: $i > $o ).
thf(func_def_631,type,
sK348: ( $i > $o ) > $i > $i ).
thf(func_def_656,type,
sK373: $i > $o ).
thf(func_def_658,type,
sK375: ( $i > $o ) > $i > $i ).
thf(func_def_659,type,
sK376: ( $i > $o ) > $i > $i ).
thf(func_def_660,type,
sK377: $i > $i ).
thf(func_def_664,type,
sK381: $i > $i ).
thf(func_def_675,type,
sK392: $i > $i > $i > $i > $i ).
thf(func_def_676,type,
sK393: $i > $i > $i > $i > $i ).
thf(func_def_683,type,
sK400: $i > $o ).
thf(func_def_695,type,
sK412: $i > $o ).
thf(func_def_705,type,
sK422: $i > $o ).
thf(func_def_707,type,
sK424: $i > ( $i > $o ) > $i ).
thf(func_def_720,type,
sK437: $i > $o ).
thf(func_def_722,type,
sK439: ( $i > $o ) > $i > $i ).
thf(func_def_738,type,
sK455: $i > $i > $i ).
thf(func_def_743,type,
sK460: $i > $i > ( $i > $i ) > $i ).
thf(func_def_744,type,
sK461: $i > $i ).
thf(func_def_748,type,
sK465: $i > $i ).
thf(func_def_750,type,
sK467: $i > $i ).
thf(func_def_752,type,
sK469: $i > $o ).
thf(func_def_755,type,
sK472: $i > ( $i > $o ) > $i ).
thf(func_def_757,type,
sK474: $i > $i > $o ).
thf(func_def_761,type,
sK478: $i > $o ).
thf(func_def_764,type,
sK481: $i > ( $i > $o ) > $i ).
thf(func_def_770,type,
sK487: $o > $i > $i > $i ).
thf(func_def_774,type,
sK491: $i > $i > $i ).
thf(func_def_775,type,
sK492: $i > $o ).
thf(func_def_793,type,
sK510: $i > $i ).
thf(func_def_794,type,
sK511: ( $i > $i ) > $i > $i > $i ).
thf(func_def_803,type,
sK520: $i > $i > $o ).
thf(func_def_805,type,
sK522: ( $i > $o ) > $i ).
thf(func_def_806,type,
sK523: $i > $o ).
thf(func_def_828,type,
sK545: $i > $o ).
thf(func_def_833,type,
sK550: $i > $o ).
thf(func_def_834,type,
sK551: $i > $o ).
thf(func_def_835,type,
sK552: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_836,type,
sK553: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_837,type,
sK554: $i > $o ).
thf(func_def_838,type,
sK555: $i > $i ).
thf(func_def_839,type,
sK556: ( $i > $o ) > $i ).
thf(func_def_840,type,
sK557: $i > ( $i > $o ) > $i ).
thf(func_def_841,type,
sK558: $i > $o ).
thf(func_def_845,type,
sK562: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_846,type,
sK563: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_847,type,
sK564: $i > $o ).
thf(func_def_848,type,
sK565: $i > $o ).
thf(func_def_862,type,
sK579: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_863,type,
sK580: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_867,type,
sK584: $i > $o ).
thf(func_def_873,type,
sK590: $i > $i > $i > $i > $i ).
thf(func_def_874,type,
sK591: $i > $i > $i > $i > $i ).
thf(func_def_875,type,
sK592: $i > $i > $i > $i > $i ).
thf(func_def_876,type,
sK593: $i > $i > $i > $i > $i ).
thf(func_def_881,type,
sK598: $i > $i > $i ).
thf(func_def_882,type,
sK599: $i > $i > $i ).
thf(func_def_883,type,
sK600: $i > $i > $i ).
thf(func_def_884,type,
sK601: $i > $i > $i ).
thf(func_def_885,type,
sK602: $i > $i > $i ).
thf(func_def_886,type,
sK603: $i > $i > $i > $i ).
thf(func_def_887,type,
sK604: $i > $i ).
thf(func_def_888,type,
sK605: $i > $i ).
thf(func_def_889,type,
sK606: $i > $i ).
thf(func_def_890,type,
sK607: $i > $i ).
thf(func_def_891,type,
sK608: $i > $i > $i > $i ).
thf(func_def_892,type,
sK609: $i > $i > $i > $i ).
thf(func_def_893,type,
sK610: $i > $i > $i ).
thf(func_def_894,type,
sK611: $i > $i > $i ).
thf(func_def_895,type,
sK612: $i > $i > $i ).
thf(func_def_897,type,
sK614: $i > $i ).
thf(func_def_898,type,
sK615: $i > $i ).
thf(func_def_899,type,
sK616: $i > $i ).
thf(func_def_908,type,
sK625: ( $i > $o ) > $i ).
thf(func_def_909,type,
sK626: $i > $o ).
thf(func_def_910,type,
sK627: $i > $i ).
thf(func_def_917,type,
sK634: $i > $o ).
thf(func_def_922,type,
sK639: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_923,type,
sK640: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_927,type,
sK644: $i > $o ).
thf(func_def_936,type,
sK653: $i > ( $i > $o ) > $i ).
thf(func_def_937,type,
sK654: $i > $o ).
thf(func_def_971,type,
sK688: $i > $i ).
thf(func_def_975,type,
sK692: $i > $i > ( $i > $i ) > $i ).
thf(func_def_981,type,
sK698: $i > $i ).
thf(func_def_984,type,
sK701: $i > $i > ( $i > $i ) > $i ).
thf(func_def_995,type,
sK712: $i > $i > $i > $i > $i ).
thf(func_def_1004,type,
sK721: $i > $i > $i ).
thf(func_def_1006,type,
sK723: $i > $i ).
thf(func_def_1010,type,
ph727:
!>[X0: $tType] : X0 ).
thf(f30477,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f4995,f7585,f7711,f7914,f7943,f30470]) ).
thf(f30470,plain,
( spl726_87
| spl726_88 ),
inference(avatar_split_clause,[status(thm)],[f30469,f4992,f4988]) ).
thf(f4988,definition,
( spl726_87
<=> ( ( subset @ sK652 @ sK650 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl726_87])],[avatar_definition]) ).
thf(f4992,definition,
( spl726_88
<=> ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK651 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl726_88])],[avatar_definition]) ).
thf(f30469,plain,
( ( ( subset @ sK652 @ sK650 )
= $true )
| spl726_88 ),
inference(trivial_inequality_removal,[status(thm)],[f30468]) ).
thf(f30468,plain,
( ( $true != $true )
| ( ( subset @ sK652 @ sK650 )
= $true )
| spl726_88 ),
inference(forward_demodulation,[status(thm)],[f30465,f3115]) ).
thf(f3115,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f2007,plain,
( ( complementT_lem = $true )
& ( dsetconstr__Cong = $true )
& ( binunionT_lem = $true )
& ( funcGraphProp2 = $true )
& ( upairsubunion = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem1 = $true )
& ( ex1E2 = $true )
& ( omegaIndAx = $true )
& ( exuEu = $true )
& ( setbeta = $true )
& ( setukpairinjR2 = $true )
& ( singletoninpowerset = $true )
& ( upairset2IR = $true )
& ( setukpairinjR = $true )
& ( emptyinPowerset = $true )
& ( omega__Cong = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstrEL = $true )
& ( notdexE = $true )
& ( iffalse = $true )
& ( setminusT_lem = $true )
& ( setadjoinOr = $true )
& ( notdallE = $true )
& ( binunionLsub = $true )
& ( cartprodpairmemER = $true )
& ( notinemptyset = $true )
& ( setukpairIL = $true )
& ( theprop = $true )
& ( subsetE2 = $true )
& ( cartprodmempair = $true )
& ( upairset2E = $true )
& ( quantDeMorgan4 = $true )
& ( setminusELneg = $true )
& ( symdiffI2 = $true )
& ( powerset__Cong = $true )
& ( prop2setI = $true )
& ( cartprodpairmemEL = $true )
& ( upairsetIR = $true )
& ( emptyset__Cong = $true )
& ( dpsetconstrEL1 = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( dsetconstrER = $true )
& ( brelnall1 = $true )
& ( binintersectSubset3 = $true )
& ( disjointsetsI1 = $true )
& ( beta2 = $true )
& ( emptysetsubset = $true )
& ( omega0Ax = $true )
& ( upairinpowunion = $true )
& ( wellorderingAx = $true )
& ( eqinunit = $true )
& ( exuI2 = $true )
& ( eqbreln = $true )
& ( iftrue = $true )
& ( cartprodsndin = $true )
& ( lamProp = $true )
& ( setunionsingleton2 = $true )
& ( binunionEcases = $true )
& ( singletonsubset = $true )
& ( funcext2 = $true )
& ( kpairsurjEq = $true )
& ( funcextLem = $true )
& ( symdiffIneg1 = $true )
& ( powersetI = $true )
& ( singletonsuniq = $true )
& ( dpsetconstrEL2 = $true )
& ( setminusI = $true )
& ( dpsetconstrSub = $true )
& ( kfstsingleton = $true )
& ( subsetTrans = $true )
& ( ifSingleton = $true )
& ( lam2lamEq = $true )
& ( singletonprop = $true )
& ( emptyInPowerset = $true )
& ( cartprodsndpairEq = $true )
& ( setadjoinAx = $true )
& ( sepSubset = $true )
& ( subsetI1 = $true )
& ( binunionE = $true )
& ( nonemptyI1 = $true )
& ( ap2apEq2 = $true )
& ( quantDeMorgan1 = $true )
& ( subPowSU = $true )
& ( ksndsingleton = $true )
& ( kpairiskpair = $true )
& ( lamp = $true )
& ( binintersectSubset1 = $true )
& ( subsetRefl = $true )
& ( prop2setE = $true )
& ( setminusIRneg = $true )
& ( nonemptyImpWitness = $true )
& ( setminusLsub = $true )
& ( dpsetconstrI = $true )
& ( exuI3 = $true )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( ksndpairEq = $true )
& ( kpairp = $true )
& ( cartprodmempaircEq = $true )
& ( prop2set2propI = $true )
& ( eqimpsubset1 = $true )
& ( binintersectSubset5 = $true )
& ( setextAx = $true )
& ( subset2powerset = $true )
& ( lam2p = $true )
& ( apProp = $true )
& ( binintersectER = $true )
& ( exu__Cong = $true )
& ( setukpairinjL = $true )
& ( setminusSubset2 = $true )
& ( setextsub = $true )
& ( setukpairinjL1 = $true )
& ( eta1 = $true )
& ( infuncsetfunc = $true )
& ( setadjoinSub = $true )
& ( notequalI1 = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( binunionRsub = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( dpsetconstrER = $true )
& ( setunionE = $true )
& ( cartprodpairsurjEq = $true )
& ( setunionE2 = $true )
& ( exuE3u = $true )
& ( binintersectI = $true )
& ( emptysetE = $true )
& ( setukpairIR = $true )
& ( setminusSubset1 = $true )
& ( singletonsswitch = $true )
& ( setadjoin__Cong = $true )
& ( setunionI = $true )
& ( ex1I2 = $true )
& ( setunionsingleton1 = $true )
& ( binunionIR = $true )
& ( funcGraphProp3 = $true )
& ( notinsingleton = $true )
& ( funcImageSingleton = $true )
& ( brelnall2 = $true )
& ( ubforcartprodlem2 = $true )
& ( theeq = $true )
& ( binintersectRsub = $true )
& ( subsetI2 = $true )
& ( exuI1 = $true )
& ( emptyinunitempty = $true )
& ( setunion__Cong = $true )
& ( dpsetconstrERa = $true )
& ( setunionsingleton = $true )
& ( cartprodpairin = $true )
& ( emptyI = $true )
& ( iftrueProp1 = $true )
& ( beta1 = $true )
& ( vacuousDall = $true )
& ( subsetE = $true )
& ( bs114d = $true )
& ( ex1I = $true )
& ( funcGraphProp1 = $true )
& ( singletoninpowunion = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectLsub = $true )
& ( kfstpairEq = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem3 = $true )
& ( cartprodfstpairEq = $true )
& ( uniqinunit = $true )
& ( binintersectSubset2 = $true )
& ( inCongP = $true )
& ( ex1E1 = $true )
& ( iffalseProp1 = $true )
& ( secondinupair = $true )
& ( setadjoinIR = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( descrp = $true )
& ( in__Cong = $true )
& ( $true
= ( in @ sK652 @ ( powerset @ sK651 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK651 )
!= $true )
| ( ( in @ X3 @ sK652 )
!= $true )
| ( ( in @ X3 @ sK650 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ X4 @ sK650 )
!= $true )
| ( ( in @ X4 @ sK651 )
!= $true )
| ( ( in @ X4 @ sK652 )
= $true ) )
& ( sK650 != sK652 )
& ( $true
= ( in @ sK650 @ ( powerset @ sK651 ) ) )
& ( powersetsubset = $true )
& ( setext = $true )
& ( symdiffI1 = $true )
& ( cartprodfstin = $true )
& ( ifp = $true )
& ( iftrueorfalse = $true )
& ( omegaSAx = $true )
& ( setminusER = $true )
& ( powersetE = $true )
& ( notequalI2 = $true )
& ( cartprodmempair1 = $true )
& ( setminusERneg = $true )
& ( eta2 = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjL2 = $true )
& ( exuE2 = $true )
& ( symdiffE = $true )
& ( binintersectEL = $true )
& ( funcext = $true )
& ( nonemptyI = $true )
& ( powersetT_lem = $true )
& ( nonemptyE1 = $true )
& ( funcGraphProp4 = $true )
& ( setunionAx = $true )
& ( setukpairinjR12 = $true )
& ( powersetI1 = $true )
& ( ap2apEq1 = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( eqimpsubset2 = $true )
& ( binintersectT_lem = $true )
& ( noeltsimpempty = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairinjR11 = $true )
& ( sepInPowerset = $true )
& ( foundationAx = $true )
& ( exuE1 = $true )
& ( subbreln = $true )
& ( setukpairinjR1 = $true )
& ( iffalseProp2 = $true )
& ( app = $true )
& ( upairequniteq = $true )
& ( quantDeMorgan2 = $true )
& ( iftrueProp2 = $true )
& ( descr__Cong = $true )
& ( setOfPairsIsBReln = $true )
& ( setadjoinIL = $true )
& ( setminusILneg = $true )
& ( emptysetimpfalse = $true )
& ( binunionIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK650,sK651,sK652])],[f2004,f2006,f2005]) ).
thf(f2005,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ X0 ) ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ X4 @ X2 )
= $true ) )
& ( X0 != X2 ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK651 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK651 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ sK650 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ X4 @ sK650 )
!= $true )
| ( ( in @ X4 @ sK651 )
!= $true )
| ( ( in @ X4 @ X2 )
= $true ) )
& ( sK650 != X2 ) )
& ( $true
= ( in @ sK650 @ ( powerset @ sK651 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2006,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK651 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK651 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ sK650 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ X4 @ sK650 )
!= $true )
| ( ( in @ X4 @ sK651 )
!= $true )
| ( ( in @ X4 @ X2 )
= $true ) )
& ( sK650 != X2 ) )
=> ( ( $true
= ( in @ sK652 @ ( powerset @ sK651 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK651 )
!= $true )
| ( ( in @ X3 @ sK652 )
!= $true )
| ( ( in @ X3 @ sK650 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ X4 @ sK650 )
!= $true )
| ( ( in @ X4 @ sK651 )
!= $true )
| ( ( in @ X4 @ sK652 )
= $true ) )
& ( sK650 != sK652 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2004,plain,
( ( complementT_lem = $true )
& ( dsetconstr__Cong = $true )
& ( binunionT_lem = $true )
& ( funcGraphProp2 = $true )
& ( upairsubunion = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem1 = $true )
& ( ex1E2 = $true )
& ( omegaIndAx = $true )
& ( exuEu = $true )
& ( setbeta = $true )
& ( setukpairinjR2 = $true )
& ( singletoninpowerset = $true )
& ( upairset2IR = $true )
& ( setukpairinjR = $true )
& ( emptyinPowerset = $true )
& ( omega__Cong = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstrEL = $true )
& ( notdexE = $true )
& ( iffalse = $true )
& ( setminusT_lem = $true )
& ( setadjoinOr = $true )
& ( notdallE = $true )
& ( binunionLsub = $true )
& ( cartprodpairmemER = $true )
& ( notinemptyset = $true )
& ( setukpairIL = $true )
& ( theprop = $true )
& ( subsetE2 = $true )
& ( cartprodmempair = $true )
& ( upairset2E = $true )
& ( quantDeMorgan4 = $true )
& ( setminusELneg = $true )
& ( symdiffI2 = $true )
& ( powerset__Cong = $true )
& ( prop2setI = $true )
& ( cartprodpairmemEL = $true )
& ( upairsetIR = $true )
& ( emptyset__Cong = $true )
& ( dpsetconstrEL1 = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( dsetconstrER = $true )
& ( brelnall1 = $true )
& ( binintersectSubset3 = $true )
& ( disjointsetsI1 = $true )
& ( beta2 = $true )
& ( emptysetsubset = $true )
& ( omega0Ax = $true )
& ( upairinpowunion = $true )
& ( wellorderingAx = $true )
& ( eqinunit = $true )
& ( exuI2 = $true )
& ( eqbreln = $true )
& ( iftrue = $true )
& ( cartprodsndin = $true )
& ( lamProp = $true )
& ( setunionsingleton2 = $true )
& ( binunionEcases = $true )
& ( singletonsubset = $true )
& ( funcext2 = $true )
& ( kpairsurjEq = $true )
& ( funcextLem = $true )
& ( symdiffIneg1 = $true )
& ( powersetI = $true )
& ( singletonsuniq = $true )
& ( dpsetconstrEL2 = $true )
& ( setminusI = $true )
& ( dpsetconstrSub = $true )
& ( kfstsingleton = $true )
& ( subsetTrans = $true )
& ( ifSingleton = $true )
& ( lam2lamEq = $true )
& ( singletonprop = $true )
& ( emptyInPowerset = $true )
& ( cartprodsndpairEq = $true )
& ( setadjoinAx = $true )
& ( sepSubset = $true )
& ( subsetI1 = $true )
& ( binunionE = $true )
& ( nonemptyI1 = $true )
& ( ap2apEq2 = $true )
& ( quantDeMorgan1 = $true )
& ( subPowSU = $true )
& ( ksndsingleton = $true )
& ( kpairiskpair = $true )
& ( lamp = $true )
& ( binintersectSubset1 = $true )
& ( subsetRefl = $true )
& ( prop2setE = $true )
& ( setminusIRneg = $true )
& ( nonemptyImpWitness = $true )
& ( setminusLsub = $true )
& ( dpsetconstrI = $true )
& ( exuI3 = $true )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( ksndpairEq = $true )
& ( kpairp = $true )
& ( cartprodmempaircEq = $true )
& ( prop2set2propI = $true )
& ( eqimpsubset1 = $true )
& ( binintersectSubset5 = $true )
& ( setextAx = $true )
& ( subset2powerset = $true )
& ( lam2p = $true )
& ( apProp = $true )
& ( binintersectER = $true )
& ( exu__Cong = $true )
& ( setukpairinjL = $true )
& ( setminusSubset2 = $true )
& ( setextsub = $true )
& ( setukpairinjL1 = $true )
& ( eta1 = $true )
& ( infuncsetfunc = $true )
& ( setadjoinSub = $true )
& ( notequalI1 = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( binunionRsub = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( dpsetconstrER = $true )
& ( setunionE = $true )
& ( cartprodpairsurjEq = $true )
& ( setunionE2 = $true )
& ( exuE3u = $true )
& ( binintersectI = $true )
& ( emptysetE = $true )
& ( setukpairIR = $true )
& ( setminusSubset1 = $true )
& ( singletonsswitch = $true )
& ( setadjoin__Cong = $true )
& ( setunionI = $true )
& ( ex1I2 = $true )
& ( setunionsingleton1 = $true )
& ( binunionIR = $true )
& ( funcGraphProp3 = $true )
& ( notinsingleton = $true )
& ( funcImageSingleton = $true )
& ( brelnall2 = $true )
& ( ubforcartprodlem2 = $true )
& ( theeq = $true )
& ( binintersectRsub = $true )
& ( subsetI2 = $true )
& ( exuI1 = $true )
& ( emptyinunitempty = $true )
& ( setunion__Cong = $true )
& ( dpsetconstrERa = $true )
& ( setunionsingleton = $true )
& ( cartprodpairin = $true )
& ( emptyI = $true )
& ( iftrueProp1 = $true )
& ( beta1 = $true )
& ( vacuousDall = $true )
& ( subsetE = $true )
& ( bs114d = $true )
& ( ex1I = $true )
& ( funcGraphProp1 = $true )
& ( singletoninpowunion = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectLsub = $true )
& ( kfstpairEq = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem3 = $true )
& ( cartprodfstpairEq = $true )
& ( uniqinunit = $true )
& ( binintersectSubset2 = $true )
& ( inCongP = $true )
& ( ex1E1 = $true )
& ( iffalseProp1 = $true )
& ( secondinupair = $true )
& ( setadjoinIR = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( descrp = $true )
& ( in__Cong = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ X0 ) ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ X4 @ X2 )
= $true ) )
& ( X0 != X2 ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( powersetsubset = $true )
& ( setext = $true )
& ( symdiffI1 = $true )
& ( cartprodfstin = $true )
& ( ifp = $true )
& ( iftrueorfalse = $true )
& ( omegaSAx = $true )
& ( setminusER = $true )
& ( powersetE = $true )
& ( notequalI2 = $true )
& ( cartprodmempair1 = $true )
& ( setminusERneg = $true )
& ( eta2 = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjL2 = $true )
& ( exuE2 = $true )
& ( symdiffE = $true )
& ( binintersectEL = $true )
& ( funcext = $true )
& ( nonemptyI = $true )
& ( powersetT_lem = $true )
& ( nonemptyE1 = $true )
& ( funcGraphProp4 = $true )
& ( setunionAx = $true )
& ( setukpairinjR12 = $true )
& ( powersetI1 = $true )
& ( ap2apEq1 = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( eqimpsubset2 = $true )
& ( binintersectT_lem = $true )
& ( noeltsimpempty = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairinjR11 = $true )
& ( sepInPowerset = $true )
& ( foundationAx = $true )
& ( exuE1 = $true )
& ( subbreln = $true )
& ( setukpairinjR1 = $true )
& ( iffalseProp2 = $true )
& ( app = $true )
& ( upairequniteq = $true )
& ( quantDeMorgan2 = $true )
& ( iftrueProp2 = $true )
& ( descr__Cong = $true )
& ( setOfPairsIsBReln = $true )
& ( setadjoinIL = $true )
& ( setminusILneg = $true )
& ( emptysetimpfalse = $true )
& ( binunionIL = $true ) ),
inference(rectify,[status(thm)],[f886]) ).
thf(f886,plain,
( ( complementT_lem = $true )
& ( dsetconstr__Cong = $true )
& ( binunionT_lem = $true )
& ( funcGraphProp2 = $true )
& ( upairsubunion = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem1 = $true )
& ( ex1E2 = $true )
& ( omegaIndAx = $true )
& ( exuEu = $true )
& ( setbeta = $true )
& ( setukpairinjR2 = $true )
& ( singletoninpowerset = $true )
& ( upairset2IR = $true )
& ( setukpairinjR = $true )
& ( emptyinPowerset = $true )
& ( omega__Cong = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstrEL = $true )
& ( notdexE = $true )
& ( iffalse = $true )
& ( setminusT_lem = $true )
& ( setadjoinOr = $true )
& ( notdallE = $true )
& ( binunionLsub = $true )
& ( cartprodpairmemER = $true )
& ( notinemptyset = $true )
& ( setukpairIL = $true )
& ( theprop = $true )
& ( subsetE2 = $true )
& ( cartprodmempair = $true )
& ( upairset2E = $true )
& ( quantDeMorgan4 = $true )
& ( setminusELneg = $true )
& ( symdiffI2 = $true )
& ( powerset__Cong = $true )
& ( prop2setI = $true )
& ( cartprodpairmemEL = $true )
& ( upairsetIR = $true )
& ( emptyset__Cong = $true )
& ( dpsetconstrEL1 = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( dsetconstrER = $true )
& ( brelnall1 = $true )
& ( binintersectSubset3 = $true )
& ( disjointsetsI1 = $true )
& ( beta2 = $true )
& ( emptysetsubset = $true )
& ( omega0Ax = $true )
& ( upairinpowunion = $true )
& ( wellorderingAx = $true )
& ( eqinunit = $true )
& ( exuI2 = $true )
& ( eqbreln = $true )
& ( iftrue = $true )
& ( cartprodsndin = $true )
& ( lamProp = $true )
& ( setunionsingleton2 = $true )
& ( binunionEcases = $true )
& ( singletonsubset = $true )
& ( funcext2 = $true )
& ( kpairsurjEq = $true )
& ( funcextLem = $true )
& ( symdiffIneg1 = $true )
& ( powersetI = $true )
& ( singletonsuniq = $true )
& ( dpsetconstrEL2 = $true )
& ( setminusI = $true )
& ( dpsetconstrSub = $true )
& ( kfstsingleton = $true )
& ( subsetTrans = $true )
& ( ifSingleton = $true )
& ( lam2lamEq = $true )
& ( singletonprop = $true )
& ( emptyInPowerset = $true )
& ( cartprodsndpairEq = $true )
& ( setadjoinAx = $true )
& ( sepSubset = $true )
& ( subsetI1 = $true )
& ( binunionE = $true )
& ( nonemptyI1 = $true )
& ( ap2apEq2 = $true )
& ( quantDeMorgan1 = $true )
& ( subPowSU = $true )
& ( ksndsingleton = $true )
& ( kpairiskpair = $true )
& ( lamp = $true )
& ( binintersectSubset1 = $true )
& ( subsetRefl = $true )
& ( prop2setE = $true )
& ( setminusIRneg = $true )
& ( nonemptyImpWitness = $true )
& ( setminusLsub = $true )
& ( dpsetconstrI = $true )
& ( exuI3 = $true )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( ksndpairEq = $true )
& ( kpairp = $true )
& ( cartprodmempaircEq = $true )
& ( prop2set2propI = $true )
& ( eqimpsubset1 = $true )
& ( binintersectSubset5 = $true )
& ( setextAx = $true )
& ( subset2powerset = $true )
& ( lam2p = $true )
& ( apProp = $true )
& ( binintersectER = $true )
& ( exu__Cong = $true )
& ( setukpairinjL = $true )
& ( setminusSubset2 = $true )
& ( setextsub = $true )
& ( setukpairinjL1 = $true )
& ( eta1 = $true )
& ( infuncsetfunc = $true )
& ( setadjoinSub = $true )
& ( notequalI1 = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( binunionRsub = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( dpsetconstrER = $true )
& ( setunionE = $true )
& ( cartprodpairsurjEq = $true )
& ( setunionE2 = $true )
& ( exuE3u = $true )
& ( binintersectI = $true )
& ( emptysetE = $true )
& ( setukpairIR = $true )
& ( setminusSubset1 = $true )
& ( singletonsswitch = $true )
& ( setadjoin__Cong = $true )
& ( setunionI = $true )
& ( ex1I2 = $true )
& ( setunionsingleton1 = $true )
& ( binunionIR = $true )
& ( funcGraphProp3 = $true )
& ( notinsingleton = $true )
& ( funcImageSingleton = $true )
& ( brelnall2 = $true )
& ( ubforcartprodlem2 = $true )
& ( theeq = $true )
& ( binintersectRsub = $true )
& ( subsetI2 = $true )
& ( exuI1 = $true )
& ( emptyinunitempty = $true )
& ( setunion__Cong = $true )
& ( dpsetconstrERa = $true )
& ( setunionsingleton = $true )
& ( cartprodpairin = $true )
& ( emptyI = $true )
& ( iftrueProp1 = $true )
& ( beta1 = $true )
& ( vacuousDall = $true )
& ( subsetE = $true )
& ( bs114d = $true )
& ( ex1I = $true )
& ( funcGraphProp1 = $true )
& ( singletoninpowunion = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectLsub = $true )
& ( kfstpairEq = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem3 = $true )
& ( cartprodfstpairEq = $true )
& ( uniqinunit = $true )
& ( binintersectSubset2 = $true )
& ( inCongP = $true )
& ( ex1E1 = $true )
& ( iffalseProp1 = $true )
& ( secondinupair = $true )
& ( setadjoinIR = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( descrp = $true )
& ( in__Cong = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ X4 @ X2 )
!= $true )
| ( $true
= ( in @ X4 @ X0 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
= $true ) )
& ( X0 != X2 ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( powersetsubset = $true )
& ( setext = $true )
& ( symdiffI1 = $true )
& ( cartprodfstin = $true )
& ( ifp = $true )
& ( iftrueorfalse = $true )
& ( omegaSAx = $true )
& ( setminusER = $true )
& ( powersetE = $true )
& ( notequalI2 = $true )
& ( cartprodmempair1 = $true )
& ( setminusERneg = $true )
& ( eta2 = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjL2 = $true )
& ( exuE2 = $true )
& ( symdiffE = $true )
& ( binintersectEL = $true )
& ( funcext = $true )
& ( nonemptyI = $true )
& ( powersetT_lem = $true )
& ( nonemptyE1 = $true )
& ( funcGraphProp4 = $true )
& ( setunionAx = $true )
& ( setukpairinjR12 = $true )
& ( powersetI1 = $true )
& ( ap2apEq1 = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( eqimpsubset2 = $true )
& ( binintersectT_lem = $true )
& ( noeltsimpempty = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairinjR11 = $true )
& ( sepInPowerset = $true )
& ( foundationAx = $true )
& ( exuE1 = $true )
& ( subbreln = $true )
& ( setukpairinjR1 = $true )
& ( iffalseProp2 = $true )
& ( app = $true )
& ( upairequniteq = $true )
& ( quantDeMorgan2 = $true )
& ( iftrueProp2 = $true )
& ( descr__Cong = $true )
& ( setOfPairsIsBReln = $true )
& ( setadjoinIL = $true )
& ( setminusILneg = $true )
& ( emptysetimpfalse = $true )
& ( binunionIL = $true ) ),
inference(flattening,[status(thm)],[f885]) ).
thf(f885,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( X0 != X2 )
& ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
| ( ( in @ X4 @ X2 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( $true
!= ( in @ X3 @ X0 ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f504]) ).
thf(f504,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( in @ X3 @ X0 ) )
=> ( ( in @ X3 @ X2 )
= $true ) ) )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( in @ X4 @ X2 )
= $true )
=> ( $true
= ( in @ X4 @ X0 ) ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f503]) ).
thf(f503,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X0 ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f237]) ).
thf(f237,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X11 )
=> ( in @ X1 @ X16 ) ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X16 )
=> ( in @ X1 @ X11 ) ) )
=> ( X11 = X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f236]) ).
thf(f236,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X11 )
=> ( in @ X1 @ X16 ) ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X16 )
=> ( in @ X1 @ X11 ) ) )
=> ( X11 = X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',setextT) ).
thf(f30465,plain,
( ( subsetI1 != $true )
| ( ( subset @ sK652 @ sK650 )
= $true )
| spl726_88 ),
inference(trivial_inequality_removal,[status(thm)],[f30455]) ).
thf(f30455,plain,
( ( $true != $true )
| ( ( subset @ sK652 @ sK650 )
= $true )
| ( subsetI1 != $true )
| spl726_88 ),
inference(superposition,[status(thm)],[f6457,f2133]) ).
thf(f2133,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK26 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( subset @ X3 @ X4 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1041]) ).
thf(f1041,plain,
( ( ( subsetI1 = $true )
| ( ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK25 ) )
| ( ( in @ X2 @ sK24 )
!= $true ) )
& ( ( subset @ sK24 @ sK25 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( ( in @ ( sK26 @ X4 @ X3 ) @ X4 )
!= $true )
& ( ( in @ ( sK26 @ X4 @ X3 ) @ X3 )
= $true ) )
| ( ( subset @ X3 @ X4 )
= $true ) )
| ( subsetI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f1038,f1040,f1039]) ).
thf(f1039,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( $true
!= ( subset @ X0 @ X1 ) ) )
=> ( ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK25 ) )
| ( ( in @ X2 @ sK24 )
!= $true ) )
& ( ( subset @ sK24 @ sK25 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1040,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( $true
= ( in @ X5 @ X3 ) ) )
=> ( ( ( in @ ( sK26 @ X4 @ X3 ) @ X4 )
!= $true )
& ( ( in @ ( sK26 @ X4 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1038,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( $true
!= ( subset @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( $true
= ( in @ X5 @ X3 ) ) )
| ( ( subset @ X3 @ X4 )
= $true ) )
| ( subsetI1 != $true ) ) ),
inference(rectify,[status(thm)],[f1037]) ).
thf(f1037,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( $true
!= ( subset @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( $true
= ( subset @ X0 @ X1 ) ) )
| ( subsetI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f928]) ).
thf(f928,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
| ( $true
= ( subset @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f266]) ).
thf(f266,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( $true
= ( subset @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f265]) ).
thf(f265,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f78]) ).
thf(f78,axiom,
! [X3: $i,X4: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( subset @ X3 @ X4 ) )
= subsetI1 ),
file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',subsetI1) ).
thf(f6457,plain,
( ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK652 )
!= $true )
| spl726_88 ),
inference(trivial_inequality_removal,[status(thm)],[f6450]) ).
thf(f6450,plain,
( ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK652 )
!= $true )
| ( $true != $true )
| spl726_88 ),
inference(superposition,[status(thm)],[f4994,f3501]) ).
thf(f3501,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK651 )
= $true )
| ( ( in @ X0 @ sK652 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3500]) ).
thf(f3500,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ sK652 )
!= $true )
| ( ( in @ X0 @ sK651 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f3488,f3002]) ).
thf(f3002,plain,
powersetE = $true,
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f3488,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK651 )
= $true )
| ( ( in @ X0 @ sK652 )
!= $true )
| ( powersetE != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3483]) ).
thf(f3483,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK652 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ sK651 )
= $true )
| ( powersetE != $true ) ),
inference(superposition,[status(thm)],[f2666,f3015]) ).
thf(f3015,plain,
( $true
= ( in @ sK652 @ ( powerset @ sK651 ) ) ),
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f2666,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( powersetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f1669]) ).
thf(f1669,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ( ( ( in @ sK434 @ sK432 )
= $true )
& ( ( in @ sK434 @ sK433 )
!= $true )
& ( ( in @ sK432 @ ( powerset @ sK433 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK432,sK433,sK434])],[f1667,f1668]) ).
thf(f1668,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
& ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X4 ) )
= $true ) )
=> ( ( ( in @ sK434 @ sK432 )
= $true )
& ( ( in @ sK434 @ sK433 )
!= $true )
& ( ( in @ sK432 @ ( powerset @ sK433 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1667,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
& ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X3 @ ( powerset @ X4 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1666]) ).
thf(f1666,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( powersetE != $true ) )
& ( ( powersetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f842]) ).
thf(f842,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( powersetE = $true ) ),
inference(flattening,[status(thm)],[f841]) ).
thf(f841,plain,
( ( powersetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f408]) ).
thf(f408,plain,
( ( powersetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f407]) ).
thf(f407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= powersetE ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,axiom,
! [X4: $i,X3: $i,X1: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
=> ( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) ) )
= powersetE ),
file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',powersetE) ).
thf(f4994,plain,
( ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK651 )
!= $true )
| spl726_88 ),
inference(avatar_component_clause,[status(thm)],[f4992]) ).
thf(f7943,plain,
spl726_91,
inference(avatar_split_clause,[status(thm)],[f7942,f5050]) ).
thf(f5050,definition,
( spl726_91
<=> ( ( in @ sK650 @ ( powerset @ sK652 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl726_91])],[avatar_definition]) ).
thf(f7942,plain,
( ( in @ sK650 @ ( powerset @ sK652 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f7941]) ).
thf(f7941,plain,
( ( $true != $true )
| ( ( in @ sK650 @ ( powerset @ sK652 ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f7939,f3129]) ).
thf(f3129,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f7939,plain,
( ( ( in @ sK650 @ ( powerset @ sK652 ) )
= $true )
| ( powersetI != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f7938]) ).
thf(f7938,plain,
( ( $true != $true )
| ( ( in @ sK650 @ ( powerset @ sK652 ) )
= $true )
| ( powersetI != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f7929]) ).
thf(f7929,plain,
( ( ( in @ sK650 @ ( powerset @ sK652 ) )
= $true )
| ( $true != $true )
| ( powersetI != $true )
| ( ( in @ sK650 @ ( powerset @ sK652 ) )
= $true ) ),
inference(superposition,[status(thm)],[f5079,f2698]) ).
thf(f2698,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK455 @ X1 @ X0 ) @ X1 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( powersetI != $true ) ),
inference(cnf_transformation,[status(thm)],[f1709]) ).
thf(f1709,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ ( sK455 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK455 @ X1 @ X0 ) @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ( ! [X5: $i] :
( ( ( in @ X5 @ sK457 )
!= $true )
| ( ( in @ X5 @ sK456 )
= $true ) )
& ( ( in @ sK457 @ ( powerset @ sK456 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK455,sK456,sK457])],[f1706,f1708,f1707]) ).
thf(f1707,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
=> ( ( ( in @ ( sK455 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK455 @ X1 @ X0 ) @ X0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1708,plain,
( ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) )
& ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true ) )
=> ( ! [X5: $i] :
( ( ( in @ X5 @ sK457 )
!= $true )
| ( ( in @ X5 @ sK456 )
= $true ) )
& ( ( in @ sK457 @ ( powerset @ sK456 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1706,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) )
& ( ( in @ X4 @ ( powerset @ X3 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f1705]) ).
thf(f1705,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI != $true ) )
& ( ( powersetI = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f815]) ).
thf(f815,plain,
( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetI = $true ) ),
inference(ennf_transformation,[status(thm)],[f326]) ).
thf(f326,plain,
( ( powersetI = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f325]) ).
thf(f325,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X1 @ ( powerset @ X0 ) ) )
= powersetI ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,axiom,
! [X3: $i,X4: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
=> ( in @ X4 @ ( powerset @ X3 ) ) )
= powersetI ),
file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',powersetI) ).
thf(f5079,plain,
! [X0: $i] :
( ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK650 )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK652 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5078]) ).
thf(f5078,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( powerset @ sK652 ) )
= $true )
| ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK650 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f5063]) ).
thf(f5063,plain,
! [X0: $i] :
( ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK650 )
!= $true )
| ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK650 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ sK652 ) )
= $true ) ),
inference(superposition,[status(thm)],[f3573,f3476]) ).
thf(f3476,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK651 )
= $true )
| ( $true
!= ( in @ X0 @ sK650 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3475]) ).
thf(f3475,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X0 @ sK650 ) )
| ( ( in @ X0 @ sK651 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f3459,f3002]) ).
thf(f3459,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK650 ) )
| ( ( in @ X0 @ sK651 )
= $true )
| ( powersetE != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3454]) ).
thf(f3454,plain,
! [X0: $i] :
( ( powersetE != $true )
| ( ( in @ X0 @ sK651 )
= $true )
| ( $true
!= ( in @ X0 @ sK650 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2666,f3011]) ).
thf(f3011,plain,
( $true
= ( in @ sK650 @ ( powerset @ sK651 ) ) ),
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f3573,plain,
! [X0: $i] :
( ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK651 )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK652 ) )
= $true )
| ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK650 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3572]) ).
thf(f3572,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK650 )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK652 ) )
= $true )
| ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK651 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f3530,f3129]) ).
thf(f3530,plain,
! [X0: $i] :
( ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK650 )
!= $true )
| ( powersetI != $true )
| ( ( in @ X0 @ ( powerset @ sK652 ) )
= $true )
| ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK651 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3522]) ).
thf(f3522,plain,
! [X0: $i] :
( ( powersetI != $true )
| ( ( in @ X0 @ ( powerset @ sK652 ) )
= $true )
| ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK651 )
!= $true )
| ( ( in @ ( sK455 @ X0 @ sK652 ) @ sK650 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2697,f3013]) ).
thf(f3013,plain,
! [X4: $i] :
( ( ( in @ X4 @ sK652 )
= $true )
| ( ( in @ X4 @ sK651 )
!= $true )
| ( ( in @ X4 @ sK650 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f2697,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK455 @ X1 @ X0 ) @ X0 )
!= $true )
| ( powersetI != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1709]) ).
thf(f7914,plain,
( spl726_124
| ~ spl726_91 ),
inference(avatar_split_clause,[status(thm)],[f7913,f5050,f6290]) ).
thf(f6290,definition,
( spl726_124
<=> ( ( subset @ sK650 @ sK652 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl726_124])],[avatar_definition]) ).
thf(f7913,plain,
( ( ( subset @ sK650 @ sK652 )
= $true )
| ~ spl726_91 ),
inference(trivial_inequality_removal,[status(thm)],[f7912]) ).
thf(f7912,plain,
( ( ( subset @ sK650 @ sK652 )
= $true )
| ( $true != $true )
| ~ spl726_91 ),
inference(forward_demodulation,[status(thm)],[f7905,f2997]) ).
thf(f2997,plain,
powersetE1 = $true,
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f7905,plain,
( ( powersetE1 != $true )
| ( ( subset @ sK650 @ sK652 )
= $true )
| ~ spl726_91 ),
inference(trivial_inequality_removal,[status(thm)],[f7898]) ).
thf(f7898,plain,
( ( $true != $true )
| ( powersetE1 != $true )
| ( ( subset @ sK650 @ sK652 )
= $true )
| ~ spl726_91 ),
inference(superposition,[status(thm)],[f2384,f5052]) ).
thf(f5052,plain,
( ( ( in @ sK650 @ ( powerset @ sK652 ) )
= $true )
| ~ spl726_91 ),
inference(avatar_component_clause,[status(thm)],[f5050]) ).
thf(f2384,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true )
| ( ( subset @ X3 @ X2 )
= $true )
| ( powersetE1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1348]) ).
thf(f1348,plain,
( ( ( powersetE1 = $true )
| ( ( ( subset @ sK224 @ sK223 )
!= $true )
& ( ( in @ sK224 @ ( powerset @ sK223 ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
| ( powersetE1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK223,sK224])],[f1346,f1347]) ).
thf(f1347,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ( ( subset @ sK224 @ sK223 )
!= $true )
& ( ( in @ sK224 @ ( powerset @ sK223 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1346,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
| ( powersetE1 != $true ) ) ),
inference(rectify,[status(thm)],[f1345]) ).
thf(f1345,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( powersetE1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f921]) ).
thf(f921,plain,
( ( powersetE1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f298]) ).
thf(f298,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(fool_elimination,[status(thm)],[f297]) ).
thf(f297,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
inference(rectify,[status(thm)],[f96]) ).
thf(f96,axiom,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) )
= powersetE1 ),
file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',powersetE1) ).
thf(f7711,plain,
( spl726_100
| ~ spl726_87
| ~ spl726_124 ),
inference(avatar_split_clause,[status(thm)],[f7710,f6290,f4988,f5331]) ).
thf(f5331,definition,
( spl726_100
<=> ( sK650 = sK652 ) ),
introduced(definition,[new_symbols(naming,[spl726_100])],[avatar_definition]) ).
thf(f7710,plain,
( ( ( subset @ sK652 @ sK650 )
!= $true )
| ( sK650 = sK652 )
| ~ spl726_124 ),
inference(trivial_inequality_removal,[status(thm)],[f7709]) ).
thf(f7709,plain,
( ( $true != $true )
| ( ( subset @ sK652 @ sK650 )
!= $true )
| ( sK650 = sK652 )
| ~ spl726_124 ),
inference(forward_demodulation,[status(thm)],[f7708,f3082]) ).
thf(f3082,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f7708,plain,
( ( sK650 = sK652 )
| ( setextsub != $true )
| ( ( subset @ sK652 @ sK650 )
!= $true )
| ~ spl726_124 ),
inference(trivial_inequality_removal,[status(thm)],[f7704]) ).
thf(f7704,plain,
( ( ( subset @ sK652 @ sK650 )
!= $true )
| ( sK650 = sK652 )
| ( setextsub != $true )
| ( $true != $true )
| ~ spl726_124 ),
inference(superposition,[status(thm)],[f2115,f6291]) ).
thf(f6291,plain,
( ( ( subset @ sK650 @ sK652 )
= $true )
| ~ spl726_124 ),
inference(avatar_component_clause,[status(thm)],[f6290]) ).
thf(f2115,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
!= $true )
| ( setextsub != $true )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( X2 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f1019]) ).
thf(f1019,plain,
( ( ( setextsub = $true )
| ( ( ( subset @ sK11 @ sK12 )
= $true )
& ( ( subset @ sK12 @ sK11 )
= $true )
& ( sK11 != sK12 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 ) )
| ( setextsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f1017,f1018]) ).
thf(f1018,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) )
=> ( ( ( subset @ sK11 @ sK12 )
= $true )
& ( ( subset @ sK12 @ sK11 )
= $true )
& ( sK11 != sK12 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1017,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 ) )
| ( setextsub != $true ) ) ),
inference(rectify,[status(thm)],[f1016]) ).
thf(f1016,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) )
| ( setextsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f951]) ).
thf(f951,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) ) ),
inference(flattening,[status(thm)],[f950]) ).
thf(f950,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
!= ( subset @ X0 @ X1 ) )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f394]) ).
thf(f394,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( $true
= ( subset @ X0 @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f393]) ).
thf(f393,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
! [X4: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) )
= setextsub ),
file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',setextsub) ).
thf(f7585,plain,
~ spl726_100,
inference(avatar_contradiction_clause,[status(thm)],[f7584]) ).
thf(f7584,plain,
( $false
| ~ spl726_100 ),
inference(trivial_inequality_removal,[status(thm)],[f7518]) ).
thf(f7518,plain,
( ( sK650 != sK650 )
| ~ spl726_100 ),
inference(superposition,[status(thm)],[f3012,f5333]) ).
thf(f5333,plain,
( ( sK650 = sK652 )
| ~ spl726_100 ),
inference(avatar_component_clause,[status(thm)],[f5331]) ).
thf(f3012,plain,
sK650 != sK652,
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f4995,plain,
( spl726_87
| ~ spl726_88 ),
inference(avatar_split_clause,[status(thm)],[f4986,f4992,f4988]) ).
thf(f4986,plain,
( ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK651 )
!= $true )
| ( ( subset @ sK652 @ sK650 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4985]) ).
thf(f4985,plain,
( ( $true != $true )
| ( ( subset @ sK652 @ sK650 )
= $true )
| ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK651 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4981,f3115]) ).
thf(f4981,plain,
( ( ( subset @ sK652 @ sK650 )
= $true )
| ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK651 )
!= $true )
| ( subsetI1 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4980]) ).
thf(f4980,plain,
( ( ( subset @ sK652 @ sK650 )
= $true )
| ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK651 )
!= $true )
| ( $true != $true )
| ( subsetI1 != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f4970]) ).
thf(f4970,plain,
( ( ( subset @ sK652 @ sK650 )
= $true )
| ( ( subset @ sK652 @ sK650 )
= $true )
| ( subsetI1 != $true )
| ( $true != $true )
| ( ( in @ ( sK26 @ sK650 @ sK652 ) @ sK651 )
!= $true ) ),
inference(superposition,[status(thm)],[f3645,f2133]) ).
thf(f3645,plain,
! [X0: $i] :
( ( ( in @ ( sK26 @ sK650 @ X0 ) @ sK652 )
!= $true )
| ( ( in @ ( sK26 @ sK650 @ X0 ) @ sK651 )
!= $true )
| ( ( subset @ X0 @ sK650 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3644]) ).
thf(f3644,plain,
! [X0: $i] :
( ( ( in @ ( sK26 @ sK650 @ X0 ) @ sK651 )
!= $true )
| ( ( in @ ( sK26 @ sK650 @ X0 ) @ sK652 )
!= $true )
| ( ( subset @ X0 @ sK650 )
= $true )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f3642,f3115]) ).
thf(f3642,plain,
! [X0: $i] :
( ( ( in @ ( sK26 @ sK650 @ X0 ) @ sK652 )
!= $true )
| ( ( subset @ X0 @ sK650 )
= $true )
| ( ( in @ ( sK26 @ sK650 @ X0 ) @ sK651 )
!= $true )
| ( subsetI1 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3609]) ).
thf(f3609,plain,
! [X0: $i] :
( ( ( in @ ( sK26 @ sK650 @ X0 ) @ sK652 )
!= $true )
| ( ( in @ ( sK26 @ sK650 @ X0 ) @ sK651 )
!= $true )
| ( ( subset @ X0 @ sK650 )
= $true )
| ( $true != $true )
| ( subsetI1 != $true ) ),
inference(superposition,[status(thm)],[f2134,f3014]) ).
thf(f3014,plain,
! [X3: $i] :
( ( ( in @ X3 @ sK650 )
= $true )
| ( ( in @ X3 @ sK651 )
!= $true )
| ( ( in @ X3 @ sK652 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f2007]) ).
thf(f2134,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK26 @ X4 @ X3 ) @ X4 )
!= $true )
| ( ( subset @ X3 @ X4 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1041]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU715^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:31:08 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU715^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.28/0.46 % (! x:i.in x A -> in x X -> in x Y) -> (! x:i.in x A -> in x Y ->
% 0.28/0.46 % in x X) -> X = Y))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC217g [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.86 v6.1.0, 1.00 v6.0.0, 0.86 v5.5.0, 0.83 v5.4.0, 1.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 505 ( 235 unt; 269 typ; 235 def)
% 0.28/0.46 % Number of atoms : 1321 ( 360 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 240 ( 5 avg)
% 0.28/0.46 % Number of connectives : 2568 ( 55 ~; 12 |; 44 &;1818 @)
% 0.28/0.46 % ( 14 <=>; 625 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 244 ( 2 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 272 ( 269 usr; 235 con; 0-4 aty)
% 0.28/0.46 % Number of variables : 790 ( 74 ^; 681 !; 35 ?; 790 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=273
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu_type,type,
% 0.28/0.46 exu: ( $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu,definition,
% 0.28/0.46 ( exu
% 0.28/0.46 = ( ^ [Xphi: $i > $o] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx_type,type,
% 0.28/0.46 setextAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx,definition,
% 0.28/0.46 ( setextAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 <=> ( in @ Xx @ B ) )
% 0.28/0.46 => ( A = B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset_type,type,
% 0.28/0.46 emptyset: $i ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx_type,type,
% 0.28/0.46 emptysetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx,definition,
% 0.28/0.46 ( emptysetAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin_type,type,
% 0.28/0.46 setadjoin: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx_type,type,
% 0.28/0.46 setadjoinAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx,definition,
% 0.28/0.46 ( setadjoinAx
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 <=> ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powerset_type,type,
% 0.28/0.46 powerset: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx_type,type,
% 0.28/0.46 powersetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx,definition,
% 0.28/0.46 ( powersetAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 <=> ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunion_type,type,
% 0.28/0.46 setunion: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx_type,type,
% 0.28/0.46 setunionAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx,definition,
% 0.28/0.46 ( setunionAx
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.46 <=> ? [B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omega_type,type,
% 0.28/0.46 omega: $i ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax_type,type,
% 0.28/0.46 omega0Ax: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax,definition,
% 0.28/0.46 ( omega0Ax
% 0.28/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx_type,type,
% 0.28/0.46 omegaSAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx,definition,
% 0.28/0.46 ( omegaSAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx_type,type,
% 0.28/0.46 omegaIndAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx,definition,
% 0.28/0.46 ( omegaIndAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( ( in @ emptyset @ A )
% 0.28/0.46 & ! [Xx: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ omega )
% 0.28/0.46 & ( in @ Xx @ A ) )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(replAx_type,type,
% 0.28/0.46 replAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(replAx,definition,
% 0.28/0.46 ( replAx
% 0.28/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 <=> ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx_type,type,
% 0.28/0.46 foundationAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx,definition,
% 0.28/0.46 ( foundationAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ( ( in @ B @ A )
% 0.28/0.46 & ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx_type,type,
% 0.28/0.46 wellorderingAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx,definition,
% 0.28/0.46 ( wellorderingAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ? [B: $i] :
% 0.28/0.46 ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ A )
% 0.28/0.46 & ( in @ Xy @ A ) )
% 0.28/0.46 => ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ( ( in @ Xx @ C )
% 0.28/0.46 <=> ( in @ Xy @ C ) ) )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 & ! [C: $i,D: $i] :
% 0.28/0.46 ( ( ( in @ C @ B )
% 0.28/0.46 & ( in @ D @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ D ) )
% 0.28/0.46 | ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ D )
% 0.28/0.46 => ( in @ Xx @ C ) ) ) )
% 0.28/0.46 & ! [C: $i] :
% 0.28/0.46 ( ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.46 => ? [D: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ D @ B )
% 0.28/0.46 & ( in @ Xx @ C )
% 0.28/0.46 & ~ ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ D )
% 0.28/0.46 & ( in @ Xy @ C ) )
% 0.28/0.46 & ! [E: $i] :
% 0.28/0.46 ( ( in @ E @ B )
% 0.28/0.46 => ( ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ E )
% 0.28/0.46 => ( in @ Xy @ D ) )
% 0.28/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(descr_type,type,
% 0.28/0.46 descr: ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(descrp_type,type,
% 0.28/0.46 descrp: $o ).
% 0.28/0.46
% 0.28/0.46 thf(descrp,definition,
% 0.28/0.46 ( descrp
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ( Xphi
% 0.28/0.46 @ ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr_type,type,
% 0.28/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI_type,type,
% 0.28/0.46 dsetconstrI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI,definition,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL_type,type,
% 0.28/0.46 dsetconstrEL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL,definition,
% 0.28/0.46 ( dsetconstrEL
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER_type,type,
% 0.28/0.46 dsetconstrER: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER,definition,
% 0.28/0.46 ( dsetconstrER
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1_type,type,
% 0.28/0.46 exuE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1,definition,
% 0.28/0.46 ( exuE1
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set_type,type,
% 0.28/0.46 prop2set: $o > $i ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE_type,type,
% 0.28/0.46 prop2setE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE,definition,
% 0.28/0.46 ( prop2setE
% 0.28/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.46 => Xphi ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetE_type,type,
% 0.28/0.46 emptysetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetE,definition,
% 0.28/0.46 ( emptysetE
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetimpfalse_type,type,
% 0.28/0.46 emptysetimpfalse: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetimpfalse,definition,
% 0.28/0.46 ( emptysetimpfalse
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => $false ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notinemptyset_type,type,
% 0.28/0.46 notinemptyset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notinemptyset,definition,
% 0.28/0.46 ( notinemptyset
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e_type,type,
% 0.28/0.46 exuE3e: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e,definition,
% 0.28/0.46 ( exuE3e
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setext_type,type,
% 0.28/0.46 setext: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setext,definition,
% 0.28/0.46 ( setext
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 => ( A = B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyI_type,type,
% 0.28/0.46 emptyI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyI,definition,
% 0.28/0.46 ( emptyI
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ A )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(noeltsimpempty_type,type,
% 0.28/0.46 noeltsimpempty: $o ).
% 0.28/0.46
% 0.28/0.46 thf(noeltsimpempty,definition,
% 0.28/0.46 ( noeltsimpempty
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ A )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setbeta_type,type,
% 0.28/0.46 setbeta: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setbeta,definition,
% 0.28/0.46 ( setbeta
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonempty_type,type,
% 0.28/0.46 nonempty: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonempty,definition,
% 0.28/0.46 ( nonempty
% 0.28/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyE1_type,type,
% 0.28/0.46 nonemptyE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyE1,definition,
% 0.28/0.46 ( nonemptyE1
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( nonempty @ A )
% 0.28/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI_type,type,
% 0.28/0.46 nonemptyI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI,definition,
% 0.28/0.46 ( nonemptyI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( nonempty
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI1_type,type,
% 0.28/0.46 nonemptyI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI1,definition,
% 0.28/0.46 ( nonemptyI1
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIL_type,type,
% 0.28/0.46 setadjoinIL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIL,definition,
% 0.28/0.46 ( setadjoinIL
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinunitempty_type,type,
% 0.28/0.46 emptyinunitempty: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinunitempty,definition,
% 0.28/0.46 ( emptyinunitempty
% 0.28/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIR_type,type,
% 0.28/0.46 setadjoinIR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIR,definition,
% 0.28/0.46 ( setadjoinIR
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinE_type,type,
% 0.28/0.46 setadjoinE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinE,definition,
% 0.28/0.46 ( setadjoinE
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 => ! [Xphi: $o] :
% 0.28/0.46 ( ( ( Xy = Xx )
% 0.28/0.46 => Xphi )
% 0.28/0.46 => ( ( ( in @ Xy @ A )
% 0.28/0.46 => Xphi )
% 0.28/0.46 => Xphi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinOr_type,type,
% 0.28/0.46 setadjoinOr: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinOr,definition,
% 0.28/0.46 ( setadjoinOr
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 => ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setoftrueEq_type,type,
% 0.28/0.46 setoftrueEq: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setoftrueEq,definition,
% 0.28/0.46 ( setoftrueEq
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : $true )
% 0.28/0.46 = A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetI_type,type,
% 0.28/0.46 powersetI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetI,definition,
% 0.28/0.46 ( powersetI
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinPowerset_type,type,
% 0.28/0.46 emptyinPowerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinPowerset,definition,
% 0.28/0.46 ( emptyinPowerset
% 0.28/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyInPowerset_type,type,
% 0.28/0.46 emptyInPowerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyInPowerset,definition,
% 0.28/0.46 ( emptyInPowerset
% 0.28/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetE_type,type,
% 0.28/0.46 powersetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetE,definition,
% 0.28/0.46 ( powersetE
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 => ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunionI_type,type,
% 0.28/0.46 setunionI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionI,definition,
% 0.28/0.46 ( setunionI
% 0.28/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( ( in @ B @ A )
% 0.28/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunionE_type,type,
% 0.28/0.46 setunionE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionE,definition,
% 0.28/0.46 ( setunionE
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.46 => ! [Xphi: $o] :
% 0.28/0.46 ( ! [B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( ( in @ B @ A )
% 0.28/0.46 => Xphi ) )
% 0.28/0.46 => Xphi ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subPowSU_type,type,
% 0.28/0.46 subPowSU: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subPowSU,definition,
% 0.28/0.46 ( subPowSU
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE2_type,type,
% 0.28/0.46 exuE2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE2,definition,
% 0.28/0.46 ( exuE2
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyImpWitness_type,type,
% 0.28/0.46 nonemptyImpWitness: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyImpWitness,definition,
% 0.28/0.46 ( nonemptyImpWitness
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( nonempty @ A )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & $true ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(uniqinunit_type,type,
% 0.28/0.46 uniqinunit: $o ).
% 0.28/0.46
% 0.28/0.46 thf(uniqinunit,definition,
% 0.28/0.46 ( uniqinunit
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notinsingleton_type,type,
% 0.28/0.46 notinsingleton: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notinsingleton,definition,
% 0.28/0.46 ( notinsingleton
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx != Xy )
% 0.28/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(eqinunit_type,type,
% 0.28/0.46 eqinunit: $o ).
% 0.28/0.46
% 0.28/0.46 thf(eqinunit,definition,
% 0.28/0.46 ( eqinunit
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(singletonsswitch_type,type,
% 0.28/0.46 singletonsswitch: $o ).
% 0.28/0.46
% 0.28/0.46 thf(singletonsswitch,definition,
% 0.28/0.46 ( singletonsswitch
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetE_type,type,
% 0.28/0.46 upairsetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetE,definition,
% 0.28/0.46 ( upairsetE
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.46 => ( ( Xz = Xx )
% 0.28/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIL_type,type,
% 0.28/0.46 upairsetIL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIL,definition,
% 0.28/0.46 ( upairsetIL
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIR_type,type,
% 0.28/0.46 upairsetIR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIR,definition,
% 0.28/0.46 ( upairsetIR
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyE1_type,type,
% 0.28/0.46 emptyE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyE1,definition,
% 0.28/0.46 ( emptyE1
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) )
% 0.28/0.46 => ( ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 = emptyset )
% 0.28/0.46 => $false ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(vacuousDall_type,type,
% 0.28/0.46 vacuousDall: $o ).
% 0.28/0.46
% 0.28/0.46 thf(vacuousDall,definition,
% 0.28/0.46 ( vacuousDall
% 0.28/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan1_type,type,
% 0.28/0.46 quantDeMorgan1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan1,definition,
% 0.28/0.46 ( quantDeMorgan1
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan2_type,type,
% 0.28/0.46 quantDeMorgan2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan2,definition,
% 0.28/0.46 ( quantDeMorgan2
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ~ ( Xphi @ Xx ) )
% 0.28/0.46 => ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan3_type,type,
% 0.28/0.46 quantDeMorgan3: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan3,definition,
% 0.28/0.46 ( quantDeMorgan3
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan4_type,type,
% 0.28/0.46 quantDeMorgan4: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan4,definition,
% 0.28/0.46 ( quantDeMorgan4
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ~ ( Xphi @ Xx ) )
% 0.28/0.46 => ~ ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setI_type,type,
% 0.28/0.46 prop2setI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setI,definition,
% 0.28/0.46 ( prop2setI
% 0.28/0.46 = ( ! [Xphi: $o] :
% 0.28/0.46 ( Xphi
% 0.28/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(set2prop_type,type,
% 0.28/0.46 set2prop: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set2propI_type,type,
% 0.28/0.46 prop2set2propI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set2propI,definition,
% 0.28/0.46 ( prop2set2propI
% 0.28/0.46 = ( ! [Xphi: $o] :
% 0.28/0.46 ( Xphi
% 0.28/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notdexE_type,type,
% 0.28/0.46 notdexE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notdexE,definition,
% 0.28/0.46 ( notdexE
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notdallE_type,type,
% 0.28/0.46 notdallE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notdallE,definition,
% 0.28/0.46 ( notdallE
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuI1_type,type,
% 0.28/0.46 exuI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuI1,definition,
% 0.28/0.46 ( exuI1
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuI3_type,type,
% 0.28/0.46 exuI3: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuI3,definition,
% 0.28/0.46 ( exuI3
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 => ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuI2_type,type,
% 0.28/0.46 exuI2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuI2,definition,
% 0.28/0.46 ( exuI2
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 <=> ( Xy = Xx ) )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(inCongP_type,type,
% 0.28/0.46 inCongP: $o ).
% 0.28/0.46
% 0.28/0.46 thf(inCongP,definition,
% 0.28/0.46 ( inCongP
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(in__Cong_type,type,
% 0.28/0.46 in__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(in__Cong,definition,
% 0.28/0.46 ( in__Cong
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( ( in @ Xx @ A )
% 0.28/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3u_type,type,
% 0.28/0.46 exuE3u: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3u,definition,
% 0.28/0.46 ( exuE3u
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 => ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exu__Cong_type,type,
% 0.28/0.46 exu__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu__Cong,definition,
% 0.28/0.46 ( exu__Cong
% 0.28/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.46 => ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 <=> ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset__Cong_type,type,
% 0.28/0.46 emptyset__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset__Cong,definition,
% 0.28/0.46 ( emptyset__Cong
% 0.28/0.46 = ( emptyset = emptyset ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin__Cong_type,type,
% 0.28/0.46 setadjoin__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin__Cong,definition,
% 0.28/0.46 ( setadjoin__Cong
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ! [Xz: $i,Xu: $i] :
% 0.28/0.46 ( ( Xz = Xu )
% 0.28/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powerset__Cong_type,type,
% 0.28/0.46 powerset__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powerset__Cong,definition,
% 0.28/0.46 ( powerset__Cong
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ( ( powerset @ A )
% 0.28/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunion__Cong_type,type,
% 0.28/0.46 setunion__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunion__Cong,definition,
% 0.28/0.46 ( setunion__Cong
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ( ( setunion @ A )
% 0.28/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omega__Cong_type,type,
% 0.28/0.46 omega__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omega__Cong,definition,
% 0.28/0.46 ( omega__Cong
% 0.28/0.46 = ( omega = omega ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuEu_type,type,
% 0.28/0.46 exuEu: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuEu,definition,
% 0.28/0.46 ( exuEu
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 => ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(descr__Cong_type,type,
% 0.28/0.46 descr__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(descr__Cong,definition,
% 0.28/0.46 ( descr__Cong
% 0.28/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.46 => ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.46 => ( ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 = ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr__Cong_type,type,
% 0.28/0.46 dsetconstr__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr__Cong,definition,
% 0.28/0.46 ( dsetconstr__Cong
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ B )
% 0.28/0.46 => ( ( Xx = Xy )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.46 => ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 = ( dsetconstr @ B
% 0.28/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subset_type,type,
% 0.28/0.46 subset: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(disjoint_type,type,
% 0.28/0.46 disjoint: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(setsmeet_type,type,
% 0.28/0.46 setsmeet: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetI1_type,type,
% 0.28/0.46 subsetI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetI1,definition,
% 0.28/0.46 ( subsetI1
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(eqimpsubset2_type,type,
% 0.28/0.46 eqimpsubset2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(eqimpsubset2,definition,
% 0.28/0.46 ( eqimpsubset2
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(eqimpsubset1_type,type,
% 0.28/0.46 eqimpsubset1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(eqimpsubset1,definition,
% 0.28/0.46 ( eqimpsubset1
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetI2_type,type,
% 0.28/0.46 subsetI2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetI2,definition,
% 0.28/0.46 ( subsetI2
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetsubset_type,type,
% 0.28/0.46 emptysetsubset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetsubset,definition,
% 0.28/0.46 ( emptysetsubset
% 0.28/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetE_type,type,
% 0.28/0.46 subsetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetE,definition,
% 0.28/0.46 ( subsetE
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetE2_type,type,
% 0.28/0.46 subsetE2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetE2,definition,
% 0.28/0.46 ( subsetE2
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( ~ ( in @ Xx @ B )
% 0.28/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notsubsetI_type,type,
% 0.28/0.46 notsubsetI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notsubsetI,definition,
% 0.28/0.46 ( notsubsetI
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ~ ( in @ Xx @ B )
% 0.28/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notequalI1_type,type,
% 0.28/0.46 notequalI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notequalI1,definition,
% 0.28/0.46 ( notequalI1
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ~ ( subset @ A @ B )
% 0.28/0.46 => ( A != B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notequalI2_type,type,
% 0.28/0.46 notequalI2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notequalI2,definition,
% 0.28/0.46 ( notequalI2
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ~ ( in @ Xx @ B )
% 0.28/0.46 => ( A != B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetRefl_type,type,
% 0.28/0.46 subsetRefl: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetRefl,definition,
% 0.28/0.46 ( subsetRefl
% 0.28/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetTrans_type,type,
% 0.28/0.46 subsetTrans: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetTrans,definition,
% 0.28/0.46 ( subsetTrans
% 0.28/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( ( subset @ B @ C )
% 0.28/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinSub_type,type,
% 0.28/0.46 setadjoinSub: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinSub,definition,
% 0.28/0.46 ( setadjoinSub
% 0.28/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinSub2_type,type,
% 0.28/0.46 setadjoinSub2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinSub2,definition,
% 0.28/0.46 ( setadjoinSub2
% 0.28/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subset2powerset_type,type,
% 0.28/0.46 subset2powerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subset2powerset,definition,
% 0.28/0.46 ( subset2powerset
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setextsub_type,type,
% 0.28/0.46 setextsub: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setextsub,definition,
% 0.28/0.46 ( setextsub
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( ( subset @ B @ A )
% 0.28/0.46 => ( A = B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetemptysetimpeq_type,type,
% 0.28/0.46 subsetemptysetimpeq: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetemptysetimpeq,definition,
% 0.28/0.46 ( subsetemptysetimpeq
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( subset @ A @ emptyset )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetI1_type,type,
% 0.28/0.46 powersetI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetI1,definition,
% 0.28/0.46 ( powersetI1
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( subset @ B @ A )
% 0.28/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetE1_type,type,
% 0.28/0.46 powersetE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetE1,definition,
% 0.28/0.46 ( powersetE1
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(inPowerset_type,type,
% 0.28/0.46 inPowerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(inPowerset,definition,
% 0.28/0.46 ( inPowerset
% 0.28/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetsubset_type,type,
% 0.28/0.46 powersetsubset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetsubset,definition,
% 0.28/0.46 ( powersetsubset
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sepInPowerset_type,type,
% 0.28/0.46 sepInPowerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(sepInPowerset,definition,
% 0.28/0.46 ( sepInPowerset
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( in
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sepSubset_type,type,
% 0.28/0.46 sepSubset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(sepSubset,definition,
% 0.28/0.46 ( sepSubset
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( subset
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binunion_type,type,
% 0.28/0.46 binunion: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(binunionIL_type,type,
% 0.28/0.46 binunionIL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binunionIL,definition,
% 0.28/0.46 ( binunionIL
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairset2IR_type,type,
% 0.28/0.46 upairset2IR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairset2IR,definition,
% 0.28/0.46 ( upairset2IR
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binunionIR_type,type,
% 0.28/0.46 binunionIR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binunionIR,definition,
% 0.28/0.46 ( binunionIR
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binunionEcases_type,type,
% 0.28/0.46 binunionEcases: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binunionEcases,definition,
% 0.28/0.46 ( binunionEcases
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( ( in @ Xx @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE_type,type,
% 0.28/0.47 binunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE,definition,
% 0.28/0.47 ( binunionE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub_type,type,
% 0.28/0.47 binunionLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub,definition,
% 0.28/0.47 ( binunionLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub_type,type,
% 0.28/0.47 binunionRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub,definition,
% 0.28/0.47 ( binunionRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersect_type,type,
% 0.28/0.47 binintersect: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI_type,type,
% 0.28/0.47 binintersectI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI,definition,
% 0.28/0.47 ( binintersectI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5_type,type,
% 0.28/0.47 binintersectSubset5: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5,definition,
% 0.28/0.47 ( binintersectSubset5
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ C @ A )
% 0.28/0.47 => ( ( subset @ C @ B )
% 0.28/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL_type,type,
% 0.28/0.47 binintersectEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL,definition,
% 0.28/0.47 ( binintersectEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub_type,type,
% 0.28/0.47 binintersectLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub,definition,
% 0.28/0.47 ( binintersectLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2_type,type,
% 0.28/0.47 binintersectSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2,definition,
% 0.28/0.47 ( binintersectSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3_type,type,
% 0.28/0.47 binintersectSubset3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3,definition,
% 0.28/0.47 ( binintersectSubset3
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER_type,type,
% 0.28/0.47 binintersectER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER,definition,
% 0.28/0.47 ( binintersectER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(disjointsetsI1_type,type,
% 0.28/0.47 disjointsetsI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(disjointsetsI1,definition,
% 0.28/0.47 ( disjointsetsI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( in @ Xx @ B ) )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectRsub_type,type,
% 0.28/0.47 binintersectRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectRsub,definition,
% 0.28/0.47 ( binintersectRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset4_type,type,
% 0.28/0.47 binintersectSubset4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset4,definition,
% 0.28/0.47 ( binintersectSubset4
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset1_type,type,
% 0.28/0.47 binintersectSubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset1,definition,
% 0.28/0.47 ( binintersectSubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = A )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(bs114d_type,type,
% 0.28/0.47 bs114d: $o ).
% 0.28/0.47
% 0.28/0.47 thf(bs114d,definition,
% 0.28/0.47 ( bs114d
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.28/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(regular_type,type,
% 0.28/0.47 regular: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminus_type,type,
% 0.28/0.47 setminus: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setminusI_type,type,
% 0.28/0.47 setminusI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusI,definition,
% 0.28/0.47 ( setminusI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusEL_type,type,
% 0.28/0.47 setminusEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusEL,definition,
% 0.28/0.47 ( setminusEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusER_type,type,
% 0.28/0.47 setminusER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusER,definition,
% 0.28/0.47 ( setminusER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset2_type,type,
% 0.28/0.47 setminusSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset2,definition,
% 0.28/0.47 ( setminusSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( setminus @ A @ B )
% 0.28/0.47 = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusERneg_type,type,
% 0.28/0.47 setminusERneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusERneg,definition,
% 0.28/0.47 ( setminusERneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusELneg_type,type,
% 0.28/0.47 setminusELneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusELneg,definition,
% 0.28/0.47 ( setminusELneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusILneg_type,type,
% 0.28/0.47 setminusILneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusILneg,definition,
% 0.28/0.47 ( setminusILneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusIRneg_type,type,
% 0.28/0.47 setminusIRneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusIRneg,definition,
% 0.28/0.47 ( setminusIRneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusLsub_type,type,
% 0.28/0.47 setminusLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusLsub,definition,
% 0.28/0.47 ( setminusLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset1_type,type,
% 0.28/0.47 setminusSubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset1,definition,
% 0.28/0.47 ( setminusSubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( setminus @ A @ B )
% 0.28/0.47 = emptyset )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiff_type,type,
% 0.28/0.47 symdiff: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffE_type,type,
% 0.28/0.47 symdiffE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffE,definition,
% 0.28/0.47 ( symdiffE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI1_type,type,
% 0.28/0.47 symdiffI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI1,definition,
% 0.28/0.47 ( symdiffI1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI2_type,type,
% 0.28/0.47 symdiffI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI2,definition,
% 0.28/0.47 ( symdiffI2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg1_type,type,
% 0.28/0.47 symdiffIneg1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg1,definition,
% 0.28/0.47 ( symdiffIneg1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg2_type,type,
% 0.28/0.47 symdiffIneg2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg2,definition,
% 0.28/0.47 ( symdiffIneg2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair_type,type,
% 0.28/0.47 iskpair: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(secondinupair_type,type,
% 0.28/0.47 secondinupair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(secondinupair,definition,
% 0.28/0.47 ( secondinupair
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL_type,type,
% 0.28/0.47 setukpairIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL,definition,
% 0.28/0.47 ( setukpairIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR_type,type,
% 0.28/0.47 setukpairIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR,definition,
% 0.28/0.47 ( setukpairIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair_type,type,
% 0.28/0.47 kpairiskpair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair,definition,
% 0.28/0.47 ( kpairiskpair
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpair_type,type,
% 0.28/0.47 kpair: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp_type,type,
% 0.28/0.47 kpairp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp,definition,
% 0.28/0.47 ( kpairp
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprod_type,type,
% 0.28/0.47 cartprod: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsubset_type,type,
% 0.28/0.47 singletonsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsubset,definition,
% 0.28/0.47 ( singletonsubset
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowerset_type,type,
% 0.28/0.47 singletoninpowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowerset,definition,
% 0.28/0.47 ( singletoninpowerset
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowunion_type,type,
% 0.28/0.47 singletoninpowunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowunion,definition,
% 0.28/0.47 ( singletoninpowunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2E_type,type,
% 0.28/0.47 upairset2E: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2E,definition,
% 0.28/0.47 ( upairset2E
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsubunion_type,type,
% 0.28/0.47 upairsubunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsubunion,definition,
% 0.28/0.47 ( upairsubunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairinpowunion_type,type,
% 0.28/0.47 upairinpowunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairinpowunion,definition,
% 0.28/0.47 ( upairinpowunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem1_type,type,
% 0.28/0.47 ubforcartprodlem1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem1,definition,
% 0.28/0.47 ( ubforcartprodlem1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem2_type,type,
% 0.28/0.47 ubforcartprodlem2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem2,definition,
% 0.28/0.47 ( ubforcartprodlem2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem3_type,type,
% 0.28/0.47 ubforcartprodlem3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem3,definition,
% 0.28/0.47 ( ubforcartprodlem3
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairin_type,type,
% 0.28/0.47 cartprodpairin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairin,definition,
% 0.28/0.47 ( cartprodpairin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair1_type,type,
% 0.28/0.47 cartprodmempair1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair1,definition,
% 0.28/0.47 ( cartprodmempair1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 & ( Xu
% 0.28/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair_type,type,
% 0.28/0.47 cartprodmempair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair,definition,
% 0.28/0.47 ( cartprodmempair
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE2_type,type,
% 0.28/0.47 setunionE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE2,definition,
% 0.28/0.47 ( setunionE2
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ? [X: $i] :
% 0.28/0.47 ( ( in @ X @ A )
% 0.28/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton1_type,type,
% 0.28/0.47 setunionsingleton1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton1,definition,
% 0.28/0.47 ( setunionsingleton1
% 0.28/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton2_type,type,
% 0.28/0.47 setunionsingleton2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton2,definition,
% 0.28/0.47 ( setunionsingleton2
% 0.28/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton_type,type,
% 0.28/0.47 setunionsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton,definition,
% 0.28/0.47 ( setunionsingleton
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.28/0.47 = Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singleton_type,type,
% 0.28/0.47 singleton: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonprop_type,type,
% 0.28/0.47 singletonprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonprop,definition,
% 0.28/0.47 ( singletonprop
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) )
% 0.28/0.47 => ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1_type,type,
% 0.28/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1,definition,
% 0.28/0.47 ( ex1
% 0.28/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E1_type,type,
% 0.28/0.47 ex1E1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E1,definition,
% 0.28/0.47 ( ex1E1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I_type,type,
% 0.28/0.47 ex1I: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I,definition,
% 0.28/0.47 ( ex1I
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xy = Xx ) ) )
% 0.28/0.47 => ( ex1 @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I2_type,type,
% 0.28/0.47 ex1I2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I2,definition,
% 0.28/0.47 ( ex1I2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) )
% 0.28/0.47 => ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsuniq_type,type,
% 0.28/0.47 singletonsuniq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsuniq,definition,
% 0.28/0.47 ( singletonsuniq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.28/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(atmost1p_type,type,
% 0.28/0.47 atmost1p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(atleast2p_type,type,
% 0.28/0.47 atleast2p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(atmost2p_type,type,
% 0.28/0.47 atmost2p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetp_type,type,
% 0.28/0.47 upairsetp: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL1_type,type,
% 0.28/0.47 setukpairinjL1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL1,definition,
% 0.28/0.47 ( setukpairinjL1
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kfstsingleton_type,type,
% 0.28/0.47 kfstsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kfstsingleton,definition,
% 0.28/0.47 ( kfstsingleton
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(theprop_type,type,
% 0.28/0.47 theprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(theprop,definition,
% 0.28/0.47 ( theprop
% 0.28/0.47 = ( ! [X: $i] :
% 0.28/0.47 ( ( singleton @ X )
% 0.28/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kfst_type,type,
% 0.28/0.47 kfst: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(kfstpairEq_type,type,
% 0.28/0.47 kfstpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kfstpairEq,definition,
% 0.28/0.47 ( kfstpairEq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstin_type,type,
% 0.28/0.47 cartprodfstin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstin,definition,
% 0.28/0.47 ( cartprodfstin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL2_type,type,
% 0.28/0.47 setukpairinjL2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL2,definition,
% 0.28/0.47 ( setukpairinjL2
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL_type,type,
% 0.28/0.47 setukpairinjL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL,definition,
% 0.28/0.47 ( setukpairinjL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xz @ Xu ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR11_type,type,
% 0.28/0.47 setukpairinjR11: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR11,definition,
% 0.28/0.47 ( setukpairinjR11
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR12_type,type,
% 0.28/0.47 setukpairinjR12: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR12,definition,
% 0.28/0.47 ( setukpairinjR12
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR1_type,type,
% 0.28/0.47 setukpairinjR1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR1,definition,
% 0.28/0.47 ( setukpairinjR1
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xu )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairequniteq_type,type,
% 0.28/0.47 upairequniteq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairequniteq,definition,
% 0.28/0.47 ( upairequniteq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR2_type,type,
% 0.28/0.47 setukpairinjR2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR2,definition,
% 0.28/0.47 ( setukpairinjR2
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR_type,type,
% 0.28/0.47 setukpairinjR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR,definition,
% 0.28/0.47 ( setukpairinjR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xz @ Xu ) )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksndsingleton_type,type,
% 0.28/0.47 ksndsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ksndsingleton,definition,
% 0.28/0.47 ( ksndsingleton
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.47 @ ^ [Xx: $i] :
% 0.28/0.47 ( Xu
% 0.28/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksnd_type,type,
% 0.28/0.47 ksnd: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(ksndpairEq_type,type,
% 0.28/0.47 ksndpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ksndpairEq,definition,
% 0.28/0.47 ( ksndpairEq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xy ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairsurjEq_type,type,
% 0.28/0.47 kpairsurjEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairsurjEq,definition,
% 0.28/0.47 ( kpairsurjEq
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.28/0.47 = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndin_type,type,
% 0.28/0.47 cartprodsndin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndin,definition,
% 0.28/0.47 ( cartprodsndin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairmemEL_type,type,
% 0.28/0.47 cartprodpairmemEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairmemEL,definition,
% 0.28/0.47 ( cartprodpairmemEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairmemER_type,type,
% 0.28/0.47 cartprodpairmemER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairmemER,definition,
% 0.28/0.47 ( cartprodpairmemER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempaircEq_type,type,
% 0.28/0.47 cartprodmempaircEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempaircEq,definition,
% 0.28/0.47 ( cartprodmempaircEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstpairEq_type,type,
% 0.28/0.47 cartprodfstpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstpairEq,definition,
% 0.28/0.47 ( cartprodfstpairEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndpairEq_type,type,
% 0.28/0.47 cartprodsndpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndpairEq,definition,
% 0.28/0.47 ( cartprodsndpairEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairsurjEq_type,type,
% 0.28/0.47 cartprodpairsurjEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairsurjEq,definition,
% 0.28/0.47 ( cartprodpairsurjEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.28/0.47 = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln_type,type,
% 0.28/0.47 breln: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln,definition,
% 0.28/0.47 ( breln
% 0.28/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstr_type,type,
% 0.28/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrI_type,type,
% 0.28/0.47 dpsetconstrI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrI,definition,
% 0.28/0.47 ( dpsetconstrI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrSub_type,type,
% 0.28/0.47 dpsetconstrSub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrSub,definition,
% 0.28/0.47 ( dpsetconstrSub
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.28/0.47 ( subset
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.28/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setOfPairsIsBReln_type,type,
% 0.28/0.47 setOfPairsIsBReln: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setOfPairsIsBReln,definition,
% 0.28/0.47 ( setOfPairsIsBReln
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.28/0.47 ( breln @ A @ B
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrERa_type,type,
% 0.28/0.47 dpsetconstrERa: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrERa,definition,
% 0.28/0.47 ( dpsetconstrERa
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrEL1_type,type,
% 0.28/0.47 dpsetconstrEL1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrEL1,definition,
% 0.28/0.47 ( dpsetconstrEL1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrEL2_type,type,
% 0.28/0.47 dpsetconstrEL2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrEL2,definition,
% 0.28/0.47 ( dpsetconstrEL2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrER_type,type,
% 0.28/0.47 dpsetconstrER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrER,definition,
% 0.28/0.47 ( dpsetconstrER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(func_type,type,
% 0.28/0.47 func: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcSet_type,type,
% 0.28/0.47 funcSet: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(funcImageSingleton_type,type,
% 0.28/0.47 funcImageSingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcImageSingleton,definition,
% 0.28/0.47 ( funcImageSingleton
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(apProp_type,type,
% 0.28/0.47 apProp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(apProp,definition,
% 0.28/0.47 ( apProp
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in
% 0.28/0.47 @ ( setunion
% 0.28/0.47 @ ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.28/0.47 @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ap_type,type,
% 0.28/0.47 ap: $i > $i > $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(app_type,type,
% 0.28/0.47 app: $o ).
% 0.28/0.47
% 0.28/0.47 thf(app,definition,
% 0.28/0.47 ( app
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(infuncsetfunc_type,type,
% 0.28/0.47 infuncsetfunc: $o ).
% 0.28/0.47
% 0.28/0.47 thf(infuncsetfunc,definition,
% 0.28/0.47 ( infuncsetfunc
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ap2p_type,type,
% 0.28/0.47 ap2p: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ap2p,definition,
% 0.28/0.47 ( ap2p
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcinfuncset_type,type,
% 0.28/0.47 funcinfuncset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcinfuncset,definition,
% 0.28/0.47 ( funcinfuncset
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(lamProp_type,type,
% 0.28/0.47 lamProp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lamProp,definition,
% 0.28/0.47 ( lamProp
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ( func @ A @ B
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xf @ Xx )
% 0.28/0.47 = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(lam_type,type,
% 0.28/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(lamp_type,type,
% 0.28/0.47 lamp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lamp,definition,
% 0.28/0.47 ( lamp
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ( func @ A @ B
% 0.28/0.47 @ ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(lam2p_type,type,
% 0.28/0.47 lam2p: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lam2p,definition,
% 0.28/0.47 ( lam2p
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ( in
% 0.28/0.47 @ ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.28/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(brelnall1_type,type,
% 0.28/0.47 brelnall1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(brelnall1,definition,
% 0.28/0.47 ( brelnall1
% 0.28/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ R )
% 0.28/0.47 => ! [Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ R )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(brelnall2_type,type,
% 0.28/0.47 brelnall2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(brelnall2,definition,
% 0.28/0.47 ( brelnall2
% 0.28/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ R )
% 0.28/0.47 => ! [Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ R )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E2_type,type,
% 0.28/0.47 ex1E2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E2,definition,
% 0.28/0.47 ( ex1E2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp1_type,type,
% 0.28/0.47 funcGraphProp1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp1,definition,
% 0.28/0.47 ( funcGraphProp1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp3_type,type,
% 0.28/0.47 funcGraphProp3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp3,definition,
% 0.28/0.47 ( funcGraphProp3
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp2_type,type,
% 0.28/0.47 funcGraphProp2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp2,definition,
% 0.28/0.47 ( funcGraphProp2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcextLem_type,type,
% 0.28/0.47 funcextLem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcextLem,definition,
% 0.28/0.47 ( funcextLem
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xg: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xg )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp4_type,type,
% 0.28/0.47 funcGraphProp4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp4,definition,
% 0.28/0.47 ( funcGraphProp4
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subbreln_type,type,
% 0.28/0.47 subbreln: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subbreln,definition,
% 0.28/0.47 ( subbreln
% 0.28/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ S )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqbreln_type,type,
% 0.28/0.47 eqbreln: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqbreln,definition,
% 0.28/0.47 ( eqbreln
% 0.28/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ S )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.28/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcext_type,type,
% 0.28/0.47 funcext: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcext,definition,
% 0.28/0.47 ( funcext
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xg: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xg )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcext2_type,type,
% 0.28/0.47 funcext2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcext2,definition,
% 0.28/0.47 ( funcext2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xg: $i] :
% 0.28/0.47 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ap2apEq1_type,type,
% 0.28/0.47 ap2apEq1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ap2apEq1,definition,
% 0.28/0.47 ( ap2apEq1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ap2apEq2_type,type,
% 0.28/0.47 ap2apEq2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ap2apEq2,definition,
% 0.28/0.47 ( ap2apEq2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(beta1_type,type,
% 0.28/0.47 beta1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(beta1,definition,
% 0.28/0.47 ( beta1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B
% 0.28/0.47 @ ( lam @ A @ B
% 0.28/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.28/0.47 @ Xx )
% 0.28/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eta1_type,type,
% 0.28/0.47 eta1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eta1,definition,
% 0.28/0.47 ( eta1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ( ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.28/0.47 = Xf ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(lam2lamEq_type,type,
% 0.28/0.47 lam2lamEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lam2lamEq,definition,
% 0.28/0.47 ( lam2lamEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ( ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.28/0.47 = ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(beta2_type,type,
% 0.28/0.47 beta2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(beta2,definition,
% 0.28/0.47 ( beta2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B
% 0.28/0.47 @ ( lam @ A @ B
% 0.28/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.28/0.47 @ Xx )
% 0.28/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eta2_type,type,
% 0.28/0.47 eta2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eta2,definition,
% 0.28/0.47 ( eta2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ( ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.28/0.47 = Xf ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iffalseProp1_type,type,
% 0.28/0.47 iffalseProp1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iffalseProp1,definition,
% 0.28/0.47 ( iffalseProp1
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ~ Xphi
% 0.28/0.47 => ( in @ Xy
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iffalseProp2_type,type,
% 0.28/0.47 iffalseProp2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iffalseProp2,definition,
% 0.28/0.47 ( iffalseProp2
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ~ Xphi
% 0.28/0.47 => ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) )
% 0.28/0.47 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueProp1_type,type,
% 0.28/0.47 iftrueProp1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueProp1,definition,
% 0.28/0.47 ( iftrueProp1
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 => ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueProp2_type,type,
% 0.28/0.47 iftrueProp2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueProp2,definition,
% 0.28/0.47 ( iftrueProp2
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 => ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) )
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ifSingleton_type,type,
% 0.28/0.47 ifSingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ifSingleton,definition,
% 0.28/0.47 ( ifSingleton
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(if_type,type,
% 0.28/0.47 if: $i > $o > $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(ifp_type,type,
% 0.28/0.47 ifp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ifp,definition,
% 0.28/0.47 ( ifp
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(theeq_type,type,
% 0.28/0.47 theeq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(theeq,definition,
% 0.28/0.47 ( theeq
% 0.28/0.47 = ( ! [X: $i] :
% 0.28/0.47 ( ( singleton @ X )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ X )
% 0.28/0.47 => ( ( setunion @ X )
% 0.28/0.47 = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iftrue_type,type,
% 0.28/0.47 iftrue: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iftrue,definition,
% 0.28/0.47 ( iftrue
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.28/0.47 = Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iffalse_type,type,
% 0.28/0.47 iffalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iffalse,definition,
% 0.28/0.47 ( iffalse
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ~ Xphi
% 0.28/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.28/0.47 = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueorfalse_type,type,
% 0.28/0.47 iftrueorfalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueorfalse,definition,
% 0.28/0.47 ( iftrueorfalse
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectT_lem_type,type,
% 0.28/0.47 binintersectT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectT_lem,definition,
% 0.28/0.47 ( binintersectT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionT_lem_type,type,
% 0.28/0.47 binunionT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionT_lem,definition,
% 0.28/0.47 ( binunionT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetT_lem_type,type,
% 0.28/0.47 powersetT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetT_lem,definition,
% 0.28/0.47 ( powersetT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusT_lem_type,type,
% 0.28/0.47 setminusT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusT_lem,definition,
% 0.28/0.47 ( setminusT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementT_lem_type,type,
% 0.28/0.47 complementT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementT_lem,definition,
% 0.28/0.47 ( complementT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextT,conjecture,
% 0.28/0.47 ( setextAx
% 0.28/0.47 => ( emptysetAx
% 0.28/0.47 => ( setadjoinAx
% 0.28/0.47 => ( powersetAx
% 0.28/0.47 => ( setunionAx
% 0.28/0.47 => ( omega0Ax
% 0.28/0.47 => ( omegaSAx
% 0.28/0.47 => ( omegaIndAx
% 0.28/0.47 => ( replAx
% 0.28/0.47 => ( foundationAx
% 0.28/0.47 => ( wellorderingAx
% 0.28/0.47 => ( descrp
% 0.28/0.47 => ( dsetconstrI
% 0.28/0.47 => ( dsetconstrEL
% 0.28/0.47 => ( dsetconstrER
% 0.28/0.47 => ( exuE1
% 0.28/0.47 => ( prop2setE
% 0.28/0.47 => ( emptysetE
% 0.28/0.47 => ( emptysetimpfalse
% 0.28/0.47 => ( notinemptyset
% 0.28/0.47 => ( exuE3e
% 0.28/0.47 => ( setext
% 0.28/0.47 => ( emptyI
% 0.28/0.47 => ( noeltsimpempty
% 0.28/0.47 => ( setbeta
% 0.28/0.47 => ( nonemptyE1
% 0.28/0.47 => ( nonemptyI
% 0.28/0.47 => ( nonemptyI1
% 0.28/0.47 => ( setadjoinIL
% 0.28/0.47 => ( emptyinunitempty
% 0.28/0.47 => ( setadjoinIR
% 0.28/0.47 => ( setadjoinE
% 0.28/0.47 => ( setadjoinOr
% 0.28/0.47 => ( setoftrueEq
% 0.28/0.47 => ( powersetI
% 0.28/0.47 => ( emptyinPowerset
% 0.28/0.47 => ( emptyInPowerset
% 0.28/0.47 => ( powersetE
% 0.28/0.47 => ( setunionI
% 0.28/0.47 => ( setunionE
% 0.28/0.47 => ( subPowSU
% 0.28/0.47 => ( exuE2
% 0.28/0.47 => ( nonemptyImpWitness
% 0.28/0.47 => ( uniqinunit
% 0.28/0.47 => ( notinsingleton
% 0.28/0.47 => ( eqinunit
% 0.28/0.47 => ( singletonsswitch
% 0.28/0.47 => ( upairsetE
% 0.28/0.47 => ( upairsetIL
% 0.28/0.47 => ( upairsetIR
% 0.28/0.47 => ( emptyE1
% 0.28/0.47 => ( vacuousDall
% 0.28/0.47 => ( quantDeMorgan1
% 0.28/0.47 => ( quantDeMorgan2
% 0.28/0.47 => ( quantDeMorgan3
% 0.28/0.47 => ( quantDeMorgan4
% 0.28/0.47 => ( prop2setI
% 0.28/0.47 => ( prop2set2propI
% 0.28/0.47 => ( notdexE
% 0.28/0.47 => ( notdallE
% 0.28/0.47 => ( exuI1
% 0.28/0.47 => ( exuI3
% 0.28/0.47 => ( exuI2
% 0.28/0.47 => ( inCongP
% 0.28/0.47 => ( in__Cong
% 0.28/0.47 => ( exuE3u
% 0.28/0.47 => ( exu__Cong
% 0.28/0.47 => ( emptyset__Cong
% 0.28/0.47 => ( setadjoin__Cong
% 0.28/0.47 => ( powerset__Cong
% 0.28/0.47 => ( setunion__Cong
% 0.28/0.47 => ( omega__Cong
% 0.28/0.47 => ( exuEu
% 0.28/0.47 => ( descr__Cong
% 0.28/0.47 => ( dsetconstr__Cong
% 0.28/0.47 => ( subsetI1
% 0.28/0.47 => ( eqimpsubset2
% 0.28/0.47 => ( eqimpsubset1
% 0.28/0.47 => ( subsetI2
% 0.28/0.47 => ( emptysetsubset
% 0.28/0.47 => ( subsetE
% 0.28/0.47 => ( subsetE2
% 0.28/0.47 => ( notsubsetI
% 0.28/0.47 => ( notequalI1
% 0.28/0.47 => ( notequalI2
% 0.28/0.47 => ( subsetRefl
% 0.28/0.47 => ( subsetTrans
% 0.28/0.47 => ( setadjoinSub
% 0.28/0.47 => ( setadjoinSub2
% 0.28/0.47 => ( subset2powerset
% 0.28/0.47 => ( setextsub
% 0.28/0.47 => ( subsetemptysetimpeq
% 0.28/0.47 => ( powersetI1
% 0.28/0.47 => ( powersetE1
% 0.28/0.47 => ( inPowerset
% 0.28/0.47 => ( powersetsubset
% 0.28/0.47 => ( sepInPowerset
% 0.28/0.47 => ( sepSubset
% 0.28/0.47 => ( binunionIL
% 0.28/0.47 => ( upairset2IR
% 0.28/0.47 => ( binunionIR
% 0.28/0.47 => ( binunionEcases
% 0.28/0.47 => ( binunionE
% 0.28/0.47 => ( binunionLsub
% 0.28/0.47 => ( binunionRsub
% 0.28/0.47 => ( binintersectI
% 0.28/0.47 => ( binintersectSubset5
% 0.28/0.47 => ( binintersectEL
% 0.28/0.47 => ( binintersectLsub
% 0.28/0.47 => ( binintersectSubset2
% 0.28/0.47 => ( binintersectSubset3
% 0.28/0.47 => ( binintersectER
% 0.28/0.47 => ( disjointsetsI1
% 0.28/0.47 => ( binintersectRsub
% 0.28/0.47 => ( binintersectSubset4
% 0.28/0.47 => ( binintersectSubset1
% 0.28/0.47 => ( bs114d
% 0.28/0.47 => ( setminusI
% 0.28/0.47 => ( setminusEL
% 0.28/0.47 => ( setminusER
% 0.28/0.47 => ( setminusSubset2
% 0.28/0.47 => ( setminusERneg
% 0.28/0.47 => ( setminusELneg
% 0.28/0.47 => ( setminusILneg
% 0.28/0.47 => ( setminusIRneg
% 0.28/0.47 => ( setminusLsub
% 0.28/0.47 => ( setminusSubset1
% 0.28/0.47 => ( symdiffE
% 0.28/0.47 => ( symdiffI1
% 0.28/0.47 => ( symdiffI2
% 0.28/0.47 => ( symdiffIneg1
% 0.28/0.47 => ( symdiffIneg2
% 0.28/0.47 => ( secondinupair
% 0.28/0.47 => ( setukpairIL
% 0.28/0.47 => ( setukpairIR
% 0.28/0.47 => ( kpairiskpair
% 0.28/0.47 => ( kpairp
% 0.28/0.47 => ( singletonsubset
% 0.28/0.47 => ( singletoninpowerset
% 0.28/0.47 => ( singletoninpowunion
% 0.28/0.47 => ( upairset2E
% 0.28/0.47 => ( upairsubunion
% 0.28/0.47 => ( upairinpowunion
% 0.28/0.47 => ( ubforcartprodlem1
% 0.28/0.47 => ( ubforcartprodlem2
% 0.28/0.47 => ( ubforcartprodlem3
% 0.28/0.47 => ( cartprodpairin
% 0.28/0.47 => ( cartprodmempair1
% 0.28/0.47 => ( cartprodmempair
% 0.28/0.47 => ( setunionE2
% 0.28/0.47 => ( setunionsingleton1
% 0.28/0.47 => ( setunionsingleton2
% 0.28/0.47 => ( setunionsingleton
% 0.28/0.47 => ( singletonprop
% 0.28/0.47 => ( ex1E1
% 0.28/0.47 => ( ex1I
% 0.28/0.47 => ( ex1I2
% 0.28/0.47 => ( singletonsuniq
% 0.28/0.47 => ( setukpairinjL1
% 0.28/0.47 => ( kfstsingleton
% 0.28/0.47 => ( theprop
% 0.28/0.47 => ( kfstpairEq
% 0.28/0.47 => ( cartprodfstin
% 0.28/0.47 => ( setukpairinjL2
% 0.28/0.47 => ( setukpairinjL
% 0.28/0.47 => ( setukpairinjR11
% 0.28/0.47 => ( setukpairinjR12
% 0.28/0.47 => ( setukpairinjR1
% 0.28/0.47 => ( upairequniteq
% 0.28/0.47 => ( setukpairinjR2
% 0.28/0.47 => ( setukpairinjR
% 0.28/0.47 => ( ksndsingleton
% 0.28/0.47 => ( ksndpairEq
% 0.28/0.47 => ( kpairsurjEq
% 0.28/0.47 => ( cartprodsndin
% 0.28/0.47 => ( cartprodpairmemEL
% 0.28/0.47 => ( cartprodpairmemER
% 0.28/0.47 => ( cartprodmempaircEq
% 0.28/0.47 => ( cartprodfstpairEq
% 0.28/0.47 => ( cartprodsndpairEq
% 0.28/0.47 => ( cartprodpairsurjEq
% 0.28/0.47 => ( dpsetconstrI
% 0.28/0.47 => ( dpsetconstrSub
% 0.28/0.47 => ( setOfPairsIsBReln
% 0.28/0.47 => ( dpsetconstrERa
% 0.28/0.47 => ( dpsetconstrEL1
% 0.28/0.47 => ( dpsetconstrEL2
% 0.28/0.47 => ( dpsetconstrER
% 0.28/0.47 => ( funcImageSingleton
% 0.28/0.47 => ( apProp
% 0.28/0.47 => ( app
% 0.28/0.47 => ( infuncsetfunc
% 0.28/0.47 => ( ap2p
% 0.28/0.47 => ( funcinfuncset
% 0.28/0.47 => ( lamProp
% 0.28/0.47 => ( lamp
% 0.28/0.47 => ( lam2p
% 0.28/0.47 => ( brelnall1
% 0.28/0.47 => ( brelnall2
% 0.28/0.47 => ( ex1E2
% 0.28/0.47 => ( funcGraphProp1
% 0.28/0.47 => ( funcGraphProp3
% 0.28/0.47 => ( funcGraphProp2
% 0.28/0.47 => ( funcextLem
% 0.28/0.47 => ( funcGraphProp4
% 0.28/0.47 => ( subbreln
% 0.28/0.47 => ( eqbreln
% 0.28/0.47 => ( funcext
% 0.28/0.47 => ( funcext2
% 0.28/0.47 => ( ap2apEq1
% 0.28/0.47 => ( ap2apEq2
% 0.28/0.47 => ( beta1
% 0.28/0.47 => ( eta1
% 0.28/0.47 => ( lam2lamEq
% 0.28/0.47 => ( beta2
% 0.28/0.47 => ( eta2
% 0.28/0.47 => ( iffalseProp1
% 0.28/0.47 => ( iffalseProp2
% 0.28/0.47 => ( iftrueProp1
% 0.28/0.47 => ( iftrueProp2
% 0.28/0.47 => ( ifSingleton
% 0.28/0.47 => ( ifp
% 0.28/0.47 => ( theeq
% 0.28/0.47 => ( iftrue
% 0.28/0.47 => ( iffalse
% 0.28/0.47 => ( iftrueorfalse
% 0.28/0.47 => ( binintersectT_lem
% 0.28/0.47 => ( binunionT_lem
% 0.28/0.47 => ( powersetT_lem
% 0.28/0.47 => ( setminusT_lem
% 0.28/0.47 => ( complementT_lem
% 0.28/0.47 => ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ( in @ Xx @ Y ) ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ Y )
% 0.28/0.47 => ( in @ Xx @ X ) ) )
% 0.28/0.47 => ( X = Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.43/1.46 ---- Embedded in THF ---
% 2.43/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.43/1.46 %%% Generated on Tue Feb 24 12:31:09 EST 2026
% 2.43/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.43/1.46 %%% Logic specification used:
% 2.43/1.46 %%% thf(spec, logic, $$dhol).
% 2.43/1.46
% 2.43/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2DTF1611.p
% See solution above
% 2.43/1.46 ------------------------
% 2.65/1.51 ---- Cleaned THF ---
% 2.65/1.51 thf(in_type,type,
% 2.65/1.51 in: $i > $i > $o ).
% 2.65/1.51
% 2.65/1.51 thf(exu_type,type,
% 2.65/1.51 exu: ( $i > $o ) > $o ).
% 2.65/1.51
% 2.65/1.51 thf(exu,definition,
% 2.65/1.51 ( exu
% 2.65/1.51 = ( ^ [Xphi: $i > $o] :
% 2.65/1.51 ? [Xx: $i] :
% 2.65/1.51 ( ( Xphi @ Xx )
% 2.65/1.51 & ! [Xy: $i] :
% 2.65/1.51 ( ( Xphi @ Xy )
% 2.65/1.51 => ( Xx = Xy ) ) ) ) ) ).
% 2.65/1.51
% 2.65/1.51 thf(setextAx_type,type,
% 2.65/1.51 setextAx: $o ).
% 2.65/1.51
% 2.65/1.51 thf(setextAx,definition,
% 2.65/1.51 ( setextAx
% 2.65/1.51 = ( ! [A: $i,B: $i] :
% 2.65/1.51 ( ! [Xx: $i] :
% 2.65/1.51 ( ( in @ Xx @ A )
% 2.65/1.51 <=> ( in @ Xx @ B ) )
% 2.65/1.51 => ( A = B ) ) ) ) ).
% 2.65/1.51
% 2.65/1.51 thf(emptyset_type,type,
% 2.65/1.51 emptyset: $i ).
% 2.65/1.51
% 2.65/1.51 thf(emptysetAx_type,type,
% 2.65/1.51 emptysetAx: $o ).
% 2.65/1.51
% 2.65/1.51 thf(emptysetAx,definition,
% 2.65/1.51 ( emptysetAx
% 2.65/1.51 = ( ! [Xx: $i] :
% 2.65/1.51 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.65/1.51
% 2.65/1.51 thf(setadjoin_type,type,
% 2.65/1.51 setadjoin: $i > $i > $i ).
% 2.65/1.51
% 2.65/1.51 thf(setadjoinAx_type,type,
% 2.65/1.51 setadjoinAx: $o ).
% 2.65/1.51
% 2.65/1.51 thf(setadjoinAx,definition,
% 2.65/1.51 ( setadjoinAx
% 2.65/1.51 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.65/1.51 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.65/1.51 <=> ( ( Xy = Xx )
% 2.65/1.51 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(powerset_type,type,
% 2.65/1.52 powerset: $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(powersetAx_type,type,
% 2.65/1.52 powersetAx: $o ).
% 2.65/1.52
% 2.65/1.52 thf(powersetAx,definition,
% 2.65/1.52 ( powersetAx
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.65/1.52 <=> ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setunion_type,type,
% 2.65/1.52 setunion: $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(setunionAx_type,type,
% 2.65/1.52 setunionAx: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setunionAx,definition,
% 2.65/1.52 ( setunionAx
% 2.65/1.52 = ( ! [A: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.65/1.52 <=> ? [B: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 & ( in @ B @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(omega_type,type,
% 2.65/1.52 omega: $i ).
% 2.65/1.52
% 2.65/1.52 thf(omega0Ax_type,type,
% 2.65/1.52 omega0Ax: $o ).
% 2.65/1.52
% 2.65/1.52 thf(omega0Ax,definition,
% 2.65/1.52 ( omega0Ax
% 2.65/1.52 = ( in @ emptyset @ omega ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(omegaSAx_type,type,
% 2.65/1.52 omegaSAx: $o ).
% 2.65/1.52
% 2.65/1.52 thf(omegaSAx,definition,
% 2.65/1.52 ( omegaSAx
% 2.65/1.52 = ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ omega )
% 2.65/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(omegaIndAx_type,type,
% 2.65/1.52 omegaIndAx: $o ).
% 2.65/1.52
% 2.65/1.52 thf(omegaIndAx,definition,
% 2.65/1.52 ( omegaIndAx
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ( ( in @ emptyset @ A )
% 2.65/1.52 & ! [Xx: $i] :
% 2.65/1.52 ( ( ( in @ Xx @ omega )
% 2.65/1.52 & ( in @ Xx @ A ) )
% 2.65/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ omega )
% 2.65/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(replAx_type,type,
% 2.65/1.52 replAx: $o ).
% 2.65/1.52
% 2.65/1.52 thf(replAx,definition,
% 2.65/1.52 ( replAx
% 2.65/1.52 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( exu
% 2.65/1.52 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.65/1.52 => ? [B: $i] :
% 2.65/1.52 ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 <=> ? [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(foundationAx_type,type,
% 2.65/1.52 foundationAx: $o ).
% 2.65/1.52
% 2.65/1.52 thf(foundationAx,definition,
% 2.65/1.52 ( foundationAx
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.65/1.52 => ? [B: $i] :
% 2.65/1.52 ( ( in @ B @ A )
% 2.65/1.52 & ~ ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(wellorderingAx_type,type,
% 2.65/1.52 wellorderingAx: $o ).
% 2.65/1.52
% 2.65/1.52 thf(wellorderingAx,definition,
% 2.65/1.52 ( wellorderingAx
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ? [B: $i] :
% 2.65/1.52 ( ! [C: $i] :
% 2.65/1.52 ( ( in @ C @ B )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ C )
% 2.65/1.52 => ( in @ Xx @ A ) ) )
% 2.65/1.52 & ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( ( in @ Xx @ A )
% 2.65/1.52 & ( in @ Xy @ A ) )
% 2.65/1.52 => ( ! [C: $i] :
% 2.65/1.52 ( ( in @ C @ B )
% 2.65/1.52 => ( ( in @ Xx @ C )
% 2.65/1.52 <=> ( in @ Xy @ C ) ) )
% 2.65/1.52 => ( Xx = Xy ) ) )
% 2.65/1.52 & ! [C: $i,D: $i] :
% 2.65/1.52 ( ( ( in @ C @ B )
% 2.65/1.52 & ( in @ D @ B ) )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ C )
% 2.65/1.52 => ( in @ Xx @ D ) )
% 2.65/1.52 | ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ D )
% 2.65/1.52 => ( in @ Xx @ C ) ) ) )
% 2.65/1.52 & ! [C: $i] :
% 2.65/1.52 ( ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ C )
% 2.65/1.52 => ( in @ Xx @ A ) )
% 2.65/1.52 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.65/1.52 => ? [D: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ D @ B )
% 2.65/1.52 & ( in @ Xx @ C )
% 2.65/1.52 & ~ ? [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ D )
% 2.65/1.52 & ( in @ Xy @ C ) )
% 2.65/1.52 & ! [E: $i] :
% 2.65/1.52 ( ( in @ E @ B )
% 2.65/1.52 => ( ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ E )
% 2.65/1.52 => ( in @ Xy @ D ) )
% 2.65/1.52 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(descr_type,type,
% 2.65/1.52 descr: ( $i > $o ) > $i ).
% 2.65/1.52
% 2.65/1.52 thf(descrp_type,type,
% 2.65/1.52 descrp: $o ).
% 2.65/1.52
% 2.65/1.52 thf(descrp,definition,
% 2.65/1.52 ( descrp
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ( Xphi
% 2.65/1.52 @ ( descr
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstr_type,type,
% 2.65/1.52 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstrI_type,type,
% 2.65/1.52 dsetconstrI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstrI,definition,
% 2.65/1.52 ( dsetconstrI
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 => ( in @ Xx
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstrEL_type,type,
% 2.65/1.52 dsetconstrEL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstrEL,definition,
% 2.65/1.52 ( dsetconstrEL
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.65/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstrER_type,type,
% 2.65/1.52 dsetconstrER: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstrER,definition,
% 2.65/1.52 ( dsetconstrER
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.65/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exuE1_type,type,
% 2.65/1.52 exuE1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exuE1,definition,
% 2.65/1.52 ( exuE1
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ? [Xx: $i] :
% 2.65/1.52 ( ( Xphi @ Xx )
% 2.65/1.52 & ! [Xy: $i] :
% 2.65/1.52 ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(prop2set_type,type,
% 2.65/1.52 prop2set: $o > $i ).
% 2.65/1.52
% 2.65/1.52 thf(prop2setE_type,type,
% 2.65/1.52 prop2setE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(prop2setE,definition,
% 2.65/1.52 ( prop2setE
% 2.65/1.52 = ( ! [Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.65/1.52 => Xphi ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptysetE_type,type,
% 2.65/1.52 emptysetE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptysetE,definition,
% 2.65/1.52 ( emptysetE
% 2.65/1.52 = ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ emptyset )
% 2.65/1.52 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptysetimpfalse_type,type,
% 2.65/1.52 emptysetimpfalse: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptysetimpfalse,definition,
% 2.65/1.52 ( emptysetimpfalse
% 2.65/1.52 = ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ emptyset )
% 2.65/1.52 => $false ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(notinemptyset_type,type,
% 2.65/1.52 notinemptyset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(notinemptyset,definition,
% 2.65/1.52 ( notinemptyset
% 2.65/1.52 = ( ! [Xx: $i] :
% 2.65/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exuE3e_type,type,
% 2.65/1.52 exuE3e: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exuE3e,definition,
% 2.65/1.52 ( exuE3e
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setext_type,type,
% 2.65/1.52 setext: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setext,definition,
% 2.65/1.52 ( setext
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ Xx @ B ) )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ A ) )
% 2.65/1.52 => ( A = B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptyI_type,type,
% 2.65/1.52 emptyI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptyI,definition,
% 2.65/1.52 ( emptyI
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ~ ( in @ Xx @ A )
% 2.65/1.52 => ( A = emptyset ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(noeltsimpempty_type,type,
% 2.65/1.52 noeltsimpempty: $o ).
% 2.65/1.52
% 2.65/1.52 thf(noeltsimpempty,definition,
% 2.65/1.52 ( noeltsimpempty
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ~ ( in @ Xx @ A )
% 2.65/1.52 => ( A = emptyset ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setbeta_type,type,
% 2.65/1.52 setbeta: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setbeta,definition,
% 2.65/1.52 ( setbeta
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( in @ Xx
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.65/1.52 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(nonempty_type,type,
% 2.65/1.52 nonempty: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(nonempty,definition,
% 2.65/1.52 ( nonempty
% 2.65/1.52 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(nonemptyE1_type,type,
% 2.65/1.52 nonemptyE1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(nonemptyE1,definition,
% 2.65/1.52 ( nonemptyE1
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ( nonempty @ A )
% 2.65/1.52 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(nonemptyI_type,type,
% 2.65/1.52 nonemptyI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(nonemptyI,definition,
% 2.65/1.52 ( nonemptyI
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 => ( nonempty
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(nonemptyI1_type,type,
% 2.65/1.52 nonemptyI1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(nonemptyI1,definition,
% 2.65/1.52 ( nonemptyI1
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.65/1.52 => ( nonempty @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinIL_type,type,
% 2.65/1.52 setadjoinIL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinIL,definition,
% 2.65/1.52 ( setadjoinIL
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptyinunitempty_type,type,
% 2.65/1.52 emptyinunitempty: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptyinunitempty,definition,
% 2.65/1.52 ( emptyinunitempty
% 2.65/1.52 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinIR_type,type,
% 2.65/1.52 setadjoinIR: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinIR,definition,
% 2.65/1.52 ( setadjoinIR
% 2.65/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinE_type,type,
% 2.65/1.52 setadjoinE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinE,definition,
% 2.65/1.52 ( setadjoinE
% 2.65/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.65/1.52 => ! [Xphi: $o] :
% 2.65/1.52 ( ( ( Xy = Xx )
% 2.65/1.52 => Xphi )
% 2.65/1.52 => ( ( ( in @ Xy @ A )
% 2.65/1.52 => Xphi )
% 2.65/1.52 => Xphi ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinOr_type,type,
% 2.65/1.52 setadjoinOr: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinOr,definition,
% 2.65/1.52 ( setadjoinOr
% 2.65/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.65/1.52 => ( ( Xy = Xx )
% 2.65/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setoftrueEq_type,type,
% 2.65/1.52 setoftrueEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setoftrueEq,definition,
% 2.65/1.52 ( setoftrueEq
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xx: $i] : $true )
% 2.65/1.52 = A ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(powersetI_type,type,
% 2.65/1.52 powersetI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(powersetI,definition,
% 2.65/1.52 ( powersetI
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ A ) )
% 2.65/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptyinPowerset_type,type,
% 2.65/1.52 emptyinPowerset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptyinPowerset,definition,
% 2.65/1.52 ( emptyinPowerset
% 2.65/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptyInPowerset_type,type,
% 2.65/1.52 emptyInPowerset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptyInPowerset,definition,
% 2.65/1.52 ( emptyInPowerset
% 2.65/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(powersetE_type,type,
% 2.65/1.52 powersetE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(powersetE,definition,
% 2.65/1.52 ( powersetE
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.65/1.52 => ( ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setunionI_type,type,
% 2.65/1.52 setunionI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setunionI,definition,
% 2.65/1.52 ( setunionI
% 2.65/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 => ( ( in @ B @ A )
% 2.65/1.52 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setunionE_type,type,
% 2.65/1.52 setunionE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setunionE,definition,
% 2.65/1.52 ( setunionE
% 2.65/1.52 = ( ! [A: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.65/1.52 => ! [Xphi: $o] :
% 2.65/1.52 ( ! [B: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 => ( ( in @ B @ A )
% 2.65/1.52 => Xphi ) )
% 2.65/1.52 => Xphi ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subPowSU_type,type,
% 2.65/1.52 subPowSU: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subPowSU,definition,
% 2.65/1.52 ( subPowSU
% 2.65/1.52 = ( ! [A: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exuE2_type,type,
% 2.65/1.52 exuE2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exuE2,definition,
% 2.65/1.52 ( exuE2
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ? [Xx: $i] :
% 2.65/1.52 ! [Xy: $i] :
% 2.65/1.52 ( ( Xphi @ Xy )
% 2.65/1.52 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(nonemptyImpWitness_type,type,
% 2.65/1.52 nonemptyImpWitness: $o ).
% 2.65/1.52
% 2.65/1.52 thf(nonemptyImpWitness,definition,
% 2.65/1.52 ( nonemptyImpWitness
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ( nonempty @ A )
% 2.65/1.52 => ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & $true ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(uniqinunit_type,type,
% 2.65/1.52 uniqinunit: $o ).
% 2.65/1.52
% 2.65/1.52 thf(uniqinunit,definition,
% 2.65/1.52 ( uniqinunit
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(notinsingleton_type,type,
% 2.65/1.52 notinsingleton: $o ).
% 2.65/1.52
% 2.65/1.52 thf(notinsingleton,definition,
% 2.65/1.52 ( notinsingleton
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx != Xy )
% 2.65/1.52 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(eqinunit_type,type,
% 2.65/1.52 eqinunit: $o ).
% 2.65/1.52
% 2.65/1.52 thf(eqinunit,definition,
% 2.65/1.52 ( eqinunit
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx = Xy )
% 2.65/1.52 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(singletonsswitch_type,type,
% 2.65/1.52 singletonsswitch: $o ).
% 2.65/1.52
% 2.65/1.52 thf(singletonsswitch,definition,
% 2.65/1.52 ( singletonsswitch
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.65/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(upairsetE_type,type,
% 2.65/1.52 upairsetE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairsetE,definition,
% 2.65/1.52 ( upairsetE
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.65/1.52 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.65/1.52 => ( ( Xz = Xx )
% 2.65/1.52 | ( Xz = Xy ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(upairsetIL_type,type,
% 2.65/1.52 upairsetIL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairsetIL,definition,
% 2.65/1.52 ( upairsetIL
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(upairsetIR_type,type,
% 2.65/1.52 upairsetIR: $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairsetIR,definition,
% 2.65/1.52 ( upairsetIR
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptyE1_type,type,
% 2.65/1.52 emptyE1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptyE1,definition,
% 2.65/1.52 ( emptyE1
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ( Xphi @ Xx ) )
% 2.65/1.52 => ( ( ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 = emptyset )
% 2.65/1.52 => $false ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(vacuousDall_type,type,
% 2.65/1.52 vacuousDall: $o ).
% 2.65/1.52
% 2.65/1.52 thf(vacuousDall,definition,
% 2.65/1.52 ( vacuousDall
% 2.65/1.52 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ emptyset )
% 2.65/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(quantDeMorgan1_type,type,
% 2.65/1.52 quantDeMorgan1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(quantDeMorgan1,definition,
% 2.65/1.52 ( quantDeMorgan1
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ~ ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( Xphi @ Xx ) )
% 2.65/1.52 => ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(quantDeMorgan2_type,type,
% 2.65/1.52 quantDeMorgan2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(quantDeMorgan2,definition,
% 2.65/1.52 ( quantDeMorgan2
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ~ ( Xphi @ Xx ) )
% 2.65/1.52 => ~ ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(quantDeMorgan3_type,type,
% 2.65/1.52 quantDeMorgan3: $o ).
% 2.65/1.52
% 2.65/1.52 thf(quantDeMorgan3,definition,
% 2.65/1.52 ( quantDeMorgan3
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ~ ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ( Xphi @ Xx ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(quantDeMorgan4_type,type,
% 2.65/1.52 quantDeMorgan4: $o ).
% 2.65/1.52
% 2.65/1.52 thf(quantDeMorgan4,definition,
% 2.65/1.52 ( quantDeMorgan4
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ~ ( Xphi @ Xx ) )
% 2.65/1.52 => ~ ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(prop2setI_type,type,
% 2.65/1.52 prop2setI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(prop2setI,definition,
% 2.65/1.52 ( prop2setI
% 2.65/1.52 = ( ! [Xphi: $o] :
% 2.65/1.52 ( Xphi
% 2.65/1.52 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(set2prop_type,type,
% 2.65/1.52 set2prop: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(prop2set2propI_type,type,
% 2.65/1.52 prop2set2propI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(prop2set2propI,definition,
% 2.65/1.52 ( prop2set2propI
% 2.65/1.52 = ( ! [Xphi: $o] :
% 2.65/1.52 ( Xphi
% 2.65/1.52 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(notdexE_type,type,
% 2.65/1.52 notdexE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(notdexE,definition,
% 2.65/1.52 ( notdexE
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ~ ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ( Xphi @ Xx ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(notdallE_type,type,
% 2.65/1.52 notdallE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(notdallE,definition,
% 2.65/1.52 ( notdallE
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ~ ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( Xphi @ Xx ) )
% 2.65/1.52 => ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exuI1_type,type,
% 2.65/1.52 exuI1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exuI1,definition,
% 2.65/1.52 ( exuI1
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ? [Xx: $i] :
% 2.65/1.52 ( ( Xphi @ Xx )
% 2.65/1.52 & ! [Xy: $i] :
% 2.65/1.52 ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xx = Xy ) ) )
% 2.65/1.52 => ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exuI3_type,type,
% 2.65/1.52 exuI3: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exuI3,definition,
% 2.65/1.52 ( exuI3
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.65/1.52 => ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xphi @ Xx )
% 2.65/1.52 => ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xx = Xy ) ) )
% 2.65/1.52 => ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exuI2_type,type,
% 2.65/1.52 exuI2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exuI2,definition,
% 2.65/1.52 ( exuI2
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ? [Xx: $i] :
% 2.65/1.52 ! [Xy: $i] :
% 2.65/1.52 ( ( Xphi @ Xy )
% 2.65/1.52 <=> ( Xy = Xx ) )
% 2.65/1.52 => ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(inCongP_type,type,
% 2.65/1.52 inCongP: $o ).
% 2.65/1.52
% 2.65/1.52 thf(inCongP,definition,
% 2.65/1.52 ( inCongP
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( A = B )
% 2.65/1.52 => ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx = Xy )
% 2.65/1.52 => ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(in__Cong_type,type,
% 2.65/1.52 in__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(in__Cong,definition,
% 2.65/1.52 ( in__Cong
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( A = B )
% 2.65/1.52 => ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx = Xy )
% 2.65/1.52 => ( ( in @ Xx @ A )
% 2.65/1.52 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exuE3u_type,type,
% 2.65/1.52 exuE3u: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exuE3u,definition,
% 2.65/1.52 ( exuE3u
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xphi @ Xx )
% 2.65/1.52 => ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exu__Cong_type,type,
% 2.65/1.52 exu__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exu__Cong,definition,
% 2.65/1.52 ( exu__Cong
% 2.65/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.65/1.52 ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx = Xy )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 <=> ( Xpsi @ Xy ) ) )
% 2.65/1.52 => ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 <=> ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptyset__Cong_type,type,
% 2.65/1.52 emptyset__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptyset__Cong,definition,
% 2.65/1.52 ( emptyset__Cong
% 2.65/1.52 = ( emptyset = emptyset ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoin__Cong_type,type,
% 2.65/1.52 setadjoin__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoin__Cong,definition,
% 2.65/1.52 ( setadjoin__Cong
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx = Xy )
% 2.65/1.52 => ! [Xz: $i,Xu: $i] :
% 2.65/1.52 ( ( Xz = Xu )
% 2.65/1.52 => ( ( setadjoin @ Xx @ Xz )
% 2.65/1.52 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(powerset__Cong_type,type,
% 2.65/1.52 powerset__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(powerset__Cong,definition,
% 2.65/1.52 ( powerset__Cong
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( A = B )
% 2.65/1.52 => ( ( powerset @ A )
% 2.65/1.52 = ( powerset @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setunion__Cong_type,type,
% 2.65/1.52 setunion__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setunion__Cong,definition,
% 2.65/1.52 ( setunion__Cong
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( A = B )
% 2.65/1.52 => ( ( setunion @ A )
% 2.65/1.52 = ( setunion @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(omega__Cong_type,type,
% 2.65/1.52 omega__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(omega__Cong,definition,
% 2.65/1.52 ( omega__Cong
% 2.65/1.52 = ( omega = omega ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(exuEu_type,type,
% 2.65/1.52 exuEu: $o ).
% 2.65/1.52
% 2.65/1.52 thf(exuEu,definition,
% 2.65/1.52 ( exuEu
% 2.65/1.52 = ( ! [Xphi: $i > $o] :
% 2.65/1.52 ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xphi @ Xx )
% 2.65/1.52 => ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(descr__Cong_type,type,
% 2.65/1.52 descr__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(descr__Cong,definition,
% 2.65/1.52 ( descr__Cong
% 2.65/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.65/1.52 ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx = Xy )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 <=> ( Xpsi @ Xy ) ) )
% 2.65/1.52 => ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ( ( exu
% 2.65/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.65/1.52 => ( ( descr
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 = ( descr
% 2.65/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstr__Cong_type,type,
% 2.65/1.52 dsetconstr__Cong: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dsetconstr__Cong,definition,
% 2.65/1.52 ( dsetconstr__Cong
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( A = B )
% 2.65/1.52 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( Xx = Xy )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.65/1.52 => ( ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 = ( dsetconstr @ B
% 2.65/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subset_type,type,
% 2.65/1.52 subset: $i > $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(disjoint_type,type,
% 2.65/1.52 disjoint: $i > $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(setsmeet_type,type,
% 2.65/1.52 setsmeet: $i > $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(subsetI1_type,type,
% 2.65/1.52 subsetI1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subsetI1,definition,
% 2.65/1.52 ( subsetI1
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ Xx @ B ) )
% 2.65/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(eqimpsubset2_type,type,
% 2.65/1.52 eqimpsubset2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(eqimpsubset2,definition,
% 2.65/1.52 ( eqimpsubset2
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( A = B )
% 2.65/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(eqimpsubset1_type,type,
% 2.65/1.52 eqimpsubset1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(eqimpsubset1,definition,
% 2.65/1.52 ( eqimpsubset1
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( A = B )
% 2.65/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subsetI2_type,type,
% 2.65/1.52 subsetI2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subsetI2,definition,
% 2.65/1.52 ( subsetI2
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ Xx @ B ) )
% 2.65/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(emptysetsubset_type,type,
% 2.65/1.52 emptysetsubset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(emptysetsubset,definition,
% 2.65/1.52 ( emptysetsubset
% 2.65/1.52 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subsetE_type,type,
% 2.65/1.52 subsetE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subsetE,definition,
% 2.65/1.52 ( subsetE
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subsetE2_type,type,
% 2.65/1.52 subsetE2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subsetE2,definition,
% 2.65/1.52 ( subsetE2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( ~ ( in @ Xx @ B )
% 2.65/1.52 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(notsubsetI_type,type,
% 2.65/1.52 notsubsetI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(notsubsetI,definition,
% 2.65/1.52 ( notsubsetI
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ~ ( in @ Xx @ B )
% 2.65/1.52 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(notequalI1_type,type,
% 2.65/1.52 notequalI1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(notequalI1,definition,
% 2.65/1.52 ( notequalI1
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ~ ( subset @ A @ B )
% 2.65/1.52 => ( A != B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(notequalI2_type,type,
% 2.65/1.52 notequalI2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(notequalI2,definition,
% 2.65/1.52 ( notequalI2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ~ ( in @ Xx @ B )
% 2.65/1.52 => ( A != B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subsetRefl_type,type,
% 2.65/1.52 subsetRefl: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subsetRefl,definition,
% 2.65/1.52 ( subsetRefl
% 2.65/1.52 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subsetTrans_type,type,
% 2.65/1.52 subsetTrans: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subsetTrans,definition,
% 2.65/1.52 ( subsetTrans
% 2.65/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( ( subset @ B @ C )
% 2.65/1.52 => ( subset @ A @ C ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinSub_type,type,
% 2.65/1.52 setadjoinSub: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinSub,definition,
% 2.65/1.52 ( setadjoinSub
% 2.65/1.52 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinSub2_type,type,
% 2.65/1.52 setadjoinSub2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setadjoinSub2,definition,
% 2.65/1.52 ( setadjoinSub2
% 2.65/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subset2powerset_type,type,
% 2.65/1.52 subset2powerset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subset2powerset,definition,
% 2.65/1.52 ( subset2powerset
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setextsub_type,type,
% 2.65/1.52 setextsub: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setextsub,definition,
% 2.65/1.52 ( setextsub
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( ( subset @ B @ A )
% 2.65/1.52 => ( A = B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subsetemptysetimpeq_type,type,
% 2.65/1.52 subsetemptysetimpeq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subsetemptysetimpeq,definition,
% 2.65/1.52 ( subsetemptysetimpeq
% 2.65/1.52 = ( ! [A: $i] :
% 2.65/1.52 ( ( subset @ A @ emptyset )
% 2.65/1.52 => ( A = emptyset ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(powersetI1_type,type,
% 2.65/1.52 powersetI1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(powersetI1,definition,
% 2.65/1.52 ( powersetI1
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( subset @ B @ A )
% 2.65/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(powersetE1_type,type,
% 2.65/1.52 powersetE1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(powersetE1,definition,
% 2.65/1.52 ( powersetE1
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.65/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(inPowerset_type,type,
% 2.65/1.52 inPowerset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(inPowerset,definition,
% 2.65/1.52 ( inPowerset
% 2.65/1.52 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(powersetsubset_type,type,
% 2.65/1.52 powersetsubset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(powersetsubset,definition,
% 2.65/1.52 ( powersetsubset
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(sepInPowerset_type,type,
% 2.65/1.52 sepInPowerset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(sepInPowerset,definition,
% 2.65/1.52 ( sepInPowerset
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( in
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 @ ( powerset @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(sepSubset_type,type,
% 2.65/1.52 sepSubset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(sepSubset,definition,
% 2.65/1.52 ( sepSubset
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( subset
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 @ A ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binunion_type,type,
% 2.65/1.52 binunion: $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(binunionIL_type,type,
% 2.65/1.52 binunionIL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binunionIL,definition,
% 2.65/1.52 ( binunionIL
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(upairset2IR_type,type,
% 2.65/1.52 upairset2IR: $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairset2IR,definition,
% 2.65/1.52 ( upairset2IR
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binunionIR_type,type,
% 2.65/1.52 binunionIR: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binunionIR,definition,
% 2.65/1.52 ( binunionIR
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binunionEcases_type,type,
% 2.65/1.52 binunionEcases: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binunionEcases,definition,
% 2.65/1.52 ( binunionEcases
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.65/1.52 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.65/1.52 => ( ( ( in @ Xx @ A )
% 2.65/1.52 => Xphi )
% 2.65/1.52 => ( ( ( in @ Xx @ B )
% 2.65/1.52 => Xphi )
% 2.65/1.52 => Xphi ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binunionE_type,type,
% 2.65/1.52 binunionE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binunionE,definition,
% 2.65/1.52 ( binunionE
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.65/1.52 => ( ( in @ Xx @ A )
% 2.65/1.52 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binunionLsub_type,type,
% 2.65/1.52 binunionLsub: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binunionLsub,definition,
% 2.65/1.52 ( binunionLsub
% 2.65/1.52 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binunionRsub_type,type,
% 2.65/1.52 binunionRsub: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binunionRsub,definition,
% 2.65/1.52 ( binunionRsub
% 2.65/1.52 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersect_type,type,
% 2.65/1.52 binintersect: $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectI_type,type,
% 2.65/1.52 binintersectI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectI,definition,
% 2.65/1.52 ( binintersectI
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset5_type,type,
% 2.65/1.52 binintersectSubset5: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset5,definition,
% 2.65/1.52 ( binintersectSubset5
% 2.65/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.65/1.52 ( ( subset @ C @ A )
% 2.65/1.52 => ( ( subset @ C @ B )
% 2.65/1.52 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectEL_type,type,
% 2.65/1.52 binintersectEL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectEL,definition,
% 2.65/1.52 ( binintersectEL
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.65/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectLsub_type,type,
% 2.65/1.52 binintersectLsub: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectLsub,definition,
% 2.65/1.52 ( binintersectLsub
% 2.65/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset2_type,type,
% 2.65/1.52 binintersectSubset2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset2,definition,
% 2.65/1.52 ( binintersectSubset2
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( ( binintersect @ A @ B )
% 2.65/1.52 = A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset3_type,type,
% 2.65/1.52 binintersectSubset3: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset3,definition,
% 2.65/1.52 ( binintersectSubset3
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( ( binintersect @ A @ B )
% 2.65/1.52 = B )
% 2.65/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectER_type,type,
% 2.65/1.52 binintersectER: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectER,definition,
% 2.65/1.52 ( binintersectER
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.65/1.52 => ( in @ Xx @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(disjointsetsI1_type,type,
% 2.65/1.52 disjointsetsI1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(disjointsetsI1,definition,
% 2.65/1.52 ( disjointsetsI1
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ~ ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ( in @ Xx @ B ) )
% 2.65/1.52 => ( ( binintersect @ A @ B )
% 2.65/1.52 = emptyset ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectRsub_type,type,
% 2.65/1.52 binintersectRsub: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectRsub,definition,
% 2.65/1.52 ( binintersectRsub
% 2.65/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset4_type,type,
% 2.65/1.52 binintersectSubset4: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset4,definition,
% 2.65/1.52 ( binintersectSubset4
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( subset @ B @ A )
% 2.65/1.52 => ( ( binintersect @ A @ B )
% 2.65/1.52 = B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset1_type,type,
% 2.65/1.52 binintersectSubset1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectSubset1,definition,
% 2.65/1.52 ( binintersectSubset1
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( ( binintersect @ A @ B )
% 2.65/1.52 = A )
% 2.65/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(bs114d_type,type,
% 2.65/1.52 bs114d: $o ).
% 2.65/1.52
% 2.65/1.52 thf(bs114d,definition,
% 2.65/1.52 ( bs114d
% 2.65/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.65/1.52 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.65/1.52 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(regular_type,type,
% 2.65/1.52 regular: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminus_type,type,
% 2.65/1.52 setminus: $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(setminusI_type,type,
% 2.65/1.52 setminusI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusI,definition,
% 2.65/1.52 ( setminusI
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ~ ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusEL_type,type,
% 2.65/1.52 setminusEL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusEL,definition,
% 2.65/1.52 ( setminusEL
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.65/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusER_type,type,
% 2.65/1.52 setminusER: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusER,definition,
% 2.65/1.52 ( setminusER
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.65/1.52 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusSubset2_type,type,
% 2.65/1.52 setminusSubset2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusSubset2,definition,
% 2.65/1.52 ( setminusSubset2
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( subset @ A @ B )
% 2.65/1.52 => ( ( setminus @ A @ B )
% 2.65/1.52 = emptyset ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusERneg_type,type,
% 2.65/1.52 setminusERneg: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusERneg,definition,
% 2.65/1.52 ( setminusERneg
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.65/1.52 => ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusELneg_type,type,
% 2.65/1.52 setminusELneg: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusELneg,definition,
% 2.65/1.52 ( setminusELneg
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.65/1.52 => ( ~ ( in @ Xx @ B )
% 2.65/1.52 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusILneg_type,type,
% 2.65/1.52 setminusILneg: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusILneg,definition,
% 2.65/1.52 ( setminusILneg
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ~ ( in @ Xx @ A )
% 2.65/1.52 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusIRneg_type,type,
% 2.65/1.52 setminusIRneg: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusIRneg,definition,
% 2.65/1.52 ( setminusIRneg
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ B )
% 2.65/1.52 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusLsub_type,type,
% 2.65/1.52 setminusLsub: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusLsub,definition,
% 2.65/1.52 ( setminusLsub
% 2.65/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusSubset1_type,type,
% 2.65/1.52 setminusSubset1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusSubset1,definition,
% 2.65/1.52 ( setminusSubset1
% 2.65/1.52 = ( ! [A: $i,B: $i] :
% 2.65/1.52 ( ( ( setminus @ A @ B )
% 2.65/1.52 = emptyset )
% 2.65/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(symdiff_type,type,
% 2.65/1.52 symdiff: $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffE_type,type,
% 2.65/1.52 symdiffE: $o ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffE,definition,
% 2.65/1.52 ( symdiffE
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.65/1.52 => ! [Xphi: $o] :
% 2.65/1.52 ( ( ( in @ Xx @ A )
% 2.65/1.52 => ( ~ ( in @ Xx @ B )
% 2.65/1.52 => Xphi ) )
% 2.65/1.52 => ( ( ~ ( in @ Xx @ A )
% 2.65/1.52 => ( ( in @ Xx @ B )
% 2.65/1.52 => Xphi ) )
% 2.65/1.52 => Xphi ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffI1_type,type,
% 2.65/1.52 symdiffI1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffI1,definition,
% 2.65/1.52 ( symdiffI1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ~ ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffI2_type,type,
% 2.65/1.52 symdiffI2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffI2,definition,
% 2.65/1.52 ( symdiffI2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ~ ( in @ Xx @ A )
% 2.65/1.52 => ( ( in @ Xx @ B )
% 2.65/1.52 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffIneg1_type,type,
% 2.65/1.52 symdiffIneg1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffIneg1,definition,
% 2.65/1.52 ( symdiffIneg1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( in @ Xx @ B )
% 2.65/1.52 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffIneg2_type,type,
% 2.65/1.52 symdiffIneg2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(symdiffIneg2,definition,
% 2.65/1.52 ( symdiffIneg2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ~ ( in @ Xx @ A )
% 2.65/1.52 => ( ~ ( in @ Xx @ B )
% 2.65/1.52 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(iskpair_type,type,
% 2.65/1.52 iskpair: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(secondinupair_type,type,
% 2.65/1.52 secondinupair: $o ).
% 2.65/1.52
% 2.65/1.52 thf(secondinupair,definition,
% 2.65/1.52 ( secondinupair
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairIL_type,type,
% 2.65/1.52 setukpairIL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairIL,definition,
% 2.65/1.52 ( setukpairIL
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairIR_type,type,
% 2.65/1.52 setukpairIR: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairIR,definition,
% 2.65/1.52 ( setukpairIR
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(kpairiskpair_type,type,
% 2.65/1.52 kpairiskpair: $o ).
% 2.65/1.52
% 2.65/1.52 thf(kpairiskpair,definition,
% 2.65/1.52 ( kpairiskpair
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(kpair_type,type,
% 2.65/1.52 kpair: $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(kpairp_type,type,
% 2.65/1.52 kpairp: $o ).
% 2.65/1.52
% 2.65/1.52 thf(kpairp,definition,
% 2.65/1.52 ( kpairp
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprod_type,type,
% 2.65/1.52 cartprod: $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(singletonsubset_type,type,
% 2.65/1.52 singletonsubset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(singletonsubset,definition,
% 2.65/1.52 ( singletonsubset
% 2.65/1.52 = ( ! [A: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(singletoninpowerset_type,type,
% 2.65/1.52 singletoninpowerset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(singletoninpowerset,definition,
% 2.65/1.52 ( singletoninpowerset
% 2.65/1.52 = ( ! [A: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(singletoninpowunion_type,type,
% 2.65/1.52 singletoninpowunion: $o ).
% 2.65/1.52
% 2.65/1.52 thf(singletoninpowunion,definition,
% 2.65/1.52 ( singletoninpowunion
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(upairset2E_type,type,
% 2.65/1.52 upairset2E: $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairset2E,definition,
% 2.65/1.52 ( upairset2E
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.65/1.52 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.65/1.52 => ( ( Xz = Xx )
% 2.65/1.52 | ( Xz = Xy ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(upairsubunion_type,type,
% 2.65/1.52 upairsubunion: $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairsubunion,definition,
% 2.65/1.52 ( upairsubunion
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(upairinpowunion_type,type,
% 2.65/1.52 upairinpowunion: $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairinpowunion,definition,
% 2.65/1.52 ( upairinpowunion
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ubforcartprodlem1_type,type,
% 2.65/1.52 ubforcartprodlem1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ubforcartprodlem1,definition,
% 2.65/1.52 ( ubforcartprodlem1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ubforcartprodlem2_type,type,
% 2.65/1.52 ubforcartprodlem2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ubforcartprodlem2,definition,
% 2.65/1.52 ( ubforcartprodlem2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ubforcartprodlem3_type,type,
% 2.65/1.52 ubforcartprodlem3: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ubforcartprodlem3,definition,
% 2.65/1.52 ( ubforcartprodlem3
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodpairin_type,type,
% 2.65/1.52 cartprodpairin: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodpairin,definition,
% 2.65/1.52 ( cartprodpairin
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodmempair1_type,type,
% 2.65/1.52 cartprodmempair1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodmempair1,definition,
% 2.65/1.52 ( cartprodmempair1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.65/1.52 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.65/1.52 => ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ? [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 & ( Xu
% 2.65/1.52 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodmempair_type,type,
% 2.65/1.52 cartprodmempair: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodmempair,definition,
% 2.65/1.52 ( cartprodmempair
% 2.65/1.52 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.65/1.52 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.65/1.52 => ( iskpair @ Xu ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setunionE2_type,type,
% 2.65/1.52 setunionE2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setunionE2,definition,
% 2.65/1.52 ( setunionE2
% 2.65/1.52 = ( ! [A: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.65/1.52 => ? [X: $i] :
% 2.65/1.52 ( ( in @ X @ A )
% 2.65/1.52 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setunionsingleton1_type,type,
% 2.65/1.52 setunionsingleton1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setunionsingleton1,definition,
% 2.65/1.52 ( setunionsingleton1
% 2.65/1.52 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setunionsingleton2_type,type,
% 2.65/1.52 setunionsingleton2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setunionsingleton2,definition,
% 2.65/1.52 ( setunionsingleton2
% 2.65/1.52 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setunionsingleton_type,type,
% 2.65/1.52 setunionsingleton: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setunionsingleton,definition,
% 2.65/1.52 ( setunionsingleton
% 2.65/1.52 = ( ! [Xx: $i] :
% 2.65/1.52 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.65/1.52 = Xx ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(singleton_type,type,
% 2.65/1.52 singleton: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(singletonprop_type,type,
% 2.65/1.52 singletonprop: $o ).
% 2.65/1.52
% 2.65/1.52 thf(singletonprop,definition,
% 2.65/1.52 ( singletonprop
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 => ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) )
% 2.65/1.52 => ( ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ( Xphi @ Xx ) )
% 2.65/1.52 => ( singleton
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ex1_type,type,
% 2.65/1.52 ex1: $i > ( $i > $o ) > $o ).
% 2.65/1.52
% 2.65/1.52 thf(ex1,definition,
% 2.65/1.52 ( ex1
% 2.65/1.52 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( singleton
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ex1E1_type,type,
% 2.65/1.52 ex1E1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ex1E1,definition,
% 2.65/1.52 ( ex1E1
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ( ex1 @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ex1I_type,type,
% 2.65/1.52 ex1I: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ex1I,definition,
% 2.65/1.52 ( ex1I
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 => ( ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xy = Xx ) ) )
% 2.65/1.52 => ( ex1 @ A
% 2.65/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ex1I2_type,type,
% 2.65/1.52 ex1I2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ex1I2,definition,
% 2.65/1.52 ( ex1I2
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 => ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) )
% 2.65/1.52 => ( ? [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 & ( Xphi @ Xx ) )
% 2.65/1.52 => ( ex1 @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(singletonsuniq_type,type,
% 2.65/1.52 singletonsuniq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(singletonsuniq,definition,
% 2.65/1.52 ( singletonsuniq
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( ( setadjoin @ Xx @ emptyset )
% 2.65/1.52 = ( setadjoin @ Xy @ emptyset ) )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(atmost1p_type,type,
% 2.65/1.52 atmost1p: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(atleast2p_type,type,
% 2.65/1.52 atleast2p: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(atmost2p_type,type,
% 2.65/1.52 atmost2p: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairsetp_type,type,
% 2.65/1.52 upairsetp: $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjL1_type,type,
% 2.65/1.52 setukpairinjL1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjL1,definition,
% 2.65/1.52 ( setukpairinjL1
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.65/1.52 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.65/1.52 => ( Xx = Xz ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(kfstsingleton_type,type,
% 2.65/1.52 kfstsingleton: $o ).
% 2.65/1.52
% 2.65/1.52 thf(kfstsingleton,definition,
% 2.65/1.52 ( kfstsingleton
% 2.65/1.52 = ( ! [Xu: $i] :
% 2.65/1.52 ( ( iskpair @ Xu )
% 2.65/1.52 => ( singleton
% 2.65/1.52 @ ( dsetconstr @ ( setunion @ Xu )
% 2.65/1.52 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(theprop_type,type,
% 2.65/1.52 theprop: $o ).
% 2.65/1.52
% 2.65/1.52 thf(theprop,definition,
% 2.65/1.52 ( theprop
% 2.65/1.52 = ( ! [X: $i] :
% 2.65/1.52 ( ( singleton @ X )
% 2.65/1.52 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(kfst_type,type,
% 2.65/1.52 kfst: $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(kfstpairEq_type,type,
% 2.65/1.52 kfstpairEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(kfstpairEq,definition,
% 2.65/1.52 ( kfstpairEq
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.65/1.52 = Xx ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodfstin_type,type,
% 2.65/1.52 cartprodfstin: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodfstin,definition,
% 2.65/1.52 ( cartprodfstin
% 2.65/1.52 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.65/1.52 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.65/1.52 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjL2_type,type,
% 2.65/1.52 setukpairinjL2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjL2,definition,
% 2.65/1.52 ( setukpairinjL2
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.65/1.52 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.65/1.52 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.65/1.52 => ( Xx = Xz ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjL_type,type,
% 2.65/1.52 setukpairinjL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjL,definition,
% 2.65/1.52 ( setukpairinjL
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.65/1.52 ( ( ( kpair @ Xx @ Xy )
% 2.65/1.52 = ( kpair @ Xz @ Xu ) )
% 2.65/1.52 => ( Xx = Xz ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR11_type,type,
% 2.65/1.52 setukpairinjR11: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR11,definition,
% 2.65/1.52 ( setukpairinjR11
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx = Xy )
% 2.65/1.52 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.65/1.52 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR12_type,type,
% 2.65/1.52 setukpairinjR12: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR12,definition,
% 2.65/1.52 ( setukpairinjR12
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xx = Xy )
% 2.65/1.52 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.65/1.52 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR1_type,type,
% 2.65/1.52 setukpairinjR1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR1,definition,
% 2.65/1.52 ( setukpairinjR1
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.65/1.52 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.65/1.52 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.65/1.52 => ( ( Xz = Xu )
% 2.65/1.52 => ( Xy = Xu ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(upairequniteq_type,type,
% 2.65/1.52 upairequniteq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(upairequniteq,definition,
% 2.65/1.52 ( upairequniteq
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.65/1.52 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.65/1.52 = ( setadjoin @ Xz @ emptyset ) )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR2_type,type,
% 2.65/1.52 setukpairinjR2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR2,definition,
% 2.65/1.52 ( setukpairinjR2
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.65/1.52 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.65/1.52 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.65/1.52 => ( Xy = Xu ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR_type,type,
% 2.65/1.52 setukpairinjR: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setukpairinjR,definition,
% 2.65/1.52 ( setukpairinjR
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.65/1.52 ( ( ( kpair @ Xx @ Xy )
% 2.65/1.52 = ( kpair @ Xz @ Xu ) )
% 2.65/1.52 => ( Xy = Xu ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ksndsingleton_type,type,
% 2.65/1.52 ksndsingleton: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ksndsingleton,definition,
% 2.65/1.52 ( ksndsingleton
% 2.65/1.52 = ( ! [Xu: $i] :
% 2.65/1.52 ( ( iskpair @ Xu )
% 2.65/1.52 => ( singleton
% 2.65/1.52 @ ( dsetconstr @ ( setunion @ Xu )
% 2.65/1.52 @ ^ [Xx: $i] :
% 2.65/1.52 ( Xu
% 2.65/1.52 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ksnd_type,type,
% 2.65/1.52 ksnd: $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(ksndpairEq_type,type,
% 2.65/1.52 ksndpairEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ksndpairEq,definition,
% 2.65/1.52 ( ksndpairEq
% 2.65/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.65/1.52 = Xy ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(kpairsurjEq_type,type,
% 2.65/1.52 kpairsurjEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(kpairsurjEq,definition,
% 2.65/1.52 ( kpairsurjEq
% 2.65/1.52 = ( ! [Xu: $i] :
% 2.65/1.52 ( ( iskpair @ Xu )
% 2.65/1.52 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.65/1.52 = Xu ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodsndin_type,type,
% 2.65/1.52 cartprodsndin: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodsndin,definition,
% 2.65/1.52 ( cartprodsndin
% 2.65/1.52 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.65/1.52 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.65/1.52 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodpairmemEL_type,type,
% 2.65/1.52 cartprodpairmemEL: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodpairmemEL,definition,
% 2.65/1.52 ( cartprodpairmemEL
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.65/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodpairmemER_type,type,
% 2.65/1.52 cartprodpairmemER: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodpairmemER,definition,
% 2.65/1.52 ( cartprodpairmemER
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.65/1.52 => ( in @ Xy @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodmempaircEq_type,type,
% 2.65/1.52 cartprodmempaircEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodmempaircEq,definition,
% 2.65/1.52 ( cartprodmempaircEq
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( kpair @ Xx @ Xy )
% 2.65/1.52 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodfstpairEq_type,type,
% 2.65/1.52 cartprodfstpairEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodfstpairEq,definition,
% 2.65/1.52 ( cartprodfstpairEq
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.65/1.52 = Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodsndpairEq_type,type,
% 2.65/1.52 cartprodsndpairEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodsndpairEq,definition,
% 2.65/1.52 ( cartprodsndpairEq
% 2.65/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.65/1.52 = Xy ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodpairsurjEq_type,type,
% 2.65/1.52 cartprodpairsurjEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(cartprodpairsurjEq,definition,
% 2.65/1.52 ( cartprodpairsurjEq
% 2.65/1.52 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.65/1.52 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.65/1.52 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.65/1.52 = Xu ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(breln_type,type,
% 2.65/1.52 breln: $i > $i > $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(breln,definition,
% 2.65/1.52 ( breln
% 2.65/1.52 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstr_type,type,
% 2.65/1.52 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrI_type,type,
% 2.65/1.52 dpsetconstrI: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrI,definition,
% 2.65/1.52 ( dpsetconstrI
% 2.65/1.52 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( Xphi @ Xx @ Xy )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ Xy )
% 2.65/1.52 @ ( dpsetconstr @ A @ B
% 2.65/1.52 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrSub_type,type,
% 2.65/1.52 dpsetconstrSub: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrSub,definition,
% 2.65/1.52 ( dpsetconstrSub
% 2.65/1.52 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.65/1.52 ( subset
% 2.65/1.52 @ ( dpsetconstr @ A @ B
% 2.65/1.52 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.65/1.52 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setOfPairsIsBReln_type,type,
% 2.65/1.52 setOfPairsIsBReln: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setOfPairsIsBReln,definition,
% 2.65/1.52 ( setOfPairsIsBReln
% 2.65/1.52 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.65/1.52 ( breln @ A @ B
% 2.65/1.52 @ ( dpsetconstr @ A @ B
% 2.65/1.52 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrERa_type,type,
% 2.65/1.52 dpsetconstrERa: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrERa,definition,
% 2.65/1.52 ( dpsetconstrERa
% 2.65/1.52 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.65/1.52 @ ( dpsetconstr @ A @ B
% 2.65/1.52 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.65/1.52 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrEL1_type,type,
% 2.65/1.52 dpsetconstrEL1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrEL1,definition,
% 2.65/1.52 ( dpsetconstrEL1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ ( kpair @ Xx @ Xy )
% 2.65/1.52 @ ( dpsetconstr @ A @ B
% 2.65/1.52 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.65/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrEL2_type,type,
% 2.65/1.52 dpsetconstrEL2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrEL2,definition,
% 2.65/1.52 ( dpsetconstrEL2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ ( kpair @ Xx @ Xy )
% 2.65/1.52 @ ( dpsetconstr @ A @ B
% 2.65/1.52 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.65/1.52 => ( in @ Xy @ B ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrER_type,type,
% 2.65/1.52 dpsetconstrER: $o ).
% 2.65/1.52
% 2.65/1.52 thf(dpsetconstrER,definition,
% 2.65/1.52 ( dpsetconstrER
% 2.65/1.52 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( in @ ( kpair @ Xx @ Xy )
% 2.65/1.52 @ ( dpsetconstr @ A @ B
% 2.65/1.52 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.65/1.52 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(func_type,type,
% 2.65/1.52 func: $i > $i > $i > $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcSet_type,type,
% 2.65/1.52 funcSet: $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(funcImageSingleton_type,type,
% 2.65/1.52 funcImageSingleton: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcImageSingleton,definition,
% 2.65/1.52 ( funcImageSingleton
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( singleton
% 2.65/1.52 @ ( dsetconstr @ B
% 2.65/1.52 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(apProp_type,type,
% 2.65/1.52 apProp: $o ).
% 2.65/1.52
% 2.65/1.52 thf(apProp,definition,
% 2.65/1.52 ( apProp
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in
% 2.65/1.52 @ ( setunion
% 2.65/1.52 @ ( dsetconstr @ B
% 2.65/1.52 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.65/1.52 @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ap_type,type,
% 2.65/1.52 ap: $i > $i > $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(app_type,type,
% 2.65/1.52 app: $o ).
% 2.65/1.52
% 2.65/1.52 thf(app,definition,
% 2.65/1.52 ( app
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(infuncsetfunc_type,type,
% 2.65/1.52 infuncsetfunc: $o ).
% 2.65/1.52
% 2.65/1.52 thf(infuncsetfunc,definition,
% 2.65/1.52 ( infuncsetfunc
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.65/1.52 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ap2p_type,type,
% 2.65/1.52 ap2p: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ap2p,definition,
% 2.65/1.52 ( ap2p
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(funcinfuncset_type,type,
% 2.65/1.52 funcinfuncset: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcinfuncset,definition,
% 2.65/1.52 ( funcinfuncset
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(lamProp_type,type,
% 2.65/1.52 lamProp: $o ).
% 2.65/1.52
% 2.65/1.52 thf(lamProp,definition,
% 2.65/1.52 ( lamProp
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.65/1.52 => ( func @ A @ B
% 2.65/1.52 @ ( dpsetconstr @ A @ B
% 2.65/1.52 @ ^ [Xx: $i,Xy: $i] :
% 2.65/1.52 ( ( Xf @ Xx )
% 2.65/1.52 = Xy ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(lam_type,type,
% 2.65/1.52 lam: $i > $i > ( $i > $i ) > $i ).
% 2.65/1.52
% 2.65/1.52 thf(lamp_type,type,
% 2.65/1.52 lamp: $o ).
% 2.65/1.52
% 2.65/1.52 thf(lamp,definition,
% 2.65/1.52 ( lamp
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.65/1.52 => ( func @ A @ B
% 2.65/1.52 @ ( lam @ A @ B
% 2.65/1.52 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(lam2p_type,type,
% 2.65/1.52 lam2p: $o ).
% 2.65/1.52
% 2.65/1.52 thf(lam2p,definition,
% 2.65/1.52 ( lam2p
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.65/1.52 => ( in
% 2.65/1.52 @ ( lam @ A @ B
% 2.65/1.52 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.65/1.52 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(brelnall1_type,type,
% 2.65/1.52 brelnall1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(brelnall1,definition,
% 2.65/1.52 ( brelnall1
% 2.65/1.52 = ( ! [A: $i,B: $i,R: $i] :
% 2.65/1.52 ( ( breln @ A @ B @ R )
% 2.65/1.52 => ! [Xphi: $i > $o] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.65/1.52 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ R )
% 2.65/1.52 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(brelnall2_type,type,
% 2.65/1.52 brelnall2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(brelnall2,definition,
% 2.65/1.52 ( brelnall2
% 2.65/1.52 = ( ! [A: $i,B: $i,R: $i] :
% 2.65/1.52 ( ( breln @ A @ B @ R )
% 2.65/1.52 => ! [Xphi: $i > $o] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.65/1.52 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ R )
% 2.65/1.52 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ex1E2_type,type,
% 2.65/1.52 ex1E2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ex1E2,definition,
% 2.65/1.52 ( ex1E2
% 2.65/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.65/1.52 ( ( ex1 @ A
% 2.65/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( ( Xphi @ Xx )
% 2.65/1.52 => ( ( Xphi @ Xy )
% 2.65/1.52 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(funcGraphProp1_type,type,
% 2.65/1.52 funcGraphProp1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcGraphProp1,definition,
% 2.65/1.52 ( funcGraphProp1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(funcGraphProp3_type,type,
% 2.65/1.52 funcGraphProp3: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcGraphProp3,definition,
% 2.65/1.52 ( funcGraphProp3
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(funcGraphProp2_type,type,
% 2.65/1.52 funcGraphProp2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcGraphProp2,definition,
% 2.65/1.52 ( funcGraphProp2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.65/1.52 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.65/1.52 = Xy ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(funcextLem_type,type,
% 2.65/1.52 funcextLem: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcextLem,definition,
% 2.65/1.52 ( funcextLem
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ! [Xg: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xg )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.65/1.52 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(funcGraphProp4_type,type,
% 2.65/1.52 funcGraphProp4: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcGraphProp4,definition,
% 2.65/1.52 ( funcGraphProp4
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.65/1.52 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.65/1.52 = Xy ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(subbreln_type,type,
% 2.65/1.52 subbreln: $o ).
% 2.65/1.52
% 2.65/1.52 thf(subbreln,definition,
% 2.65/1.52 ( subbreln
% 2.65/1.52 = ( ! [A: $i,B: $i,R: $i] :
% 2.65/1.52 ( ( breln @ A @ B @ R )
% 2.65/1.52 => ! [S: $i] :
% 2.65/1.52 ( ( breln @ A @ B @ S )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.65/1.52 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(eqbreln_type,type,
% 2.65/1.52 eqbreln: $o ).
% 2.65/1.52
% 2.65/1.52 thf(eqbreln,definition,
% 2.65/1.52 ( eqbreln
% 2.65/1.52 = ( ! [A: $i,B: $i,R: $i] :
% 2.65/1.52 ( ( breln @ A @ B @ R )
% 2.65/1.52 => ! [S: $i] :
% 2.65/1.52 ( ( breln @ A @ B @ S )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ B )
% 2.65/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.65/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.65/1.52 => ( R = S ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(funcext_type,type,
% 2.65/1.52 funcext: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcext,definition,
% 2.65/1.52 ( funcext
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ! [Xg: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xg )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.65/1.52 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.65/1.52 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(funcext2_type,type,
% 2.65/1.52 funcext2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(funcext2,definition,
% 2.65/1.52 ( funcext2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.65/1.52 => ! [Xg: $i] :
% 2.65/1.52 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.65/1.52 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.65/1.52 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ap2apEq1_type,type,
% 2.65/1.52 ap2apEq1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ap2apEq1,definition,
% 2.65/1.52 ( ap2apEq1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.65/1.52 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ap2apEq2_type,type,
% 2.65/1.52 ap2apEq2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ap2apEq2,definition,
% 2.65/1.52 ( ap2apEq2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.65/1.52 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(beta1_type,type,
% 2.65/1.52 beta1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(beta1,definition,
% 2.65/1.52 ( beta1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( ap @ A @ B
% 2.65/1.52 @ ( lam @ A @ B
% 2.65/1.52 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.65/1.52 @ Xx )
% 2.65/1.52 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(eta1_type,type,
% 2.65/1.52 eta1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(eta1,definition,
% 2.65/1.52 ( eta1
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( func @ A @ B @ Xf )
% 2.65/1.52 => ( ( lam @ A @ B
% 2.65/1.52 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.65/1.52 = Xf ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(lam2lamEq_type,type,
% 2.65/1.52 lam2lamEq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(lam2lamEq,definition,
% 2.65/1.52 ( lam2lamEq
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.65/1.52 => ( ( lam @ A @ B
% 2.65/1.52 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.65/1.52 = ( lam @ A @ B
% 2.65/1.52 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(beta2_type,type,
% 2.65/1.52 beta2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(beta2,definition,
% 2.65/1.52 ( beta2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.65/1.52 ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( ap @ A @ B
% 2.65/1.52 @ ( lam @ A @ B
% 2.65/1.52 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.65/1.52 @ Xx )
% 2.65/1.52 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(eta2_type,type,
% 2.65/1.52 eta2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(eta2,definition,
% 2.65/1.52 ( eta2
% 2.65/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.65/1.52 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.65/1.52 => ( ( lam @ A @ B
% 2.65/1.52 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.65/1.52 = Xf ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(iffalseProp1_type,type,
% 2.65/1.52 iffalseProp1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(iffalseProp1,definition,
% 2.65/1.52 ( iffalseProp1
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( ~ Xphi
% 2.65/1.52 => ( in @ Xy
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xz: $i] :
% 2.65/1.52 ( ( Xphi
% 2.65/1.52 & ( Xz = Xx ) )
% 2.65/1.52 | ( ~ Xphi
% 2.65/1.52 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(iffalseProp2_type,type,
% 2.65/1.52 iffalseProp2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(iffalseProp2,definition,
% 2.65/1.52 ( iffalseProp2
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( ~ Xphi
% 2.65/1.52 => ( ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xz: $i] :
% 2.65/1.52 ( ( Xphi
% 2.65/1.52 & ( Xz = Xx ) )
% 2.65/1.52 | ( ~ Xphi
% 2.65/1.52 & ( Xz = Xy ) ) ) )
% 2.65/1.52 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(iftrueProp1_type,type,
% 2.65/1.52 iftrueProp1: $o ).
% 2.65/1.52
% 2.65/1.52 thf(iftrueProp1,definition,
% 2.65/1.52 ( iftrueProp1
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( Xphi
% 2.65/1.52 => ( in @ Xx
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xz: $i] :
% 2.65/1.52 ( ( Xphi
% 2.65/1.52 & ( Xz = Xx ) )
% 2.65/1.52 | ( ~ Xphi
% 2.65/1.52 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(iftrueProp2_type,type,
% 2.65/1.52 iftrueProp2: $o ).
% 2.65/1.52
% 2.65/1.52 thf(iftrueProp2,definition,
% 2.65/1.52 ( iftrueProp2
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( Xphi
% 2.65/1.52 => ( ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xz: $i] :
% 2.65/1.52 ( ( Xphi
% 2.65/1.52 & ( Xz = Xx ) )
% 2.65/1.52 | ( ~ Xphi
% 2.65/1.52 & ( Xz = Xy ) ) ) )
% 2.65/1.52 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(ifSingleton_type,type,
% 2.65/1.52 ifSingleton: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ifSingleton,definition,
% 2.65/1.52 ( ifSingleton
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( singleton
% 2.65/1.52 @ ( dsetconstr @ A
% 2.65/1.52 @ ^ [Xz: $i] :
% 2.65/1.52 ( ( Xphi
% 2.65/1.52 & ( Xz = Xx ) )
% 2.65/1.52 | ( ~ Xphi
% 2.65/1.52 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(if_type,type,
% 2.65/1.52 if: $i > $o > $i > $i > $i ).
% 2.65/1.52
% 2.65/1.52 thf(ifp_type,type,
% 2.65/1.52 ifp: $o ).
% 2.65/1.52
% 2.65/1.52 thf(ifp,definition,
% 2.65/1.52 ( ifp
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(theeq_type,type,
% 2.65/1.52 theeq: $o ).
% 2.65/1.52
% 2.65/1.52 thf(theeq,definition,
% 2.65/1.52 ( theeq
% 2.65/1.52 = ( ! [X: $i] :
% 2.65/1.52 ( ( singleton @ X )
% 2.65/1.52 => ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ X )
% 2.65/1.52 => ( ( setunion @ X )
% 2.65/1.52 = Xx ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(iftrue_type,type,
% 2.65/1.52 iftrue: $o ).
% 2.65/1.52
% 2.65/1.52 thf(iftrue,definition,
% 2.65/1.52 ( iftrue
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( Xphi
% 2.65/1.52 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.65/1.52 = Xx ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(iffalse_type,type,
% 2.65/1.52 iffalse: $o ).
% 2.65/1.52
% 2.65/1.52 thf(iffalse,definition,
% 2.65/1.52 ( iffalse
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( ~ Xphi
% 2.65/1.52 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.65/1.52 = Xy ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(iftrueorfalse_type,type,
% 2.65/1.52 iftrueorfalse: $o ).
% 2.65/1.52
% 2.65/1.52 thf(iftrueorfalse,definition,
% 2.65/1.52 ( iftrueorfalse
% 2.65/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ! [Xy: $i] :
% 2.65/1.52 ( ( in @ Xy @ A )
% 2.65/1.52 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectT_lem_type,type,
% 2.65/1.52 binintersectT_lem: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binintersectT_lem,definition,
% 2.65/1.52 ( binintersectT_lem
% 2.65/1.52 = ( ! [A: $i,X: $i] :
% 2.65/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.65/1.52 => ! [Y: $i] :
% 2.65/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.65/1.52 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(binunionT_lem_type,type,
% 2.65/1.52 binunionT_lem: $o ).
% 2.65/1.52
% 2.65/1.52 thf(binunionT_lem,definition,
% 2.65/1.52 ( binunionT_lem
% 2.65/1.52 = ( ! [A: $i,X: $i] :
% 2.65/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.65/1.52 => ! [Y: $i] :
% 2.65/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.65/1.52 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(powersetT_lem_type,type,
% 2.65/1.52 powersetT_lem: $o ).
% 2.65/1.52
% 2.65/1.52 thf(powersetT_lem,definition,
% 2.65/1.52 ( powersetT_lem
% 2.65/1.52 = ( ! [A: $i,X: $i] :
% 2.65/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.65/1.52 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setminusT_lem_type,type,
% 2.65/1.52 setminusT_lem: $o ).
% 2.65/1.52
% 2.65/1.52 thf(setminusT_lem,definition,
% 2.65/1.52 ( setminusT_lem
% 2.65/1.52 = ( ! [A: $i,X: $i] :
% 2.65/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.65/1.52 => ! [Y: $i] :
% 2.65/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.65/1.52 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(complementT_lem_type,type,
% 2.65/1.52 complementT_lem: $o ).
% 2.65/1.52
% 2.65/1.52 thf(complementT_lem,definition,
% 2.65/1.52 ( complementT_lem
% 2.65/1.52 = ( ! [A: $i,X: $i] :
% 2.65/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.65/1.52 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.65/1.52
% 2.65/1.52 thf(setextT,conjecture,
% 2.65/1.52 ( setextAx
% 2.65/1.52 => ( emptysetAx
% 2.65/1.52 => ( setadjoinAx
% 2.65/1.52 => ( powersetAx
% 2.65/1.52 => ( setunionAx
% 2.65/1.52 => ( omega0Ax
% 2.65/1.52 => ( omegaSAx
% 2.65/1.52 => ( omegaIndAx
% 2.65/1.52 => ( replAx
% 2.65/1.52 => ( foundationAx
% 2.65/1.52 => ( wellorderingAx
% 2.65/1.52 => ( descrp
% 2.65/1.52 => ( dsetconstrI
% 2.65/1.52 => ( dsetconstrEL
% 2.65/1.52 => ( dsetconstrER
% 2.65/1.52 => ( exuE1
% 2.65/1.52 => ( prop2setE
% 2.65/1.52 => ( emptysetE
% 2.65/1.52 => ( emptysetimpfalse
% 2.65/1.52 => ( notinemptyset
% 2.65/1.52 => ( exuE3e
% 2.65/1.52 => ( setext
% 2.65/1.52 => ( emptyI
% 2.65/1.52 => ( noeltsimpempty
% 2.65/1.52 => ( setbeta
% 2.65/1.52 => ( nonemptyE1
% 2.65/1.52 => ( nonemptyI
% 2.65/1.52 => ( nonemptyI1
% 2.65/1.52 => ( setadjoinIL
% 2.65/1.52 => ( emptyinunitempty
% 2.65/1.52 => ( setadjoinIR
% 2.65/1.52 => ( setadjoinE
% 2.65/1.52 => ( setadjoinOr
% 2.65/1.52 => ( setoftrueEq
% 2.65/1.52 => ( powersetI
% 2.65/1.52 => ( emptyinPowerset
% 2.65/1.52 => ( emptyInPowerset
% 2.65/1.52 => ( powersetE
% 2.65/1.52 => ( setunionI
% 2.65/1.52 => ( setunionE
% 2.65/1.52 => ( subPowSU
% 2.65/1.52 => ( exuE2
% 2.65/1.52 => ( nonemptyImpWitness
% 2.65/1.52 => ( uniqinunit
% 2.65/1.52 => ( notinsingleton
% 2.65/1.52 => ( eqinunit
% 2.65/1.52 => ( singletonsswitch
% 2.65/1.52 => ( upairsetE
% 2.65/1.52 => ( upairsetIL
% 2.65/1.52 => ( upairsetIR
% 2.65/1.52 => ( emptyE1
% 2.65/1.52 => ( vacuousDall
% 2.65/1.52 => ( quantDeMorgan1
% 2.65/1.52 => ( quantDeMorgan2
% 2.65/1.52 => ( quantDeMorgan3
% 2.65/1.52 => ( quantDeMorgan4
% 2.65/1.52 => ( prop2setI
% 2.65/1.52 => ( prop2set2propI
% 2.65/1.52 => ( notdexE
% 2.65/1.52 => ( notdallE
% 2.65/1.52 => ( exuI1
% 2.65/1.52 => ( exuI3
% 2.65/1.52 => ( exuI2
% 2.65/1.52 => ( inCongP
% 2.65/1.52 => ( in__Cong
% 2.65/1.52 => ( exuE3u
% 2.65/1.52 => ( exu__Cong
% 2.65/1.52 => ( emptyset__Cong
% 2.65/1.52 => ( setadjoin__Cong
% 2.65/1.52 => ( powerset__Cong
% 2.65/1.52 => ( setunion__Cong
% 2.65/1.52 => ( omega__Cong
% 2.65/1.52 => ( exuEu
% 2.65/1.52 => ( descr__Cong
% 2.65/1.52 => ( dsetconstr__Cong
% 2.65/1.52 => ( subsetI1
% 2.65/1.52 => ( eqimpsubset2
% 2.65/1.52 => ( eqimpsubset1
% 2.65/1.52 => ( subsetI2
% 2.65/1.52 => ( emptysetsubset
% 2.65/1.52 => ( subsetE
% 2.65/1.52 => ( subsetE2
% 2.65/1.52 => ( notsubsetI
% 2.65/1.52 => ( notequalI1
% 2.65/1.52 => ( notequalI2
% 2.65/1.52 => ( subsetRefl
% 2.65/1.52 => ( subsetTrans
% 2.65/1.52 => ( setadjoinSub
% 2.65/1.52 => ( setadjoinSub2
% 2.65/1.52 => ( subset2powerset
% 2.65/1.52 => ( setextsub
% 2.65/1.52 => ( subsetemptysetimpeq
% 2.65/1.52 => ( powersetI1
% 2.65/1.52 => ( powersetE1
% 2.65/1.52 => ( inPowerset
% 2.65/1.52 => ( powersetsubset
% 2.65/1.52 => ( sepInPowerset
% 2.65/1.52 => ( sepSubset
% 2.65/1.52 => ( binunionIL
% 2.65/1.52 => ( upairset2IR
% 2.65/1.52 => ( binunionIR
% 2.65/1.52 => ( binunionEcases
% 2.65/1.52 => ( binunionE
% 2.65/1.52 => ( binunionLsub
% 2.65/1.52 => ( binunionRsub
% 2.65/1.52 => ( binintersectI
% 2.65/1.52 => ( binintersectSubset5
% 2.65/1.52 => ( binintersectEL
% 2.65/1.52 => ( binintersectLsub
% 2.65/1.52 => ( binintersectSubset2
% 2.65/1.52 => ( binintersectSubset3
% 2.65/1.52 => ( binintersectER
% 2.65/1.52 => ( disjointsetsI1
% 2.65/1.52 => ( binintersectRsub
% 2.65/1.52 => ( binintersectSubset4
% 2.65/1.52 => ( binintersectSubset1
% 2.65/1.52 => ( bs114d
% 2.65/1.52 => ( setminusI
% 2.65/1.52 => ( setminusEL
% 2.65/1.52 => ( setminusER
% 2.65/1.52 => ( setminusSubset2
% 2.65/1.52 => ( setminusERneg
% 2.65/1.52 => ( setminusELneg
% 2.65/1.52 => ( setminusILneg
% 2.65/1.52 => ( setminusIRneg
% 2.65/1.52 => ( setminusLsub
% 2.65/1.52 => ( setminusSubset1
% 2.65/1.52 => ( symdiffE
% 2.65/1.52 => ( symdiffI1
% 2.65/1.52 => ( symdiffI2
% 2.65/1.52 => ( symdiffIneg1
% 2.65/1.52 => ( symdiffIneg2
% 2.65/1.52 => ( secondinupair
% 2.65/1.52 => ( setukpairIL
% 2.65/1.52 => ( setukpairIR
% 2.65/1.52 => ( kpairiskpair
% 2.65/1.52 => ( kpairp
% 2.65/1.52 => ( singletonsubset
% 2.65/1.52 => ( singletoninpowerset
% 2.65/1.52 => ( singletoninpowunion
% 2.65/1.52 => ( upairset2E
% 2.65/1.52 => ( upairsubunion
% 2.65/1.52 => ( upairinpowunion
% 2.65/1.52 => ( ubforcartprodlem1
% 2.65/1.52 => ( ubforcartprodlem2
% 2.65/1.52 => ( ubforcartprodlem3
% 2.65/1.52 => ( cartprodpairin
% 2.65/1.52 => ( cartprodmempair1
% 2.65/1.52 => ( cartprodmempair
% 2.65/1.52 => ( setunionE2
% 2.65/1.52 => ( setunionsingleton1
% 2.65/1.52 => ( setunionsingleton2
% 2.65/1.52 => ( setunionsingleton
% 2.65/1.52 => ( singletonprop
% 2.65/1.52 => ( ex1E1
% 2.65/1.52 => ( ex1I
% 2.65/1.52 => ( ex1I2
% 2.65/1.52 => ( singletonsuniq
% 2.65/1.52 => ( setukpairinjL1
% 2.65/1.52 => ( kfstsingleton
% 2.65/1.52 => ( theprop
% 2.65/1.52 => ( kfstpairEq
% 2.65/1.52 => ( cartprodfstin
% 2.65/1.52 => ( setukpairinjL2
% 2.65/1.52 => ( setukpairinjL
% 2.65/1.52 => ( setukpairinjR11
% 2.65/1.52 => ( setukpairinjR12
% 2.65/1.52 => ( setukpairinjR1
% 2.65/1.52 => ( upairequniteq
% 2.65/1.52 => ( setukpairinjR2
% 2.65/1.52 => ( setukpairinjR
% 2.65/1.52 => ( ksndsingleton
% 2.65/1.52 => ( ksndpairEq
% 2.65/1.52 => ( kpairsurjEq
% 2.65/1.52 => ( cartprodsndin
% 2.65/1.52 => ( cartprodpairmemEL
% 2.65/1.52 => ( cartprodpairmemER
% 2.65/1.52 => ( cartprodmempaircEq
% 2.65/1.52 => ( cartprodfstpairEq
% 2.65/1.52 => ( cartprodsndpairEq
% 2.65/1.52 => ( cartprodpairsurjEq
% 2.65/1.52 => ( dpsetconstrI
% 2.65/1.52 => ( dpsetconstrSub
% 2.65/1.52 => ( setOfPairsIsBReln
% 2.65/1.52 => ( dpsetconstrERa
% 2.65/1.52 => ( dpsetconstrEL1
% 2.65/1.52 => ( dpsetconstrEL2
% 2.65/1.52 => ( dpsetconstrER
% 2.65/1.52 => ( funcImageSingleton
% 2.65/1.52 => ( apProp
% 2.65/1.52 => ( app
% 2.65/1.52 => ( infuncsetfunc
% 2.65/1.52 => ( ap2p
% 2.65/1.52 => ( funcinfuncset
% 2.65/1.52 => ( lamProp
% 2.65/1.52 => ( lamp
% 2.65/1.52 => ( lam2p
% 2.65/1.52 => ( brelnall1
% 2.65/1.52 => ( brelnall2
% 2.65/1.52 => ( ex1E2
% 2.65/1.52 => ( funcGraphProp1
% 2.65/1.52 => ( funcGraphProp3
% 2.65/1.52 => ( funcGraphProp2
% 2.65/1.52 => ( funcextLem
% 2.65/1.52 => ( funcGraphProp4
% 2.65/1.52 => ( subbreln
% 2.65/1.52 => ( eqbreln
% 2.65/1.52 => ( funcext
% 2.65/1.52 => ( funcext2
% 2.65/1.52 => ( ap2apEq1
% 2.65/1.52 => ( ap2apEq2
% 2.65/1.52 => ( beta1
% 2.65/1.52 => ( eta1
% 2.65/1.52 => ( lam2lamEq
% 2.65/1.52 => ( beta2
% 2.65/1.52 => ( eta2
% 2.65/1.52 => ( iffalseProp1
% 2.65/1.52 => ( iffalseProp2
% 2.65/1.52 => ( iftrueProp1
% 2.65/1.52 => ( iftrueProp2
% 2.65/1.52 => ( ifSingleton
% 2.65/1.52 => ( ifp
% 2.65/1.52 => ( theeq
% 2.65/1.52 => ( iftrue
% 2.65/1.52 => ( iffalse
% 2.65/1.52 => ( iftrueorfalse
% 2.65/1.52 => ( binintersectT_lem
% 2.65/1.52 => ( binunionT_lem
% 2.65/1.52 => ( powersetT_lem
% 2.65/1.52 => ( setminusT_lem
% 2.65/1.52 => ( complementT_lem
% 2.65/1.52 => ! [A: $i,X: $i] :
% 2.65/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.65/1.52 => ! [Y: $i] :
% 2.65/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( in @ Xx @ X )
% 2.65/1.52 => ( in @ Xx @ Y ) ) )
% 2.65/1.52 => ( ! [Xx: $i] :
% 2.65/1.52 ( ( in @ Xx @ A )
% 2.65/1.52 => ( ( in @ Xx @ Y )
% 2.65/1.52 => ( in @ Xx @ X ) ) )
% 2.65/1.52 => ( X = Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.65/1.52 ------------------------
% 2.65/1.56 % (1906)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_1611 for (2999ds/2Mi)
% 2.65/1.56 % (1908)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/18Mi)
% 2.65/1.56 % (1906)Instruction limit reached!
% 2.65/1.56 % (1906)------------------------------
% 2.65/1.56 % (1906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.56 % (1906)Termination reason: Unknown
% 2.65/1.56 % (1906)Termination phase: shuffling
% 2.65/1.56
% 2.65/1.56 % (1906)Memory used [KB]: 1407
% 2.65/1.56 % (1906)Time elapsed: 0.003 s
% 2.65/1.56 % (1906)Instructions burned: 4 (million)
% 2.65/1.56 % (1906)------------------------------
% 2.65/1.56 % (1906)------------------------------
% 2.65/1.56 % (1908)Instruction limit reached!
% 2.65/1.56 % (1908)------------------------------
% 2.65/1.56 % (1908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.56 % (1908)Termination reason: Unknown
% 2.65/1.56 % (1908)Termination phase: shuffling
% 2.65/1.56
% 2.65/1.56 % (1908)Memory used [KB]: 1791
% 2.65/1.56 % (1908)Time elapsed: 0.008 s
% 2.65/1.56 % (1908)Instructions burned: 19 (million)
% 2.65/1.56 % (1908)------------------------------
% 2.65/1.56 % (1908)------------------------------
% 2.65/1.56 % (1902)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/183Mi)
% 2.65/1.56 % (1903)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_1611 for (2999ds/4Mi)
% 2.65/1.56 % (1904)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_1611 for (2999ds/27Mi)
% 2.65/1.56 % (1905)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/2Mi)
% 2.65/1.56 % (1907)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_1611 for (2999ds/275Mi)
% 2.65/1.57 % (1905)Instruction limit reached!
% 2.65/1.57 % (1905)------------------------------
% 2.65/1.57 % (1905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.57 % (1905)Termination reason: Unknown
% 2.65/1.57 % (1905)Termination phase: shuffling
% 2.65/1.57
% 2.65/1.57 % (1905)Memory used [KB]: 1407
% 2.65/1.57 % (1905)Time elapsed: 0.003 s
% 2.65/1.57 % (1905)Instructions burned: 3 (million)
% 2.65/1.57 % (1905)------------------------------
% 2.65/1.57 % (1905)------------------------------
% 2.65/1.57 % (1903)Instruction limit reached!
% 2.65/1.57 % (1903)------------------------------
% 2.65/1.57 % (1903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.57 % (1903)Termination reason: Unknown
% 2.65/1.57 % (1903)Termination phase: shuffling
% 2.65/1.57
% 2.65/1.57 % (1903)Memory used [KB]: 1407
% 2.65/1.57 % (1903)Time elapsed: 0.005 s
% 2.65/1.57 % (1903)Instructions burned: 5 (million)
% 2.65/1.57 % (1903)------------------------------
% 2.65/1.57 % (1903)------------------------------
% 2.65/1.57 % (1909)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/3Mi)
% 2.65/1.57 % (1909)Instruction limit reached!
% 2.65/1.57 % (1909)------------------------------
% 2.65/1.57 % (1909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.57 % (1909)Termination reason: Unknown
% 2.65/1.57 % (1909)Termination phase: shuffling
% 2.65/1.57
% 2.65/1.57 % (1909)Memory used [KB]: 1407
% 2.65/1.57 % (1909)Time elapsed: 0.002 s
% 2.65/1.57 % (1909)Instructions burned: 3 (million)
% 2.65/1.57 % (1909)------------------------------
% 2.65/1.57 % (1909)------------------------------
% 2.65/1.58 % (1913)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_1611 for (2999ds/1041Mi)
% 2.65/1.58 % (1904)Instruction limit reached!
% 2.65/1.58 % (1904)------------------------------
% 2.65/1.58 % (1904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.58 % (1904)Termination reason: Unknown
% 2.65/1.58 % (1904)Termination phase: shuffling
% 2.65/1.58
% 2.65/1.58 % (1904)Memory used [KB]: 1918
% 2.65/1.58 % (1904)Time elapsed: 0.016 s
% 2.65/1.58 % (1904)Instructions burned: 28 (million)
% 2.65/1.58 % (1904)------------------------------
% 2.65/1.58 % (1904)------------------------------
% 2.65/1.58 % (1910)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_1611 for (2999ds/37Mi)
% 2.65/1.58 % (1911)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_1611 for (2999ds/15Mi)
% 2.65/1.58 % (1912)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_1611 for (2999ds/3Mi)
% 2.65/1.59 % (1912)Instruction limit reached!
% 2.65/1.59 % (1912)------------------------------
% 2.65/1.59 % (1912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.59 % (1912)Termination reason: Unknown
% 2.65/1.59 % (1912)Termination phase: shuffling
% 2.65/1.59
% 2.65/1.59 % (1912)Memory used [KB]: 1407
% 2.65/1.59 % (1912)Time elapsed: 0.004 s
% 2.65/1.59 % (1912)Instructions burned: 3 (million)
% 2.65/1.59 % (1912)------------------------------
% 2.65/1.59 % (1912)------------------------------
% 2.65/1.59 % (1911)Instruction limit reached!
% 2.65/1.59 % (1911)------------------------------
% 2.65/1.59 % (1911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.59 % (1911)Termination reason: Unknown
% 2.65/1.59 % (1911)Termination phase: shuffling
% 2.65/1.59
% 2.65/1.59 % (1911)Memory used [KB]: 1663
% 2.65/1.59 % (1911)Time elapsed: 0.011 s
% 2.65/1.59 % (1911)Instructions burned: 15 (million)
% 2.65/1.59 % (1911)------------------------------
% 2.65/1.59 % (1911)------------------------------
% 2.70/1.60 % (1914)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/7Mi)
% 2.70/1.60 % (1914)Instruction limit reached!
% 2.70/1.60 % (1914)------------------------------
% 2.70/1.60 % (1914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.60 % (1914)Termination reason: Unknown
% 2.70/1.60 % (1914)Termination phase: shuffling
% 2.70/1.60
% 2.70/1.60 % (1914)Memory used [KB]: 1535
% 2.70/1.60 % (1914)Time elapsed: 0.006 s
% 2.70/1.60 % (1914)Instructions burned: 7 (million)
% 2.70/1.60 % (1914)------------------------------
% 2.70/1.60 % (1914)------------------------------
% 2.70/1.60 % (1910)Instruction limit reached!
% 2.70/1.60 % (1910)------------------------------
% 2.70/1.60 % (1910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.60 % (1910)Termination reason: Unknown
% 2.70/1.60 % (1910)Termination phase: shuffling
% 2.70/1.60
% 2.70/1.60 % (1910)Memory used [KB]: 2174
% 2.70/1.60 % (1910)Time elapsed: 0.020 s
% 2.70/1.60 % (1910)Instructions burned: 37 (million)
% 2.70/1.60 % (1910)------------------------------
% 2.70/1.60 % (1910)------------------------------
% 2.70/1.60 % (1915)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/16Mi)
% 2.70/1.61 % (1916)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_1611 for (2999ds/3Mi)
% 2.70/1.61 % (1916)Instruction limit reached!
% 2.70/1.61 % (1916)------------------------------
% 2.70/1.61 % (1916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.61 % (1916)Termination reason: Unknown
% 2.70/1.61 % (1916)Termination phase: shuffling
% 2.70/1.61
% 2.70/1.61 % (1916)Memory used [KB]: 1407
% 2.70/1.61 % (1916)Time elapsed: 0.003 s
% 2.70/1.61 % (1916)Instructions burned: 3 (million)
% 2.70/1.61 % (1916)------------------------------
% 2.70/1.61 % (1916)------------------------------
% 2.70/1.61 % (1915)Instruction limit reached!
% 2.70/1.61 % (1915)------------------------------
% 2.70/1.61 % (1915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.61 % (1915)Termination reason: Unknown
% 2.70/1.61 % (1915)Termination phase: shuffling
% 2.70/1.61
% 2.70/1.61 % (1915)Memory used [KB]: 1791
% 2.70/1.61 % (1915)Time elapsed: 0.011 s
% 2.70/1.61 % (1915)Instructions burned: 17 (million)
% 2.70/1.61 % (1915)------------------------------
% 2.70/1.61 % (1915)------------------------------
% 2.70/1.61 % (1918)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/7Mi)
% 2.70/1.62 % (1918)Instruction limit reached!
% 2.70/1.62 % (1918)------------------------------
% 2.70/1.62 % (1918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.62 % (1918)Termination reason: Unknown
% 2.70/1.62 % (1918)Termination phase: shuffling
% 2.70/1.62
% 2.70/1.62 % (1918)Memory used [KB]: 1535
% 2.70/1.62 % (1918)Time elapsed: 0.004 s
% 2.70/1.62 % (1918)Instructions burned: 8 (million)
% 2.70/1.62 % (1918)------------------------------
% 2.70/1.62 % (1918)------------------------------
% 2.70/1.62 % (1917)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_1611 for (2999ds/3Mi)
% 2.70/1.62 % (1917)Instruction limit reached!
% 2.70/1.62 % (1917)------------------------------
% 2.70/1.62 % (1917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.62 % (1917)Termination reason: Unknown
% 2.70/1.62 % (1917)Termination phase: shuffling
% 2.70/1.62
% 2.70/1.62 % (1917)Memory used [KB]: 1407
% 2.70/1.62 % (1917)Time elapsed: 0.004 s
% 2.70/1.62 % (1917)Instructions burned: 3 (million)
% 2.70/1.62 % (1917)------------------------------
% 2.70/1.62 % (1917)------------------------------
% 2.70/1.63 % (1921)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/18Mi)
% 2.70/1.63 % (1919)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/3Mi)
% 2.70/1.63 % (1920)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/4Mi)
% 2.70/1.63 % (1919)Instruction limit reached!
% 2.70/1.63 % (1919)------------------------------
% 2.70/1.63 % (1919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.63 % (1919)Termination reason: Unknown
% 2.70/1.63 % (1919)Termination phase: shuffling
% 2.70/1.63
% 2.70/1.63 % (1919)Memory used [KB]: 1407
% 2.70/1.63 % (1919)Time elapsed: 0.004 s
% 2.70/1.63 % (1919)Instructions burned: 4 (million)
% 2.70/1.63 % (1919)------------------------------
% 2.70/1.63 % (1919)------------------------------
% 2.70/1.63 % (1920)Instruction limit reached!
% 2.70/1.63 % (1920)------------------------------
% 2.70/1.63 % (1920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.63 % (1920)Termination reason: Unknown
% 2.70/1.63 % (1920)Termination phase: shuffling
% 2.70/1.63
% 2.70/1.63 % (1920)Memory used [KB]: 1407
% 2.70/1.63 % (1920)Time elapsed: 0.004 s
% 2.70/1.63 % (1920)Instructions burned: 4 (million)
% 2.70/1.63 % (1920)------------------------------
% 2.70/1.63 % (1920)------------------------------
% 2.70/1.63 % (1921)Instruction limit reached!
% 2.70/1.63 % (1921)------------------------------
% 2.70/1.63 % (1921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.63 % (1921)Termination reason: Unknown
% 2.70/1.63 % (1921)Termination phase: shuffling
% 2.70/1.63
% 2.70/1.63 % (1921)Memory used [KB]: 1791
% 2.70/1.63 % (1921)Time elapsed: 0.007 s
% 2.70/1.63 % (1921)Instructions burned: 20 (million)
% 2.70/1.63 % (1921)------------------------------
% 2.70/1.63 % (1921)------------------------------
% 2.70/1.63 % (1922)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/710Mi)
% 2.70/1.64 % (1925)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_1611 for (2999ds/21Mi)
% 2.70/1.65 % (1924)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_1611 for (2999ds/902Mi)
% 2.70/1.65 % (1923)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1611 for (2999ds/6Mi)
% 2.70/1.65 % (1902)Instruction limit reached!
% 2.70/1.65 % (1902)------------------------------
% 2.70/1.65 % (1902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.65 % (1902)Termination reason: Unknown
% 2.70/1.65 % (1902)Termination phase: Saturation
% 2.70/1.65
% 2.70/1.65 % (1902)Memory used [KB]: 7547
% 2.70/1.65 % (1902)Time elapsed: 0.088 s
% 2.70/1.65 % (1902)Instructions burned: 185 (million)
% 2.70/1.65 % (1902)------------------------------
% 2.70/1.65 % (1902)------------------------------
% 2.70/1.65 % (1925)Instruction limit reached!
% 2.70/1.65 % (1925)------------------------------
% 2.70/1.65 % (1925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.65 % (1925)Termination reason: Unknown
% 2.70/1.65 % (1925)Termination phase: shuffling
% 2.70/1.65
% 2.70/1.65 % (1925)Memory used [KB]: 1791
% 2.70/1.65 % (1925)Time elapsed: 0.007 s
% 2.70/1.65 % (1925)Instructions burned: 21 (million)
% 2.70/1.65 % (1925)------------------------------
% 2.70/1.65 % (1925)------------------------------
% 2.70/1.65 % (1923)Instruction limit reached!
% 2.70/1.65 % (1923)------------------------------
% 2.70/1.65 % (1923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.65 % (1923)Termination reason: Unknown
% 2.70/1.65 % (1923)Termination phase: shuffling
% 2.70/1.65
% 2.70/1.65 % (1923)Memory used [KB]: 1535
% 2.70/1.65 % (1923)Time elapsed: 0.004 s
% 2.70/1.65 % (1923)Instructions burned: 7 (million)
% 2.70/1.65 % (1923)------------------------------
% 2.70/1.65 % (1923)------------------------------
% 2.70/1.66 % (1926)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1611 for (2998ds/5Mi)
% 2.70/1.66 % (1927)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_1611 for (2998ds/6Mi)
% 2.70/1.66 % (1928)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1611 for (2998ds/377Mi)
% 2.70/1.66 % (1926)Instruction limit reached!
% 2.70/1.66 % (1926)------------------------------
% 2.70/1.66 % (1926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.66 % (1926)Termination reason: Unknown
% 2.70/1.66 % (1926)Termination phase: shuffling
% 2.70/1.66
% 2.70/1.66 % (1926)Memory used [KB]: 1535
% 2.70/1.66 % (1926)Time elapsed: 0.003 s
% 2.70/1.66 % (1926)Instructions burned: 7 (million)
% 2.70/1.66 % (1926)------------------------------
% 2.70/1.66 % (1926)------------------------------
% 2.70/1.66 % (1927)Instruction limit reached!
% 2.70/1.66 % (1927)------------------------------
% 2.70/1.66 % (1927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.66 % (1927)Termination reason: Unknown
% 2.70/1.66 % (1927)Termination phase: shuffling
% 2.70/1.66
% 2.70/1.66 % (1927)Memory used [KB]: 1535
% 2.70/1.66 % (1927)Time elapsed: 0.003 s
% 2.70/1.66 % (1927)Instructions burned: 7 (million)
% 2.70/1.66 % (1927)------------------------------
% 2.70/1.66 % (1927)------------------------------
% 2.70/1.67 % (1930)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_1611 for (2998ds/779Mi)
% 2.70/1.67 % (1931)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_1611 for (2998ds/19Mi)
% 2.70/1.67 % (1907)Instruction limit reached!
% 2.70/1.67 % (1907)------------------------------
% 2.70/1.67 % (1907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.67 % (1907)Termination reason: Unknown
% 2.70/1.67 % (1907)Termination phase: Saturation
% 2.70/1.67
% 2.70/1.67 % (1907)Memory used [KB]: 9210
% 2.70/1.67 % (1907)Time elapsed: 0.110 s
% 2.70/1.67 % (1907)Instructions burned: 277 (million)
% 2.70/1.67 % (1907)------------------------------
% 2.70/1.67 % (1907)------------------------------
% 2.70/1.68 % (1931)Instruction limit reached!
% 2.70/1.68 % (1931)------------------------------
% 2.70/1.68 % (1931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.68 % (1931)Termination reason: Unknown
% 2.70/1.68 % (1931)Termination phase: shuffling
% 2.70/1.68
% 2.70/1.68 % (1931)Memory used [KB]: 1791
% 2.70/1.68 % (1931)Time elapsed: 0.008 s
% 2.70/1.68 % (1931)Instructions burned: 21 (million)
% 2.70/1.68 % (1931)------------------------------
% 2.70/1.68 % (1931)------------------------------
% 2.70/1.68 % (1932)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1611 for (2998ds/879Mi)
% 2.70/1.69 % (1933)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1611 for (2998ds/17Mi)
% 2.70/1.69 % (1933)Instruction limit reached!
% 2.70/1.69 % (1933)------------------------------
% 2.70/1.69 % (1933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.69 % (1933)Termination reason: Unknown
% 2.70/1.69 % (1933)Termination phase: shuffling
% 2.70/1.69
% 2.70/1.69 % (1933)Memory used [KB]: 1791
% 2.70/1.69 % (1933)Time elapsed: 0.007 s
% 2.70/1.69 % (1933)Instructions burned: 18 (million)
% 2.70/1.69 % (1933)------------------------------
% 2.70/1.69 % (1933)------------------------------
% 2.70/1.70 % (1934)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1611 for (2998ds/3Mi)
% 2.70/1.71 % (1934)Instruction limit reached!
% 2.70/1.71 % (1934)------------------------------
% 2.70/1.71 % (1934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.71 % (1934)Termination reason: Unknown
% 2.70/1.71 % (1934)Termination phase: shuffling
% 2.70/1.71
% 2.70/1.71 % (1934)Memory used [KB]: 1407
% 2.70/1.71 % (1934)Time elapsed: 0.003 s
% 2.70/1.71 % (1934)Instructions burned: 4 (million)
% 2.70/1.71 % (1934)------------------------------
% 2.70/1.71 % (1934)------------------------------
% 2.70/1.72 % (1935)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1611 for (2998ds/30Mi)
% 2.70/1.73 % (1935)Instruction limit reached!
% 2.70/1.73 % (1935)------------------------------
% 2.70/1.73 % (1935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.73 % (1935)Termination reason: Unknown
% 2.70/1.73 % (1935)Termination phase: shuffling
% 2.70/1.73
% 2.70/1.73 % (1935)Memory used [KB]: 1918
% 2.70/1.73 % (1935)Time elapsed: 0.010 s
% 2.70/1.73 % (1935)Instructions burned: 30 (million)
% 2.70/1.73 % (1935)------------------------------
% 2.70/1.73 % (1935)------------------------------
% 2.70/1.74 % (1936)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1611 for (2998ds/127Mi)
% 2.70/1.77 % (1936)Instruction limit reached!
% 2.70/1.77 % (1936)------------------------------
% 2.70/1.77 % (1936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.77 % (1936)Termination reason: Unknown
% 2.70/1.77 % (1936)Termination phase: Property scanning
% 2.70/1.77
% 2.70/1.77 % (1936)Memory used [KB]: 2558
% 2.70/1.77 % (1936)Time elapsed: 0.037 s
% 2.70/1.77 % (1936)Instructions burned: 129 (million)
% 2.70/1.77 % (1936)------------------------------
% 2.70/1.77 % (1936)------------------------------
% 2.70/1.78 % (1928)Instruction limit reached!
% 2.70/1.78 % (1928)------------------------------
% 2.70/1.78 % (1928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.78 % (1928)Termination reason: Unknown
% 2.70/1.78 % (1928)Termination phase: Saturation
% 2.70/1.78
% 2.70/1.78 % (1928)Memory used [KB]: 8699
% 2.70/1.78 % (1928)Time elapsed: 0.116 s
% 2.70/1.78 % (1928)Instructions burned: 379 (million)
% 2.70/1.78 % (1928)------------------------------
% 2.70/1.78 % (1928)------------------------------
% 2.70/1.78 % (1937)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1611 for (2997ds/100Mi)
% 2.70/1.79 % (1938)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_1611 for (2997ds/3Mi)
% 2.70/1.79 % (1938)Instruction limit reached!
% 2.70/1.79 % (1938)------------------------------
% 2.70/1.79 % (1938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.79 % (1938)Termination reason: Unknown
% 2.70/1.79 % (1938)Termination phase: shuffling
% 2.70/1.79
% 2.70/1.79 % (1938)Memory used [KB]: 1407
% 2.70/1.79 % (1938)Time elapsed: 0.002 s
% 2.70/1.79 % (1938)Instructions burned: 3 (million)
% 2.70/1.79 % (1938)------------------------------
% 2.70/1.79 % (1938)------------------------------
% 2.70/1.80 % (1939)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_1611 for (2997ds/20Mi)
% 2.70/1.80 % (1939)Instruction limit reached!
% 2.70/1.80 % (1939)------------------------------
% 2.70/1.80 % (1939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.80 % (1939)Termination reason: Unknown
% 2.70/1.80 % (1939)Termination phase: shuffling
% 2.70/1.80
% 2.70/1.80 % (1939)Memory used [KB]: 1791
% 2.70/1.80 % (1939)Time elapsed: 0.008 s
% 2.70/1.80 % (1939)Instructions burned: 20 (million)
% 2.70/1.80 % (1939)------------------------------
% 2.70/1.80 % (1939)------------------------------
% 2.70/1.81 % (1937)Instruction limit reached!
% 2.70/1.81 % (1937)------------------------------
% 2.70/1.81 % (1937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.81 % (1937)Termination reason: Unknown
% 2.70/1.81 % (1937)Termination phase: Property scanning
% 2.70/1.81
% 2.70/1.81 % (1937)Memory used [KB]: 2430
% 2.70/1.81 % (1937)Time elapsed: 0.029 s
% 2.70/1.81 % (1937)Instructions burned: 101 (million)
% 2.70/1.81 % (1937)------------------------------
% 2.70/1.81 % (1937)------------------------------
% 2.70/1.82 % (1940)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_1611 for (2997ds/86Mi)
% 2.70/1.82 % (1941)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_1611 for (2997ds/107Mi)
% 2.70/1.84 % (1940)Instruction limit reached!
% 2.70/1.84 % (1940)------------------------------
% 2.70/1.84 % (1940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.84 % (1940)Termination reason: Unknown
% 2.70/1.84 % (1940)Termination phase: Property scanning
% 2.70/1.84
% 2.70/1.84 % (1940)Memory used [KB]: 2430
% 2.70/1.84 % (1940)Time elapsed: 0.025 s
% 2.70/1.84 % (1940)Instructions burned: 87 (million)
% 2.70/1.84 % (1940)------------------------------
% 2.70/1.84 % (1940)------------------------------
% 2.70/1.85 % (1913)Instruction limit reached!
% 2.70/1.85 % (1913)------------------------------
% 2.70/1.85 % (1913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.85 % (1913)Termination reason: Unknown
% 2.70/1.85 % (1913)Termination phase: Saturation
% 2.70/1.85
% 2.70/1.85 % (1913)Memory used [KB]: 13432
% 2.70/1.85 % (1913)Time elapsed: 0.269 s
% 2.70/1.85 % (1913)Instructions burned: 1041 (million)
% 2.70/1.85 % (1913)------------------------------
% 2.70/1.85 % (1913)------------------------------
% 2.70/1.85 % (1941)Instruction limit reached!
% 2.70/1.85 % (1941)------------------------------
% 2.70/1.85 % (1941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.85 % (1941)Termination reason: Unknown
% 2.70/1.85 % (1941)Termination phase: Property scanning
% 2.70/1.85
% 2.70/1.85 % (1941)Memory used [KB]: 2430
% 2.70/1.85 % (1941)Time elapsed: 0.031 s
% 2.70/1.85 % (1941)Instructions burned: 107 (million)
% 2.70/1.85 % (1941)------------------------------
% 2.70/1.85 % (1941)------------------------------
% 2.70/1.85 % (1942)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_1611 for (2997ds/39Mi)
% 2.70/1.86 % (1943)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_1611 for (2996ds/448Mi)
% 2.70/1.86 % (1944)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_1611 for (2996ds/46Mi)
% 2.70/1.86 % (1942)Instruction limit reached!
% 2.70/1.86 % (1942)------------------------------
% 2.70/1.86 % (1942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.86 % (1942)Termination reason: Unknown
% 2.70/1.86 % (1942)Termination phase: shuffling
% 2.70/1.86
% 2.70/1.86 % (1942)Memory used [KB]: 2174
% 2.70/1.86 % (1942)Time elapsed: 0.012 s
% 2.70/1.86 % (1942)Instructions burned: 39 (million)
% 2.70/1.86 % (1942)------------------------------
% 2.70/1.86 % (1942)------------------------------
% 2.70/1.87 % (1945)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_1611 for (2996ds/98Mi)
% 2.70/1.87 % (1944)Instruction limit reached!
% 2.70/1.87 % (1944)------------------------------
% 2.70/1.87 % (1944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.87 % (1944)Termination reason: Unknown
% 2.70/1.87 % (1944)Termination phase: Property scanning
% 2.70/1.87
% 2.70/1.87 % (1944)Memory used [KB]: 2302
% 2.70/1.87 % (1944)Time elapsed: 0.015 s
% 2.70/1.87 % (1944)Instructions burned: 49 (million)
% 2.70/1.87 % (1944)------------------------------
% 2.70/1.87 % (1944)------------------------------
% 2.70/1.87 % (1922)Instruction limit reached!
% 2.70/1.87 % (1922)------------------------------
% 2.70/1.87 % (1922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.87 % (1922)Termination reason: Unknown
% 2.70/1.87 % (1922)Termination phase: Saturation
% 2.70/1.87
% 2.70/1.87 % (1922)Memory used [KB]: 10106
% 2.70/1.87 % (1922)Time elapsed: 0.241 s
% 2.70/1.87 % (1922)Instructions burned: 713 (million)
% 2.70/1.87 % (1922)------------------------------
% 2.70/1.87 % (1922)------------------------------
% 2.70/1.88 % (1930)Instruction limit reached!
% 2.70/1.88 % (1930)------------------------------
% 2.70/1.88 % (1930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.88 % (1930)Termination reason: Unknown
% 2.70/1.88 % (1930)Termination phase: Saturation
% 2.70/1.88
% 2.70/1.88 % (1930)Memory used [KB]: 7291
% 2.70/1.88 % (1930)Time elapsed: 0.209 s
% 2.70/1.88 % (1930)Instructions burned: 779 (million)
% 2.70/1.88 % (1930)------------------------------
% 2.70/1.88 % (1930)------------------------------
% 2.70/1.88 % (1946)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_1611 for (2996ds/507Mi)
% 2.70/1.88 % (1947)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_1611 for (2996ds/149Mi)
% 2.70/1.89 % (1948)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_1611 for (2996ds/39Mi)
% 2.70/1.90 % (1945)Instruction limit reached!
% 2.70/1.90 % (1945)------------------------------
% 2.70/1.90 % (1945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.90 % (1945)Termination reason: Unknown
% 2.70/1.90 % (1945)Termination phase: Function definition elimination
% 2.70/1.90
% 2.70/1.90 % (1945)Memory used [KB]: 2430
% 2.70/1.90 % (1945)Time elapsed: 0.029 s
% 2.70/1.90 % (1945)Instructions burned: 99 (million)
% 2.70/1.90 % (1945)------------------------------
% 2.70/1.90 % (1945)------------------------------
% 2.70/1.90 % (1948)Instruction limit reached!
% 2.70/1.90 % (1948)------------------------------
% 2.70/1.90 % (1948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.90 % (1948)Termination reason: Unknown
% 2.70/1.90 % (1948)Termination phase: shuffling
% 2.70/1.90
% 2.70/1.90 % (1948)Memory used [KB]: 2302
% 2.70/1.90 % (1948)Time elapsed: 0.013 s
% 2.70/1.90 % (1948)Instructions burned: 41 (million)
% 2.70/1.90 % (1948)------------------------------
% 2.70/1.90 % (1948)------------------------------
% 2.70/1.91 % (1949)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_1611 for (2996ds/6Mi)
% 2.70/1.91 % (1949)Instruction limit reached!
% 2.70/1.91 % (1949)------------------------------
% 2.70/1.91 % (1949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.91 % (1949)Termination reason: Unknown
% 2.70/1.91 % (1949)Termination phase: shuffling
% 2.70/1.91
% 2.70/1.91 % (1949)Memory used [KB]: 1535
% 2.70/1.91 % (1949)Time elapsed: 0.003 s
% 2.70/1.91 % (1949)Instructions burned: 7 (million)
% 2.70/1.91 % (1949)------------------------------
% 2.70/1.91 % (1949)------------------------------
% 2.70/1.91 % (1950)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_1611 for (2996ds/1087Mi)
% 2.70/1.92 % (1951)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_1611 for (2996ds/47Mi)
% 2.70/1.93 % (1947)Instruction limit reached!
% 2.70/1.93 % (1947)------------------------------
% 2.70/1.93 % (1947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.93 % (1947)Termination reason: Unknown
% 2.70/1.93 % (1947)Termination phase: Saturation
% 2.70/1.93
% 2.70/1.93 % (1947)Memory used [KB]: 7419
% 2.70/1.93 % (1947)Time elapsed: 0.043 s
% 2.70/1.93 % (1947)Instructions burned: 150 (million)
% 2.70/1.93 % (1947)------------------------------
% 2.70/1.93 % (1947)------------------------------
% 2.70/1.93 % (1951)Instruction limit reached!
% 2.70/1.93 % (1951)------------------------------
% 2.70/1.93 % (1951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.93 % (1951)Termination reason: Unknown
% 2.70/1.93 % (1951)Termination phase: Property scanning
% 2.70/1.93
% 2.70/1.93 % (1951)Memory used [KB]: 2302
% 2.70/1.93 % (1951)Time elapsed: 0.016 s
% 2.70/1.93 % (1951)Instructions burned: 49 (million)
% 2.70/1.93 % (1951)------------------------------
% 2.70/1.93 % (1951)------------------------------
% 2.70/1.94 % (1952)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_1611 for (2995ds/44Mi)
% 2.70/1.94 % (1924)Instruction limit reached!
% 2.70/1.94 % (1924)------------------------------
% 2.70/1.94 % (1924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.94 % (1924)Termination reason: Unknown
% 2.70/1.94 % (1924)Termination phase: Saturation
% 2.70/1.94
% 2.70/1.94 % (1924)Memory used [KB]: 11385
% 2.70/1.94 % (1924)Time elapsed: 0.295 s
% 2.70/1.94 % (1924)Instructions burned: 904 (million)
% 2.70/1.94 % (1924)------------------------------
% 2.70/1.94 % (1924)------------------------------
% 2.70/1.95 % (1953)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_1611 for (2995ds/432Mi)
% 2.70/1.95 % (1954)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_1611 for (2995ds/62Mi)
% 2.70/1.95 % (1952)Instruction limit reached!
% 2.70/1.95 % (1952)------------------------------
% 2.70/1.95 % (1952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.95 % (1952)Termination reason: Unknown
% 2.70/1.95 % (1952)Termination phase: Property scanning
% 2.70/1.95
% 2.70/1.95 % (1952)Memory used [KB]: 2302
% 2.70/1.95 % (1952)Time elapsed: 0.014 s
% 2.70/1.95 % (1952)Instructions burned: 46 (million)
% 2.70/1.95 % (1952)------------------------------
% 2.70/1.95 % (1952)------------------------------
% 2.70/1.95 % (1932)Refutation not found, non-redundant clauses discarded% (1932)------------------------------
% 2.70/1.95 % (1932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.95 % (1932)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.70/1.95
% 2.70/1.95 % (1932)Memory used [KB]: 9466
% 2.70/1.95 % (1932)Time elapsed: 0.267 s
% 2.70/1.95 % (1932)Instructions burned: 865 (million)
% 2.70/1.95 % (1932)------------------------------
% 2.70/1.95 % (1932)------------------------------
% 2.70/1.96 % (1955)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_1611 for (2995ds/31Mi)
% 2.70/1.96 % (1956)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_1611 for (2995ds/96Mi)
% 2.70/1.97 % (1954)Instruction limit reached!
% 2.70/1.97 % (1954)------------------------------
% 2.70/1.97 % (1954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.97 % (1954)Termination reason: Unknown
% 2.70/1.97 % (1954)Termination phase: Property scanning
% 2.70/1.97
% 2.70/1.97 % (1954)Memory used [KB]: 2302
% 2.70/1.97 % (1954)Time elapsed: 0.018 s
% 2.70/1.97 % (1954)Instructions burned: 62 (million)
% 2.70/1.97 % (1954)------------------------------
% 2.70/1.97 % (1954)------------------------------
% 2.70/1.97 % (1943)Instruction limit reached!
% 2.70/1.97 % (1943)------------------------------
% 2.70/1.97 % (1943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.97 % (1943)Termination reason: Unknown
% 2.70/1.97 % (1943)Termination phase: Saturation
% 2.70/1.97
% 2.70/1.97 % (1943)Memory used [KB]: 7291
% 2.70/1.97 % (1943)Time elapsed: 0.113 s
% 2.70/1.97 % (1943)Instructions burned: 449 (million)
% 2.70/1.97 % (1943)------------------------------
% 2.70/1.97 % (1943)------------------------------
% 2.70/1.97 % (1955)Instruction limit reached!
% 2.70/1.97 % (1955)------------------------------
% 2.70/1.97 % (1955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.97 % (1955)Termination reason: Unknown
% 2.70/1.97 % (1955)Termination phase: shuffling
% 2.70/1.97
% 2.70/1.97 % (1955)Memory used [KB]: 2046
% 2.70/1.97 % (1955)Time elapsed: 0.010 s
% 2.70/1.97 % (1955)Instructions burned: 33 (million)
% 2.70/1.97 % (1955)------------------------------
% 2.70/1.97 % (1955)------------------------------
% 2.70/1.98 % (1957)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_1611 for (2995ds/453Mi)
% 2.70/1.98 % (1958)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_1611 for (2995ds/71Mi)
% 2.70/1.98 % (1959)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_1611 for (2995ds/83Mi)
% 2.70/1.99 % (1956)Instruction limit reached!
% 2.70/1.99 % (1956)------------------------------
% 2.70/1.99 % (1956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.99 % (1956)Termination reason: Unknown
% 2.70/1.99 % (1956)Termination phase: Function definition elimination
% 2.70/1.99
% 2.70/1.99 % (1956)Memory used [KB]: 2430
% 2.70/1.99 % (1956)Time elapsed: 0.026 s
% 2.70/1.99 % (1956)Instructions burned: 97 (million)
% 2.70/1.99 % (1956)------------------------------
% 2.70/1.99 % (1956)------------------------------
% 2.70/2.00 % (1960)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_1611 for (2995ds/11Mi)
% 2.70/2.00 % (1958)Instruction limit reached!
% 2.70/2.00 % (1958)------------------------------
% 2.70/2.00 % (1958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.00 % (1958)Termination reason: Unknown
% 2.70/2.00 % (1958)Termination phase: Property scanning
% 2.70/2.00
% 2.70/2.00 % (1958)Memory used [KB]: 2430
% 2.70/2.00 % (1958)Time elapsed: 0.020 s
% 2.70/2.00 % (1958)Instructions burned: 72 (million)
% 2.70/2.00 % (1958)------------------------------
% 2.70/2.00 % (1958)------------------------------
% 2.70/2.00 % (1960)Instruction limit reached!
% 2.70/2.00 % (1960)------------------------------
% 2.70/2.00 % (1960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.00 % (1960)Termination reason: Unknown
% 2.70/2.00 % (1960)Termination phase: shuffling
% 2.70/2.00
% 2.70/2.00 % (1960)Memory used [KB]: 1663
% 2.70/2.00 % (1960)Time elapsed: 0.004 s
% 2.70/2.00 % (1960)Instructions burned: 11 (million)
% 2.70/2.00 % (1960)------------------------------
% 2.70/2.00 % (1960)------------------------------
% 2.70/2.00 % (1959)Instruction limit reached!
% 2.70/2.00 % (1959)------------------------------
% 2.70/2.00 % (1959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.00 % (1959)Termination reason: Unknown
% 2.70/2.00 % (1959)Termination phase: SInE selection
% 2.70/2.00
% 2.70/2.00 % (1959)Memory used [KB]: 2302
% 2.70/2.00 % (1959)Time elapsed: 0.023 s
% 2.70/2.00 % (1959)Instructions burned: 86 (million)
% 2.70/2.00 % (1959)------------------------------
% 2.70/2.00 % (1959)------------------------------
% 2.70/2.01 % (1961)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_1611 for (2995ds/41Mi)
% 2.70/2.01 % (1962)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1611 for (2995ds/6Mi)
% 2.70/2.01 % (1962)Instruction limit reached!
% 2.70/2.01 % (1962)------------------------------
% 2.70/2.01 % (1962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.01 % (1962)Termination reason: Unknown
% 2.70/2.01 % (1962)Termination phase: shuffling
% 2.70/2.01
% 2.70/2.01 % (1962)Memory used [KB]: 1535
% 2.70/2.01 % (1962)Time elapsed: 0.003 s
% 2.70/2.01 % (1962)Instructions burned: 7 (million)
% 2.70/2.01 % (1962)------------------------------
% 2.70/2.01 % (1962)------------------------------
% 2.70/2.01 % (1963)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_1611 for (2995ds/150Mi)
% 5.90/2.02 % (1961)Instruction limit reached!
% 5.90/2.02 % (1961)------------------------------
% 5.90/2.02 % (1961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.90/2.02 % (1961)Termination reason: Unknown
% 5.90/2.02 % (1961)Termination phase: Property scanning
% 5.90/2.02
% 5.90/2.02 % (1961)Memory used [KB]: 2302
% 5.90/2.02 % (1961)Time elapsed: 0.012 s
% 5.90/2.02 % (1961)Instructions burned: 42 (million)
% 5.90/2.02 % (1961)------------------------------
% 5.90/2.02 % (1961)------------------------------
% 5.90/2.02 % (1964)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_1611 for (2995ds/343Mi)
% 5.90/2.03 % (1965)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_1611 for (2995ds/109Mi)
% 5.90/2.04 % (1946)Instruction limit reached!
% 5.90/2.04 % (1946)------------------------------
% 5.90/2.04 % (1946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.90/2.04 % (1946)Termination reason: Unknown
% 5.90/2.04 % (1946)Termination phase: Saturation
% 5.90/2.04
% 5.90/2.04 % (1946)Memory used [KB]: 7931
% 5.90/2.04 % (1946)Time elapsed: 0.158 s
% 5.90/2.04 % (1946)Instructions burned: 509 (million)
% 5.90/2.04 % (1946)------------------------------
% 5.90/2.04 % (1946)------------------------------
% 5.90/2.05 % (1966)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_1611 for (2994ds/253Mi)
% 5.90/2.05 % (1963)Instruction limit reached!
% 5.90/2.05 % (1963)------------------------------
% 5.90/2.05 % (1963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.90/2.05 % (1963)Termination reason: Unknown
% 5.90/2.05 % (1963)Termination phase: Property scanning
% 5.90/2.05
% 5.90/2.05 % (1963)Memory used [KB]: 4093
% 5.90/2.05 % (1963)Time elapsed: 0.043 s
% 5.90/2.05 % (1963)Instructions burned: 151 (million)
% 5.90/2.05 % (1963)------------------------------
% 5.90/2.05 % (1963)------------------------------
% 5.90/2.06 % (1965)Instruction limit reached!
% 5.90/2.06 % (1965)------------------------------
% 5.90/2.06 % (1965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.90/2.06 % (1965)Termination reason: Unknown
% 5.90/2.06 % (1965)Termination phase: Function definition elimination
% 5.90/2.06
% 5.90/2.06 % (1965)Memory used [KB]: 2430
% 5.90/2.06 % (1965)Time elapsed: 0.030 s
% 5.90/2.06 % (1965)Instructions burned: 112 (million)
% 5.90/2.06 % (1965)------------------------------
% 5.90/2.06 % (1965)------------------------------
% 5.90/2.06 % (1967)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_1611 for (2994ds/140Mi)
% 5.90/2.07 % (1968)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_1611 for (2994ds/614Mi)
% 5.90/2.09 % (1957)Instruction limit reached!
% 5.90/2.09 % (1957)------------------------------
% 5.90/2.09 % (1957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.90/2.09 % (1957)Termination reason: Unknown
% 5.90/2.09 % (1957)Termination phase: Saturation
% 5.90/2.09
% 5.90/2.09 % (1957)Memory used [KB]: 7419
% 5.90/2.09 % (1957)Time elapsed: 0.119 s
% 5.90/2.09 % (1957)Instructions burned: 456 (million)
% 5.90/2.09 % (1957)------------------------------
% 5.90/2.09 % (1957)------------------------------
% 5.90/2.10 % (1967)Instruction limit reached!
% 5.90/2.10 % (1967)------------------------------
% 5.90/2.10 % (1967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.90/2.10 % (1967)Termination reason: Unknown
% 5.90/2.10 % (1967)Termination phase: Saturation
% 5.90/2.10
% 5.90/2.10 % (1967)Memory used [KB]: 7036
% 5.90/2.10 % (1967)Time elapsed: 0.039 s
% 5.90/2.10 % (1967)Instructions burned: 143 (million)
% 5.90/2.10 % (1967)------------------------------
% 5.90/2.10 % (1967)------------------------------
% 5.90/2.10 % (1969)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_1611 for (2994ds/202Mi)
% 5.90/2.11 % (1953)Instruction limit reached!
% 5.90/2.11 % (1953)------------------------------
% 5.90/2.11 % (1953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.90/2.11 % (1953)Termination reason: Unknown
% 5.90/2.11 % (1953)Termination phase: Saturation
% 5.90/2.11
% 5.90/2.11 % (1953)Memory used [KB]: 2814
% 5.90/2.11 % (1953)Time elapsed: 0.163 s
% 5.90/2.11 % (1953)Instructions burned: 433 (million)
% 5.90/2.11 % (1953)------------------------------
% 5.90/2.11 % (1953)------------------------------
% 5.90/2.11 % (1970)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_1611 for (2994ds/339Mi)
% 6.40/2.11 % (1964)Instruction limit reached!
% 6.40/2.11 % (1964)------------------------------
% 6.40/2.11 % (1964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.11 % (1964)Termination reason: Unknown
% 6.40/2.11 % (1964)Termination phase: Saturation
% 6.40/2.11
% 6.40/2.11 % (1964)Memory used [KB]: 8443
% 6.40/2.11 % (1964)Time elapsed: 0.095 s
% 6.40/2.11 % (1964)Instructions burned: 343 (million)
% 6.40/2.11 % (1964)------------------------------
% 6.40/2.11 % (1964)------------------------------
% 6.40/2.12 % (1971)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_1611 for (2994ds/283Mi)
% 6.40/2.12 % (1972)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_1611 for (2994ds/134Mi)
% 6.40/2.13 % (1966)Instruction limit reached!
% 6.40/2.13 % (1966)------------------------------
% 6.40/2.13 % (1966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.13 % (1966)Termination reason: Unknown
% 6.40/2.13 % (1966)Termination phase: Saturation
% 6.40/2.13
% 6.40/2.13 % (1966)Memory used [KB]: 9338
% 6.40/2.13 % (1966)Time elapsed: 0.077 s
% 6.40/2.13 % (1966)Instructions burned: 254 (million)
% 6.40/2.13 % (1966)------------------------------
% 6.40/2.13 % (1966)------------------------------
% 6.40/2.13 % (1973)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_1611 for (2994ds/298Mi)
% 6.40/2.16 % (1972)Instruction limit reached!
% 6.40/2.16 % (1972)------------------------------
% 6.40/2.16 % (1972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.16 % (1972)Termination reason: Unknown
% 6.40/2.16 % (1972)Termination phase: Saturation
% 6.40/2.16
% 6.40/2.16 % (1972)Memory used [KB]: 7036
% 6.40/2.16 % (1972)Time elapsed: 0.036 s
% 6.40/2.16 % (1972)Instructions burned: 137 (million)
% 6.40/2.16 % (1972)------------------------------
% 6.40/2.16 % (1972)------------------------------
% 6.40/2.16 % (1969)Instruction limit reached!
% 6.40/2.16 % (1969)------------------------------
% 6.40/2.16 % (1969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.16 % (1969)Termination reason: Unknown
% 6.40/2.16 % (1969)Termination phase: Saturation
% 6.40/2.16
% 6.40/2.16 % (1969)Memory used [KB]: 4733
% 6.40/2.16 % (1969)Time elapsed: 0.058 s
% 6.40/2.16 % (1969)Instructions burned: 204 (million)
% 6.40/2.16 % (1969)------------------------------
% 6.40/2.16 % (1969)------------------------------
% 6.40/2.17 % (1974)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_1611 for (2993ds/192Mi)
% 6.40/2.17 % (1975)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_1611 for (2993ds/258Mi)
% 6.40/2.20 % (1971)Instruction limit reached!
% 6.40/2.20 % (1971)------------------------------
% 6.40/2.20 % (1971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.20 % (1971)Termination reason: Unknown
% 6.40/2.20 % (1971)Termination phase: Saturation
% 6.40/2.20
% 6.40/2.20 % (1971)Memory used [KB]: 7291
% 6.40/2.20 % (1971)Time elapsed: 0.079 s
% 6.40/2.20 % (1971)Instructions burned: 284 (million)
% 6.40/2.20 % (1971)------------------------------
% 6.40/2.20 % (1971)------------------------------
% 6.78/2.20 % (1970)Instruction limit reached!
% 6.78/2.20 % (1970)------------------------------
% 6.78/2.20 % (1970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.20 % (1970)Termination reason: Unknown
% 6.78/2.20 % (1970)Termination phase: Saturation
% 6.78/2.20
% 6.78/2.20 % (1970)Memory used [KB]: 7803
% 6.78/2.20 % (1970)Time elapsed: 0.093 s
% 6.78/2.20 % (1970)Instructions burned: 342 (million)
% 6.78/2.20 % (1970)------------------------------
% 6.78/2.20 % (1970)------------------------------
% 6.78/2.21 % (1976)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_1611 for (2993ds/90Mi)
% 6.78/2.21 % (1973)Instruction limit reached!
% 6.78/2.21 % (1973)------------------------------
% 6.78/2.21 % (1973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.21 % (1973)Termination reason: Unknown
% 6.78/2.21 % (1973)Termination phase: Saturation
% 6.78/2.21
% 6.78/2.21 % (1973)Memory used [KB]: 7291
% 6.78/2.21 % (1973)Time elapsed: 0.076 s
% 6.78/2.21 % (1973)Instructions burned: 299 (million)
% 6.78/2.21 % (1973)------------------------------
% 6.78/2.21 % (1973)------------------------------
% 6.78/2.21 % (1977)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_1611 for (2993ds/231Mi)
% 6.78/2.22 % (1974)Instruction limit reached!
% 6.78/2.22 % (1974)------------------------------
% 6.78/2.22 % (1974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.22 % (1974)Termination reason: Unknown
% 6.78/2.22 % (1974)Termination phase: Saturation
% 6.78/2.22
% 6.78/2.22 % (1974)Memory used [KB]: 7547
% 6.78/2.22 % (1974)Time elapsed: 0.052 s
% 6.78/2.22 % (1974)Instructions burned: 192 (million)
% 6.78/2.22 % (1974)------------------------------
% 6.78/2.22 % (1974)------------------------------
% 6.78/2.22 % (1978)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_1611 for (2993ds/458Mi)
% 6.78/2.23 % (1979)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_1611 for (2993ds/31Mi)
% 6.78/2.23 % (1976)Instruction limit reached!
% 6.78/2.23 % (1976)------------------------------
% 6.78/2.23 % (1976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.23 % (1976)Termination reason: Unknown
% 6.78/2.23 % (1976)Termination phase: Property scanning
% 6.78/2.23
% 6.78/2.23 % (1976)Memory used [KB]: 2430
% 6.78/2.23 % (1976)Time elapsed: 0.026 s
% 6.78/2.23 % (1976)Instructions burned: 90 (million)
% 6.78/2.23 % (1976)------------------------------
% 6.78/2.23 % (1976)------------------------------
% 6.78/2.24 % (1979)Instruction limit reached!
% 6.78/2.24 % (1979)------------------------------
% 6.78/2.24 % (1979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.24 % (1979)Termination reason: Unknown
% 6.78/2.24 % (1979)Termination phase: shuffling
% 6.78/2.24
% 6.78/2.24 % (1979)Memory used [KB]: 2046
% 6.78/2.24 % (1979)Time elapsed: 0.010 s
% 6.78/2.24 % (1979)Instructions burned: 33 (million)
% 6.78/2.24 % (1979)------------------------------
% 6.78/2.24 % (1979)------------------------------
% 6.78/2.24 % (1975)Instruction limit reached!
% 6.78/2.24 % (1975)------------------------------
% 6.78/2.24 % (1975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.24 % (1975)Termination reason: Unknown
% 6.78/2.24 % (1975)Termination phase: Saturation
% 6.78/2.24
% 6.78/2.24 % (1975)Memory used [KB]: 7931
% 6.78/2.24 % (1975)Time elapsed: 0.069 s
% 6.78/2.24 % (1975)Instructions burned: 259 (million)
% 6.78/2.24 % (1975)------------------------------
% 6.78/2.24 % (1975)------------------------------
% 6.78/2.24 % (1980)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_1611 for (2992ds/297Mi)
% 6.78/2.25 % (1981)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_1611 for (2992ds/987Mi)
% 6.78/2.25 % (1982)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_1611 for (2992ds/182Mi)
% 6.78/2.25 % (1968)Instruction limit reached!
% 6.78/2.25 % (1968)------------------------------
% 6.78/2.25 % (1968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.25 % (1968)Termination reason: Unknown
% 6.78/2.25 % (1968)Termination phase: Saturation
% 6.78/2.25
% 6.78/2.25 % (1968)Memory used [KB]: 9466
% 6.78/2.25 % (1968)Time elapsed: 0.184 s
% 6.78/2.25 % (1968)Instructions burned: 616 (million)
% 6.78/2.25 % (1968)------------------------------
% 6.78/2.25 % (1968)------------------------------
% 6.78/2.26 % (1983)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_1611 for (2992ds/182Mi)
% 6.78/2.26 % (1950)Instruction limit reached!
% 6.78/2.26 % (1950)------------------------------
% 6.78/2.26 % (1950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.26 % (1950)Termination reason: Unknown
% 6.78/2.26 % (1950)Termination phase: Saturation
% 6.78/2.26
% 6.78/2.26 % (1950)Memory used [KB]: 11129
% 6.78/2.26 % (1950)Time elapsed: 0.348 s
% 6.78/2.26 % (1950)Instructions burned: 1088 (million)
% 6.78/2.26 % (1950)------------------------------
% 6.78/2.26 % (1950)------------------------------
% 6.78/2.27 % (1984)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_1611 for (2992ds/154Mi)
% 6.78/2.27 % (1977)Instruction limit reached!
% 6.78/2.27 % (1977)------------------------------
% 6.78/2.27 % (1977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.27 % (1977)Termination reason: Unknown
% 6.78/2.27 % (1977)Termination phase: Saturation
% 6.78/2.27
% 6.78/2.27 % (1977)Memory used [KB]: 10490
% 6.78/2.27 % (1977)Time elapsed: 0.064 s
% 6.78/2.27 % (1977)Instructions burned: 232 (million)
% 6.78/2.27 % (1977)------------------------------
% 6.78/2.27 % (1977)------------------------------
% 6.78/2.28 % (1985)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_1611 for (2992ds/79Mi)
% 7.59/2.30 % (1982)Instruction limit reached!
% 7.59/2.30 % (1982)------------------------------
% 7.59/2.30 % (1982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.30 % (1982)Termination reason: Unknown
% 7.59/2.30 % (1982)Termination phase: Saturation
% 7.59/2.30
% 7.59/2.30 % (1982)Memory used [KB]: 7547
% 7.59/2.30 % (1982)Time elapsed: 0.050 s
% 7.59/2.30 % (1982)Instructions burned: 184 (million)
% 7.59/2.30 % (1982)------------------------------
% 7.59/2.30 % (1982)------------------------------
% 7.59/2.30 % (1985)Instruction limit reached!
% 7.59/2.30 % (1985)------------------------------
% 7.59/2.30 % (1985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.30 % (1985)Termination reason: Unknown
% 7.59/2.30 % (1985)Termination phase: Property scanning
% 7.59/2.30
% 7.59/2.31 % (1985)Memory used [KB]: 2430
% 7.59/2.31 % (1985)Time elapsed: 0.022 s
% 7.59/2.31 % (1985)Instructions burned: 80 (million)
% 7.59/2.31 % (1985)------------------------------
% 7.59/2.31 % (1985)------------------------------
% 7.59/2.31 % (1986)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_1611 for (2992ds/216Mi)
% 7.59/2.31 % (1984)Instruction limit reached!
% 7.59/2.31 % (1984)------------------------------
% 7.59/2.31 % (1984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.31 % (1984)Termination reason: Unknown
% 7.59/2.31 % (1984)Termination phase: Saturation
% 7.59/2.31
% 7.59/2.31 % (1984)Memory used [KB]: 7036
% 7.59/2.31 % (1984)Time elapsed: 0.040 s
% 7.59/2.31 % (1984)Instructions burned: 155 (million)
% 7.59/2.31 % (1984)------------------------------
% 7.59/2.31 % (1984)------------------------------
% 7.59/2.31 % (1983)Instruction limit reached!
% 7.59/2.31 % (1983)------------------------------
% 7.59/2.31 % (1983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.31 % (1983)Termination reason: Unknown
% 7.59/2.31 % (1983)Termination phase: Saturation
% 7.59/2.31
% 7.59/2.31 % (1983)Memory used [KB]: 8443
% 7.59/2.31 % (1983)Time elapsed: 0.052 s
% 7.59/2.31 % (1983)Instructions burned: 183 (million)
% 7.59/2.31 % (1983)------------------------------
% 7.59/2.31 % (1983)------------------------------
% 7.59/2.31 % (1987)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_1611 for (2992ds/114Mi)
% 7.59/2.32 % (1988)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_1611 for (2992ds/922Mi)
% 7.59/2.32 % (1989)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_1611 for (2992ds/182Mi)
% 7.59/2.32 % (1980)Instruction limit reached!
% 7.59/2.32 % (1980)------------------------------
% 7.59/2.32 % (1980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.32 % (1980)Termination reason: Unknown
% 7.59/2.32 % (1980)Termination phase: Saturation
% 7.59/2.32
% 7.59/2.32 % (1980)Memory used [KB]: 7291
% 7.59/2.32 % (1980)Time elapsed: 0.082 s
% 7.59/2.32 % (1980)Instructions burned: 297 (million)
% 7.59/2.32 % (1980)------------------------------
% 7.59/2.32 % (1980)------------------------------
% 7.59/2.33 % (1990)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_1611 for (2992ds/164Mi)
% 7.59/2.34 % (1987)Instruction limit reached!
% 7.59/2.34 % (1987)------------------------------
% 7.59/2.34 % (1987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.34 % (1987)Termination reason: Unknown
% 7.59/2.34 % (1987)Termination phase: Property scanning
% 7.59/2.34
% 7.59/2.34 % (1987)Memory used [KB]: 2558
% 7.59/2.34 % (1987)Time elapsed: 0.030 s
% 7.59/2.34 % (1987)Instructions burned: 114 (million)
% 7.59/2.34 % (1987)------------------------------
% 7.59/2.34 % (1987)------------------------------
% 7.59/2.35 % (1978)Instruction limit reached!
% 7.59/2.35 % (1978)------------------------------
% 7.59/2.35 % (1978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.35 % (1978)Termination reason: Unknown
% 7.59/2.35 % (1978)Termination phase: Saturation
% 7.59/2.35
% 7.59/2.35 % (1978)Memory used [KB]: 8827
% 7.59/2.35 % (1978)Time elapsed: 0.130 s
% 7.59/2.35 % (1978)Instructions burned: 458 (million)
% 7.59/2.35 % (1978)------------------------------
% 7.59/2.35 % (1978)------------------------------
% 7.59/2.35 % (1991)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_1611 for (2991ds/50Mi)
% 7.59/2.36 % (1992)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_1611 for (2991ds/368Mi)
% 7.59/2.36 % (1986)Instruction limit reached!
% 7.59/2.36 % (1986)------------------------------
% 7.59/2.36 % (1986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.36 % (1986)Termination reason: Unknown
% 7.59/2.36 % (1986)Termination phase: Saturation
% 7.59/2.36
% 7.59/2.36 % (1986)Memory used [KB]: 7291
% 7.59/2.36 % (1986)Time elapsed: 0.055 s
% 7.59/2.36 % (1986)Instructions burned: 217 (million)
% 7.59/2.36 % (1986)------------------------------
% 7.59/2.36 % (1986)------------------------------
% 7.59/2.37 % (1989)Instruction limit reached!
% 7.59/2.37 % (1989)------------------------------
% 7.59/2.37 % (1989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.37 % (1989)Termination reason: Unknown
% 7.59/2.37 % (1989)Termination phase: Saturation
% 7.59/2.37
% 7.59/2.37 % (1989)Memory used [KB]: 7291
% 7.59/2.37 % (1989)Time elapsed: 0.047 s
% 7.59/2.37 % (1989)Instructions burned: 183 (million)
% 7.59/2.37 % (1989)------------------------------
% 7.59/2.37 % (1989)------------------------------
% 7.59/2.37 % (1991)Instruction limit reached!
% 7.59/2.37 % (1991)------------------------------
% 7.59/2.37 % (1991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.37 % (1991)Termination reason: Unknown
% 7.59/2.37 % (1991)Termination phase: Property scanning
% 7.59/2.37
% 7.59/2.37 % (1991)Memory used [KB]: 2302
% 7.59/2.37 % (1991)Time elapsed: 0.015 s
% 7.59/2.37 % (1991)Instructions burned: 53 (million)
% 7.59/2.37 % (1991)------------------------------
% 7.59/2.37 % (1991)------------------------------
% 7.59/2.37 % (1993)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_1611 for (2991ds/1021Mi)
% 7.59/2.38 % (1994)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_1611 for (2991ds/267Mi)
% 7.59/2.38 % (1990)Instruction limit reached!
% 7.59/2.38 % (1990)------------------------------
% 7.59/2.38 % (1990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.38 % (1990)Termination reason: Unknown
% 7.59/2.38 % (1990)Termination phase: Saturation
% 7.59/2.38
% 7.59/2.38 % (1990)Memory used [KB]: 2558
% 7.59/2.38 % (1990)Time elapsed: 0.045 s
% 7.59/2.38 % (1990)Instructions burned: 164 (million)
% 7.59/2.38 % (1990)------------------------------
% 7.59/2.38 % (1990)------------------------------
% 7.59/2.38 % (1995)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_1611 for (2991ds/204Mi)
% 7.59/2.39 % (1996)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_1611 for (2991ds/26Mi)
% 7.59/2.40 % (1996)Instruction limit reached!
% 7.59/2.40 % (1996)------------------------------
% 7.59/2.40 % (1996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.40 % (1996)Termination reason: Unknown
% 7.59/2.40 % (1996)Termination phase: shuffling
% 7.59/2.40
% 7.59/2.40 % (1996)Memory used [KB]: 1918
% 7.59/2.40 % (1996)Time elapsed: 0.009 s
% 7.59/2.40 % (1996)Instructions burned: 28 (million)
% 7.59/2.40 % (1996)------------------------------
% 7.59/2.40 % (1996)------------------------------
% 8.27/2.41 % (1997)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_1611 for (2991ds/53Mi)
% 8.27/2.42 % (1997)Instruction limit reached!
% 8.27/2.42 % (1997)------------------------------
% 8.27/2.42 % (1997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.42 % (1997)Termination reason: Unknown
% 8.27/2.42 % (1997)Termination phase: Property scanning
% 8.27/2.42
% 8.27/2.42 % (1997)Memory used [KB]: 2302
% 8.27/2.42 % (1997)Time elapsed: 0.016 s
% 8.27/2.42 % (1997)Instructions burned: 53 (million)
% 8.27/2.42 % (1997)------------------------------
% 8.27/2.42 % (1997)------------------------------
% 8.27/2.43 % (1995)Instruction limit reached!
% 8.27/2.43 % (1995)------------------------------
% 8.27/2.43 % (1995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.43 % (1995)Termination reason: Unknown
% 8.27/2.43 % (1995)Termination phase: Saturation
% 8.27/2.43
% 8.27/2.43 % (1995)Memory used [KB]: 7547
% 8.27/2.43 % (1995)Time elapsed: 0.055 s
% 8.27/2.43 % (1995)Instructions burned: 206 (million)
% 8.27/2.43 % (1995)------------------------------
% 8.27/2.43 % (1995)------------------------------
% 8.27/2.43 % (1998)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_1611 for (2991ds/4436Mi)
% 8.27/2.44 % (1999)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_1611 for (2991ds/1539Mi)
% 8.27/2.44 % (1994)Instruction limit reached!
% 8.27/2.44 % (1994)------------------------------
% 8.27/2.44 % (1994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.44 % (1994)Termination reason: Unknown
% 8.27/2.44 % (1994)Termination phase: Saturation
% 8.27/2.44
% 8.27/2.44 % (1994)Memory used [KB]: 7291
% 8.27/2.44 % (1994)Time elapsed: 0.070 s
% 8.27/2.44 % (1994)Instructions burned: 269 (million)
% 8.27/2.44 % (1994)------------------------------
% 8.27/2.44 % (1994)------------------------------
% 8.27/2.45 % (2000)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_1611 for (2990ds/408Mi)
% 8.27/2.46 % (1992)Instruction limit reached!
% 8.27/2.46 % (1992)------------------------------
% 8.27/2.46 % (1992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.46 % (1992)Termination reason: Unknown
% 8.27/2.46 % (1992)Termination phase: Saturation
% 8.27/2.46
% 8.27/2.46 % (1992)Memory used [KB]: 8571
% 8.27/2.46 % (1992)Time elapsed: 0.106 s
% 8.27/2.46 % (1992)Instructions burned: 370 (million)
% 8.27/2.46 % (1992)------------------------------
% 8.27/2.46 % (1992)------------------------------
% 8.27/2.47 % (2001)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_1611 for (2990ds/5205Mi)
% 8.55/2.50 % (1981)Instruction limit reached!
% 8.55/2.50 % (1981)------------------------------
% 8.55/2.50 % (1981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.50 % (1981)Termination reason: Unknown
% 8.55/2.50 % (1981)Termination phase: Saturation
% 8.55/2.50
% 8.55/2.50 % (1981)Memory used [KB]: 13560
% 8.55/2.50 % (1981)Time elapsed: 0.255 s
% 8.55/2.50 % (1981)Instructions burned: 987 (million)
% 8.55/2.50 % (1981)------------------------------
% 8.55/2.50 % (1981)------------------------------
% 8.55/2.51 % (2002)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_1611 for (2990ds/1913Mi)
% 8.55/2.58 % (2000)Instruction limit reached!
% 8.55/2.58 % (2000)------------------------------
% 8.55/2.58 % (2000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.58 % (2000)Termination reason: Unknown
% 8.55/2.58 % (2000)Termination phase: Saturation
% 8.55/2.58
% 8.55/2.58 % (2000)Memory used [KB]: 10490
% 8.55/2.58 % (2000)Time elapsed: 0.127 s
% 8.55/2.58 % (2000)Instructions burned: 408 (million)
% 8.55/2.58 % (2000)------------------------------
% 8.55/2.58 % (2000)------------------------------
% 8.55/2.59 % (2003)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_1611 for (2989ds/4350Mi)
% 8.96/2.61 % (1988)Instruction limit reached!
% 8.96/2.61 % (1988)------------------------------
% 8.96/2.61 % (1988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.61 % (1988)Termination reason: Unknown
% 8.96/2.61 % (1988)Termination phase: Saturation
% 8.96/2.61
% 8.96/2.61 % (1988)Memory used [KB]: 10618
% 8.96/2.61 % (1988)Time elapsed: 0.289 s
% 8.96/2.61 % (1988)Instructions burned: 924 (million)
% 8.96/2.61 % (1988)------------------------------
% 8.96/2.61 % (1988)------------------------------
% 8.96/2.62 % (2004)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_1611 for (2989ds/68Mi)
% 8.96/2.64 % (2004)Instruction limit reached!
% 8.96/2.64 % (2004)------------------------------
% 8.96/2.64 % (2004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.64 % (2004)Termination reason: Unknown
% 8.96/2.64 % (2004)Termination phase: SInE selection
% 8.96/2.64
% 8.96/2.64 % (2004)Memory used [KB]: 2302
% 8.96/2.64 % (2004)Time elapsed: 0.020 s
% 8.96/2.64 % (2004)Instructions burned: 72 (million)
% 8.96/2.64 % (2004)------------------------------
% 8.96/2.64 % (2004)------------------------------
% 8.96/2.64 % (2005)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_1611 for (2989ds/358Mi)
% 8.96/2.69 % (1993)Instruction limit reached!
% 8.96/2.69 % (1993)------------------------------
% 8.96/2.69 % (1993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.69 % (1993)Termination reason: Unknown
% 8.96/2.69 % (1993)Termination phase: Saturation
% 8.96/2.69
% 8.96/2.69 % (1993)Memory used [KB]: 11897
% 8.96/2.69 % (1993)Time elapsed: 0.319 s
% 8.96/2.69 % (1993)Instructions burned: 1022 (million)
% 8.96/2.69 % (1993)------------------------------
% 8.96/2.69 % (1993)------------------------------
% 9.62/2.70 % (2006)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_1611 for (2988ds/31Mi)
% 9.62/2.71 % (2006)Instruction limit reached!
% 9.62/2.71 % (2006)------------------------------
% 9.62/2.71 % (2006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.62/2.71 % (2006)Termination reason: Unknown
% 9.62/2.71 % (2006)Termination phase: shuffling
% 9.62/2.71
% 9.62/2.71 % (2006)Memory used [KB]: 2046
% 9.62/2.71 % (2006)Time elapsed: 0.010 s
% 9.62/2.71 % (2006)Instructions burned: 32 (million)
% 9.62/2.71 % (2006)------------------------------
% 9.62/2.71 % (2006)------------------------------
% 9.62/2.72 % (2007)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_1611 for (2988ds/279Mi)
% 9.62/2.74 % (2005)Instruction limit reached!
% 9.62/2.74 % (2005)------------------------------
% 9.62/2.74 % (2005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.62/2.74 % (2005)Termination reason: Unknown
% 9.62/2.74 % (2005)Termination phase: Saturation
% 9.62/2.74
% 9.62/2.74 % (2005)Memory used [KB]: 8443
% 9.62/2.74 % (2005)Time elapsed: 0.098 s
% 9.62/2.74 % (2005)Instructions burned: 360 (million)
% 9.62/2.74 % (2005)------------------------------
% 9.62/2.74 % (2005)------------------------------
% 9.62/2.75 % (2008)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_1611 for (2987ds/258Mi)
% 9.62/2.79 % (2007)Instruction limit reached!
% 9.62/2.79 % (2007)------------------------------
% 9.62/2.79 % (2007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.62/2.79 % (2007)Termination reason: Unknown
% 9.62/2.79 % (2007)Termination phase: Saturation
% 9.62/2.79
% 9.62/2.79 % (2007)Memory used [KB]: 7291
% 9.62/2.79 % (2007)Time elapsed: 0.071 s
% 9.62/2.79 % (2007)Instructions burned: 280 (million)
% 9.62/2.79 % (2007)------------------------------
% 9.62/2.79 % (2007)------------------------------
% 9.82/2.80 % (2009)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_1611 for (2987ds/26Mi)
% 9.82/2.80 % (2009)Instruction limit reached!
% 9.82/2.80 % (2009)------------------------------
% 9.82/2.80 % (2009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.80 % (2009)Termination reason: Unknown
% 9.82/2.80 % (2009)Termination phase: shuffling
% 9.82/2.80
% 9.82/2.80 % (2009)Memory used [KB]: 1918
% 9.82/2.80 % (2009)Time elapsed: 0.008 s
% 9.82/2.80 % (2009)Instructions burned: 26 (million)
% 9.82/2.80 % (2009)------------------------------
% 9.82/2.80 % (2009)------------------------------
% 9.82/2.81 % (2010)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_1611 for (2987ds/995Mi)
% 9.82/2.82 % (2008)Instruction limit reached!
% 9.82/2.82 % (2008)------------------------------
% 9.82/2.82 % (2008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.82 % (2008)Termination reason: Unknown
% 9.82/2.82 % (2008)Termination phase: Saturation
% 9.82/2.82
% 9.82/2.82 % (2008)Memory used [KB]: 8443
% 9.82/2.82 % (2008)Time elapsed: 0.070 s
% 9.82/2.82 % (2008)Instructions burned: 260 (million)
% 9.82/2.82 % (2008)------------------------------
% 9.82/2.82 % (2008)------------------------------
% 9.82/2.83 % (2011)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_1611 for (2987ds/373Mi)
% 9.91/2.92 % (1999)Instruction limit reached!
% 9.91/2.92 % (1999)------------------------------
% 9.91/2.92 % (1999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.92 % (1999)Termination reason: Unknown
% 9.91/2.92 % (1999)Termination phase: Saturation
% 9.91/2.92
% 9.91/2.92 % (1999)Memory used [KB]: 10234
% 9.91/2.92 % (1999)Time elapsed: 0.480 s
% 9.91/2.92 % (1999)Instructions burned: 1540 (million)
% 9.91/2.92 % (1999)------------------------------
% 9.91/2.92 % (1999)------------------------------
% 9.91/2.93 % (2012)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_1611 for (2986ds/253Mi)
% 9.91/2.94 % (2011)Instruction limit reached!
% 9.91/2.94 % (2011)------------------------------
% 9.91/2.94 % (2011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.94 % (2011)Termination reason: Unknown
% 9.91/2.94 % (2011)Termination phase: Saturation
% 9.91/2.94
% 9.91/2.94 % (2011)Memory used [KB]: 8443
% 9.91/2.94 % (2011)Time elapsed: 0.110 s
% 9.91/2.94 % (2011)Instructions burned: 374 (million)
% 9.91/2.94 % (2011)------------------------------
% 9.91/2.94 % (2011)------------------------------
% 9.91/2.95 % (2013)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_1611 for (2986ds/832Mi)
% 9.91/2.99 % (2012)Instruction limit reached!
% 9.91/2.99 % (2012)------------------------------
% 9.91/2.99 % (2012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.91/2.99 % (2012)Termination reason: Unknown
% 9.91/2.99 % (2012)Termination phase: Saturation
% 9.91/2.99
% 9.91/2.99 % (2012)Memory used [KB]: 7291
% 9.91/2.99 % (2012)Time elapsed: 0.065 s
% 9.91/2.99 % (2012)Instructions burned: 255 (million)
% 9.91/2.99 % (2012)------------------------------
% 9.91/2.99 % (2012)------------------------------
% 9.91/3.00 % (2014)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_1611 for (2985ds/668Mi)
% 12.96/3.07 % (2010)Instruction limit reached!
% 12.96/3.07 % (2010)------------------------------
% 12.96/3.07 % (2010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.07 % (2010)Termination reason: Unknown
% 12.96/3.07 % (2010)Termination phase: Saturation
% 12.96/3.07
% 12.96/3.07 % (2010)Memory used [KB]: 13048
% 12.96/3.07 % (2010)Time elapsed: 0.256 s
% 12.96/3.07 % (2010)Instructions burned: 997 (million)
% 12.96/3.07 % (2010)------------------------------
% 12.96/3.07 % (2010)------------------------------
% 12.96/3.08 % (2015)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_1611 for (2984ds/40Mi)
% 12.96/3.09 % (2015)Instruction limit reached!
% 12.96/3.09 % (2015)------------------------------
% 12.96/3.09 % (2015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.09 % (2015)Termination reason: Unknown
% 12.96/3.09 % (2015)Termination phase: Property scanning
% 12.96/3.09
% 12.96/3.09 % (2015)Memory used [KB]: 2302
% 12.96/3.09 % (2015)Time elapsed: 0.013 s
% 12.96/3.09 % (2015)Instructions burned: 43 (million)
% 12.96/3.09 % (2015)------------------------------
% 12.96/3.09 % (2015)------------------------------
% 12.96/3.10 % (2002)Instruction limit reached!
% 12.96/3.10 % (2002)------------------------------
% 12.96/3.10 % (2002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.10 % (2002)Termination reason: Unknown
% 12.96/3.10 % (2002)Termination phase: Saturation
% 12.96/3.10
% 12.96/3.10 % (2002)Memory used [KB]: 5117
% 12.96/3.10 % (2002)Time elapsed: 0.589 s
% 12.96/3.10 % (2002)Instructions burned: 1915 (million)
% 12.96/3.10 % (2002)------------------------------
% 12.96/3.10 % (2002)------------------------------
% 12.96/3.10 % (2016)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_1611 for (2984ds/294Mi)
% 12.96/3.11 % (2017)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_1611 for (2984ds/187Mi)
% 13.66/3.16 % (2017)Instruction limit reached!
% 13.66/3.16 % (2017)------------------------------
% 13.66/3.16 % (2017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.66/3.16 % (2017)Termination reason: Unknown
% 13.66/3.16 % (2017)Termination phase: Saturation
% 13.66/3.16
% 13.66/3.16 % (2017)Memory used [KB]: 7547
% 13.66/3.16 % (2017)Time elapsed: 0.050 s
% 13.66/3.16 % (2017)Instructions burned: 187 (million)
% 13.66/3.16 % (2017)------------------------------
% 13.66/3.16 % (2017)------------------------------
% 13.66/3.17 % (2018)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_1611 for (2983ds/371Mi)
% 13.66/3.17 % (2014)Instruction limit reached!
% 13.66/3.17 % (2014)------------------------------
% 13.66/3.17 % (2014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.66/3.17 % (2014)Termination reason: Unknown
% 13.66/3.17 % (2014)Termination phase: Saturation
% 13.66/3.17
% 13.66/3.17 % (2014)Memory used [KB]: 17910
% 13.66/3.17 % (2014)Time elapsed: 0.192 s
% 13.66/3.17 % (2014)Instructions burned: 668 (million)
% 13.66/3.17 % (2014)------------------------------
% 13.66/3.17 % (2014)------------------------------
% 13.66/3.17 % (2016)Instruction limit reached!
% 13.66/3.17 % (2016)------------------------------
% 13.66/3.17 % (2016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.66/3.17 % (2016)Termination reason: Unknown
% 13.66/3.17 % (2016)Termination phase: Saturation
% 13.66/3.17
% 13.66/3.17 % (2016)Memory used [KB]: 7291
% 13.66/3.17 % (2016)Time elapsed: 0.075 s
% 13.66/3.17 % (2016)Instructions burned: 295 (million)
% 13.66/3.17 % (2016)------------------------------
% 13.66/3.17 % (2016)------------------------------
% 13.66/3.18 % (2020)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_1611 for (2983ds/70Mi)
% 13.66/3.19 % (2019)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_1611 for (2983ds/1827Mi)
% 14.15/3.20 % (2020)Instruction limit reached!
% 14.15/3.20 % (2020)------------------------------
% 14.15/3.20 % (2020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.15/3.20 % (2020)Termination reason: Unknown
% 14.15/3.20 % (2020)Termination phase: Property scanning
% 14.15/3.20
% 14.15/3.20 % (2020)Memory used [KB]: 2302
% 14.15/3.20 % (2020)Time elapsed: 0.019 s
% 14.15/3.20 % (2020)Instructions burned: 70 (million)
% 14.15/3.20 % (2020)------------------------------
% 14.15/3.20 % (2020)------------------------------
% 14.15/3.21 % (2013)Instruction limit reached!
% 14.15/3.21 % (2013)------------------------------
% 14.15/3.21 % (2013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.15/3.21 % (2013)Termination reason: Unknown
% 14.15/3.21 % (2013)Termination phase: Saturation
% 14.15/3.21
% 14.15/3.21 % (2013)Memory used [KB]: 10490
% 14.15/3.21 % (2013)Time elapsed: 0.279 s
% 14.15/3.21 % (2013)Instructions burned: 833 (million)
% 14.15/3.21 % (2013)------------------------------
% 14.15/3.21 % (2013)------------------------------
% 14.15/3.21 % (2021)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_1611 for (2983ds/316Mi)
% 14.15/3.22 % (2022)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_1611 for (2983ds/932Mi)
% 14.15/3.27 % (2018)Instruction limit reached!
% 14.15/3.27 % (2018)------------------------------
% 14.15/3.27 % (2018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.15/3.27 % (2018)Termination reason: Unknown
% 14.15/3.27 % (2018)Termination phase: Saturation
% 14.15/3.27
% 14.15/3.27 % (2018)Memory used [KB]: 8699
% 14.15/3.27 % (2018)Time elapsed: 0.104 s
% 14.15/3.27 % (2018)Instructions burned: 373 (million)
% 14.15/3.27 % (2018)------------------------------
% 14.15/3.27 % (2018)------------------------------
% 14.15/3.28 % (2023)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_1611 for (2982ds/4714Mi)
% 14.15/3.29 % (2021)Instruction limit reached!
% 14.15/3.29 % (2021)------------------------------
% 14.15/3.29 % (2021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.15/3.29 % (2021)Termination reason: Unknown
% 14.15/3.29 % (2021)Termination phase: Saturation
% 14.15/3.29
% 14.15/3.29 % (2021)Memory used [KB]: 7291
% 14.15/3.29 % (2021)Time elapsed: 0.082 s
% 14.15/3.29 % (2021)Instructions burned: 319 (million)
% 14.15/3.29 % (2021)------------------------------
% 14.15/3.29 % (2021)------------------------------
% 14.70/3.30 % (2024)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_1611 for (2982ds/8250Mi)
% 15.00/3.45 % (2022)Instruction limit reached!
% 15.00/3.45 % (2022)------------------------------
% 15.00/3.45 % (2022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.00/3.45 % (2022)Termination reason: Unknown
% 15.00/3.45 % (2022)Termination phase: Saturation
% 15.00/3.45
% 15.00/3.45 % (2022)Memory used [KB]: 14072
% 15.00/3.45 % (2022)Time elapsed: 0.238 s
% 15.00/3.45 % (2022)Instructions burned: 932 (million)
% 15.00/3.45 % (2022)------------------------------
% 15.00/3.45 % (2022)------------------------------
% 15.00/3.46 % (2025)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_1611 for (2980ds/770Mi)
% 15.87/3.67 % (2025)Instruction limit reached!
% 15.87/3.67 % (2025)------------------------------
% 15.87/3.67 % (2025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.87/3.67 % (2025)Termination reason: Unknown
% 15.87/3.67 % (2025)Termination phase: Saturation
% 15.87/3.67
% 15.87/3.67 % (2025)Memory used [KB]: 7547
% 15.87/3.67 % (2025)Time elapsed: 0.212 s
% 15.87/3.67 % (2025)Instructions burned: 771 (million)
% 15.87/3.67 % (2025)------------------------------
% 15.87/3.67 % (2025)------------------------------
% 15.87/3.68 % (2026)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_1611 for (2978ds/794Mi)
% 16.38/3.78 % (2001)Instruction limit reached!
% 16.38/3.78 % (2001)------------------------------
% 16.38/3.78 % (2001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.38/3.78 % (2001)Termination reason: Unknown
% 16.38/3.78 % (2001)Termination phase: Saturation
% 16.38/3.78
% 16.38/3.78 % (2001)Memory used [KB]: 13688
% 16.38/3.78 % (2001)Time elapsed: 1.308 s
% 16.38/3.78 % (2001)Instructions burned: 5209 (million)
% 16.38/3.78 % (2001)------------------------------
% 16.38/3.78 % (2001)------------------------------
% 16.38/3.79 % (2027)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_1611 for (2977ds/464Mi)
% 16.38/3.79 % (2019)Instruction limit reached!
% 16.38/3.79 % (2019)------------------------------
% 16.38/3.79 % (2019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.38/3.79 % (2019)Termination reason: Unknown
% 16.38/3.79 % (2019)Termination phase: Saturation
% 16.38/3.79
% 16.38/3.79 % (2019)Memory used [KB]: 19445
% 16.38/3.79 % (2019)Time elapsed: 0.604 s
% 16.38/3.79 % (2019)Instructions burned: 1828 (million)
% 16.38/3.79 % (2019)------------------------------
% 16.38/3.79 % (2019)------------------------------
% 17.31/3.80 % (2028)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_1611 for (2977ds/1376Mi)
% 17.31/3.82 % (1998)Instruction limit reached!
% 17.31/3.82 % (1998)------------------------------
% 17.31/3.82 % (1998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.31/3.82 % (1998)Termination reason: Unknown
% 17.31/3.82 % (1998)Termination phase: Saturation
% 17.31/3.82
% 17.31/3.82 % (1998)Memory used [KB]: 17142
% 17.31/3.82 % (1998)Time elapsed: 1.390 s
% 17.31/3.82 % (1998)Instructions burned: 4437 (million)
% 17.31/3.82 % (1998)------------------------------
% 17.31/3.82 % (1998)------------------------------
% 17.31/3.83 % (2029)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_1611 for (2977ds/906Mi)
% 17.45/3.92 % (2026)Instruction limit reached!
% 17.45/3.92 % (2026)------------------------------
% 17.45/3.92 % (2026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.45/3.92 % (2026)Termination reason: Unknown
% 17.45/3.92 % (2026)Termination phase: Saturation
% 17.45/3.92
% 17.45/3.92 % (2026)Memory used [KB]: 5373
% 17.45/3.92 % (2026)Time elapsed: 0.240 s
% 17.45/3.92 % (2026)Instructions burned: 795 (million)
% 17.45/3.92 % (2026)------------------------------
% 17.45/3.92 % (2026)------------------------------
% 17.45/3.92 % (2027)Instruction limit reached!
% 17.45/3.92 % (2027)------------------------------
% 17.45/3.92 % (2027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.45/3.92 % (2027)Termination reason: Unknown
% 17.45/3.92 % (2027)Termination phase: Saturation
% 17.45/3.92
% 17.45/3.92 % (2027)Memory used [KB]: 8699
% 17.45/3.92 % (2027)Time elapsed: 0.135 s
% 17.45/3.92 % (2027)Instructions burned: 466 (million)
% 17.45/3.92 % (2027)------------------------------
% 17.45/3.92 % (2027)------------------------------
% 17.45/3.93 % (2003)Instruction limit reached!
% 17.45/3.93 % (2003)------------------------------
% 17.45/3.93 % (2003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.45/3.93 % (2003)Termination reason: Unknown
% 17.45/3.93 % (2003)Termination phase: Saturation
% 17.45/3.93
% 17.45/3.93 % (2003)Memory used [KB]: 13560
% 17.45/3.93 % (2003)Time elapsed: 1.338 s
% 17.45/3.93 % (2003)Instructions burned: 4351 (million)
% 17.45/3.93 % (2003)------------------------------
% 17.45/3.93 % (2003)------------------------------
% 17.45/3.93 % (2030)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_1611 for (2976ds/434Mi)
% 17.45/3.93 % (2032)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_1611 for (2976ds/865Mi)
% 17.45/3.94 % (2033)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_1611 for (2976ds/593Mi)
% 19.91/4.05 % (2030)Refutation not found, non-redundant clauses discarded% (2030)------------------------------
% 19.91/4.05 % (2030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.05 % (2030)Termination reason: Refutation not found, non-redundant clauses discarded
% 19.91/4.05
% 19.91/4.05 % (2030)Memory used [KB]: 10106
% 19.91/4.05 % (2030)Time elapsed: 0.122 s
% 19.91/4.05 % (2030)Instructions burned: 410 (million)
% 19.91/4.05 % (2030)------------------------------
% 19.91/4.05 % (2030)------------------------------
% 19.91/4.07 % (2034)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_1611 for (2974ds/443Mi)
% 19.91/4.09 % (2033)Instruction limit reached!
% 19.91/4.09 % (2033)------------------------------
% 19.91/4.09 % (2033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.09 % (2033)Termination reason: Unknown
% 19.91/4.09 % (2033)Termination phase: Saturation
% 19.91/4.09
% 19.91/4.09 % (2033)Memory used [KB]: 7291
% 19.91/4.09 % (2033)Time elapsed: 0.150 s
% 19.91/4.09 % (2033)Instructions burned: 594 (million)
% 19.91/4.09 % (2033)------------------------------
% 19.91/4.09 % (2033)------------------------------
% 19.91/4.10 % (2035)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_1611 for (2974ds/594Mi)
% 19.91/4.11 % (2029)Instruction limit reached!
% 19.91/4.11 % (2029)------------------------------
% 19.91/4.11 % (2029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.11 % (2029)Termination reason: Unknown
% 19.91/4.11 % (2029)Termination phase: Saturation
% 19.91/4.11
% 19.91/4.11 % (2029)Memory used [KB]: 10746
% 19.91/4.11 % (2029)Time elapsed: 0.278 s
% 19.91/4.11 % (2029)Instructions burned: 906 (million)
% 19.91/4.11 % (2029)------------------------------
% 19.91/4.11 % (2029)------------------------------
% 20.59/4.12 % (2036)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_1611 for (2974ds/327Mi)
% 20.59/4.19 % (2034)Instruction limit reached!
% 20.59/4.19 % (2034)------------------------------
% 20.59/4.19 % (2034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.59/4.19 % (2034)Termination reason: Unknown
% 20.59/4.19 % (2034)Termination phase: Saturation
% 20.59/4.19
% 20.59/4.19 % (2034)Memory used [KB]: 8699
% 20.59/4.19 % (2034)Time elapsed: 0.129 s
% 20.59/4.19 % (2034)Instructions burned: 446 (million)
% 20.59/4.19 % (2034)------------------------------
% 20.59/4.19 % (2034)------------------------------
% 20.59/4.19 % (2032)Instruction limit reached!
% 20.59/4.19 % (2032)------------------------------
% 20.59/4.19 % (2032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.59/4.19 % (2032)Termination reason: Unknown
% 20.59/4.19 % (2032)Termination phase: Saturation
% 20.59/4.19
% 20.59/4.19 % (2032)Memory used [KB]: 10362
% 20.59/4.19 % (2032)Time elapsed: 0.261 s
% 20.59/4.19 % (2032)Instructions burned: 866 (million)
% 20.59/4.19 % (2032)------------------------------
% 20.59/4.19 % (2032)------------------------------
% 21.07/4.20 % (2038)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_1611 for (2973ds/5411Mi)
% 21.07/4.20 % (2039)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_1611 for (2973ds/1762Mi)
% 21.07/4.22 % (2036)Instruction limit reached!
% 21.07/4.22 % (2036)------------------------------
% 21.07/4.22 % (2036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.07/4.22 % (2036)Termination reason: Unknown
% 21.07/4.22 % (2036)Termination phase: Saturation
% 21.07/4.22
% 21.07/4.22 % (2036)Memory used [KB]: 10746
% 21.07/4.22 % (2036)Time elapsed: 0.101 s
% 21.07/4.22 % (2036)Instructions burned: 327 (million)
% 21.07/4.22 % (2036)------------------------------
% 21.07/4.22 % (2036)------------------------------
% 21.07/4.22 % (2028)Instruction limit reached!
% 21.07/4.22 % (2028)------------------------------
% 21.07/4.22 % (2028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.07/4.22 % (2028)Termination reason: Unknown
% 21.07/4.22 % (2028)Termination phase: Saturation
% 21.07/4.22
% 21.07/4.22 % (2028)Memory used [KB]: 9083
% 21.07/4.22 % (2028)Time elapsed: 0.416 s
% 21.07/4.22 % (2028)Instructions burned: 1379 (million)
% 21.07/4.22 % (2028)------------------------------
% 21.07/4.22 % (2028)------------------------------
% 21.07/4.23 % (2040)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_1611 for (2973ds/96Mi)
% 21.07/4.23 % (2041)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_1611 for (2973ds/503Mi)
% 21.07/4.25 % (2040)Instruction limit reached!
% 21.07/4.25 % (2040)------------------------------
% 21.07/4.25 % (2040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.07/4.25 % (2040)Termination reason: Unknown
% 21.07/4.25 % (2040)Termination phase: Function definition elimination
% 21.07/4.25
% 21.07/4.25 % (2040)Memory used [KB]: 2430
% 21.07/4.25 % (2040)Time elapsed: 0.026 s
% 21.07/4.25 % (2040)Instructions burned: 100 (million)
% 21.07/4.25 % (2040)------------------------------
% 21.07/4.25 % (2040)------------------------------
% 21.07/4.26 % (2042)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_1611 for (2972ds/90Mi)
% 21.07/4.27 % (2035)Instruction limit reached!
% 21.07/4.27 % (2035)------------------------------
% 21.07/4.27 % (2035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.07/4.27 % (2035)Termination reason: Unknown
% 21.07/4.27 % (2035)Termination phase: Saturation
% 21.07/4.27
% 21.07/4.27 % (2035)Memory used [KB]: 8699
% 21.07/4.27 % (2035)Time elapsed: 0.177 s
% 21.07/4.27 % (2035)Instructions burned: 596 (million)
% 21.07/4.27 % (2035)------------------------------
% 21.07/4.27 % (2035)------------------------------
% 21.07/4.28 % (2043)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_1611 for (2972ds/593Mi)
% 21.07/4.29 % (2042)Instruction limit reached!
% 21.07/4.29 % (2042)------------------------------
% 21.07/4.29 % (2042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.07/4.29 % (2042)Termination reason: Unknown
% 21.07/4.29 % (2042)Termination phase: Function definition elimination
% 21.07/4.29
% 21.07/4.29 % (2042)Memory used [KB]: 2430
% 21.07/4.29 % (2042)Time elapsed: 0.025 s
% 21.07/4.29 % (2042)Instructions burned: 93 (million)
% 21.07/4.29 % (2042)------------------------------
% 21.07/4.29 % (2042)------------------------------
% 21.07/4.30 % (2044)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_1611 for (2972ds/1512Mi)
% 21.67/4.38 % (2041)Instruction limit reached!
% 21.67/4.38 % (2041)------------------------------
% 21.67/4.38 % (2041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.67/4.38 % (2041)Termination reason: Unknown
% 21.67/4.38 % (2041)Termination phase: Saturation
% 21.67/4.38
% 21.67/4.38 % (2041)Memory used [KB]: 9466
% 21.67/4.38 % (2041)Time elapsed: 0.148 s
% 21.67/4.38 % (2041)Instructions burned: 503 (million)
% 21.67/4.38 % (2041)------------------------------
% 21.67/4.38 % (2041)------------------------------
% 21.67/4.39 % (2045)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_1611 for (2971ds/569Mi)
% 22.03/4.45 % (2023)Instruction limit reached!
% 22.03/4.45 % (2023)------------------------------
% 22.03/4.45 % (2023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.03/4.45 % (2023)Termination reason: Unknown
% 22.03/4.45 % (2023)Termination phase: Saturation
% 22.03/4.45
% 22.03/4.45 % (2023)Memory used [KB]: 7419
% 22.03/4.45 % (2023)Time elapsed: 1.173 s
% 22.03/4.45 % (2023)Instructions burned: 4717 (million)
% 22.03/4.45 % (2023)------------------------------
% 22.03/4.45 % (2023)------------------------------
% 22.03/4.46 % (2043)Instruction limit reached!
% 22.03/4.46 % (2043)------------------------------
% 22.03/4.46 % (2043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.03/4.46 % (2043)Termination reason: Unknown
% 22.03/4.46 % (2043)Termination phase: Saturation
% 22.03/4.46
% 22.03/4.46 % (2043)Memory used [KB]: 9466
% 22.03/4.46 % (2043)Time elapsed: 0.179 s
% 22.03/4.46 % (2043)Instructions burned: 595 (million)
% 22.03/4.46 % (2043)------------------------------
% 22.03/4.46 % (2043)------------------------------
% 22.03/4.46 % (2046)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_1611 for (2970ds/501Mi)
% 22.03/4.47 % (2047)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_1611 for (2970ds/562Mi)
% 22.38/4.53 % (2045)Instruction limit reached!
% 22.38/4.53 % (2045)------------------------------
% 22.38/4.53 % (2045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.38/4.53 % (2045)Termination reason: Unknown
% 22.38/4.53 % (2045)Termination phase: Saturation
% 22.38/4.53
% 22.38/4.53 % (2045)Memory used [KB]: 12920
% 22.38/4.53 % (2045)Time elapsed: 0.146 s
% 22.38/4.53 % (2045)Instructions burned: 572 (million)
% 22.38/4.53 % (2045)------------------------------
% 22.38/4.53 % (2045)------------------------------
% 22.38/4.54 % (2048)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_1611 for (2970ds/406Mi)
% 22.63/4.61 % (2046)Instruction limit reached!
% 22.63/4.61 % (2046)------------------------------
% 22.63/4.61 % (2046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.63/4.61 % (2046)Termination reason: Unknown
% 22.63/4.61 % (2046)Termination phase: Saturation
% 22.63/4.61
% 22.63/4.61 % (2046)Memory used [KB]: 9850
% 22.63/4.61 % (2046)Time elapsed: 0.151 s
% 22.63/4.61 % (2046)Instructions burned: 502 (million)
% 22.63/4.61 % (2046)------------------------------
% 22.63/4.61 % (2046)------------------------------
% 22.63/4.62 % (2049)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_1611 for (2969ds/582Mi)
% 22.63/4.63 % (2047)Instruction limit reached!
% 22.63/4.63 % (2047)------------------------------
% 22.63/4.63 % (2047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.63/4.63 % (2047)Termination reason: Unknown
% 22.63/4.63 % (2047)Termination phase: Saturation
% 22.63/4.63
% 22.63/4.63 % (2047)Memory used [KB]: 9210
% 22.63/4.63 % (2047)Time elapsed: 0.166 s
% 22.63/4.63 % (2047)Instructions burned: 564 (million)
% 22.63/4.63 % (2047)------------------------------
% 22.63/4.63 % (2047)------------------------------
% 22.63/4.64 % (2039)Instruction limit reached!
% 22.63/4.64 % (2039)------------------------------
% 22.63/4.64 % (2039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.63/4.64 % (2039)Termination reason: Unknown
% 22.63/4.64 % (2039)Termination phase: Saturation
% 22.63/4.64
% 22.63/4.64 % (2039)Memory used [KB]: 20212
% 22.63/4.64 % (2039)Time elapsed: 0.438 s
% 22.63/4.64 % (2039)Instructions burned: 1763 (million)
% 22.63/4.64 % (2039)------------------------------
% 22.63/4.64 % (2039)------------------------------
% 22.63/4.64 % (2050)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_1611 for (2969ds/456Mi)
% 22.63/4.65 % (2051)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_1611 for (2968ds/393Mi)
% 22.63/4.65 % (2048)Instruction limit reached!
% 22.63/4.65 % (2048)------------------------------
% 22.63/4.65 % (2048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.63/4.65 % (2048)Termination reason: Unknown
% 22.63/4.65 % (2048)Termination phase: Saturation
% 22.63/4.65
% 22.63/4.65 % (2048)Memory used [KB]: 7547
% 22.63/4.65 % (2048)Time elapsed: 0.113 s
% 22.63/4.65 % (2048)Instructions burned: 409 (million)
% 22.63/4.65 % (2048)------------------------------
% 22.63/4.65 % (2048)------------------------------
% 22.63/4.66 % (2052)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_1611 for (2968ds/1335Mi)
% 23.64/4.77 % (2051)Instruction limit reached!
% 23.64/4.77 % (2051)------------------------------
% 23.64/4.77 % (2051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.64/4.77 % (2051)Termination reason: Unknown
% 23.64/4.77 % (2051)Termination phase: Saturation
% 23.64/4.77
% 23.64/4.77 % (2051)Memory used [KB]: 9338
% 23.64/4.77 % (2051)Time elapsed: 0.118 s
% 23.64/4.77 % (2051)Instructions burned: 393 (million)
% 23.64/4.77 % (2051)------------------------------
% 23.64/4.77 % (2051)------------------------------
% 23.64/4.77 % (2044)Instruction limit reached!
% 23.64/4.77 % (2044)------------------------------
% 23.64/4.77 % (2044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.64/4.77 % (2044)Termination reason: Unknown
% 23.64/4.77 % (2044)Termination phase: Saturation
% 23.64/4.77
% 23.64/4.77 % (2044)Memory used [KB]: 11385
% 23.64/4.77 % (2044)Time elapsed: 0.477 s
% 23.64/4.77 % (2044)Instructions burned: 1513 (million)
% 23.64/4.77 % (2044)------------------------------
% 23.64/4.77 % (2044)------------------------------
% 23.64/4.78 % (2050)Instruction limit reached!
% 23.64/4.78 % (2050)------------------------------
% 23.64/4.78 % (2050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.64/4.78 % (2050)Termination reason: Unknown
% 23.64/4.78 % (2050)Termination phase: Saturation
% 23.64/4.78
% 23.64/4.78 % (2050)Memory used [KB]: 9338
% 23.64/4.78 % (2050)Time elapsed: 0.136 s
% 23.64/4.78 % (2050)Instructions burned: 456 (million)
% 23.64/4.78 % (2050)------------------------------
% 23.64/4.78 % (2050)------------------------------
% 23.64/4.78 % (2053)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_1611 for (2967ds/3373Mi)
% 23.64/4.78 % (2054)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_1611 for (2967ds/474Mi)
% 23.64/4.79 % (2055)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_1611 for (2967ds/157Mi)
% 24.51/4.81 % (2049)Instruction limit reached!
% 24.51/4.81 % (2049)------------------------------
% 24.51/4.81 % (2049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.81 % (2049)Termination reason: Unknown
% 24.51/4.81 % (2049)Termination phase: Saturation
% 24.51/4.81
% 24.51/4.81 % (2049)Memory used [KB]: 9978
% 24.51/4.81 % (2049)Time elapsed: 0.185 s
% 24.51/4.81 % (2049)Instructions burned: 584 (million)
% 24.51/4.81 % (2049)------------------------------
% 24.51/4.81 % (2049)------------------------------
% 24.51/4.82 % (2056)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_1611 for (2967ds/590Mi)
% 24.51/4.83 % (2055)Instruction limit reached!
% 24.51/4.83 % (2055)------------------------------
% 24.51/4.83 % (2055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.83 % (2055)Termination reason: Unknown
% 24.51/4.83 % (2055)Termination phase: Saturation
% 24.51/4.83
% 24.51/4.83 % (2055)Memory used [KB]: 7036
% 24.51/4.83 % (2055)Time elapsed: 0.041 s
% 24.51/4.83 % (2055)Instructions burned: 157 (million)
% 24.51/4.83 % (2055)------------------------------
% 24.51/4.83 % (2055)------------------------------
% 24.51/4.84 % (2057)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_1611 for (2967ds/104Mi)
% 24.51/4.86 % (2057)Instruction limit reached!
% 24.51/4.86 % (2057)------------------------------
% 24.51/4.86 % (2057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.51/4.86 % (2057)Termination reason: Unknown
% 24.51/4.86 % (2057)Termination phase: Property scanning
% 24.51/4.86
% 24.51/4.86 % (2057)Memory used [KB]: 2558
% 24.51/4.86 % (2057)Time elapsed: 0.028 s
% 24.51/4.86 % (2057)Instructions burned: 105 (million)
% 24.51/4.86 % (2057)------------------------------
% 24.51/4.86 % (2057)------------------------------
% 24.51/4.87 % (2058)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_1611 for (2966ds/414Mi)
% 24.89/4.90 % (2054)Instruction limit reached!
% 24.89/4.90 % (2054)------------------------------
% 24.89/4.90 % (2054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.89/4.90 % (2054)Termination reason: Unknown
% 24.89/4.90 % (2054)Termination phase: Saturation
% 24.89/4.90
% 24.89/4.90 % (2054)Memory used [KB]: 9594
% 24.89/4.90 % (2054)Time elapsed: 0.124 s
% 24.89/4.90 % (2054)Instructions burned: 477 (million)
% 24.89/4.90 % (2054)------------------------------
% 24.89/4.90 % (2054)------------------------------
% 24.89/4.91 % (2059)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_1611 for (2966ds/715Mi)
% 24.89/4.98 % (2058)Instruction limit reached!
% 24.89/4.98 % (2058)------------------------------
% 24.89/4.98 % (2058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.89/4.98 % (2058)Termination reason: Unknown
% 24.89/4.98 % (2058)Termination phase: Saturation
% 24.89/4.98
% 24.89/4.98 % (2058)Memory used [KB]: 7291
% 24.89/4.98 % (2058)Time elapsed: 0.106 s
% 24.89/4.98 % (2058)Instructions burned: 414 (million)
% 24.89/4.98 % (2058)------------------------------
% 24.89/4.98 % (2058)------------------------------
% 24.89/4.98 % (2056)Instruction limit reached!
% 24.89/4.98 % (2056)------------------------------
% 24.89/4.98 % (2056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.89/4.98 % (2056)Termination reason: Unknown
% 24.89/4.98 % (2056)Termination phase: Saturation
% 24.89/4.98
% 24.89/4.98 % (2056)Memory used [KB]: 8827
% 24.89/4.98 % (2056)Time elapsed: 0.168 s
% 24.89/4.98 % (2056)Instructions burned: 590 (million)
% 24.89/4.98 % (2056)------------------------------
% 24.89/4.98 % (2056)------------------------------
% 24.89/4.99 % (2060)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_1611 for (2965ds/961Mi)
% 24.89/4.99 % (2061)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_1611 for (2965ds/1213Mi)
% 26.99/5.07 % (2052)Instruction limit reached!
% 26.99/5.07 % (2052)------------------------------
% 26.99/5.07 % (2052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.99/5.07 % (2052)Termination reason: Unknown
% 26.99/5.07 % (2052)Termination phase: Saturation
% 26.99/5.07
% 26.99/5.07 % (2052)Memory used [KB]: 9850
% 26.99/5.07 % (2052)Time elapsed: 0.412 s
% 26.99/5.07 % (2052)Instructions burned: 1335 (million)
% 26.99/5.07 % (2052)------------------------------
% 26.99/5.07 % (2052)------------------------------
% 26.99/5.08 % (2062)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_1611 for (2964ds/1979Mi)
% 27.70/5.13 % (2059)Instruction limit reached!
% 27.70/5.13 % (2059)------------------------------
% 27.70/5.13 % (2059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.70/5.13 % (2059)Termination reason: Unknown
% 27.70/5.13 % (2059)Termination phase: Saturation
% 27.70/5.13
% 27.70/5.13 % (2059)Memory used [KB]: 4989
% 27.70/5.13 % (2059)Time elapsed: 0.217 s
% 27.70/5.13 % (2059)Instructions burned: 717 (million)
% 27.70/5.13 % (2059)------------------------------
% 27.70/5.13 % (2059)------------------------------
% 27.70/5.14 % (2063)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_1611 for (2963ds/481Mi)
% 28.09/5.26 % (2063)Instruction limit reached!
% 28.09/5.26 % (2063)------------------------------
% 28.09/5.26 % (2063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.09/5.26 % (2063)Termination reason: Unknown
% 28.09/5.26 % (2063)Termination phase: Saturation
% 28.09/5.26
% 28.09/5.26 % (2063)Memory used [KB]: 8187
% 28.09/5.26 % (2063)Time elapsed: 0.121 s
% 28.09/5.26 % (2063)Instructions burned: 483 (million)
% 28.09/5.26 % (2063)------------------------------
% 28.09/5.26 % (2063)------------------------------
% 28.09/5.27 % (2064)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_1611 for (2962ds/783Mi)
% 28.09/5.28 % (2060)Instruction limit reached!
% 28.09/5.28 % (2060)------------------------------
% 28.09/5.28 % (2060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.09/5.28 % (2060)Termination reason: Unknown
% 28.09/5.28 % (2060)Termination phase: Saturation
% 28.09/5.28
% 28.09/5.28 % (2060)Memory used [KB]: 9210
% 28.09/5.28 % (2060)Time elapsed: 0.317 s
% 28.09/5.28 % (2060)Instructions burned: 962 (million)
% 28.09/5.28 % (2060)------------------------------
% 28.09/5.28 % (2060)------------------------------
% 28.09/5.29 % (2065)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_1611 for (2962ds/432Mi)
% 28.71/5.37 % (2061)Instruction limit reached!
% 28.71/5.37 % (2061)------------------------------
% 28.71/5.37 % (2061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.71/5.37 % (2061)Termination reason: Unknown
% 28.71/5.37 % (2061)Termination phase: Saturation
% 28.71/5.37
% 28.71/5.37 % (2061)Memory used [KB]: 13560
% 28.71/5.37 % (2061)Time elapsed: 0.400 s
% 28.71/5.37 % (2061)Instructions burned: 1214 (million)
% 28.71/5.37 % (2061)------------------------------
% 28.71/5.37 % (2061)------------------------------
% 28.71/5.38 % (2066)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_1611 for (2961ds/1670Mi)
% 29.11/5.42 % (2065)Instruction limit reached!
% 29.11/5.42 % (2065)------------------------------
% 29.11/5.42 % (2065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.42 % (2065)Termination reason: Unknown
% 29.11/5.42 % (2065)Termination phase: Saturation
% 29.11/5.42
% 29.11/5.42 % (2065)Memory used [KB]: 8699
% 29.11/5.42 % (2065)Time elapsed: 0.124 s
% 29.11/5.42 % (2065)Instructions burned: 433 (million)
% 29.11/5.42 % (2065)------------------------------
% 29.11/5.42 % (2065)------------------------------
% 29.11/5.43 % (2067)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_1611 for (2961ds/90Mi)
% 29.11/5.45 % (2067)Instruction limit reached!
% 29.11/5.45 % (2067)------------------------------
% 29.11/5.45 % (2067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.45 % (2067)Termination reason: Unknown
% 29.11/5.45 % (2067)Termination phase: Function definition elimination
% 29.11/5.45
% 29.11/5.45 % (2067)Memory used [KB]: 2430
% 29.11/5.45 % (2067)Time elapsed: 0.026 s
% 29.11/5.45 % (2067)Instructions burned: 91 (million)
% 29.11/5.45 % (2067)------------------------------
% 29.11/5.45 % (2067)------------------------------
% 29.11/5.46 % (2068)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_1611 for (2960ds/346Mi)
% 29.58/5.51 % (2064)Instruction limit reached!
% 29.58/5.51 % (2064)------------------------------
% 29.58/5.51 % (2064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.58/5.51 % (2064)Termination reason: Unknown
% 29.58/5.51 % (2064)Termination phase: Saturation
% 29.58/5.51
% 29.58/5.51 % (2064)Memory used [KB]: 11001
% 29.58/5.51 % (2064)Time elapsed: 0.245 s
% 29.58/5.51 % (2064)Instructions burned: 784 (million)
% 29.58/5.51 % (2064)------------------------------
% 29.58/5.51 % (2064)------------------------------
% 29.58/5.52 % (2069)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_1611 for (2960ds/401Mi)
% 29.58/5.55 % (2068)Instruction limit reached!
% 29.58/5.55 % (2068)------------------------------
% 29.58/5.55 % (2068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.58/5.55 % (2068)Termination reason: Unknown
% 29.58/5.55 % (2068)Termination phase: Saturation
% 29.58/5.55
% 29.58/5.55 % (2068)Memory used [KB]: 7291
% 29.58/5.55 % (2068)Time elapsed: 0.088 s
% 29.58/5.55 % (2068)Instructions burned: 346 (million)
% 29.58/5.55 % (2068)------------------------------
% 29.58/5.55 % (2068)------------------------------
% 29.58/5.56 % (2070)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_1611 for (2959ds/6454Mi)
% 30.22/5.63 % (2069)Instruction limit reached!
% 30.22/5.63 % (2069)------------------------------
% 30.22/5.63 % (2069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.22/5.63 % (2069)Termination reason: Unknown
% 30.22/5.63 % (2069)Termination phase: Saturation
% 30.22/5.63
% 30.22/5.63 % (2069)Memory used [KB]: 7291
% 30.22/5.63 % (2069)Time elapsed: 0.103 s
% 30.22/5.63 % (2069)Instructions burned: 403 (million)
% 30.22/5.63 % (2069)------------------------------
% 30.22/5.63 % (2069)------------------------------
% 30.22/5.64 % (2071)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_1611 for (2959ds/283Mi)
% 30.22/5.69 % (2062)Instruction limit reached!
% 30.22/5.69 % (2062)------------------------------
% 30.22/5.69 % (2062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.22/5.69 % (2062)Termination reason: Unknown
% 30.22/5.69 % (2062)Termination phase: Saturation
% 30.22/5.69
% 30.22/5.69 % (2062)Memory used [KB]: 10106
% 30.22/5.69 % (2062)Time elapsed: 0.608 s
% 30.22/5.69 % (2062)Instructions burned: 1979 (million)
% 30.22/5.69 % (2062)------------------------------
% 30.22/5.69 % (2062)------------------------------
% 31.25/5.70 % (2073)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_1611 for (2958ds/865Mi)
% 31.25/5.71 % (2071)Instruction limit reached!
% 31.25/5.71 % (2071)------------------------------
% 31.25/5.71 % (2071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.25/5.71 % (2071)Termination reason: Unknown
% 31.25/5.71 % (2071)Termination phase: Saturation
% 31.25/5.71
% 31.25/5.71 % (2071)Memory used [KB]: 8315
% 31.25/5.71 % (2071)Time elapsed: 0.078 s
% 31.25/5.71 % (2071)Instructions burned: 284 (million)
% 31.25/5.71 % (2071)------------------------------
% 31.25/5.71 % (2071)------------------------------
% 31.25/5.72 % (2074)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_1611 for (2958ds/4528Mi)
% 31.65/5.81 % (2066)Instruction limit reached!
% 31.65/5.81 % (2066)------------------------------
% 31.65/5.81 % (2066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.65/5.81 % (2066)Termination reason: Unknown
% 31.65/5.81 % (2066)Termination phase: Saturation
% 31.65/5.81
% 31.65/5.81 % (2066)Memory used [KB]: 14711
% 31.65/5.81 % (2066)Time elapsed: 0.428 s
% 31.65/5.81 % (2066)Instructions burned: 1670 (million)
% 31.65/5.81 % (2066)------------------------------
% 31.65/5.81 % (2066)------------------------------
% 31.65/5.82 % (2075)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_1611 for (2957ds/1001Mi)
% 31.65/5.82 % (2053)Instruction limit reached!
% 31.65/5.82 % (2053)------------------------------
% 31.65/5.82 % (2053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.65/5.82 % (2053)Termination reason: Unknown
% 31.65/5.82 % (2053)Termination phase: Saturation
% 31.65/5.82
% 31.65/5.82 % (2053)Memory used [KB]: 12281
% 31.65/5.82 % (2053)Time elapsed: 1.045 s
% 31.65/5.82 % (2053)Instructions burned: 3373 (million)
% 31.65/5.82 % (2053)------------------------------
% 31.65/5.82 % (2053)------------------------------
% 31.65/5.83 % (2076)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_1611 for (2957ds/102Mi)
% 31.65/5.85 % (2074)Refutation not found, incomplete strategy
% 31.65/5.85 % (2074)------------------------------
% 31.65/5.85 % (2074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.65/5.85 % (2074)Termination reason: Refutation not found, incomplete strategy
% 31.65/5.85
% 31.65/5.85
% 31.65/5.85 % (2074)Memory used [KB]: 2686
% 31.65/5.85 % (2074)Time elapsed: 0.133 s
% 31.65/5.85 % (2074)Instructions burned: 515 (million)
% 31.65/5.85 % (2074)------------------------------
% 31.65/5.85 % (2074)------------------------------
% 31.65/5.86 % (2076)Instruction limit reached!
% 31.65/5.86 % (2076)------------------------------
% 31.65/5.86 % (2076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.65/5.86 % (2076)Termination reason: Unknown
% 31.65/5.86 % (2076)Termination phase: Property scanning
% 31.65/5.86
% 31.65/5.86 % (2076)Memory used [KB]: 2558
% 31.65/5.86 % (2076)Time elapsed: 0.027 s
% 31.65/5.86 % (2076)Instructions burned: 102 (million)
% 31.65/5.86 % (2076)------------------------------
% 31.65/5.86 % (2076)------------------------------
% 31.65/5.86 % (2077)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_1611 for (2956ds/952Mi)
% 31.65/5.87 % (2078)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_1611 for (2956ds/578Mi)
% 32.51/5.91 % (2038)Instruction limit reached!
% 32.51/5.91 % (2038)------------------------------
% 32.51/5.91 % (2038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.51/5.91 % (2038)Termination reason: Unknown
% 32.51/5.91 % (2038)Termination phase: Saturation
% 32.51/5.91
% 32.51/5.91 % (2038)Memory used [KB]: 15735
% 32.51/5.91 % (2038)Time elapsed: 1.709 s
% 32.51/5.91 % (2038)Instructions burned: 5412 (million)
% 32.51/5.91 % (2038)------------------------------
% 32.51/5.91 % (2038)------------------------------
% 32.51/5.92 % (2079)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_1611 for (2956ds/643Mi)
% 32.51/5.94 % (2073)Instruction limit reached!
% 32.51/5.94 % (2073)------------------------------
% 32.51/5.94 % (2073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.51/5.94 % (2073)Termination reason: Unknown
% 32.51/5.94 % (2073)Termination phase: Saturation
% 32.51/5.94
% 32.51/5.94 % (2073)Memory used [KB]: 8187
% 32.51/5.94 % (2073)Time elapsed: 0.239 s
% 32.51/5.94 % (2073)Instructions burned: 868 (million)
% 32.51/5.94 % (2073)------------------------------
% 32.51/5.94 % (2073)------------------------------
% 32.51/5.95 % (2080)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_1611 for (2955ds/865Mi)
% 32.51/5.96 % (2024)Instruction limit reached!
% 32.51/5.96 % (2024)------------------------------
% 32.51/5.96 % (2024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.51/5.96 % (2024)Termination reason: Unknown
% 32.51/5.96 % (2024)Termination phase: Saturation
% 32.51/5.96
% 32.51/5.96 % (2024)Memory used [KB]: 24818
% 32.51/5.96 % (2024)Time elapsed: 2.659 s
% 32.51/5.96 % (2024)Instructions burned: 8250 (million)
% 32.51/5.96 % (2024)------------------------------
% 32.51/5.96 % (2024)------------------------------
% 32.51/5.97 % (2081)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_1611 for (2955ds/1174Mi)
% 32.51/6.01 % (2078)Instruction limit reached!
% 32.51/6.01 % (2078)------------------------------
% 32.51/6.01 % (2078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.51/6.01 % (2078)Termination reason: Unknown
% 32.51/6.01 % (2078)Termination phase: Saturation
% 32.51/6.01
% 32.51/6.01 % (2078)Memory used [KB]: 9466
% 32.51/6.01 % (2078)Time elapsed: 0.141 s
% 32.51/6.01 % (2078)Instructions burned: 581 (million)
% 32.51/6.01 % (2078)------------------------------
% 32.51/6.01 % (2078)------------------------------
% 32.51/6.02 % (2082)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_1611 for (2955ds/644Mi)
% 34.03/6.09 % (2079)Instruction limit reached!
% 34.03/6.09 % (2079)------------------------------
% 34.03/6.09 % (2079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.03/6.09 % (2079)Termination reason: Unknown
% 34.03/6.09 % (2079)Termination phase: Saturation
% 34.03/6.09
% 34.03/6.09 % (2079)Memory used [KB]: 12792
% 34.03/6.09 % (2079)Time elapsed: 0.166 s
% 34.03/6.09 % (2079)Instructions burned: 646 (million)
% 34.03/6.09 % (2079)------------------------------
% 34.03/6.09 % (2079)------------------------------
% 34.03/6.10 % (2083)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_1611 for (2954ds/1201Mi)
% 34.64/6.12 % (2075)Instruction limit reached!
% 34.64/6.12 % (2075)------------------------------
% 34.64/6.12 % (2075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.64/6.12 % (2075)Termination reason: Unknown
% 34.64/6.12 % (2075)Termination phase: Saturation
% 34.64/6.12
% 34.64/6.12 % (2075)Memory used [KB]: 11129
% 34.64/6.12 % (2075)Time elapsed: 0.308 s
% 34.64/6.12 % (2075)Instructions burned: 1003 (million)
% 34.64/6.12 % (2075)------------------------------
% 34.64/6.12 % (2075)------------------------------
% 34.64/6.13 % (2084)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_1611 for (2953ds/1046Mi)
% 34.64/6.15 % (2077)Instruction limit reached!
% 34.64/6.15 % (2077)------------------------------
% 34.64/6.15 % (2077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.64/6.15 % (2077)Termination reason: Unknown
% 34.64/6.15 % (2077)Termination phase: Saturation
% 34.64/6.15
% 34.64/6.15 % (2077)Memory used [KB]: 9978
% 34.64/6.15 % (2077)Time elapsed: 0.291 s
% 34.64/6.15 % (2077)Instructions burned: 952 (million)
% 34.64/6.15 % (2077)------------------------------
% 34.64/6.15 % (2077)------------------------------
% 34.64/6.16 % (2085)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_1611 for (2953ds/222Mi)
% 34.64/6.18 % (2080)Instruction limit reached!
% 34.64/6.18 % (2080)------------------------------
% 34.64/6.18 % (2080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.64/6.18 % (2080)Termination reason: Unknown
% 34.64/6.18 % (2080)Termination phase: Saturation
% 34.64/6.18
% 34.64/6.18 % (2080)Memory used [KB]: 7547
% 34.64/6.18 % (2080)Time elapsed: 0.236 s
% 34.64/6.18 % (2080)Instructions burned: 868 (million)
% 34.64/6.18 % (2080)------------------------------
% 34.64/6.18 % (2080)------------------------------
% 34.64/6.19 % (2086)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_1611 for (2953ds/68Mi)
% 34.90/6.21 % (2082)Instruction limit reached!
% 34.90/6.21 % (2082)------------------------------
% 34.90/6.21 % (2082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/6.21 % (2082)Termination reason: Unknown
% 34.90/6.21 % (2082)Termination phase: Saturation
% 34.90/6.21
% 34.90/6.21 % (2082)Memory used [KB]: 7931
% 34.90/6.21 % (2082)Time elapsed: 0.190 s
% 34.90/6.21 % (2082)Instructions burned: 645 (million)
% 34.90/6.21 % (2082)------------------------------
% 34.90/6.21 % (2082)------------------------------
% 34.90/6.21 % (2086)Instruction limit reached!
% 34.90/6.21 % (2086)------------------------------
% 34.90/6.21 % (2086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/6.21 % (2086)Termination reason: Unknown
% 34.90/6.21 % (2086)Termination phase: SInE selection
% 34.90/6.21
% 34.90/6.21 % (2086)Memory used [KB]: 2302
% 34.90/6.21 % (2086)Time elapsed: 0.019 s
% 34.90/6.21 % (2086)Instructions burned: 68 (million)
% 34.90/6.21 % (2086)------------------------------
% 34.90/6.21 % (2086)------------------------------
% 34.90/6.22 % (2087)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_1611 for (2953ds/454Mi)
% 34.90/6.22 % (2085)Instruction limit reached!
% 34.90/6.22 % (2085)------------------------------
% 34.90/6.22 % (2085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/6.22 % (2085)Termination reason: Unknown
% 34.90/6.22 % (2085)Termination phase: Saturation
% 34.90/6.22
% 34.90/6.22 % (2085)Memory used [KB]: 7291
% 34.90/6.22 % (2085)Time elapsed: 0.058 s
% 34.90/6.22 % (2085)Instructions burned: 226 (million)
% 34.90/6.22 % (2085)------------------------------
% 34.90/6.22 % (2085)------------------------------
% 34.90/6.22 % (2088)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_1611 for (2953ds/360Mi)
% 34.90/6.23 % (2089)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_1611 for (2953ds/157Mi)
% 34.90/6.27 % (2089)Instruction limit reached!
% 34.90/6.27 % (2089)------------------------------
% 34.90/6.27 % (2089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/6.27 % (2089)Termination reason: Unknown
% 34.90/6.27 % (2089)Termination phase: Saturation
% 34.90/6.27
% 34.90/6.27 % (2089)Memory used [KB]: 7036
% 34.90/6.27 % (2089)Time elapsed: 0.040 s
% 34.90/6.27 % (2089)Instructions burned: 157 (million)
% 34.90/6.27 % (2089)------------------------------
% 34.90/6.27 % (2089)------------------------------
% 34.90/6.28 % (2090)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_1611 for (2952ds/5061Mi)
% 34.90/6.29 % (2081)Refutation not found, non-redundant clauses discarded% (2081)------------------------------
% 34.90/6.29 % (2081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.90/6.29 % (2081)Termination reason: Refutation not found, non-redundant clauses discarded
% 34.90/6.29
% 34.90/6.29 % (2081)Memory used [KB]: 9594
% 34.90/6.29 % (2081)Time elapsed: 0.325 s
% 34.90/6.29 % (2081)Instructions burned: 1077 (million)
% 34.90/6.29 % (2081)------------------------------
% 34.90/6.29 % (2081)------------------------------
% 35.46/6.30 % (2091)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_1611 for (2952ds/2401Mi)
% 35.46/6.31 % (2088)Instruction limit reached!
% 35.46/6.31 % (2088)------------------------------
% 35.46/6.31 % (2088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.46/6.31 % (2088)Termination reason: Unknown
% 35.46/6.31 % (2088)Termination phase: Saturation
% 35.46/6.31
% 35.46/6.31 % (2088)Memory used [KB]: 7291
% 35.46/6.31 % (2088)Time elapsed: 0.091 s
% 35.46/6.31 % (2088)Instructions burned: 360 (million)
% 35.46/6.31 % (2088)------------------------------
% 35.46/6.31 % (2088)------------------------------
% 35.46/6.32 % (2092)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_1611 for (2952ds/5798Mi)
% 35.46/6.33 % (2087)Instruction limit reached!
% 35.46/6.33 % (2087)------------------------------
% 35.46/6.33 % (2087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.46/6.33 % (2087)Termination reason: Unknown
% 35.46/6.33 % (2087)Termination phase: Saturation
% 35.46/6.33
% 35.46/6.33 % (2087)Memory used [KB]: 14200
% 35.46/6.33 % (2087)Time elapsed: 0.117 s
% 35.46/6.33 % (2087)Instructions burned: 457 (million)
% 35.46/6.33 % (2087)------------------------------
% 35.46/6.33 % (2087)------------------------------
% 35.46/6.34 % (2093)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_1611 for (2951ds/346Mi)
% 35.77/6.40 % (2084)Instruction limit reached!
% 35.77/6.40 % (2084)------------------------------
% 35.77/6.40 % (2084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.77/6.40 % (2084)Termination reason: Unknown
% 35.77/6.40 % (2084)Termination phase: Saturation
% 35.77/6.40
% 35.77/6.40 % (2084)Memory used [KB]: 7419
% 35.77/6.40 % (2084)Time elapsed: 0.267 s
% 35.77/6.40 % (2084)Instructions burned: 1049 (million)
% 35.77/6.40 % (2084)------------------------------
% 35.77/6.40 % (2084)------------------------------
% 35.77/6.41 % (2094)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_1611 for (2951ds/1321Mi)
% 35.77/6.42 % (2083)Instruction limit reached!
% 35.77/6.42 % (2083)------------------------------
% 35.77/6.42 % (2083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.77/6.42 % (2083)Termination reason: Unknown
% 35.77/6.42 % (2083)Termination phase: Saturation
% 35.77/6.42
% 35.77/6.42 % (2083)Memory used [KB]: 10234
% 35.77/6.42 % (2083)Time elapsed: 0.321 s
% 35.77/6.42 % (2083)Instructions burned: 1201 (million)
% 35.77/6.42 % (2083)------------------------------
% 35.77/6.42 % (2083)------------------------------
% 35.77/6.43 % (2095)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_1611 for (2951ds/1312Mi)
% 35.77/6.44 % (2093)Instruction limit reached!
% 35.77/6.44 % (2093)------------------------------
% 35.77/6.44 % (2093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.77/6.44 % (2093)Termination reason: Unknown
% 35.77/6.44 % (2093)Termination phase: Saturation
% 35.77/6.44
% 35.77/6.44 % (2093)Memory used [KB]: 7291
% 35.77/6.44 % (2093)Time elapsed: 0.092 s
% 35.77/6.44 % (2093)Instructions burned: 349 (million)
% 35.77/6.44 % (2093)------------------------------
% 35.77/6.44 % (2093)------------------------------
% 35.77/6.44 % (2096)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_1611 for (2950ds/672Mi)
% 36.68/6.65 % (2096)Instruction limit reached!
% 36.68/6.65 % (2096)------------------------------
% 36.68/6.65 % (2096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.68/6.65 % (2096)Termination reason: Unknown
% 36.68/6.65 % (2096)Termination phase: Saturation
% 36.68/6.65
% 36.68/6.65 % (2096)Memory used [KB]: 10362
% 36.68/6.65 % (2096)Time elapsed: 0.202 s
% 36.68/6.65 % (2096)Instructions burned: 673 (million)
% 36.68/6.65 % (2096)------------------------------
% 36.68/6.65 % (2096)------------------------------
% 36.68/6.66 % (2097)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_1611 for (2948ds/1897Mi)
% 37.00/6.76 % (2095)Instruction limit reached!
% 37.00/6.76 % (2095)------------------------------
% 37.00/6.76 % (2095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.76 % (2095)Termination reason: Unknown
% 37.00/6.76 % (2095)Termination phase: Saturation
% 37.00/6.76
% 37.00/6.76 % (2095)Memory used [KB]: 13432
% 37.00/6.76 % (2095)Time elapsed: 0.335 s
% 37.00/6.76 % (2095)Instructions burned: 1313 (million)
% 37.00/6.76 % (2095)------------------------------
% 37.00/6.76 % (2095)------------------------------
% 37.00/6.77 % (2098)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_1611 for (2947ds/1202Mi)
% 37.45/6.80 % (2094)Instruction limit reached!
% 37.45/6.80 % (2094)------------------------------
% 37.45/6.80 % (2094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.45/6.80 % (2094)Termination reason: Unknown
% 37.45/6.80 % (2094)Termination phase: Saturation
% 37.45/6.80
% 37.45/6.80 % (2094)Memory used [KB]: 8955
% 37.45/6.80 % (2094)Time elapsed: 0.392 s
% 37.45/6.80 % (2094)Instructions burned: 1321 (million)
% 37.45/6.80 % (2094)------------------------------
% 37.45/6.80 % (2094)------------------------------
% 37.45/6.81 % (2099)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_1611 for (2947ds/1493Mi)
% 41.03/7.02 % (2091)Instruction limit reached!
% 41.03/7.02 % (2091)------------------------------
% 41.03/7.02 % (2091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.03/7.02 % (2091)Termination reason: Unknown
% 41.03/7.02 % (2091)Termination phase: Saturation
% 41.03/7.02
% 41.03/7.02 % (2091)Memory used [KB]: 9466
% 41.03/7.02 % (2091)Time elapsed: 0.721 s
% 41.03/7.02 % (2091)Instructions burned: 2401 (million)
% 41.03/7.02 % (2091)------------------------------
% 41.03/7.02 % (2091)------------------------------
% 41.03/7.04 % (2100)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_1611 for (2945ds/7679Mi)
% 41.03/7.12 % (2098)Instruction limit reached!
% 41.03/7.12 % (2098)------------------------------
% 41.03/7.12 % (2098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.03/7.12 % (2098)Termination reason: Unknown
% 41.03/7.12 % (2098)Termination phase: Saturation
% 41.03/7.12
% 41.03/7.12 % (2098)Memory used [KB]: 8571
% 41.03/7.12 % (2098)Time elapsed: 0.346 s
% 41.03/7.12 % (2098)Instructions burned: 1202 (million)
% 41.03/7.12 % (2098)------------------------------
% 41.03/7.12 % (2098)------------------------------
% 41.70/7.13 % (2101)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_1611 for (2944ds/340Mi)
% 41.70/7.18 % (2099)Instruction limit reached!
% 41.70/7.18 % (2099)------------------------------
% 41.70/7.18 % (2099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.70/7.18 % (2099)Termination reason: Unknown
% 41.70/7.18 % (2099)Termination phase: Saturation
% 41.70/7.18
% 41.70/7.18 % (2099)Memory used [KB]: 7547
% 41.70/7.18 % (2099)Time elapsed: 0.369 s
% 41.70/7.18 % (2099)Instructions burned: 1495 (million)
% 41.70/7.18 % (2099)------------------------------
% 41.70/7.18 % (2099)------------------------------
% 41.70/7.19 % (2102)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_1611 for (2943ds/3672Mi)
% 42.05/7.23 % (2101)Instruction limit reached!
% 42.05/7.23 % (2101)------------------------------
% 42.05/7.23 % (2101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.05/7.23 % (2101)Termination reason: Unknown
% 42.05/7.23 % (2101)Termination phase: Saturation
% 42.05/7.23
% 42.05/7.23 % (2101)Memory used [KB]: 10106
% 42.05/7.23 % (2101)Time elapsed: 0.101 s
% 42.05/7.23 % (2101)Instructions burned: 341 (million)
% 42.05/7.23 % (2101)------------------------------
% 42.05/7.23 % (2101)------------------------------
% 42.05/7.24 % (2103)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_1611 for (2943ds/1535Mi)
% 42.05/7.24 % (2097)Instruction limit reached!
% 42.05/7.24 % (2097)------------------------------
% 42.05/7.24 % (2097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.05/7.24 % (2097)Termination reason: Unknown
% 42.05/7.24 % (2097)Termination phase: Saturation
% 42.05/7.24
% 42.05/7.24 % (2097)Memory used [KB]: 12792
% 42.05/7.24 % (2097)Time elapsed: 0.588 s
% 42.05/7.24 % (2097)Instructions burned: 1897 (million)
% 42.05/7.24 % (2097)------------------------------
% 42.05/7.24 % (2097)------------------------------
% 42.05/7.25 % (2104)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_1611 for (2942ds/4637Mi)
% 43.13/7.53 % (2090)Instruction limit reached!
% 43.13/7.53 % (2090)------------------------------
% 43.13/7.53 % (2090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.13/7.53 % (2090)Termination reason: Unknown
% 43.13/7.53 % (2090)Termination phase: Saturation
% 43.13/7.53
% 43.13/7.53 % (2090)Memory used [KB]: 7803
% 43.13/7.53 % (2090)Time elapsed: 1.254 s
% 43.13/7.53 % (2090)Instructions burned: 5063 (million)
% 43.13/7.53 % (2090)------------------------------
% 43.13/7.53 % (2090)------------------------------
% 43.13/7.54 % (2105)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_1611 for (2939ds/3174Mi)
% 43.39/7.62 % (2103)Instruction limit reached!
% 43.39/7.62 % (2103)------------------------------
% 43.39/7.62 % (2103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.39/7.62 % (2103)Termination reason: Unknown
% 43.39/7.62 % (2103)Termination phase: Saturation
% 43.39/7.62
% 43.39/7.62 % (2103)Memory used [KB]: 13176
% 43.39/7.62 % (2103)Time elapsed: 0.382 s
% 43.39/7.62 % (2103)Instructions burned: 1538 (million)
% 43.39/7.62 % (2103)------------------------------
% 43.39/7.62 % (2103)------------------------------
% 43.39/7.62 % (2070)Instruction limit reached!
% 43.39/7.62 % (2070)------------------------------
% 43.39/7.62 % (2070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.39/7.62 % (2070)Termination reason: Unknown
% 43.39/7.62 % (2070)Termination phase: Saturation
% 43.39/7.62
% 43.39/7.62 % (2070)Memory used [KB]: 13688
% 43.39/7.62 % (2070)Time elapsed: 2.063 s
% 43.39/7.62 % (2070)Instructions burned: 6454 (million)
% 43.39/7.62 % (2070)------------------------------
% 43.39/7.62 % (2070)------------------------------
% 43.39/7.63 % (2106)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_1611 for (2939ds/307Mi)
% 43.39/7.63 % (2107)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_1611 for (2939ds/3619Mi)
% 43.90/7.70 % (2106)Instruction limit reached!
% 43.90/7.70 % (2106)------------------------------
% 43.90/7.70 % (2106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.90/7.70 % (2106)Termination reason: Unknown
% 43.90/7.70 % (2106)Termination phase: Saturation
% 43.90/7.70
% 43.90/7.70 % (2106)Memory used [KB]: 7291
% 43.90/7.70 % (2106)Time elapsed: 0.079 s
% 43.90/7.70 % (2106)Instructions burned: 310 (million)
% 43.90/7.70 % (2106)------------------------------
% 43.90/7.70 % (2106)------------------------------
% 43.90/7.72 % (2108)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_1611 for (2938ds/2325Mi)
% 48.79/8.15 % (2092)Instruction limit reached!
% 48.79/8.15 % (2092)------------------------------
% 48.79/8.15 % (2092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.79/8.15 % (2092)Termination reason: Unknown
% 48.79/8.15 % (2092)Termination phase: Saturation
% 48.79/8.15
% 48.79/8.15 % (2092)Memory used [KB]: 13432
% 48.79/8.15 % (2092)Time elapsed: 1.834 s
% 48.79/8.15 % (2092)Instructions burned: 5800 (million)
% 48.79/8.15 % (2092)------------------------------
% 48.79/8.15 % (2092)------------------------------
% 48.79/8.16 % (2109)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_1611 for (2933ds/2341Mi)
% 49.87/8.34 % (2102)Instruction limit reached!
% 49.87/8.34 % (2102)------------------------------
% 49.87/8.34 % (2102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.87/8.34 % (2102)Termination reason: Unknown
% 49.87/8.34 % (2102)Termination phase: Saturation
% 49.87/8.34
% 49.87/8.34 % (2102)Memory used [KB]: 12409
% 49.87/8.34 % (2102)Time elapsed: 1.153 s
% 49.87/8.34 % (2102)Instructions burned: 3674 (million)
% 49.87/8.34 % (2102)------------------------------
% 49.87/8.34 % (2102)------------------------------
% 49.87/8.35 % (2108)Refutation not found, non-redundant clauses discarded% (2108)------------------------------
% 49.87/8.35 % (2108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.87/8.35 % (2108)Termination reason: Refutation not found, non-redundant clauses discarded
% 49.87/8.35
% 49.87/8.35 % (2108)Memory used [KB]: 18166
% 49.87/8.35 % (2108)Time elapsed: 0.636 s
% 49.87/8.35 % (2108)Instructions burned: 2044 (million)
% 49.87/8.35 % (2108)------------------------------
% 49.87/8.35 % (2108)------------------------------
% 49.87/8.35 % (2110)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_1611 for (2931ds/7257Mi)
% 49.87/8.36 % (2111)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_1611 for (2931ds/3710Mi)
% 50.81/8.52 % (2105)Instruction limit reached!
% 50.81/8.52 % (2105)------------------------------
% 50.81/8.52 % (2105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.81/8.52 % (2105)Termination reason: Unknown
% 50.81/8.52 % (2105)Termination phase: Saturation
% 50.81/8.52
% 50.81/8.52 % (2105)Memory used [KB]: 19061
% 50.81/8.52 % (2105)Time elapsed: 0.974 s
% 50.81/8.52 % (2105)Instructions burned: 3174 (million)
% 50.81/8.52 % (2105)------------------------------
% 50.81/8.52 % (2105)------------------------------
% 50.81/8.53 % (2112)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_1611 for (2930ds/326Mi)
% 51.14/8.62 % (2112)Instruction limit reached!
% 51.14/8.62 % (2112)------------------------------
% 51.14/8.62 % (2112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.14/8.62 % (2112)Termination reason: Unknown
% 51.14/8.62 % (2112)Termination phase: Saturation
% 51.14/8.62
% 51.14/8.62 % (2112)Memory used [KB]: 8443
% 51.14/8.62 % (2112)Time elapsed: 0.091 s
% 51.14/8.62 % (2112)Instructions burned: 327 (million)
% 51.14/8.62 % (2112)------------------------------
% 51.14/8.62 % (2112)------------------------------
% 51.14/8.63 % (2113)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_1611 for (2929ds/1100Mi)
% 51.14/8.68 % (2104)Instruction limit reached!
% 51.14/8.68 % (2104)------------------------------
% 51.14/8.68 % (2104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.14/8.68 % (2104)Termination reason: Unknown
% 51.14/8.68 % (2104)Termination phase: Saturation
% 51.14/8.68
% 51.14/8.68 % (2104)Memory used [KB]: 11257
% 51.14/8.68 % (2104)Time elapsed: 1.427 s
% 51.14/8.68 % (2104)Instructions burned: 4637 (million)
% 51.14/8.68 % (2104)------------------------------
% 51.14/8.68 % (2104)------------------------------
% 51.14/8.69 % (2114)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_1611 for (2928ds/406Mi)
% 51.53/8.73 % (2107)First to succeed.
% 51.53/8.73 % (2107)Refutation found. Thanks to Tanya!
% 51.53/8.73 % SZS status Theorem for DTF2THF_1611
% 51.53/8.73 % SZS output start Proof for DTF2THF_1611
% 51.53/8.73 thf(func_def_0, type, in: $i > $i > $o).
% 51.53/8.73 thf(func_def_1, type, exu: ($i > $o) > $o).
% 51.53/8.73 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 51.53/8.73 thf(func_def_8, type, powerset: $i > $i).
% 51.53/8.73 thf(func_def_10, type, setunion: $i > $i).
% 51.53/8.73 thf(func_def_19, type, descr: ($i > $o) > $i).
% 51.53/8.73 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 51.53/8.73 thf(func_def_26, type, prop2set: $o > $i).
% 51.53/8.73 thf(func_def_36, type, nonempty: $i > $o).
% 51.53/8.73 thf(func_def_69, type, set2prop: $i > $o).
% 51.53/8.73 thf(func_def_88, type, subset: $i > $i > $o).
% 51.53/8.73 thf(func_def_89, type, disjoint: $i > $i > $o).
% 51.53/8.73 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 51.53/8.73 thf(func_def_114, type, binunion: $i > $i > $i).
% 51.53/8.73 thf(func_def_122, type, binintersect: $i > $i > $i).
% 51.53/8.73 thf(func_def_135, type, regular: $i > $o).
% 51.53/8.73 thf(func_def_136, type, setminus: $i > $i > $i).
% 51.53/8.73 thf(func_def_147, type, symdiff: $i > $i > $i).
% 51.53/8.73 thf(func_def_153, type, iskpair: $i > $o).
% 51.53/8.73 thf(func_def_158, type, kpair: $i > $i > $i).
% 51.53/8.73 thf(func_def_160, type, cartprod: $i > $i > $i).
% 51.53/8.73 thf(func_def_177, type, singleton: $i > $o).
% 51.53/8.73 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 51.53/8.73 thf(func_def_184, type, atmost1p: $i > $o).
% 51.53/8.73 thf(func_def_185, type, atleast2p: $i > $o).
% 51.53/8.73 thf(func_def_186, type, atmost2p: $i > $o).
% 51.53/8.73 thf(func_def_187, type, upairsetp: $i > $o).
% 51.53/8.73 thf(func_def_191, type, kfst: $i > $i).
% 51.53/8.73 thf(func_def_203, type, ksnd: $i > $i).
% 51.53/8.73 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 51.53/8.73 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 51.53/8.73 thf(func_def_222, type, func: $i > $i > $i > $o).
% 51.53/8.73 thf(func_def_223, type, funcSet: $i > $i > $i).
% 51.53/8.73 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 51.53/8.73 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 51.53/8.73 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 51.53/8.73 thf(func_def_283, type, sP0: $i > $i > $i > $o > $o).
% 51.53/8.73 thf(func_def_288, type, sP5: $i > $i > $i > $i > $o).
% 51.53/8.73 thf(func_def_290, type, sP7: $i > $i > $o).
% 51.53/8.73 thf(func_def_291, type, sP8: $i > $o).
% 51.53/8.73 thf(func_def_292, type, sP9: $i > $i > $o).
% 51.53/8.74 thf(func_def_293, type, sP10: $i > $i > $o).
% 51.53/8.74 thf(func_def_304, type, sK21: $i > $o).
% 51.53/8.74 thf(func_def_309, type, sK26: $i > $i > $i).
% 51.53/8.74 thf(func_def_317, type, sK34: $i > $i > $o).
% 51.53/8.74 thf(func_def_322, type, sK39: $i > $i).
% 51.53/8.74 thf(func_def_325, type, sK42: $i > $i > ($i > $i) > $i).
% 51.53/8.74 thf(func_def_337, type, sK54: $i > $i > $o).
% 51.53/8.74 thf(func_def_353, type, sK70: $i > $o).
% 51.53/8.74 thf(func_def_356, type, sK73: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_360, type, sK77: $i > $o).
% 51.53/8.74 thf(func_def_361, type, sK78: $i > $o).
% 51.53/8.74 thf(func_def_362, type, sK79: ($i > $o) > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_363, type, sK80: ($i > $o) > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_371, type, sK88: $i > $o).
% 51.53/8.74 thf(func_def_376, type, sK93: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_377, type, sK94: $i > $o).
% 51.53/8.74 thf(func_def_387, type, sK104: $i > $i > $i).
% 51.53/8.74 thf(func_def_400, type, sK117: $i > $o).
% 51.53/8.74 thf(func_def_404, type, sK121: $i > $o).
% 51.53/8.74 thf(func_def_405, type, sK122: $i > ($i > $i) > $i > $i).
% 51.53/8.74 thf(func_def_407, type, sK124: $i > $i).
% 51.53/8.74 thf(func_def_418, type, sK135: $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_419, type, sK136: $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_436, type, sK153: $i > $i).
% 51.53/8.74 thf(func_def_450, type, sK167: $i > $i > $o).
% 51.53/8.74 thf(func_def_462, type, sK179: $i > $o).
% 51.53/8.74 thf(func_def_477, type, sK194: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_478, type, sK195: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_501, type, sK218: $i > $o).
% 51.53/8.74 thf(func_def_508, type, sK225: $i > $i).
% 51.53/8.74 thf(func_def_512, type, sK229: $i > $i > $o).
% 51.53/8.74 thf(func_def_530, type, sK247: $i > $i > $i).
% 51.53/8.74 thf(func_def_535, type, sK252: ($i > $o) > $i).
% 51.53/8.74 thf(func_def_536, type, sK253: ($i > $o) > $i).
% 51.53/8.74 thf(func_def_537, type, sK254: $i > $o).
% 51.53/8.74 thf(func_def_539, type, sK256: $i > $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_540, type, sK257: $i > $o).
% 51.53/8.74 thf(func_def_546, type, sK263: $i > $o).
% 51.53/8.74 thf(func_def_569, type, sK286: $i > $i > $i).
% 51.53/8.74 thf(func_def_570, type, sK287: $i > $i > $i).
% 51.53/8.74 thf(func_def_581, type, sK298: $i > $i > $i).
% 51.53/8.74 thf(func_def_582, type, sK299: $i > $o).
% 51.53/8.74 thf(func_def_587, type, sK304: $i > $i > $o).
% 51.53/8.74 thf(func_def_588, type, sK305: $i > $i > $i).
% 51.53/8.74 thf(func_def_597, type, sK314: $i > $o).
% 51.53/8.74 thf(func_def_600, type, sK317: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_601, type, sK318: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_609, type, sK326: $i > $i > $o).
% 51.53/8.74 thf(func_def_610, type, sK327: $i > $i).
% 51.53/8.74 thf(func_def_611, type, sK328: $i > $i).
% 51.53/8.74 thf(func_def_612, type, sK329: ($i > $i > $o) > $i > $i).
% 51.53/8.74 thf(func_def_613, type, sK330: ($i > $i > $o) > $i > $i).
% 51.53/8.74 thf(func_def_614, type, sK331: $i > ($i > $i > $o) > $i > $i).
% 51.53/8.74 thf(func_def_629, type, sK346: $i > $o).
% 51.53/8.74 thf(func_def_631, type, sK348: ($i > $o) > $i > $i).
% 51.53/8.74 thf(func_def_656, type, sK373: $i > $o).
% 51.53/8.74 thf(func_def_658, type, sK375: ($i > $o) > $i > $i).
% 51.53/8.74 thf(func_def_659, type, sK376: ($i > $o) > $i > $i).
% 51.53/8.74 thf(func_def_660, type, sK377: $i > $i).
% 51.53/8.74 thf(func_def_664, type, sK381: $i > $i).
% 51.53/8.74 thf(func_def_675, type, sK392: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_676, type, sK393: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_683, type, sK400: $i > $o).
% 51.53/8.74 thf(func_def_695, type, sK412: $i > $o).
% 51.53/8.74 thf(func_def_705, type, sK422: $i > $o).
% 51.53/8.74 thf(func_def_707, type, sK424: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_720, type, sK437: $i > $o).
% 51.53/8.74 thf(func_def_722, type, sK439: ($i > $o) > $i > $i).
% 51.53/8.74 thf(func_def_738, type, sK455: $i > $i > $i).
% 51.53/8.74 thf(func_def_743, type, sK460: $i > $i > ($i > $i) > $i).
% 51.53/8.74 thf(func_def_744, type, sK461: $i > $i).
% 51.53/8.74 thf(func_def_748, type, sK465: $i > $i).
% 51.53/8.74 thf(func_def_750, type, sK467: $i > $i).
% 51.53/8.74 thf(func_def_752, type, sK469: $i > $o).
% 51.53/8.74 thf(func_def_755, type, sK472: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_757, type, sK474: $i > $i > $o).
% 51.53/8.74 thf(func_def_761, type, sK478: $i > $o).
% 51.53/8.74 thf(func_def_764, type, sK481: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_770, type, sK487: $o > $i > $i > $i).
% 51.53/8.74 thf(func_def_774, type, sK491: $i > $i > $i).
% 51.53/8.74 thf(func_def_775, type, sK492: $i > $o).
% 51.53/8.74 thf(func_def_793, type, sK510: $i > $i).
% 51.53/8.74 thf(func_def_794, type, sK511: ($i > $i) > $i > $i > $i).
% 51.53/8.74 thf(func_def_803, type, sK520: $i > $i > $o).
% 51.53/8.74 thf(func_def_805, type, sK522: ($i > $o) > $i).
% 51.53/8.74 thf(func_def_806, type, sK523: $i > $o).
% 51.53/8.74 thf(func_def_828, type, sK545: $i > $o).
% 51.53/8.74 thf(func_def_833, type, sK550: $i > $o).
% 51.53/8.74 thf(func_def_834, type, sK551: $i > $o).
% 51.53/8.74 thf(func_def_835, type, sK552: ($i > $o) > ($i > $o) > $i > $i > $i).
% 51.53/8.74 thf(func_def_836, type, sK553: ($i > $o) > ($i > $o) > $i > $i > $i).
% 51.53/8.74 thf(func_def_837, type, sK554: $i > $o).
% 51.53/8.74 thf(func_def_838, type, sK555: $i > $i).
% 51.53/8.74 thf(func_def_839, type, sK556: ($i > $o) > $i).
% 51.53/8.74 thf(func_def_840, type, sK557: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_841, type, sK558: $i > $o).
% 51.53/8.74 thf(func_def_845, type, sK562: ($i > $o) > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_846, type, sK563: ($i > $o) > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_847, type, sK564: $i > $o).
% 51.53/8.74 thf(func_def_848, type, sK565: $i > $o).
% 51.53/8.74 thf(func_def_862, type, sK579: ($i > $o) > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_863, type, sK580: ($i > $o) > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_867, type, sK584: $i > $o).
% 51.53/8.74 thf(func_def_873, type, sK590: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_874, type, sK591: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_875, type, sK592: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_876, type, sK593: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_881, type, sK598: $i > $i > $i).
% 51.53/8.74 thf(func_def_882, type, sK599: $i > $i > $i).
% 51.53/8.74 thf(func_def_883, type, sK600: $i > $i > $i).
% 51.53/8.74 thf(func_def_884, type, sK601: $i > $i > $i).
% 51.53/8.74 thf(func_def_885, type, sK602: $i > $i > $i).
% 51.53/8.74 thf(func_def_886, type, sK603: $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_887, type, sK604: $i > $i).
% 51.53/8.74 thf(func_def_888, type, sK605: $i > $i).
% 51.53/8.74 thf(func_def_889, type, sK606: $i > $i).
% 51.53/8.74 thf(func_def_890, type, sK607: $i > $i).
% 51.53/8.74 thf(func_def_891, type, sK608: $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_892, type, sK609: $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_893, type, sK610: $i > $i > $i).
% 51.53/8.74 thf(func_def_894, type, sK611: $i > $i > $i).
% 51.53/8.74 thf(func_def_895, type, sK612: $i > $i > $i).
% 51.53/8.74 thf(func_def_897, type, sK614: $i > $i).
% 51.53/8.74 thf(func_def_898, type, sK615: $i > $i).
% 51.53/8.74 thf(func_def_899, type, sK616: $i > $i).
% 51.53/8.74 thf(func_def_908, type, sK625: ($i > $o) > $i).
% 51.53/8.74 thf(func_def_909, type, sK626: $i > $o).
% 51.53/8.74 thf(func_def_910, type, sK627: $i > $i).
% 51.53/8.74 thf(func_def_917, type, sK634: $i > $o).
% 51.53/8.74 thf(func_def_922, type, sK639: ($i > $o) > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_923, type, sK640: ($i > $o) > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_927, type, sK644: $i > $o).
% 51.53/8.74 thf(func_def_936, type, sK653: $i > ($i > $o) > $i).
% 51.53/8.74 thf(func_def_937, type, sK654: $i > $o).
% 51.53/8.74 thf(func_def_971, type, sK688: $i > $i).
% 51.53/8.74 thf(func_def_975, type, sK692: $i > $i > ($i > $i) > $i).
% 51.53/8.74 thf(func_def_981, type, sK698: $i > $i).
% 51.53/8.74 thf(func_def_984, type, sK701: $i > $i > ($i > $i) > $i).
% 51.53/8.74 thf(func_def_995, type, sK712: $i > $i > $i > $i > $i).
% 51.53/8.74 thf(func_def_1004, type, sK721: $i > $i > $i).
% 51.53/8.74 thf(func_def_1006, type, sK723: $i > $i).
% 51.53/8.74 thf(func_def_1010, type, ph727: !>[X0: $tType]:(X0)).
% 51.53/8.74 thf(f30477,plain,(
% 51.53/8.74 $false),
% 51.53/8.74 inference(avatar_sat_refutation,[status(thm)],[f4995,f7585,f7711,f7914,f7943,f30470])).
% 51.53/8.74 thf(f30470,plain,(
% 51.53/8.74 spl726_87 | spl726_88),
% 51.53/8.74 inference(avatar_split_clause,[status(thm)],[f30469,f4992,f4988])).
% 51.53/8.74 thf(f4988,definition,(
% 51.53/8.74 spl726_87 <=> ((subset @ sK652 @ sK650) = $true)),
% 51.53/8.74 introduced(definition,[new_symbols(naming,[spl726_87])],[avatar_definition])).
% 51.53/8.74 thf(f4992,definition,(
% 51.53/8.74 spl726_88 <=> ((in @ (sK26 @ sK650 @ sK652) @ sK651) = $true)),
% 51.53/8.74 introduced(definition,[new_symbols(naming,[spl726_88])],[avatar_definition])).
% 51.53/8.74 thf(f30469,plain,(
% 51.53/8.74 ((subset @ sK652 @ sK650) = $true) | spl726_88),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f30468])).
% 51.53/8.74 thf(f30468,plain,(
% 51.53/8.74 ($true != $true) | ((subset @ sK652 @ sK650) = $true) | spl726_88),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f30465,f3115])).
% 51.53/8.74 thf(f3115,plain,(
% 51.53/8.74 (subsetI1 = $true)),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f2007,plain,(
% 51.53/8.74 (complementT_lem = $true) & (dsetconstr__Cong = $true) & (binunionT_lem = $true) & (funcGraphProp2 = $true) & (upairsubunion = $true) & (setminusEL = $true) & (ubforcartprodlem1 = $true) & (ex1E2 = $true) & (omegaIndAx = $true) & (exuEu = $true) & (setbeta = $true) & (setukpairinjR2 = $true) & (singletoninpowerset = $true) & (upairset2IR = $true) & (setukpairinjR = $true) & (emptyinPowerset = $true) & (omega__Cong = $true) & (binintersectSubset4 = $true) & (dsetconstrEL = $true) & (notdexE = $true) & (iffalse = $true) & (setminusT_lem = $true) & (setadjoinOr = $true) & (notdallE = $true) & (binunionLsub = $true) & (cartprodpairmemER = $true) & (notinemptyset = $true) & (setukpairIL = $true) & (theprop = $true) & (subsetE2 = $true) & (cartprodmempair = $true) & (upairset2E = $true) & (quantDeMorgan4 = $true) & (setminusELneg = $true) & (symdiffI2 = $true) & (powerset__Cong = $true) & (prop2setI = $true) & (cartprodpairmemEL = $true) & (upairsetIR = $true) & (emptyset__Cong = $true) & (dpsetconstrEL1 = $true) & (emptysetAx = $true) & (emptyE1 = $true) & (dsetconstrER = $true) & (brelnall1 = $true) & (binintersectSubset3 = $true) & (disjointsetsI1 = $true) & (beta2 = $true) & (emptysetsubset = $true) & (omega0Ax = $true) & (upairinpowunion = $true) & (wellorderingAx = $true) & (eqinunit = $true) & (exuI2 = $true) & (eqbreln = $true) & (iftrue = $true) & (cartprodsndin = $true) & (lamProp = $true) & (setunionsingleton2 = $true) & (binunionEcases = $true) & (singletonsubset = $true) & (funcext2 = $true) & (kpairsurjEq = $true) & (funcextLem = $true) & (symdiffIneg1 = $true) & (powersetI = $true) & (singletonsuniq = $true) & (dpsetconstrEL2 = $true) & (setminusI = $true) & (dpsetconstrSub = $true) & (kfstsingleton = $true) & (subsetTrans = $true) & (ifSingleton = $true) & (lam2lamEq = $true) & (singletonprop = $true) & (emptyInPowerset = $true) & (cartprodsndpairEq = $true) & (setadjoinAx = $true) & (sepSubset = $true) & (subsetI1 = $true) & (binunionE = $true) & (nonemptyI1 = $true) & (ap2apEq2 = $true) & (quantDeMorgan1 = $true) & (subPowSU = $true) & (ksndsingleton = $true) & (kpairiskpair = $true) & (lamp = $true) & (binintersectSubset1 = $true) & (subsetRefl = $true) & (prop2setE = $true) & (setminusIRneg = $true) & (nonemptyImpWitness = $true) & (setminusLsub = $true) & (dpsetconstrI = $true) & (exuI3 = $true) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (ksndpairEq = $true) & (kpairp = $true) & (cartprodmempaircEq = $true) & (prop2set2propI = $true) & (eqimpsubset1 = $true) & (binintersectSubset5 = $true) & (setextAx = $true) & (subset2powerset = $true) & (lam2p = $true) & (apProp = $true) & (binintersectER = $true) & (exu__Cong = $true) & (setukpairinjL = $true) & (setminusSubset2 = $true) & (setextsub = $true) & (setukpairinjL1 = $true) & (eta1 = $true) & (infuncsetfunc = $true) & (setadjoinSub = $true) & (notequalI1 = $true) & (inPowerset = $true) & (replAx = $true) & (binunionRsub = $true) & (funcinfuncset = $true) & (ap2p = $true) & (dpsetconstrER = $true) & (setunionE = $true) & (cartprodpairsurjEq = $true) & (setunionE2 = $true) & (exuE3u = $true) & (binintersectI = $true) & (emptysetE = $true) & (setukpairIR = $true) & (setminusSubset1 = $true) & (singletonsswitch = $true) & (setadjoin__Cong = $true) & (setunionI = $true) & (ex1I2 = $true) & (setunionsingleton1 = $true) & (binunionIR = $true) & (funcGraphProp3 = $true) & (notinsingleton = $true) & (funcImageSingleton = $true) & (brelnall2 = $true) & (ubforcartprodlem2 = $true) & (theeq = $true) & (binintersectRsub = $true) & (subsetI2 = $true) & (exuI1 = $true) & (emptyinunitempty = $true) & (setunion__Cong = $true) & (dpsetconstrERa = $true) & (setunionsingleton = $true) & (cartprodpairin = $true) & (emptyI = $true) & (iftrueProp1 = $true) & (beta1 = $true) & (vacuousDall = $true) & (subsetE = $true) & (bs114d = $true) & (ex1I = $true) & (funcGraphProp1 = $true) & (singletoninpowunion = $true) & (quantDeMorgan3 = $true) & (binintersectLsub = $true) & (kfstpairEq = $true) & (notsubsetI = $true) & (ubforcartprodlem3 = $true) & (cartprodfstpairEq = $true) & (uniqinunit = $true) & (binintersectSubset2 = $true) & (inCongP = $true) & (ex1E1 = $true) & (iffalseProp1 = $true) & (secondinupair = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (dsetconstrI = $true) & (setadjoinE = $true) & (descrp = $true) & (in__Cong = $true) & ((($true = (in @ sK652 @ (powerset @ sK651))) & ! [X3 : $i] : (((in @ X3 @ sK651) != $true) | ((in @ X3 @ sK652) != $true) | ((in @ X3 @ sK650) = $true)) & ! [X4 : $i] : (((in @ X4 @ sK650) != $true) | ((in @ X4 @ sK651) != $true) | ((in @ X4 @ sK652) = $true)) & (sK650 != sK652)) & ($true = (in @ sK650 @ (powerset @ sK651)))) & (powersetsubset = $true) & (setext = $true) & (symdiffI1 = $true) & (cartprodfstin = $true) & (ifp = $true) & (iftrueorfalse = $true) & (omegaSAx = $true) & (setminusER = $true) & (powersetE = $true) & (notequalI2 = $true) & (cartprodmempair1 = $true) & (setminusERneg = $true) & (eta2 = $true) & (powersetE1 = $true) & (powersetAx = $true) & (symdiffIneg2 = $true) & (setukpairinjL2 = $true) & (exuE2 = $true) & (symdiffE = $true) & (binintersectEL = $true) & (funcext = $true) & (nonemptyI = $true) & (powersetT_lem = $true) & (nonemptyE1 = $true) & (funcGraphProp4 = $true) & (setunionAx = $true) & (setukpairinjR12 = $true) & (powersetI1 = $true) & (ap2apEq1 = $true) & (upairsetIL = $true) & (upairsetE = $true) & (eqimpsubset2 = $true) & (binintersectT_lem = $true) & (noeltsimpempty = $true) & (subsetemptysetimpeq = $true) & (setukpairinjR11 = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (exuE1 = $true) & (subbreln = $true) & (setukpairinjR1 = $true) & (iffalseProp2 = $true) & (app = $true) & (upairequniteq = $true) & (quantDeMorgan2 = $true) & (iftrueProp2 = $true) & (descr__Cong = $true) & (setOfPairsIsBReln = $true) & (setadjoinIL = $true) & (setminusILneg = $true) & (emptysetimpfalse = $true) & (binunionIL = $true)),
% 51.53/8.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK650,sK651,sK652])],[f2004,f2006,f2005])).
% 51.53/8.74 thf(f2005,plain,(
% 51.53/8.74 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) != $true) | ($true = (in @ X3 @ X0))) & ! [X4 : $i] : (($true != (in @ X4 @ X0)) | ((in @ X4 @ X1) != $true) | ((in @ X4 @ X2) = $true)) & (X0 != X2)) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2 : $i] : (((in @ X2 @ (powerset @ sK651)) = $true) & ! [X3 : $i] : (((in @ X3 @ sK651) != $true) | ((in @ X3 @ X2) != $true) | ((in @ X3 @ sK650) = $true)) & ! [X4 : $i] : (((in @ X4 @ sK650) != $true) | ((in @ X4 @ sK651) != $true) | ((in @ X4 @ X2) = $true)) & (sK650 != X2)) & ($true = (in @ sK650 @ (powerset @ sK651))))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f2006,plain,(
% 51.53/8.74 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK651)) = $true) & ! [X3 : $i] : (((in @ X3 @ sK651) != $true) | ((in @ X3 @ X2) != $true) | ((in @ X3 @ sK650) = $true)) & ! [X4 : $i] : (((in @ X4 @ sK650) != $true) | ((in @ X4 @ sK651) != $true) | ((in @ X4 @ X2) = $true)) & (sK650 != X2)) => (($true = (in @ sK652 @ (powerset @ sK651))) & ! [X3 : $i] : (((in @ X3 @ sK651) != $true) | ((in @ X3 @ sK652) != $true) | ((in @ X3 @ sK650) = $true)) & ! [X4 : $i] : (((in @ X4 @ sK650) != $true) | ((in @ X4 @ sK651) != $true) | ((in @ X4 @ sK652) = $true)) & (sK650 != sK652))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f2004,plain,(
% 51.53/8.74 (complementT_lem = $true) & (dsetconstr__Cong = $true) & (binunionT_lem = $true) & (funcGraphProp2 = $true) & (upairsubunion = $true) & (setminusEL = $true) & (ubforcartprodlem1 = $true) & (ex1E2 = $true) & (omegaIndAx = $true) & (exuEu = $true) & (setbeta = $true) & (setukpairinjR2 = $true) & (singletoninpowerset = $true) & (upairset2IR = $true) & (setukpairinjR = $true) & (emptyinPowerset = $true) & (omega__Cong = $true) & (binintersectSubset4 = $true) & (dsetconstrEL = $true) & (notdexE = $true) & (iffalse = $true) & (setminusT_lem = $true) & (setadjoinOr = $true) & (notdallE = $true) & (binunionLsub = $true) & (cartprodpairmemER = $true) & (notinemptyset = $true) & (setukpairIL = $true) & (theprop = $true) & (subsetE2 = $true) & (cartprodmempair = $true) & (upairset2E = $true) & (quantDeMorgan4 = $true) & (setminusELneg = $true) & (symdiffI2 = $true) & (powerset__Cong = $true) & (prop2setI = $true) & (cartprodpairmemEL = $true) & (upairsetIR = $true) & (emptyset__Cong = $true) & (dpsetconstrEL1 = $true) & (emptysetAx = $true) & (emptyE1 = $true) & (dsetconstrER = $true) & (brelnall1 = $true) & (binintersectSubset3 = $true) & (disjointsetsI1 = $true) & (beta2 = $true) & (emptysetsubset = $true) & (omega0Ax = $true) & (upairinpowunion = $true) & (wellorderingAx = $true) & (eqinunit = $true) & (exuI2 = $true) & (eqbreln = $true) & (iftrue = $true) & (cartprodsndin = $true) & (lamProp = $true) & (setunionsingleton2 = $true) & (binunionEcases = $true) & (singletonsubset = $true) & (funcext2 = $true) & (kpairsurjEq = $true) & (funcextLem = $true) & (symdiffIneg1 = $true) & (powersetI = $true) & (singletonsuniq = $true) & (dpsetconstrEL2 = $true) & (setminusI = $true) & (dpsetconstrSub = $true) & (kfstsingleton = $true) & (subsetTrans = $true) & (ifSingleton = $true) & (lam2lamEq = $true) & (singletonprop = $true) & (emptyInPowerset = $true) & (cartprodsndpairEq = $true) & (setadjoinAx = $true) & (sepSubset = $true) & (subsetI1 = $true) & (binunionE = $true) & (nonemptyI1 = $true) & (ap2apEq2 = $true) & (quantDeMorgan1 = $true) & (subPowSU = $true) & (ksndsingleton = $true) & (kpairiskpair = $true) & (lamp = $true) & (binintersectSubset1 = $true) & (subsetRefl = $true) & (prop2setE = $true) & (setminusIRneg = $true) & (nonemptyImpWitness = $true) & (setminusLsub = $true) & (dpsetconstrI = $true) & (exuI3 = $true) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (ksndpairEq = $true) & (kpairp = $true) & (cartprodmempaircEq = $true) & (prop2set2propI = $true) & (eqimpsubset1 = $true) & (binintersectSubset5 = $true) & (setextAx = $true) & (subset2powerset = $true) & (lam2p = $true) & (apProp = $true) & (binintersectER = $true) & (exu__Cong = $true) & (setukpairinjL = $true) & (setminusSubset2 = $true) & (setextsub = $true) & (setukpairinjL1 = $true) & (eta1 = $true) & (infuncsetfunc = $true) & (setadjoinSub = $true) & (notequalI1 = $true) & (inPowerset = $true) & (replAx = $true) & (binunionRsub = $true) & (funcinfuncset = $true) & (ap2p = $true) & (dpsetconstrER = $true) & (setunionE = $true) & (cartprodpairsurjEq = $true) & (setunionE2 = $true) & (exuE3u = $true) & (binintersectI = $true) & (emptysetE = $true) & (setukpairIR = $true) & (setminusSubset1 = $true) & (singletonsswitch = $true) & (setadjoin__Cong = $true) & (setunionI = $true) & (ex1I2 = $true) & (setunionsingleton1 = $true) & (binunionIR = $true) & (funcGraphProp3 = $true) & (notinsingleton = $true) & (funcImageSingleton = $true) & (brelnall2 = $true) & (ubforcartprodlem2 = $true) & (theeq = $true) & (binintersectRsub = $true) & (subsetI2 = $true) & (exuI1 = $true) & (emptyinunitempty = $true) & (setunion__Cong = $true) & (dpsetconstrERa = $true) & (setunionsingleton = $true) & (cartprodpairin = $true) & (emptyI = $true) & (iftrueProp1 = $true) & (beta1 = $true) & (vacuousDall = $true) & (subsetE = $true) & (bs114d = $true) & (ex1I = $true) & (funcGraphProp1 = $true) & (singletoninpowunion = $true) & (quantDeMorgan3 = $true) & (binintersectLsub = $true) & (kfstpairEq = $true) & (notsubsetI = $true) & (ubforcartprodlem3 = $true) & (cartprodfstpairEq = $true) & (uniqinunit = $true) & (binintersectSubset2 = $true) & (inCongP = $true) & (ex1E1 = $true) & (iffalseProp1 = $true) & (secondinupair = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (dsetconstrI = $true) & (setadjoinE = $true) & (descrp = $true) & (in__Cong = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) != $true) | ($true = (in @ X3 @ X0))) & ! [X4 : $i] : (($true != (in @ X4 @ X0)) | ((in @ X4 @ X1) != $true) | ((in @ X4 @ X2) = $true)) & (X0 != X2)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (powersetsubset = $true) & (setext = $true) & (symdiffI1 = $true) & (cartprodfstin = $true) & (ifp = $true) & (iftrueorfalse = $true) & (omegaSAx = $true) & (setminusER = $true) & (powersetE = $true) & (notequalI2 = $true) & (cartprodmempair1 = $true) & (setminusERneg = $true) & (eta2 = $true) & (powersetE1 = $true) & (powersetAx = $true) & (symdiffIneg2 = $true) & (setukpairinjL2 = $true) & (exuE2 = $true) & (symdiffE = $true) & (binintersectEL = $true) & (funcext = $true) & (nonemptyI = $true) & (powersetT_lem = $true) & (nonemptyE1 = $true) & (funcGraphProp4 = $true) & (setunionAx = $true) & (setukpairinjR12 = $true) & (powersetI1 = $true) & (ap2apEq1 = $true) & (upairsetIL = $true) & (upairsetE = $true) & (eqimpsubset2 = $true) & (binintersectT_lem = $true) & (noeltsimpempty = $true) & (subsetemptysetimpeq = $true) & (setukpairinjR11 = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (exuE1 = $true) & (subbreln = $true) & (setukpairinjR1 = $true) & (iffalseProp2 = $true) & (app = $true) & (upairequniteq = $true) & (quantDeMorgan2 = $true) & (iftrueProp2 = $true) & (descr__Cong = $true) & (setOfPairsIsBReln = $true) & (setadjoinIL = $true) & (setminusILneg = $true) & (emptysetimpfalse = $true) & (binunionIL = $true)),
% 51.53/8.74 inference(rectify,[status(thm)],[f886])).
% 51.53/8.74 thf(f886,plain,(
% 51.53/8.74 (complementT_lem = $true) & (dsetconstr__Cong = $true) & (binunionT_lem = $true) & (funcGraphProp2 = $true) & (upairsubunion = $true) & (setminusEL = $true) & (ubforcartprodlem1 = $true) & (ex1E2 = $true) & (omegaIndAx = $true) & (exuEu = $true) & (setbeta = $true) & (setukpairinjR2 = $true) & (singletoninpowerset = $true) & (upairset2IR = $true) & (setukpairinjR = $true) & (emptyinPowerset = $true) & (omega__Cong = $true) & (binintersectSubset4 = $true) & (dsetconstrEL = $true) & (notdexE = $true) & (iffalse = $true) & (setminusT_lem = $true) & (setadjoinOr = $true) & (notdallE = $true) & (binunionLsub = $true) & (cartprodpairmemER = $true) & (notinemptyset = $true) & (setukpairIL = $true) & (theprop = $true) & (subsetE2 = $true) & (cartprodmempair = $true) & (upairset2E = $true) & (quantDeMorgan4 = $true) & (setminusELneg = $true) & (symdiffI2 = $true) & (powerset__Cong = $true) & (prop2setI = $true) & (cartprodpairmemEL = $true) & (upairsetIR = $true) & (emptyset__Cong = $true) & (dpsetconstrEL1 = $true) & (emptysetAx = $true) & (emptyE1 = $true) & (dsetconstrER = $true) & (brelnall1 = $true) & (binintersectSubset3 = $true) & (disjointsetsI1 = $true) & (beta2 = $true) & (emptysetsubset = $true) & (omega0Ax = $true) & (upairinpowunion = $true) & (wellorderingAx = $true) & (eqinunit = $true) & (exuI2 = $true) & (eqbreln = $true) & (iftrue = $true) & (cartprodsndin = $true) & (lamProp = $true) & (setunionsingleton2 = $true) & (binunionEcases = $true) & (singletonsubset = $true) & (funcext2 = $true) & (kpairsurjEq = $true) & (funcextLem = $true) & (symdiffIneg1 = $true) & (powersetI = $true) & (singletonsuniq = $true) & (dpsetconstrEL2 = $true) & (setminusI = $true) & (dpsetconstrSub = $true) & (kfstsingleton = $true) & (subsetTrans = $true) & (ifSingleton = $true) & (lam2lamEq = $true) & (singletonprop = $true) & (emptyInPowerset = $true) & (cartprodsndpairEq = $true) & (setadjoinAx = $true) & (sepSubset = $true) & (subsetI1 = $true) & (binunionE = $true) & (nonemptyI1 = $true) & (ap2apEq2 = $true) & (quantDeMorgan1 = $true) & (subPowSU = $true) & (ksndsingleton = $true) & (kpairiskpair = $true) & (lamp = $true) & (binintersectSubset1 = $true) & (subsetRefl = $true) & (prop2setE = $true) & (setminusIRneg = $true) & (nonemptyImpWitness = $true) & (setminusLsub = $true) & (dpsetconstrI = $true) & (exuI3 = $true) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (ksndpairEq = $true) & (kpairp = $true) & (cartprodmempaircEq = $true) & (prop2set2propI = $true) & (eqimpsubset1 = $true) & (binintersectSubset5 = $true) & (setextAx = $true) & (subset2powerset = $true) & (lam2p = $true) & (apProp = $true) & (binintersectER = $true) & (exu__Cong = $true) & (setukpairinjL = $true) & (setminusSubset2 = $true) & (setextsub = $true) & (setukpairinjL1 = $true) & (eta1 = $true) & (infuncsetfunc = $true) & (setadjoinSub = $true) & (notequalI1 = $true) & (inPowerset = $true) & (replAx = $true) & (binunionRsub = $true) & (funcinfuncset = $true) & (ap2p = $true) & (dpsetconstrER = $true) & (setunionE = $true) & (cartprodpairsurjEq = $true) & (setunionE2 = $true) & (exuE3u = $true) & (binintersectI = $true) & (emptysetE = $true) & (setukpairIR = $true) & (setminusSubset1 = $true) & (singletonsswitch = $true) & (setadjoin__Cong = $true) & (setunionI = $true) & (ex1I2 = $true) & (setunionsingleton1 = $true) & (binunionIR = $true) & (funcGraphProp3 = $true) & (notinsingleton = $true) & (funcImageSingleton = $true) & (brelnall2 = $true) & (ubforcartprodlem2 = $true) & (theeq = $true) & (binintersectRsub = $true) & (subsetI2 = $true) & (exuI1 = $true) & (emptyinunitempty = $true) & (setunion__Cong = $true) & (dpsetconstrERa = $true) & (setunionsingleton = $true) & (cartprodpairin = $true) & (emptyI = $true) & (iftrueProp1 = $true) & (beta1 = $true) & (vacuousDall = $true) & (subsetE = $true) & (bs114d = $true) & (ex1I = $true) & (funcGraphProp1 = $true) & (singletoninpowunion = $true) & (quantDeMorgan3 = $true) & (binintersectLsub = $true) & (kfstpairEq = $true) & (notsubsetI = $true) & (ubforcartprodlem3 = $true) & (cartprodfstpairEq = $true) & (uniqinunit = $true) & (binintersectSubset2 = $true) & (inCongP = $true) & (ex1E1 = $true) & (iffalseProp1 = $true) & (secondinupair = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (dsetconstrI = $true) & (setadjoinE = $true) & (descrp = $true) & (in__Cong = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ! [X4 : $i] : (((in @ X4 @ X1) != $true) | ((in @ X4 @ X2) != $true) | ($true = (in @ X4 @ X0))) & ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true)) & (X0 != X2)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (powersetsubset = $true) & (setext = $true) & (symdiffI1 = $true) & (cartprodfstin = $true) & (ifp = $true) & (iftrueorfalse = $true) & (omegaSAx = $true) & (setminusER = $true) & (powersetE = $true) & (notequalI2 = $true) & (cartprodmempair1 = $true) & (setminusERneg = $true) & (eta2 = $true) & (powersetE1 = $true) & (powersetAx = $true) & (symdiffIneg2 = $true) & (setukpairinjL2 = $true) & (exuE2 = $true) & (symdiffE = $true) & (binintersectEL = $true) & (funcext = $true) & (nonemptyI = $true) & (powersetT_lem = $true) & (nonemptyE1 = $true) & (funcGraphProp4 = $true) & (setunionAx = $true) & (setukpairinjR12 = $true) & (powersetI1 = $true) & (ap2apEq1 = $true) & (upairsetIL = $true) & (upairsetE = $true) & (eqimpsubset2 = $true) & (binintersectT_lem = $true) & (noeltsimpempty = $true) & (subsetemptysetimpeq = $true) & (setukpairinjR11 = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (exuE1 = $true) & (subbreln = $true) & (setukpairinjR1 = $true) & (iffalseProp2 = $true) & (app = $true) & (upairequniteq = $true) & (quantDeMorgan2 = $true) & (iftrueProp2 = $true) & (descr__Cong = $true) & (setOfPairsIsBReln = $true) & (setadjoinIL = $true) & (setminusILneg = $true) & (emptysetimpfalse = $true) & (binunionIL = $true)),
% 51.53/8.74 inference(flattening,[status(thm)],[f885])).
% 51.53/8.74 thf(f885,plain,(
% 51.53/8.74 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((X0 != X2) & ! [X4 : $i] : ((($true = (in @ X4 @ X0)) | ((in @ X4 @ X2) != $true)) | ((in @ X4 @ X1) != $true))) & ! [X3 : $i] : ((((in @ X3 @ X2) = $true) | ($true != (in @ X3 @ X0))) | ((in @ X3 @ X1) != $true))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 51.53/8.74 inference(ennf_transformation,[status(thm)],[f504])).
% 51.53/8.74 thf(f504,plain,(
% 51.53/8.74 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => (($true = (in @ X3 @ X0)) => ((in @ X3 @ X2) = $true))) => (! [X4 : $i] : (((in @ X4 @ X1) = $true) => (((in @ X4 @ X2) = $true) => ($true = (in @ X4 @ X0)))) => (X0 = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 51.53/8.74 inference(fool_elimination,[status(thm)],[f503])).
% 51.53/8.74 thf(f503,plain,(
% 51.53/8.74 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (! [X4 : $i] : ((in @ X4 @ X1) => ((in @ X4 @ X2) => (in @ X4 @ X0))) => (X0 = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 51.53/8.74 inference(rectify,[status(thm)],[f237])).
% 51.53/8.74 thf(f237,negated_conjecture,(
% 51.53/8.74 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => (! [X1 : $i] : ((in @ X1 @ X3) => ((in @ X1 @ X11) => (in @ X1 @ X16))) => (! [X1 : $i] : ((in @ X1 @ X3) => ((in @ X1 @ X16) => (in @ X1 @ X11))) => (X11 = X16))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 51.53/8.74 inference(negated_conjecture,[status(cth)],[f236])).
% 51.53/8.74 thf(f236,conjecture,(
% 51.53/8.74 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => (! [X1 : $i] : ((in @ X1 @ X3) => ((in @ X1 @ X11) => (in @ X1 @ X16))) => (! [X1 : $i] : ((in @ X1 @ X3) => ((in @ X1 @ X16) => (in @ X1 @ X11))) => (X11 = X16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 51.53/8.74 file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',setextT)).
% 51.53/8.74 thf(f30465,plain,(
% 51.53/8.74 (subsetI1 != $true) | ((subset @ sK652 @ sK650) = $true) | spl726_88),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f30455])).
% 51.53/8.74 thf(f30455,plain,(
% 51.53/8.74 ($true != $true) | ((subset @ sK652 @ sK650) = $true) | (subsetI1 != $true) | spl726_88),
% 51.53/8.74 inference(superposition,[status(thm)],[f6457,f2133])).
% 51.53/8.74 thf(f2133,plain,(
% 51.53/8.74 ( ! [X3 : $i,X4 : $i] : (((in @ (sK26 @ X4 @ X3) @ X3) = $true) | ((subset @ X3 @ X4) = $true) | (subsetI1 != $true)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f1041])).
% 51.53/8.74 thf(f1041,plain,(
% 51.53/8.74 ((subsetI1 = $true) | (! [X2 : $i] : (($true = (in @ X2 @ sK25)) | ((in @ X2 @ sK24) != $true)) & ((subset @ sK24 @ sK25) != $true))) & (! [X3 : $i,X4 : $i] : ((((in @ (sK26 @ X4 @ X3) @ X4) != $true) & ((in @ (sK26 @ X4 @ X3) @ X3) = $true)) | ((subset @ X3 @ X4) = $true)) | (subsetI1 != $true))),
% 51.53/8.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f1038,f1040,f1039])).
% 51.53/8.74 thf(f1039,plain,(
% 51.53/8.74 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) & ($true != (subset @ X0 @ X1))) => (! [X2 : $i] : (($true = (in @ X2 @ sK25)) | ((in @ X2 @ sK24) != $true)) & ((subset @ sK24 @ sK25) != $true))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f1040,plain,(
% 51.53/8.74 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) != $true) & ($true = (in @ X5 @ X3))) => (((in @ (sK26 @ X4 @ X3) @ X4) != $true) & ((in @ (sK26 @ X4 @ X3) @ X3) = $true)))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f1038,plain,(
% 51.53/8.74 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) & ($true != (subset @ X0 @ X1)))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) != $true) & ($true = (in @ X5 @ X3))) | ((subset @ X3 @ X4) = $true)) | (subsetI1 != $true))),
% 51.53/8.74 inference(rectify,[status(thm)],[f1037])).
% 51.53/8.74 thf(f1037,plain,(
% 51.53/8.74 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) & ($true != (subset @ X0 @ X1)))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ($true = (subset @ X0 @ X1))) | (subsetI1 != $true))),
% 51.53/8.74 inference(nnf_transformation,[status(thm)],[f928])).
% 51.53/8.74 thf(f928,plain,(
% 51.53/8.74 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) | ($true = (subset @ X0 @ X1)))),
% 51.53/8.74 inference(ennf_transformation,[status(thm)],[f266])).
% 51.53/8.74 thf(f266,plain,(
% 51.53/8.74 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ($true = (subset @ X0 @ X1)))),
% 51.53/8.74 inference(fool_elimination,[status(thm)],[f265])).
% 51.53/8.74 thf(f265,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 51.53/8.74 inference(rectify,[status(thm)],[f78])).
% 51.53/8.74 thf(f78,axiom,(
% 51.53/8.74 (! [X3 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)) = subsetI1)),
% 51.53/8.74 file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',subsetI1)).
% 51.53/8.74 thf(f6457,plain,(
% 51.53/8.74 ((in @ (sK26 @ sK650 @ sK652) @ sK652) != $true) | spl726_88),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f6450])).
% 51.53/8.74 thf(f6450,plain,(
% 51.53/8.74 ((in @ (sK26 @ sK650 @ sK652) @ sK652) != $true) | ($true != $true) | spl726_88),
% 51.53/8.74 inference(superposition,[status(thm)],[f4994,f3501])).
% 51.53/8.74 thf(f3501,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ X0 @ sK651) = $true) | ((in @ X0 @ sK652) != $true)) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f3500])).
% 51.53/8.74 thf(f3500,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK652) != $true) | ((in @ X0 @ sK651) = $true)) )),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f3488,f3002])).
% 51.53/8.74 thf(f3002,plain,(
% 51.53/8.74 (powersetE = $true)),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f3488,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ X0 @ sK651) = $true) | ((in @ X0 @ sK652) != $true) | (powersetE != $true)) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f3483])).
% 51.53/8.74 thf(f3483,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ X0 @ sK652) != $true) | ($true != $true) | ((in @ X0 @ sK651) = $true) | (powersetE != $true)) )),
% 51.53/8.74 inference(superposition,[status(thm)],[f2666,f3015])).
% 51.53/8.74 thf(f3015,plain,(
% 51.53/8.74 ($true = (in @ sK652 @ (powerset @ sK651)))),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f2666,plain,(
% 51.53/8.74 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true) | (powersetE != $true)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f1669])).
% 51.53/8.74 thf(f1669,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X0 @ (powerset @ X1)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | (((in @ sK434 @ sK432) = $true) & ((in @ sK434 @ sK433) != $true) & ((in @ sK432 @ (powerset @ sK433)) = $true)))),
% 51.53/8.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK432,sK433,sK434])],[f1667,f1668])).
% 51.53/8.74 thf(f1668,plain,(
% 51.53/8.74 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ X3)) & ((in @ X5 @ X4) != $true) & ((in @ X3 @ (powerset @ X4)) = $true)) => (((in @ sK434 @ sK432) = $true) & ((in @ sK434 @ sK433) != $true) & ((in @ sK432 @ (powerset @ sK433)) = $true))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f1667,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X0 @ (powerset @ X1)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ X3)) & ((in @ X5 @ X4) != $true) & ((in @ X3 @ (powerset @ X4)) = $true)))),
% 51.53/8.74 inference(rectify,[status(thm)],[f1666])).
% 51.53/8.74 thf(f1666,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X0 @ (powerset @ X1)) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true) & ((in @ X0 @ (powerset @ X1)) = $true)))),
% 51.53/8.74 inference(nnf_transformation,[status(thm)],[f842])).
% 51.53/8.74 thf(f842,plain,(
% 51.53/8.74 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X0 @ (powerset @ X1)) != $true)) <=> (powersetE = $true)),
% 51.53/8.74 inference(flattening,[status(thm)],[f841])).
% 51.53/8.74 thf(f841,plain,(
% 51.53/8.74 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 51.53/8.74 inference(ennf_transformation,[status(thm)],[f408])).
% 51.53/8.74 thf(f408,plain,(
% 51.53/8.74 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)))),
% 51.53/8.74 inference(fool_elimination,[status(thm)],[f407])).
% 51.53/8.74 thf(f407,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (powerset @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = powersetE)),
% 51.53/8.74 inference(rectify,[status(thm)],[f40])).
% 51.53/8.74 thf(f40,axiom,(
% 51.53/8.74 (! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X4 @ (powerset @ X3)) => ((in @ X1 @ X4) => (in @ X1 @ X3))) = powersetE)),
% 51.53/8.74 file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',powersetE)).
% 51.53/8.74 thf(f4994,plain,(
% 51.53/8.74 ((in @ (sK26 @ sK650 @ sK652) @ sK651) != $true) | spl726_88),
% 51.53/8.74 inference(avatar_component_clause,[status(thm)],[f4992])).
% 51.53/8.74 thf(f7943,plain,(
% 51.53/8.74 spl726_91),
% 51.53/8.74 inference(avatar_split_clause,[status(thm)],[f7942,f5050])).
% 51.53/8.74 thf(f5050,definition,(
% 51.53/8.74 spl726_91 <=> ((in @ sK650 @ (powerset @ sK652)) = $true)),
% 51.53/8.74 introduced(definition,[new_symbols(naming,[spl726_91])],[avatar_definition])).
% 51.53/8.74 thf(f7942,plain,(
% 51.53/8.74 ((in @ sK650 @ (powerset @ sK652)) = $true)),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f7941])).
% 51.53/8.74 thf(f7941,plain,(
% 51.53/8.74 ($true != $true) | ((in @ sK650 @ (powerset @ sK652)) = $true)),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f7939,f3129])).
% 51.53/8.74 thf(f3129,plain,(
% 51.53/8.74 (powersetI = $true)),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f7939,plain,(
% 51.53/8.74 ((in @ sK650 @ (powerset @ sK652)) = $true) | (powersetI != $true)),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f7938])).
% 51.53/8.74 thf(f7938,plain,(
% 51.53/8.74 ($true != $true) | ((in @ sK650 @ (powerset @ sK652)) = $true) | (powersetI != $true)),
% 51.53/8.74 inference(duplicate_literal_removal,[status(thm)],[f7929])).
% 51.53/8.74 thf(f7929,plain,(
% 51.53/8.74 ((in @ sK650 @ (powerset @ sK652)) = $true) | ($true != $true) | (powersetI != $true) | ((in @ sK650 @ (powerset @ sK652)) = $true)),
% 51.53/8.74 inference(superposition,[status(thm)],[f5079,f2698])).
% 51.53/8.74 thf(f2698,plain,(
% 51.53/8.74 ( ! [X0 : $i,X1 : $i] : (((in @ (sK455 @ X1 @ X0) @ X1) = $true) | ((in @ X1 @ (powerset @ X0)) = $true) | (powersetI != $true)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f1709])).
% 51.53/8.74 thf(f1709,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i] : ((((in @ (sK455 @ X1 @ X0) @ X1) = $true) & ((in @ (sK455 @ X1 @ X0) @ X0) != $true)) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | (! [X5 : $i] : (((in @ X5 @ sK457) != $true) | ((in @ X5 @ sK456) = $true)) & ((in @ sK457 @ (powerset @ sK456)) != $true)))),
% 51.53/8.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK455,sK456,sK457])],[f1706,f1708,f1707])).
% 51.53/8.74 thf(f1707,plain,(
% 51.53/8.74 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) => (((in @ (sK455 @ X1 @ X0) @ X1) = $true) & ((in @ (sK455 @ X1 @ X0) @ X0) != $true)))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f1708,plain,(
% 51.53/8.74 ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ X3))) & ((in @ X4 @ (powerset @ X3)) != $true)) => (! [X5 : $i] : (((in @ X5 @ sK457) != $true) | ((in @ X5 @ sK456) = $true)) & ((in @ sK457 @ (powerset @ sK456)) != $true))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f1706,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ X3))) & ((in @ X4 @ (powerset @ X3)) != $true)))),
% 51.53/8.74 inference(rectify,[status(thm)],[f1705])).
% 51.53/8.74 thf(f1705,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ((in @ X1 @ (powerset @ X0)) != $true)))),
% 51.53/8.74 inference(nnf_transformation,[status(thm)],[f815])).
% 51.53/8.74 thf(f815,plain,(
% 51.53/8.74 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((in @ X1 @ (powerset @ X0)) = $true)) <=> (powersetI = $true)),
% 51.53/8.74 inference(ennf_transformation,[status(thm)],[f326])).
% 51.53/8.74 thf(f326,plain,(
% 51.53/8.74 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((in @ X1 @ (powerset @ X0)) = $true))),
% 51.53/8.74 inference(fool_elimination,[status(thm)],[f325])).
% 51.53/8.74 thf(f325,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 51.53/8.74 inference(rectify,[status(thm)],[f37])).
% 51.53/8.74 thf(f37,axiom,(
% 51.53/8.74 (! [X3 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (in @ X4 @ (powerset @ X3))) = powersetI)),
% 51.53/8.74 file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',powersetI)).
% 51.53/8.74 thf(f5079,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ (sK455 @ X0 @ sK652) @ sK650) != $true) | ((in @ X0 @ (powerset @ sK652)) = $true)) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f5078])).
% 51.53/8.74 thf(f5078,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ (powerset @ sK652)) = $true) | ((in @ (sK455 @ X0 @ sK652) @ sK650) != $true)) )),
% 51.53/8.74 inference(duplicate_literal_removal,[status(thm)],[f5063])).
% 51.53/8.74 thf(f5063,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ (sK455 @ X0 @ sK652) @ sK650) != $true) | ((in @ (sK455 @ X0 @ sK652) @ sK650) != $true) | ($true != $true) | ((in @ X0 @ (powerset @ sK652)) = $true)) )),
% 51.53/8.74 inference(superposition,[status(thm)],[f3573,f3476])).
% 51.53/8.74 thf(f3476,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ X0 @ sK651) = $true) | ($true != (in @ X0 @ sK650))) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f3475])).
% 51.53/8.74 thf(f3475,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ X0 @ sK650)) | ((in @ X0 @ sK651) = $true)) )),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f3459,f3002])).
% 51.53/8.74 thf(f3459,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (($true != (in @ X0 @ sK650)) | ((in @ X0 @ sK651) = $true) | (powersetE != $true)) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f3454])).
% 51.53/8.74 thf(f3454,plain,(
% 51.53/8.74 ( ! [X0 : $i] : ((powersetE != $true) | ((in @ X0 @ sK651) = $true) | ($true != (in @ X0 @ sK650)) | ($true != $true)) )),
% 51.53/8.74 inference(superposition,[status(thm)],[f2666,f3011])).
% 51.53/8.74 thf(f3011,plain,(
% 51.53/8.74 ($true = (in @ sK650 @ (powerset @ sK651)))),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f3573,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ (sK455 @ X0 @ sK652) @ sK651) != $true) | ((in @ X0 @ (powerset @ sK652)) = $true) | ((in @ (sK455 @ X0 @ sK652) @ sK650) != $true)) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f3572])).
% 51.53/8.74 thf(f3572,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (($true != $true) | ((in @ (sK455 @ X0 @ sK652) @ sK650) != $true) | ((in @ X0 @ (powerset @ sK652)) = $true) | ((in @ (sK455 @ X0 @ sK652) @ sK651) != $true)) )),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f3530,f3129])).
% 51.53/8.74 thf(f3530,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ (sK455 @ X0 @ sK652) @ sK650) != $true) | (powersetI != $true) | ((in @ X0 @ (powerset @ sK652)) = $true) | ((in @ (sK455 @ X0 @ sK652) @ sK651) != $true)) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f3522])).
% 51.53/8.74 thf(f3522,plain,(
% 51.53/8.74 ( ! [X0 : $i] : ((powersetI != $true) | ((in @ X0 @ (powerset @ sK652)) = $true) | ((in @ (sK455 @ X0 @ sK652) @ sK651) != $true) | ((in @ (sK455 @ X0 @ sK652) @ sK650) != $true) | ($true != $true)) )),
% 51.53/8.74 inference(superposition,[status(thm)],[f2697,f3013])).
% 51.53/8.74 thf(f3013,plain,(
% 51.53/8.74 ( ! [X4 : $i] : (((in @ X4 @ sK652) = $true) | ((in @ X4 @ sK651) != $true) | ((in @ X4 @ sK650) != $true)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f2697,plain,(
% 51.53/8.74 ( ! [X0 : $i,X1 : $i] : (((in @ (sK455 @ X1 @ X0) @ X0) != $true) | (powersetI != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f1709])).
% 51.53/8.74 thf(f7914,plain,(
% 51.53/8.74 spl726_124 | ~spl726_91),
% 51.53/8.74 inference(avatar_split_clause,[status(thm)],[f7913,f5050,f6290])).
% 51.53/8.74 thf(f6290,definition,(
% 51.53/8.74 spl726_124 <=> ((subset @ sK650 @ sK652) = $true)),
% 51.53/8.74 introduced(definition,[new_symbols(naming,[spl726_124])],[avatar_definition])).
% 51.53/8.74 thf(f7913,plain,(
% 51.53/8.74 ((subset @ sK650 @ sK652) = $true) | ~spl726_91),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f7912])).
% 51.53/8.74 thf(f7912,plain,(
% 51.53/8.74 ((subset @ sK650 @ sK652) = $true) | ($true != $true) | ~spl726_91),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f7905,f2997])).
% 51.53/8.74 thf(f2997,plain,(
% 51.53/8.74 (powersetE1 = $true)),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f7905,plain,(
% 51.53/8.74 (powersetE1 != $true) | ((subset @ sK650 @ sK652) = $true) | ~spl726_91),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f7898])).
% 51.53/8.74 thf(f7898,plain,(
% 51.53/8.74 ($true != $true) | (powersetE1 != $true) | ((subset @ sK650 @ sK652) = $true) | ~spl726_91),
% 51.53/8.74 inference(superposition,[status(thm)],[f2384,f5052])).
% 51.53/8.74 thf(f5052,plain,(
% 51.53/8.74 ((in @ sK650 @ (powerset @ sK652)) = $true) | ~spl726_91),
% 51.53/8.74 inference(avatar_component_clause,[status(thm)],[f5050])).
% 51.53/8.74 thf(f2384,plain,(
% 51.53/8.74 ( ! [X2 : $i,X3 : $i] : (((in @ X3 @ (powerset @ X2)) != $true) | ((subset @ X3 @ X2) = $true) | (powersetE1 != $true)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f1348])).
% 51.53/8.74 thf(f1348,plain,(
% 51.53/8.74 ((powersetE1 = $true) | (((subset @ sK224 @ sK223) != $true) & ((in @ sK224 @ (powerset @ sK223)) = $true))) & (! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | ((in @ X3 @ (powerset @ X2)) != $true)) | (powersetE1 != $true))),
% 51.53/8.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK223,sK224])],[f1346,f1347])).
% 51.53/8.74 thf(f1347,plain,(
% 51.53/8.74 ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ((in @ X1 @ (powerset @ X0)) = $true)) => (((subset @ sK224 @ sK223) != $true) & ((in @ sK224 @ (powerset @ sK223)) = $true))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f1346,plain,(
% 51.53/8.74 ((powersetE1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | ((in @ X3 @ (powerset @ X2)) != $true)) | (powersetE1 != $true))),
% 51.53/8.74 inference(rectify,[status(thm)],[f1345])).
% 51.53/8.74 thf(f1345,plain,(
% 51.53/8.74 ((powersetE1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) | (powersetE1 != $true))),
% 51.53/8.74 inference(nnf_transformation,[status(thm)],[f921])).
% 51.53/8.74 thf(f921,plain,(
% 51.53/8.74 (powersetE1 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 51.53/8.74 inference(ennf_transformation,[status(thm)],[f298])).
% 51.53/8.74 thf(f298,plain,(
% 51.53/8.74 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ((subset @ X1 @ X0) = $true)) <=> (powersetE1 = $true)),
% 51.53/8.74 inference(fool_elimination,[status(thm)],[f297])).
% 51.53/8.74 thf(f297,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)) = powersetE1)),
% 51.53/8.74 inference(rectify,[status(thm)],[f96])).
% 51.53/8.74 thf(f96,axiom,(
% 51.53/8.74 (! [X3 : $i,X4 : $i] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)) = powersetE1)),
% 51.53/8.74 file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',powersetE1)).
% 51.53/8.74 thf(f7711,plain,(
% 51.53/8.74 spl726_100 | ~spl726_87 | ~spl726_124),
% 51.53/8.74 inference(avatar_split_clause,[status(thm)],[f7710,f6290,f4988,f5331])).
% 51.53/8.74 thf(f5331,definition,(
% 51.53/8.74 spl726_100 <=> (sK650 = sK652)),
% 51.53/8.74 introduced(definition,[new_symbols(naming,[spl726_100])],[avatar_definition])).
% 51.53/8.74 thf(f7710,plain,(
% 51.53/8.74 ((subset @ sK652 @ sK650) != $true) | (sK650 = sK652) | ~spl726_124),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f7709])).
% 51.53/8.74 thf(f7709,plain,(
% 51.53/8.74 ($true != $true) | ((subset @ sK652 @ sK650) != $true) | (sK650 = sK652) | ~spl726_124),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f7708,f3082])).
% 51.53/8.74 thf(f3082,plain,(
% 51.53/8.74 (setextsub = $true)),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f7708,plain,(
% 51.53/8.74 (sK650 = sK652) | (setextsub != $true) | ((subset @ sK652 @ sK650) != $true) | ~spl726_124),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f7704])).
% 51.53/8.74 thf(f7704,plain,(
% 51.53/8.74 ((subset @ sK652 @ sK650) != $true) | (sK650 = sK652) | (setextsub != $true) | ($true != $true) | ~spl726_124),
% 51.53/8.74 inference(superposition,[status(thm)],[f2115,f6291])).
% 51.53/8.74 thf(f6291,plain,(
% 51.53/8.74 ((subset @ sK650 @ sK652) = $true) | ~spl726_124),
% 51.53/8.74 inference(avatar_component_clause,[status(thm)],[f6290])).
% 51.53/8.74 thf(f2115,plain,(
% 51.53/8.74 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) != $true) | (setextsub != $true) | ((subset @ X2 @ X3) != $true) | (X2 = X3)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f1019])).
% 51.53/8.74 thf(f1019,plain,(
% 51.53/8.74 ((setextsub = $true) | (((subset @ sK11 @ sK12) = $true) & ((subset @ sK12 @ sK11) = $true) & (sK11 != sK12))) & (! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true) | (X2 = X3)) | (setextsub != $true))),
% 51.53/8.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f1017,f1018])).
% 51.53/8.74 thf(f1018,plain,(
% 51.53/8.74 ? [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) & ((subset @ X1 @ X0) = $true) & (X0 != X1)) => (((subset @ sK11 @ sK12) = $true) & ((subset @ sK12 @ sK11) = $true) & (sK11 != sK12))),
% 51.53/8.74 introduced(definition,[],[choice_axiom])).
% 51.53/8.74 thf(f1017,plain,(
% 51.53/8.74 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) & ((subset @ X1 @ X0) = $true) & (X0 != X1))) & (! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true) | (X2 = X3)) | (setextsub != $true))),
% 51.53/8.74 inference(rectify,[status(thm)],[f1016])).
% 51.53/8.74 thf(f1016,plain,(
% 51.53/8.74 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) & ((subset @ X1 @ X0) = $true) & (X0 != X1))) & (! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ((subset @ X1 @ X0) != $true) | (X0 = X1)) | (setextsub != $true))),
% 51.53/8.74 inference(nnf_transformation,[status(thm)],[f951])).
% 51.53/8.74 thf(f951,plain,(
% 51.53/8.74 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ((subset @ X1 @ X0) != $true) | (X0 = X1))),
% 51.53/8.74 inference(flattening,[status(thm)],[f950])).
% 51.53/8.74 thf(f950,plain,(
% 51.53/8.74 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ($true != (subset @ X0 @ X1))) | ((subset @ X1 @ X0) != $true))),
% 51.53/8.74 inference(ennf_transformation,[status(thm)],[f394])).
% 51.53/8.74 thf(f394,plain,(
% 51.53/8.74 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => (($true = (subset @ X0 @ X1)) => (X0 = X1)))),
% 51.53/8.74 inference(fool_elimination,[status(thm)],[f393])).
% 51.53/8.74 thf(f393,plain,(
% 51.53/8.74 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))) = setextsub)),
% 51.53/8.74 inference(rectify,[status(thm)],[f93])).
% 51.53/8.74 thf(f93,axiom,(
% 51.53/8.74 (! [X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))) = setextsub)),
% 51.53/8.74 file('/export/starexec/sandbox2/tmp/tmp.74aQ65bPP2/DTF2THF_1611.p',setextsub)).
% 51.53/8.74 thf(f7585,plain,(
% 51.53/8.74 ~spl726_100),
% 51.53/8.74 inference(avatar_contradiction_clause,[status(thm)],[f7584])).
% 51.53/8.74 thf(f7584,plain,(
% 51.53/8.74 $false | ~spl726_100),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f7518])).
% 51.53/8.74 thf(f7518,plain,(
% 51.53/8.74 (sK650 != sK650) | ~spl726_100),
% 51.53/8.74 inference(superposition,[status(thm)],[f3012,f5333])).
% 51.53/8.74 thf(f5333,plain,(
% 51.53/8.74 (sK650 = sK652) | ~spl726_100),
% 51.53/8.74 inference(avatar_component_clause,[status(thm)],[f5331])).
% 51.53/8.74 thf(f3012,plain,(
% 51.53/8.74 (sK650 != sK652)),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f4995,plain,(
% 51.53/8.74 spl726_87 | ~spl726_88),
% 51.53/8.74 inference(avatar_split_clause,[status(thm)],[f4986,f4992,f4988])).
% 51.53/8.74 thf(f4986,plain,(
% 51.53/8.74 ((in @ (sK26 @ sK650 @ sK652) @ sK651) != $true) | ((subset @ sK652 @ sK650) = $true)),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f4985])).
% 51.53/8.74 thf(f4985,plain,(
% 51.53/8.74 ($true != $true) | ((subset @ sK652 @ sK650) = $true) | ((in @ (sK26 @ sK650 @ sK652) @ sK651) != $true)),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f4981,f3115])).
% 51.53/8.74 thf(f4981,plain,(
% 51.53/8.74 ((subset @ sK652 @ sK650) = $true) | ((in @ (sK26 @ sK650 @ sK652) @ sK651) != $true) | (subsetI1 != $true)),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f4980])).
% 51.53/8.74 thf(f4980,plain,(
% 51.53/8.74 ((subset @ sK652 @ sK650) = $true) | ((in @ (sK26 @ sK650 @ sK652) @ sK651) != $true) | ($true != $true) | (subsetI1 != $true)),
% 51.53/8.74 inference(duplicate_literal_removal,[status(thm)],[f4970])).
% 51.53/8.74 thf(f4970,plain,(
% 51.53/8.74 ((subset @ sK652 @ sK650) = $true) | ((subset @ sK652 @ sK650) = $true) | (subsetI1 != $true) | ($true != $true) | ((in @ (sK26 @ sK650 @ sK652) @ sK651) != $true)),
% 51.53/8.74 inference(superposition,[status(thm)],[f3645,f2133])).
% 51.53/8.74 thf(f3645,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ (sK26 @ sK650 @ X0) @ sK652) != $true) | ((in @ (sK26 @ sK650 @ X0) @ sK651) != $true) | ((subset @ X0 @ sK650) = $true)) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f3644])).
% 51.53/8.74 thf(f3644,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ (sK26 @ sK650 @ X0) @ sK651) != $true) | ((in @ (sK26 @ sK650 @ X0) @ sK652) != $true) | ((subset @ X0 @ sK650) = $true) | ($true != $true)) )),
% 51.53/8.74 inference(forward_demodulation,[status(thm)],[f3642,f3115])).
% 51.53/8.74 thf(f3642,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ (sK26 @ sK650 @ X0) @ sK652) != $true) | ((subset @ X0 @ sK650) = $true) | ((in @ (sK26 @ sK650 @ X0) @ sK651) != $true) | (subsetI1 != $true)) )),
% 51.53/8.74 inference(trivial_inequality_removal,[status(thm)],[f3609])).
% 51.53/8.74 thf(f3609,plain,(
% 51.53/8.74 ( ! [X0 : $i] : (((in @ (sK26 @ sK650 @ X0) @ sK652) != $true) | ((in @ (sK26 @ sK650 @ X0) @ sK651) != $true) | ((subset @ X0 @ sK650) = $true) | ($true != $true) | (subsetI1 != $true)) )),
% 51.53/8.74 inference(superposition,[status(thm)],[f2134,f3014])).
% 51.53/8.74 thf(f3014,plain,(
% 51.53/8.74 ( ! [X3 : $i] : (((in @ X3 @ sK650) = $true) | ((in @ X3 @ sK651) != $true) | ((in @ X3 @ sK652) != $true)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f2007])).
% 51.53/8.74 thf(f2134,plain,(
% 51.53/8.74 ( ! [X3 : $i,X4 : $i] : (((in @ (sK26 @ X4 @ X3) @ X4) != $true) | ((subset @ X3 @ X4) = $true) | (subsetI1 != $true)) )),
% 51.53/8.74 inference(cnf_transformation,[status(thm)],[f1041])).
% 51.53/8.74 % SZS output end Proof for DTF2THF_1611
% 51.53/8.74 % (2107)------------------------------
% 51.53/8.74 % (2107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.53/8.74 % (2107)Termination reason: Refutation
% 51.53/8.74
% 51.53/8.74 % (2107)Memory used [KB]: 17782
% 51.53/8.74 % (2107)Time elapsed: 1.104 s
% 51.53/8.74 % (2107)Instructions burned: 3563 (million)
% 51.53/8.74 % (2107)------------------------------
% 51.53/8.74 % (2107)------------------------------
% 51.53/8.74 % (1901)Success in time 7.21 s
%------------------------------------------------------------------------------